Ricardo Viola

M Jean-Yves

Hascoët Professeur

Mme Sandra

Chevret Mc

Examinatrice M Frédéric

HDR Vignat Mc

Rapporteur M Bertrand

Wattrisse Professeur

M Emmanuel

Duc Professeur

M Xavier

Balandraud Professeur

M Pierre

Encadrant M Fabien

Poulhaon Ir

Estia Encadrant

Modelling of WAAM process and expression of performance indicators

➢ Le troisième chapitre est consacré à l'étude des conditions thermiques avant le dépôt de chaque couche. Un modèle y est également présenté, qui démontre l'influence que les trajectoires ont pendant la construction de la pièce. Quelques résultats du modèle sont également présentés. ➢ Le quatrième chapitre est consacré à la présentation de la construction de neuf murs à l'aide de plusieurs équipements de surveillance pour la collecte de données. Ce chapitre est également consacré à la présentation des paramètres d'entrée utilisés et des résultats obtenus lors des essais mécaniques effectués sur des échantillons prélevés sur ces murs. ➢ Le cinquième chapitre est celui où les indicateurs des chapitres 2, 3 et 4 sont assemblés dans une formule qui permet d'évaluer la performance globale du processus de dépôt. ➢ Le sixième chapitre est consacré aux conclusions générales de la thèse.

Contribution

L'objectif de cette recherche est de proposer des modèles d'estimation des indicateurs clés de performance, dans le cadre d'une optimisation du processus de fabrication, basée sur une stratégie de prise de décision. Un indicateur clé de performance (ICP) est une grandeur qui permet d'évaluer la performance d'un processus de production, d'une organisation, d'un secteur d'activité, ou autres. L'indicateur clé de performance doit permettre aux parties prenantes de connaître facilement et de manière explicite la performance du processus. La "valeur" de l'ICP doit être mise à jour fréquemment ou en temps réel, afin d'adapter le processus aux besoins exprimés par l'indicateur. Lorsqu'ils sont appliqués à un processus de production, les indicateurs clés de performance doivent avoir comme source d'information d'autres indicateurs clés de performance d'un degré inférieur qui sont le produit d'une évaluation de chaque étape du processus de production.

Introduction générale

L'émergence de nouveaux processus en fabrication additive métallique (AM) et de nouvelles technologies associées au contrôle de ces processus a permis à de grandes entreprises du secteur aérospatial et aéronautique à intégrer ces procédés dans leurs lignes de production. La mise en oeuvre de l'AM dans l'industrie va aujourd'hui au-delà de la production de prototypes. Qu'il s'agisse de réparation ou de production, les avantages de l'AM commencent à être perçus par l'industrie comme un avantage évident pour la personnalisation des pièces, l'augmentation de la complexité des pièces, la réduction des délais et la réduction des coûts pour la production de petites et moyennes séries. Aux procédés déjà utilisés dans l'industrie, connus sous le nom de fabrication soustractive, s'ajoutent maintenant des procédés de fabrication additive. Ces procédés ont pour origine la construction de la géométrie souhaitée par dépôt de couches successives de matière. Il est désormais important d'évaluer les performances de ces procédés additifs dans leurs différentes phases, afin de définir des indicateurs permettant de choisir entre les différents procédés de production, qu'ils soient additifs ou soustractifs. La mise en oeuvre de plusieurs procédés additifs nécessitent l'usage de cellules robotisées permettant le déplacement de l'effecteur. La qualité de dépose du matériau et donc du procédé dépend de la qualité du mouvement du robot. Pour évaluer la performance du procédé et obtenir un indicateur de performance (ICP), il convient d'établir un modèle de prédiction du comportement du robot. Par ailleurs, le comportement thermique de la matière joue un rôle clé sur la performance du procédé pendant la dépose. En effet, le gradient de température impacte la santé matière et la qualité métallurgique du produit. Celui-ci est lié à la stratégie de dépose et aux trajectoires parcourues par le robot. Il est, alors, nécessaire de proposer un modèle thermocinétique qui permet une prédiction précise du temps de dépôt (DT) de chaque stratégie. Simultanément, le modèle doit afficher des indicateurs thermiques permettant d'évaluer les conditions thermiques avant et après le dépôt de la première couche. Pour vérifier expérimentalement l'influence des conditions thermiques sur la qualité du matériau obtenu, des murs sont construits avec différentes températures entre les couches. Plusieurs essais mécaniques sont réalisés pour caractériser le matériau, à savoir la micro-dureté, la dureté, la contrainte-déformation et la fatigue à l'aide d'une caméra infrarouge. Les résultats recueillis nous permettront de comprendre si l'introduction de temps d'attente entre les couches (appelés temps inter-couches) affecte réellement la qualité du matériau et ses caractéristiques mécaniques, ainsi que d'extraire une ICP de la qualité du matériau. Sur la base de ces études, une formule d'évaluation de la performance globale du processus devrait émerger pour permettre l'évaluation de la performance.

Structure de la thèse

La thèse présentée est divisée en six chapitres.

➢ Dans le premier chapitre, tous les concepts nécessaires à la compréhension du procédé étudié sont fournis, ainsi que son origine. Il présente également les avantages et les inconvénients du procédé WAAM, le type de matériau utilisé, des informations générales sur les gaz de protection utilisés et leur importance. ➢ Le deuxième chapitre présente l'étude cinématique du robot et de ses paramètres, ainsi que sa programmation. Les stratégies utilisées, les résultats obtenus, la procédure de traitement des données qui a été nécessaire pour obtenir les résultats et les conclusions spécifiques sur la cinématique du robot sont également présentés.

Dans un processus de fabrication additive tel que le WAAM, l'intérêt est de définir des ICP pour les différentes phases du processus de production, ce qui permet d'analyser ces phases séparément afin de détecter facilement l'origine d'un problème s'il survient. Chaque phase du processus doit donc être analysée séparément, et plus précisément lors de la préproduction, de la production effective et de la postproduction. Au sein d'un processus de production efficace, la même distinction peut être faite en analysant les différents facteurs qui contribuent à sa performance. Pour le processus WAAM, les facteurs cinématiques et thermiques ont tous deux une influence sur le processus. En ce qui concerne la qualité du matériau, les murs sont généralement fabriqués sous forme d'échantillons afin d'évaluer les propriétés mécaniques du matériau. Ceux-ci résultent des variations des innombrables paramètres d'entrée et des conditions de dépôt qui interviennent dans les processus AM. L'objectif de la thèse est l'identification d'indicateurs de performance après une analyse et une paramétrisation minutieuses du processus. Bien que pour certains matériaux la relation entre les paramètres d'entrée soit déjà définie, les méthodes de production ne sont pas standardisées. Pour définir des indicateurs de performance, l'étude doit nécessairement passer par une évaluation du processus dans toutes ses phases. Après cette évaluation, les facteurs les plus influents émergent naturellement, et ce sont ces facteurs qui constituent l'objet principal de cette enquête. Certains facteurs sont déjà connus pour être des points de recherche centraux, tels que la cinématique de l'équipement de déplacement, ainsi que le comportement thermique du matériau pendant et après le dépôt du matériau.

Principaux résultats / développements

Deux ICP de premier ordre ont été identifiés et étudiés : i) la cinématique du robot utilisé pour déposer les couches de matériau, avec une interaction potentielle entre l'équipement de transfert de métal à froid (CMT) et les contrôleurs du robot ; ii) la cinématique du robot utilisé pour déposer les couches de matériau; ii) la réponse thermique pendant la construction d'une pièce (nécessité d'un temps de refroidissement entre les couches). Ces deux aspects jouent un rôle sur la qualité finale de la pièce (précision géométrique, propriétés mécaniques). Elles ont également un impact sur le coût de fabrication, notamment en termes de productivité du processus, en raison du temps de dépôt du matériau et du temps d'intercalation. Après avoir effectué des analyses bibliographiques spécifiques sur le processus WAAM, le CMT et les matériaux élaborés par ces techniques, le travail de recherche a été divisé en trois études (analyse cinématique, analyse thermique et mesures des propriétés mécaniques) et une dernière partie (développement de formules de score pour évaluer la performance de chaque indicateur, ainsi que proposition d'un score global agrégeant les différentes contributions). Dans le processus WAAM, la précision du parcours d'outil est primordiale. Un manque de précision entraîne des défauts dans la pièce, tels que des vides ou des volumes non remplis. Elle a également un impact sur la qualité de la pièce finale et sur ses propriétés mécaniques. Cette précision dépend du comportement cinématique du robot, ainsi que de l'interaction entre l'équipement CMT et les contrôleurs du robot. Dans le chapitre 2, une analyse des mouvements de l'effecteur est réalisée à l'aide d'un robot KUKA KR 100-2 HA 2000 avec un contrôleur KRC2, sans dépôt de matériau (dépôt "virtuel" comprenant des transitions entre l'arc activé et l'arc désactivé.

Un indicateur important est la durée totale de fabrication, y compris le temps inter-couches (ITi). Ce dernier est le temps nécessaire pour que le matériau refroidisse à une température donnée, appelée "température intercouche" (ITe), entre deux couches consécutives de dépôt de matériau en fusion. La température intercouche est définie à l'aide de diagrammes temps-température-transformation (TTT). L'objectif est d'éviter l'apparition de phases indésirables qui pourraient conduire à une diminution des propriétés mécaniques du matériau. La difficulté de prévoir le temps de refroidissement provient de la corrélation complexe entre la géométrie de la pièce, la stratégie de dépôt et les dimensions du substrat. Cette corrélation doit être comprise afin de minimiser le gradient thermique à travers la pièce tout en utilisant le temps de dépôt (Dt) le plus bas possible et en assurant en même temps une qualité de matériau acceptable. Dans le chapitre 3, deux indicateurs différents sont proposés. L'un pour l'indicateur de préchauffage, basé sur une formulation analytique, pour lequel les avantages du modèle sont liés à la capacité de comparer différentes stratégies sous une forme rapide. Le modèle thermocinétique s'est avéré plus rapide et moins coûteux à calculer qu'une simulation FEM complète. Son coût de calcul réduit en fait un bon candidat pour le processus itératif qui permet d'identifier les trajectoires présentant les meilleures stratégies cinématiques (solution la plus efficace en termes de temps de fabrication) ou thermiques (la plus efficace sur le plan thermique, permettant d'obtenir la plus faible variation de température à travers la pièce). Le second modèle est lié au comportement de refroidissement et a été formé à l'aide des informations obtenues par la modélisation FEM. Ce modèle basé sur un réseau de neurone vise à fournir des prédictions sur les temps de séjour et les taux de refroidissement à travers la géométrie de la pièce. Pour ce faire, il prend en compte les critères cinématiques et thermiques du WAAM. Ce modèle permettra d'avoir une estimation rapide du temps de séjour nécessaire en chaque point de la stratégie. L'estimation obtenue est valable pour des géométries similaires aux géométries utilisées comme référence pour entraîner le modèle. En ce qui concerne la vitesse de refroidissement, une formation plus approfondie est nécessaire. Une bonne stratégie du point de vue thermique ne correspond pas nécessairement à une bonne stratégie du point de vue de la productivité. Par conséquence, les modèles développés peuvent aider à sélectionner (pour une géométrie donnée) un parcours d'outil qui offre la meilleure option cinématique ou thermique, ou même un compromis entre les deux. Une formule d'optimisation multi-critères est également proposée, permettant une évaluation thermique quantitative de chaque parcours d'outil et fournissant un score utile pour la prise de décision. La maîtrise des propriétés mécaniques du matériau déposé est d'une importance capitale pour le procédé WAAM. Dans le chapitre 4, des murs en acier inoxydable duplex 2209 sont construits en utilisant trois températures d'intercouche (150°C, 350°C et 550°C). Des échantillons sont ensuite prélevés horizontalement et verticalement. Trois types de caractérisation mécanique sont réalisés à cette fin : mesure de la dureté, essais de traction quasi-statiques (jusqu'à la rupture) et essais de fatigue accélérée (basés sur les mesures d'auto-échauffement). Les essais de fatigue accélérée ont permis de comparer la durabilité mécanique à long terme attendue des différents matériaux en fonction de l'orientation de l'échantillon et de la durée de l'intercalaire. Les résultats ont montré que la diminution de la température de la couche intermédiaire entraîne une dureté et une limite d'élasticité plus élevées, une ductilité plus faible, une résistance presque similaire et une meilleure performance en fatigue. Il est également démontré que les échantillons prélevés horizontalement ont de meilleures performances mécaniques que ceux prélevés verticalement. Ainsi, les résultats montrent que des compromis doivent être faits concernant la qualité du matériau (dans ce cas, un acier inoxydable duplex 2209) et la productivité du processus WAAM. Afin de permettre une évaluation correcte de la contribution de chaque indicateur, des formules sont proposées au chapitre 5 pour définir un score à obtenir en tenant compte de chaque domaine d'étude (cinématique, thermique et qualité du matériau). Ces scores sont finalement assemblés en un score global qui permet d'évaluer l'ensemble des performances du processus en général. Enfin, les formules développées nous ont permis de comparer l'impact des trois températures intercalaires testées (150°C, 350°C et 550°C). Les résultats montrent que le score le plus bas est obtenu avec la température intercalaire de 550°C, bien qu'il s'agisse du processus le plus rapide. La température intercalaire de 150°C a donné la meilleure qualité de matériau. Le score obtenu avec la température d'intercouche de 350°C a montré qu'il est possible d'obtenir un compromis avantageux entre la productivité et la qualité.

Perspectives

Différentes perspectives à ce travail peuvent être proposés: ➢ Il est nécessaire de structurer deux indicateurs importants pour la production : un indicateur géométrique et un indicateur de coût. L'indicateur géométrique est nécessaire en raison des différents types de géométrie des pièces qui peuvent être obtenus grâce au processus WAAM. L'indicateur de coût est mentionné à plusieurs reprises tout au long de cette thèse, où plusieurs relations l'affectant ont été révélées. Dans le calcul de l'indicateur de coût, les indicateurs de performance obtenus ici doivent être pris en compte. ➢ Compte tenu des derniers développements de la technologie WAAM avec la mise en oeuvre de positionneurs, il est désormais possible de produire des pièces en utilisant les six axes du robot plus deux axes du positionneur. Cela signifie que le modèle cinématique doit être amélioré en tenant compte des mouvements de ce nouveau type d'équipement. Par ailleurs, en ce qui concerne l'indicateur cinématique, il est possible d'améliorer la résolution des mesures permettant d'alimenter le modèle. Pour cela, il est nécessaire d'utiliser des appareils de mesure externes au robot. ➢ Dans le domaine thermique, il serait intéressant de tester les modèles développés sur des pièces ayant d'autres configurations, afin de vérifier leur applicabilité et la véracité des résultats. Il serait également intéressant d'identifier clairement le contexte dans lequel les phases nuisibles se forment, et si l'exposition consécutive pendant de courtes périodes de temps aux températures identifiées dans le diagramme TTT est suffisante pour leur formation. Il s'agit également d'améliorer le modèle de réseau de neurone, en fournissant davantage d'informations pour l'entraînement du modèle, ce qui permettrait une prédiction plus précise des temps d'attente nécessaires. Du point de vue du matériau, il serait également intéressant d'étudier en profondeur les caractéristiques métallographiques du matériau, les pourcentages de chaque phase (ferrite, austénite et éventuellement sigma), et d'essayer de relier les résultats de cette analyse aux températures inter-couches auxquelles les échantillons ont été soumis.

I would like to thank the opportunity that was given to me by the Agence Nationale de la recherche (ANR) to do this PhD, bringing together in one perfect opportunity the two subjects that I am professionally passionate about. I must therefore express my sincere gratitude to my thesis director Prof. Emmanuel Duc for the opportunity given, and for the trust placed in me. I would also like to thank him for the light and cheerful way he helped me overcome all the administrative, linguistic, and personal challenges by demonstrating his continuous institutional and personal support.

It is also with great pleasure that I thank Dr. Xavier Balandraud for the immense patience, availability, and friendship with which he always made himself available to work. It is with pleasure that I remember the time spent in the countless meetings in the writing of the scientific publication, in the thesis or even in the execution of the innumerable mechanical tests that extended even beyond working hours during some days. I want to mention that the work framework that he instilled in me, as well as his method, were well registered and will certainly help me throughout my future professional career. I would also like to thank Dr. Pierre Michaud for his exceptional reception within his team, and for his approachability in always allowing an open sharing of knowledge. I must also thank him for his help, advice, and guidance in the treatment of data and results obtained, as well as in the writing of scientific publications and the thesis manuscript. I also owe a great debt of gratitude to Dr. Fabien Poulhaon, for the enormous patience he had with me, the countless lunches talking about work, the countless half-hour meetings that would end up taking 2 hours, all while keeping the focus and good mood. It was a great source of pleasure and inspiration to work closely with Dr Fabien, who contributed a lot to the advancement of the thesis and dissipation of the countless doubts that arose over time.

I would also like to thank the members of the jury for the time they spent reading the manuscript and writing the reports to help me improve the manuscript, as well as for their willingness to come to Bidart for my thesis defense. Special thanks go to the president of the jury, Jean-Yves Hascoët, as it was a pleasure to have a renowned professor in the field of metal additive manufacturing of metal in France on the jury, and also for his understanding and help in finalizing the entire process of writing the manuscript.

Finally, I would like to thank the entire Addimadour team in the persons of Pierre Diaz, Valentin Peigne, Thomas Elcrin, Génole Braz, Henri Bernard, Pierre Seze, Antoine Lauvray, Cécile Dubief, Pierre Joyot and Anais Domergue who make Addimadour a research center of excellence with an extremely pleasant working environment. My thanks to all of them for their friendship and companionship demonstrated throughout these 3 years, both professionally and personally.

Last but not least, I want to thank my family, especially my parents, sister, brother-in-law, and nephews for all the love and unconditional support they gave me during this journey.

Index

List of figures

List of tables

General Introduction

Additive manufacturing (AM) has been undergoing developments in its various branches, plastics, metals, among others. In the case of metal additive manufacturing (MAM), the emergence of new subprocesses and new technologies associated with the control of these processes has allowed large companies in the aerospace and aviation sector to gain interest in implementing these processes in their production lines. The implementation of AM in industry today goes beyond the production of prototypes. Whether it is for repair or production purposes, the advantages of AM are now beginning to be seen by industry as a clear advantage for part customization, increased part complexity, shorter lead times, and the reduced cost for small to medium batch production. In addition to the already existing processes used in industry, known as subtractive manufacturing, AM processes are now being added. These processes have at their genesis the construction of the desired geometry by depositing successive layers of material. It is now important to evaluate the performance of the additive processes in their different phases, in order to define indicators that allow us to choose between the different production processes, whether additive or subtractive.

In what concerns the robot kinematics, several parameters with influence on its movement were tested, with the objective of extracting information which allows to build prediction model of the robot behavior, and consequently obtain a KPI.

As for the thermal behavior during deposition, the focus was on the relationship between the trajectories traveled by the robot and the thermal gradient generated by each one. The objective of this analysis is to obtain a thermo-kinematic model that will allow an accurate prediction of the deposition time (DT) for each deposition strategy. Simultaneously, the model should also display thermal indicators that allow the evaluation of the thermal conditions before and after the deposition of the first layer. To verify the influence of the thermal conditions on the quality of the resulting material, walls were built with different temperatures between layers. Several mechanical tests were performed to characterize the material, namely, microhardness, hardness, stress-strain, and fatigue using an infrared camera. The results collected will allow us to understand if the introduction of waiting times between layers (called interlayer times) really affects the quality of the material and its mechanical characteristics, as well as to extract a KPI of the material quality.

Based on these studies, a techno-economic model of the process should emerge to allow the evaluation of the process performance.

Manuscript outline

The thesis presented here is divided into five chapters. ➢ In the first chapter all the concepts necessary to understand the process studied are provided, as well as its origin. It is also presented the advantages and disadvantages of the WAAM process, and the type of material used. ➢ The second chapter presents the kinematic study done to the robot and its parameters, as well as its programming. The strategies used, results obtained, the data processing procedure that was necessary to be done to obtain the results and specific conclusions about the robot's kinematics are also presented. ➢ The third chapter is devoted to the study of thermal conditions prior to the deposition of each layer. A model is also presented here, which demonstrates the influence that the trajectories have during the construction of the part. Some results from the model are also presented. ➢ The fourth chapter is dedicated to presenting the nine walls built using several monitoring equipment for data collection. This chapter is also devoted to the presentation of input parameters used and results obtained in mechanical tests performed on samples taken from these walls. ➢ The fifth chapter is where the indicators from chapters 2, 3 and 4 are assembled in the technoeconomic model developed addressing correlations with the last indicator cost.

A specific bibliography is presented at the beginning of each chapter.

Chapter -WAAM Process presentation

Introduction

In this section, the direct energy deposition (DED) wire arc additive manufacturing (WAAM) process is introduced. An introduction is also given to the WAAM subprocess, Cold metal transfer (CMT) and its variants, used in this research. The equipment essential to operate a CMT cell, the materials, and some important characteristics of these are presented and explained. The central theme of the thesis under study, the performance of the CMT process is introduced here through the problematic faced by the industry. The context of the thesis is also presented here, in which the notion of Key Performance Indicator is defined for the CMT process and more generally for the WAAM process.

Chapter one outline

This chapter provides concepts and information that are important for understanding the origin and functioning of the sub-process studied here and its co-relationships among the variables that belong to the process or have a direct influence on it. Information regarding performance indicators and their application is also detailed here. This chapter is thus organized in six subchapters in which the information is distributed as follows: ➢ In the first sub-chapter is given the definition of the WAAM process, its history, its advantages, and disadvantages, an overview of the filler material and the gases used. ➢ In the second sub-chapter the CMT sub-process is presented, as well as the equipment used, some characteristics, and the different work modes. ➢ The third sub-chapter presents the materials used in the process, their main characteristics, and the relevant mechanical properties. ➢ The fourth sub-chapter presents the industrial problematic, the context of the thesis, the thesis problematics, as well as the definition of KPI's, their application, and the different tests to which the samples made using the WAAM process are subjected to. ➢ Sub-chapter five is dedicated to the contribution made by this thesis to solve the industrial problematic. ➢ To close chapter 1, we have subchapter six where a brief summary and conclusion of the data provided is made.

1.1.

Wire arc additive manufacturing (WAAM)

1.1.1. Definition of WAAM
WAAM is a gas metal arc welding (GMAW) production process that uses wire as feedstock to build or repair metal parts in three dimensions. This process is included on the Direct Energy Deposition (DED) classification made by the American society for testing and materials (ASTM). WAAM is a production process suitable for medium to large parts in the aeronautics field [1][2][3][4]. This process is characterized by high metal deposition capacity and reduced material waste, part cost and iteration time compared with standard processes [2][3][4]. The method consists of depositing molten metal through an electric arc between the nozzle and the already-deposited material in a sequence of two-dimensional (2D) layers using a robot to perform the movements [5]. The quality of the weld bead (WB) depends on various parameters, such as the quality of the wire, the wire feed speed (WFS), the travel speed (TS) and the heat input [1]. Weld bead geometry is controlled by optimizing the values of the deposition parameters [1,6]. Models can also be used to simulate the solidification process of the metal [7]. To limit high residual stresses, internal defects, porosities, and lack of fusion between adjacent weld beads, it is possible to control the deposition parameters or tilt the nozzle along the trajectory [8][9][10]. The mechanical quality of the final part depends on the combination of all the manufacturing input parameters [5].

1.1.2. Brief history of WAAM process The history of the WAAM process goes back to 1925 with the first publication by Baker R. [11] Figure 1 describing the deposition procedure of decorative parts with several layers. The process used was an electric arc formed between a non-adherent substrate and a fused metal electrode. This process was already stated before in a patent registered in 1919 by Noble P. O. for an economical method of enlarging shaft machines [12] and in 1920 by Eschholz O. H., where he disclosed an invention relating to ornamental arc welding using an electric arc [13]. Eschholz already understood the important relationship between width, height, depth and the arc current values, the electrode current densities, the electrode melting points, the speed of the arc travel and the influence of the tool travel.

Five years later in 1930 H. K. Shockey filed a patent [14] describing a machine dedicated to rebuilding the brake drums of cars of that time. The technology used would be the same as the one used by Baker R. using an electric arc between a fused metal electrode and a rotating metal brake drum. This patent also mentions the need for coordination between the wire speed, the rotation speed of the drum, and an overlap of one third between WB to achieve a satisfactory result. In 1943 a new patent was submitted, this time by Carpenter R. et al. for-metal pipe coating by submerged electric arc welding (SAW) [15]. The equipment in this patent was intended for the manufacture of large shafts with higher strength and one of its strengths was that it had a high deposition capability. This same process would be used by White, J. W. D. with the intention of producing rollers for the food processing industry [16]. White, J. W. D. improved the process by using rollers that pressed down the previously deposited layer.

Later, in 1967 a new patent for additive metal fabrication equipment is submitted by Ujiie A. [17] for the production of circular cross section vessels by welding. The purpose of this equipment was to permit the production of high-capacity pressure vessels with thicker walls. The advantages would be to increase the capacity achieved by this type of container, which until then had been made of curved plates welded together. Also Ujiie A. [18] submitted a new patent in 1972, this time for a process using three simultaneously deposited wires, focusing on the material deposition rate. In 1976 a patent was filed by Brandi and Luckow on the method of making large structural one-piece parts of metal particularly one-piece shafts and rotors for turbines and electric generator applications [19]. With this process they achieved nearly isotropic mechanical properties and identified a correlation between welding power, the temperature of the substrate and the subsequent layers.

Over the years, the process has been increasingly explored and parameterized, allowing its use in other applications. In 1989 a groundbreaking patent was submitted by Acheson, R. for the development of the process. This patent marks the start of the automation of the wire deposition process including a torch with gas supply and wire feeder similar to Gas Metal Arc Welding (GMAW) [20]. Until nowadays there were several advancements and patents submitted stating the advance of the process. Over time the process has been automated over the different parameters, but the advances are not limited to this field. Many works on various materials have been done to better understand how the interaction between parameters works, their influence during the process, and also their influence on the quality of the material, which has also been the subject of many studies.

Advantages and disadvantages

One of the great advantages of the WAAM process is the possibility to manufacture large volume parts with a deposition capacity of 1 to 10 kg per hour. The size of the parts depends on the type of cell installed in the manufacturing unit. The basic cell has the size limit of the reach of the robot used, but it can be improved with welding manipulators and welding tracks. Being a layered additive manufacturing process, it allows greater design freedom allowing complex part designs to be achieved. This technology also allows you to topologically optimize the design of parts by reducing the amount of material needed in their production, and even produce generatively designed parts affordably. One of the main characteristics of this process is that material is deposited only in those areas where it is needed according to the part geometry. But the fact that less material is deposited also means that less material must be post-processed to get the finished part. For these reasons, the wastage of material when compared to the production of parts using standard processes can be as high as 50%.

The WAAM process, when compared with other additive manufacturing processes, namely those in its category with direct energy deposition (DED), has a low cost of equipment acquisition and cell implementation. This affordability coupled with the high material deposition rate allows for a costeffective process.

Another advantage of WAAM is that you can build parts with different materials if they are compatible. Thus, the possibility of designing functionally graded components allows to achieve various mechanical characteristics, allowing the reduction of components and eventually improving its performance.

There is also the possibility to perform hybrid manufacturing of parts, combining WAAM with other production methods.

The number of materials available for this process is also considered a great advantage. This advantage is since the process uses metal wire as filler material. Since the process uses the same type of filler material as the welding process, there is a wide range of materials available.

In addition, one of the great advantages is the fact that the mechanical properties achieved through WAAM can exceed the performance achieved by parts manufactured by conventional processes.

Filler material transfer

The transfer of material between wire and substrate and subsequently between wire and already deposited material can be done in several different transfer modes as shown in Figure 2. There are important factors to consider when it comes to the metal transfer, like the current, tension, shielding gas and the filler material having the greatest influence. Figure 2, named transfer mode map, presents a graph showing the different transfer modes, as well as their relationship to current and tension. The line "Transition current" determines the working conditions by establishing the limit between the globular transition and the spray arc [22].

In the WAAM process, the transfer of the filler material is usually done in the short circuit mode by forming a drop of molten metal on the tip of the filler wire.

The molten metal droplet is formed due to the high temperatures reached by the electric arc between the wire and the substrate (for the first layer). Subsequently the migration of the drop from the wire tip to the molten bath is done by short-circuit where various forces act. The forces that exist during the transfer of the molten metal drop allow deposition to take place in various positions other than those that take advantage of the gravitational forces.

Types of filler material transfer

The type of transfer of the filler material depends on several factors as mentioned above. In the case of the WAAM process particularly for the CMT sub-process, the goal is to always have a short circuit transfer, which is helped by the retraction movement of the wire. This type of transfer allows the process to remain stable, without projections or wave bumping. Figure 3 shows the different types of transfer that may exist for the filler material. The selection of filler material transfer mode in Gas Metal Arc Welding (GMAW) depends on various factors such as welding position, material type, thickness, and desired weld quality. Each transfer mode has its unique advantages and limitations. ➢ Short-circuit transfer: In this transfer mode, the filler wire is melted and transferred to the weld pool through a short circuit with the base metal. This transfer mode is suitable for welding thin materials and produces a relatively low heat input. It also creates a stable arc with good control over the welding process [24][25]. ➢ Bridging transfer: Bridging transfer is similar to short-circuit transfer, but the electrode is kept at a slightly larger distance from the workpiece, which allows for a larger droplet to form. This transfer mode is used for welding thicker materials, and it produces a higher deposition rate than short-circuit transfer [26][27]. ➢ Forced short-circuit transfer: In this transfer mode, the short-circuit transfer is modified by using a pulsating current. The wire is pushed forward into the weld pool, which creates a more significant amount of molten metal transfer, and hence, a higher deposition rate. This transfer mode is suitable for welding thicker materials [28]. ➢ Globular transfer: In this transfer mode, the filler wire melts and forms large droplets that fall into the weld pool. This transfer mode produces a high deposition rate but results in a less stable arc and more spatter. It is suitable for welding thicker materials [29][30]. ➢ Repelled globular transfer: Repelled globular transfer is similar to globular transfer, but it uses a reverse polarity current. The droplets are repelled away from the workpiece and create a larger arc length, which results in a higher heat input. This transfer mode is suitable for welding thicker materials and produces a high deposition rate [31]. ➢ Projected spray transfer: In this transfer mode, the filler wire is melted and atomized into fine droplets that are projected onto the weld pool. This transfer mode produces a high deposition rate, produces less spatter, and creates a stable arc. It is suitable for welding thicker materials and produces a high-quality weld.

➢ Explosive transfer: In this transfer mode, a high current is used to vaporize the wire tip, which produces a plasma that melts the filler wire. The wire is propelled into the weld pool by a magnetic force, creating a high deposition rate. This transfer mode is suitable for welding thicker materials but requires high current and produces more spatter.

In conclusion, the selection of filler material transfer mode depends on the specific requirements of the welding application. Each transfer mode has its unique advantages and limitations, and the choice of transfer mode should be based on the material type, thickness, and desired weld quality.

Cold metal transfer (CMT)

This section will present the WAAM sub-process called CMT used for this study, with some of its variants, main characteristics, and advantages of each variant.

The cold metal transfer is a sub-process of WAAM that has as a base the processes Metal Inert Gas /Metal Active Gas (MIG/MAG). The particularity of this process is in its control, which allows to induce lower amounts of heat during the metal deposition. This advanced control system has a built-in system that detects when the tip of the wire comes into contact with the melt pool and activates the servomotor movement that retracts the wire, facilitating the transfer of the droplet [32].

The wire retraction frequency varies between 50 and 130Hz and depends on various factors such as the shielding gas, the electrode diameter, the characteristics of the filler material and the CMT mode [START_REF]Flux Corred Wire" Indiamart[END_REF]. Figure 4 shows the range of values for wire speed, current, tension and the corresponding behavior of the wire where the retraction can be seen during a section of the deposition cycle. The fact that there is a Wire retraction movement during the process implies that the heat supply associated with the electric arc is not continuous. As a result, there is a reduction in the intrinsic heat of the process.

CMT equipment

The main equipment's that constitutes the WAAM cell are the Fronius TP 3200 and the Kuka robot Figure 5. The CMT equipment controls all the manufacturing parameters except the TS. This equipment consists of a remote-control unit (RCU), where the synergic law, wire speed, current and tension are defined, as well as other parameters that are within the synergic law and closed to the user's knowledge. The RCU is connected to the TransPuls Synergic (TP) 3200 which in turn controls the gas flow it receives from the gas supply point. The controller TP 3200 is also connected to the wire feeder, and to the KRC2 robot controller. All the existing connections between equipment are represented in the scheme of Figure 6.

CMT main characteristic

The wire retraction movement is only possible because the CMT equipment is equipped with two servomotors dedicated to the unwinding of the wire spool, and to the wire retraction movement in the torch. Between these servomotors, a buffer allows the accumulation of the wire when the second servomotor makes the retraction movement (Figure 7). Another characteristic of this process is that it reduces the amount of metal projections, reducing waste while increasing efficiency, because the transfer of molten metal droplets into the melt pool as well as the re-ignition of the arc, take place practically without current during the retraction movement of the wire. The short circuit and wire retraction are also used to adjust the arc length dynamically and mechanically.

CMT variants

The CMT process also has several variants such as CMT Pulse, CMT Advanced, CMT Pulse Advanced, CMT SynchroPulse among others. ➢ The CMT Pulse variant is a combination of the CMT process and pulsed arc. In this type of process there is an increment of deposited heat since there are several pulses between each CMT cycle. One of the advantages of this process is its greater stability. ➢ The CMT Advanced variant has the particularity of alternating polarity in the short-circuit phase. An arc with reversed polarity takes place after the wire is removed from the melting bath. The reversal of polarity allows a greater deposition of material due to the increased size of the droplet and lower heat input due to the negative phase of the process. ➢ The CMT Advanced Pulse variant is a combination of the two previously mentioned subprocess types. In CMT Advanced Pulse sub-process there are not only the two types of CMT and Pulse cycles, but there is also a change of polarity between each of the cycles.

➢ The CMT SynchroPulse variant has the peculiarity of having two different types of cycles, one with low performance and low to medium WFS that is followed by a cycle with higher performance and higher WFS.

Each of the variants of the CMT process has a specific application, which depends on several factors, including base material, addition material, etc.

Materials used in WAAM

The materials available for use in the WAAM process are the wires that are commercially available to the welding industry. These metal wires can have various diameters and are supplied on spools containing different amounts of wire Figure 8. Although there are many materials available for use in the WAAM process, research efforts are largely devoted to the more expensive ones, or difficult to machine, materials such as titanium alloys or aluminum alloys. These materials are used in the aeronautic and aerospace context for part designs that allow the achievement of a high buy to flight ratio through additive manufacturing, allowing a reduction in production time and cost [START_REF] Martina | Welding Engineering and Laser Processing Centre[END_REF].

The WAAM process also allows the development of new part types using two or more directly bonded compatible materials. This is clearly an advantage from the part quality point of view, as it makes it possible to include new functions in the same part, optimizing its functions and potentially increasing its performance. The chemical composition of the material and the percentages in which they are introduced in the wire construction are of immense importance and directly affect the deposition process. Naturally, the composition of the wire is one of the most important parameters in achieving a quality part. Wire manufacturers have already stipulated the relationships between base metal and filler material that should be used given the desired characteristics of the part [START_REF][END_REF]. Underlying the composition and manufacturing process of the wire are other important characteristics such as mechanical properties like Young's modulus, material tensile stress/strain, impact, and corrosion resistance.

The physical properties of the wire such as electrical conductivity, heat conductivity and thermal expansion are also very important. In the case of the material property "electrical conductivity", this is fundamental because the process is based on an electric arc. Heat conductivity can have a considerable influence on productivity, and thermal expansion will have an effect on part quality. Given the production target, it is also necessary to consider the wire diameter factor, as this is a straightforward way to increase the volume of material deposited per unit of time, using the right set of input parameters. It must also be said that this type of material bought in coils can be transported in any vehicle due to the quantities and weight, meaning that there is an important potential for stock optimization, which is impossible to achieve when buying massive blocks of metal. Due to the characteristics of the process, it is easy from a management point of view to optimize the delivery of material according to needs, minimizing the investment in primary material (wire spools).

The WAAM process is based on a heat source that moves according to a defined strategy, while depositing metal. This means that a heat source moves over the substrate initially, and subsequently over the other layers already deposited generating a thermal gradient across the part. There are thus several heating/cooling cycles that will result in different cooling curves at different points on the part, leading to different microstructures forming at and between these points. Since the microstructure of a material determines its mechanical properties, it is very important to control the process to obtain the desired microstructure after deposition. The characteristic microstructures of the WAAM process are large columns that form from the base and grow in the direction of the deposition growth. Since the maximum temperature gradient is in this direction, there is no need for nucleation sites [30]. This type of grain growth leads to the material having anisotropic properties that are undesirable in parts with multi-axial stresses. But since we want to obtain isotropic properties, it would be necessary to obtain equiaxed grains, because they improve ductility and reduce the appearance of cracks. For these reasons heat treatments are often used to achieve the desired homogeneous microstructure. Thus, when the mechanical properties are analyzed in samples coming from walls made by the WAAM process, it is taken into account the direction in which the samples were withdrawn, if heat treatment was done, or any other type of procedure that may have influenced the mechanical properties (example in the table presented in the Figure taken from [START_REF] Jin | Wire Arc Additive Manufacturing of Stainless Steels: A Review[END_REF]).

Figure 9 -Example of a table comparing mechanical results [START_REF] Jin | Wire Arc Additive Manufacturing of Stainless Steels: A Review[END_REF].

Performance of the WAAM process

The application of Metal additive manufacturing (MAM) method in the industry still needs extensive adaptation work. In a first phase it is necessary to provide the industries with a correct perception of the advantages that this new type of process has to offer. The best way to highlight these advantages is a direct comparison of production time, cost, and final part quality for both additive and subtractive manufacturing.

It is necessary to have in mind that the application of MAM should only be applied to parts with geometry indicators that allow the part to be built to the same or better standards of quality and mechanical performance than those achieved by subtractive process (SP). The geometry of the part and its mechanical requirements are very important for the choice of the AM technology that will be used in its construction.

To provide a comparison between the two types of processes (additive and subtractive), it is crucial to identify the different phases of the AM process, taking from each one of them a performance indicator.

A detailed description of the MAM process in all its phases, describing the pros and cons, is then necessary. Associated to each of these phases should be described the needs for production and monitoring equipment, as well as other tools necessary for the cell to work. But to be able to take the maximum advantage of an AM process like WAAM, there are still some technical challenges to face, for example the development of: ➢ Input parameter sets, suitable for each material and each part geometry. ➢ Methods to obtain an accurate prediction of production times. ➢ Methods that allow minimizing the thermal phenomenon that this type of process imposes. ➢ Production methods that allow obtaining the best mechanical characteristics as well as the least possible distortion. The relationship between input parameters, part manufacturing conditions, and final results is not yet established. In order to apply WAAM technology in the industry with repeatability and accuracy there is also the need to develop the correct work procedures and methodologies. A precise evaluation of all process phases will allow us to obtain reliable performance indicators that will result in a model that will translate the entire process performance.

Thesis research issues

The work of this thesis was done in the context of INDUS-ADDI project, funded by the ANR "Agence Nationale de la Recherche", a partnership between the "Clermont Auvergne INP / Sigma Clermont" and the "École Supérieure des Technologies Industrielles Avancées" (ESTIA) through one of its research centers named Compositadour.

The main aim of the project is to propose a decision-making methodology for choosing a manufacturing process for the industrialization or re-industrialization of a product. In particular, this implies solving two problems: what decision-making methodology to use? and what performance indicators to use to characterize an additive manufacturing process? Thus, the goal of this research work is to identify performance indicators for characterizing the WAAM additive manufacturing process. The additive manufacturing process using the WAAM process can be divided into 3 phases, as shown in Figure XX: Pre-processing, processing, and post-processing. Our work focuses on phase 2: processing. To qualify the process, we can first define 3 first-level Key Performance Indicators (KPIs): Time, Quality and Cost (See Figure 11). The time KPI is a function of two second level KPIs, relating to the kinematic behavior of the robot and the thermal behavior of the part during manufacture.

As the WAAM process is operated on a robot station, the robot's kinematics are of central importance to the performance of the process, and to the quality of the material deposited. Toolpath programming thus becomes a matter of the utmost importance, the reason why it must be carefully analyzed. The robot trajectory is thus the result of the operator's decision that defines the trajectories, but it is also the result of the parameterization instilled in the construction of the program that works in articulation with the basic parameterization performed on the robot. Moreover, due to the type of deposition (layer by layer) characteristic of AM, the cooling conditions are changing throughout the part. Thermal history is dependent on various factors (such as deposition strategy for example) that influences the microstructure of the material as well as its mechanical properties. The influence that thermal history has on process performance is thus evident, making this a very important topic to study. The literature shows that there are also several uncertainties about the relationship between the set of input parameters used, the deposition conditions, and the quality achieved by the deposited material [41] [42]. The main input parameters are power (P), robot speed or travel speed (TS), and wire feed speed (WFS). There are however several other parameters that, similarly to the main ones, have an influence on the result, and on the stability of the process (tool to workpiece distance, shielding gas flow…).

The Quality KPI concerns the mechanical strength of the part. In particular, quasi-static and fatigue behavior are assessed. Finally, the last KPI concerns cost, which will not be discussed here. However, we note that the Time KPI has an influence on the mechanical behavior of the part, due to cooling times, and on the cost of the part, due to the total manufacturing time. The figure shows that it is necessary to characterize different parameters of the process in order to identify KPIs.

WAAM process can be split in 3 phases: To identify the Time KPI, the following methodology is used (See Figure 12). The Time KPI is based on an estimation model, built from experimental measurements. "Dry" runs (arc always off) are performed on the robot using different strategies to identify both the kinematic and geometric behavior laws. Both laws influence the uniformity of the material deposit. Time KPI also depends on a thermal factor linked to part cooling. Two numerical models can be used to predict the cooling time between layers required to maintain a stable interlayer temperature. They feed a neural network to predict interlayer cooling time. Quality KPI is expressed by comparison with material reference data or by mechanical testing. The most commonly used mechanical tests are microhardness, hardness, strain and fatigue. It is important to check whether the values obtained in microhardness and hardness tests are consistent with each other, and whether they serve as indicators of strength. The classical tensile test provides us with the yield strength, the elongation, and the ultimate tensile strength necessary to verify the values obtained in the hardness and microhardness tests, but it also enables us to compare these results with others in the bibliography. Fatigue testing is of great importance in the aeronautical and aerospace context, because of all the dynamic stresses that the parts are subjected to. But the high cost and time required to perform a conventional fatigue analysis, either for the tests themselves or for the material needed to build all the necessary samples ends up being a restriction. Stromeyer [START_REF] Stromeyer | The determination of Fatigue Limits under Alternating Stress Conditions[END_REF] shows that the material temperature varies when subjected to mechanical loads according to the thermomechanical couplings. In the particular case of fatigue, when a specimen is subjected to cyclic mechanical loading, a characteristic thermal signature of damage is quickly identified. According to [START_REF] Rosa | Thermographic methodology for rapid determination of the fatigue limit of materials and mechanical components[END_REF][START_REF] Luong | Infrared thermographic scanning of fatigue in metals[END_REF][START_REF] Luong | Fatigue limit evaluation of metals using an infrared thermographic technique[END_REF] this thermal signature can be correlated with the fatigue limit of the material. In this research, the "heat source reconstruction" is used, to track heat released or absorbed by the material, during a cyclic mechanical loading, in order to estimate the fatigue threshold. In conclusion, the work focuses initially on the kinematic behavior of the robot, before tackling thermal cooling problems. Both phenomena have an influence on the Time KPI. Thirdly, Quality KPI is addressed by means of mechanical tests.

WAAM cell (Addimadour)
1.6.

Summary and conclusion

In summary, AM still faces many challenges to be integrated into the industry some of which will be addressed here. The thesis presented here focuses in particular on the industrial problem that the WAAM process faces, which is centered on the creation of performance indicators that allow a correct evaluation of the production of parts, permitting a comparison with the conventional processes. In the first sub-chapter (1.1) the definition, history, advantages, and disadvantages of the WAAM process were presented, then some of the key factors and the influence they have on the course of the deposition process are described. In subchapter 1.2 the CMT technology used in this study was presented as well as the equipment associated with this technology. The characteristics that differentiate this subprocess from others were also described, and its variants were presented. Subchapter 1.3 is dedicated to the materials used in the WAAM process, their important characteristics, and the mechanical properties of the material after deposition. In subchapter 1.4 the industrial problematics is introduced, providing an overview of the challenges of implementing the WAAM process in industry. The context of the thesis is presented in subchapter 1.5. The concept of KPI is introduced and it is explained how it is intended to adapt this concept to the process evaluation.

Chapter -Kinematic analysis

Introduction

This chapter will present a study of robot kinematics, and the influence on the performance and precision of the process. Various programming parameters, speeds and trajectories tested are presented along with their results.

Chapter two outline

The various campaigns of different tests start with basic tests to identify how it performs in the most basic form of movement, and the impact that some key parameters have. The following tests are made based on the most used geometries, sectioning them afterwards and making new robot motion tests focusing on each of these sections. Thus, chapter 2 is organized as follows: ➢ Section 2.1 is dedicated to a literature review specifically on the problematics of kinematic research and its relevant developments. ➢ In section 2.2 the research problematics relevant to the context of this thesis is presented. ➢ In section 2.3 the experimental approach is detailed, as are the main questions we intend to answer. Furthermore, the importance of this study in the overall context of the thesis, as well as its relation to industrial problematics, is described. ➢ In section 2.4 the objectives we intend to achieve with this study are presented ➢ In section 2.5 presents the experimental process ➢ In section 2.6 the collected data is presented ➢ Section 2.7 presents the results obtained for the different tests with the different parameters. ➢ In section 2.8 are presented the time estimation models for the different strategies. ➢ In section 2.9 are presented the conclusions that it was possible to achieve 2.1.

Kinematic Bibliography

Wire arc additive manufacturing (WAAM) is a production process suitable for medium to large parts in the aeronautics field [1][2][3][4]. This process is characterized by high metal deposition capacity and reduced material waste, part cost and iteration time compared with standard processes [2][3][4]. The method consists of depositing molten metal through an electric arc between the nozzle and the alreadydeposited material in a sequence of two-dimensional (2D) layers using a robot to perform the movements [5]. The quality of the welded bead depends on various parameters, such as the quality of the wire, the wire feed speed (WFS), the travel speed (TS) and the heat input [1]. Weld bead geometry is controlled by optimizing the values of the deposition parameters [1,6]. Models can also be used to simulate the solidification process of the metal [7]. To limit high residual stresses, internal defects, porosities, and lack of fusion between adjacent weld beads, it is possible to control the deposition parameters or tilt the nozzle along the trajectory [8][9][10]. The mechanical quality of the final part depends on the combination of all the manufacturing input parameters [5].

In the case of a robotized process, the robot's kinematic behavior along the toolpath programmed to build the part is a determining factor [11]. In particular, slowing down the robot at constant WFS can lead to too much material being added locally: the layer is no longer regular [12]. It has been established that the quality of the metal deposited is directly related to the strategy used, which makes toolpath planning of paramount interest for the WAAM process [1]. An adequate toolpath is essential to ensure that the geometry of the deposit is close to or greater than the theoretical volume to be built [14]. The literature refers to various types of strategies, such as raster-pass, zigzag, contour or spiral in relation to material health, mechanical properties (such as strength and hardness) and geometric quality (shrinkage and warpage) [15][16][17][18]. The control of the volume of material deposited is also of great importance [19]. The most commonly used strategies to achieve a constant deposition thickness are based on equidistant path generation methods [16,18,20]. Toolpath planning is crucial and should be focused on the accuracy of the robot's movements in order to have a direct impact on the geometrical, material, and mechanical qualities of the built part [10,21,22,23].

Comments can be made about the continuous/discontinuous character of the deposition: ➢ When the geometry of the 2D layer allows it, metal deposition is preferably composed of several straight sections without intermediate stops or restarts [24]. This procedure, widely used in toolpath programming, allows the continuity of the arc, avoiding stops that usually create defects [25]. Curved sections are often broken down into linear segments when the toolpath is computed [2]. Continuous deposition may have some disadvantages due to the high heat input [26]; the latter impacts the weld bead size and by consequence the geometry of the material deposit [3]. In practice, the higher the heat input, the higher the roughness of the part (due to a higher fluidity of the melt pool and spreading of the drop) and consequently the higher the costs associated with post-processing [11,26,28]. ➢ For discontinuous deposition, a specific command (which is named arc ON/OFF for the KRC2 controller of the robot used in this study [29]) enables us to start (arc ON) and stop (arc OFF) metal deposition in specific sections of the toolpath. For example, the raster-pass strategy consists of depositing the metal along straight parallel sections in the same direction (deposition being stopped between these sections). Stops and restarts are inevitable to produce all kinds of parts, as for most rib-web structures such as flaps, wing ribs, stiffeners or landing gear ribs in aircraft and aerospace parts [2,3,25]. Since these structures cannot be created with Eulerian paths, it is impossible to produce them through continuous deposition [4]. Discontinuous depositions may lead to specific problems, such as longer deposition times, local defects, and material accumulation, but they are unavoidable for many part geometries [16]. It should be noted that WAAM robotic systems offer such a feature, which is necessary to stop the wire feed. In general, the robot controller manages the cold metal transfer (CMT) equipment through a sequence of commands including the deposition parameters (e.g. arc ON/OFF). The real-time processing of this sequential action and the management of the wire feed can induce randomness in the regularity of the weld bead deposit.

Thus, the literature shows that the use of WAAM processes necessarily imposes the precise control of the material input throughout the process. For this, it is necessary to study the kinematic behavior of the robot, which generates the variations in speed and position of the end effector. In the present study, the movement of the nozzle to create a rectangular layer was experimentally analyzed without physically depositing material (trajectory performance only). Different strategies, nozzle speeds and layer areas were compared in terms of deposition time, toolpath length and volume of "deposited" material. The consequences of discontinuous deposition (switching between arc ON and arc OFF) were also studied. The originality of this study is to better understand the complex interaction between CMT equipment and robot controllers. Another objective is to propose a model to calculate the manufacturing time of any layer area from a preliminary identification for a single area.

Research problematic

The performance of WAAM process is directly affected by the speed and accuracy of movements performed by the robot used. It is then necessary to understand how exactly the robot behaves when performing the most known strategies and the accuracy of its movements. As for each strategy they are normally composed by straight lines intercalated by different types of transitions, where curves are performed.

It is also important to understand if outside the domain to be filled the transitions can be performed without material deposition to reduce the cost, while maintaining the performance of the process. For this a clarification of the command arc ON/OFF is utterly necessary. The dynamic comportment of the robot in the transitions when the speed is increased is also addressed in this chapter.

In order to measure the performance of the process, as well as to be able to perform simulations that predict the deposition time, it is necessary to collect real information about velocities reached as well as areas of the trajectory where there is an error of precision in the positioning of the torch tip. The importance of this information is correlated with the construction of a kinematic numerical simulation model to predict deposition time for the different types of strategies.

Experimental approach

Having as a principle that the deposition time is the sum of times associated to each movement performed by the robot to produce the part. This principle allows us to split a given trajectory into sections. Then each section can be quantifiable in different physical quantities such as length and time and standardize the way it is calculated. The sum of all the sections should naturally result in the deposition time in the case of time, and in the case of length, it should result in the total length of the toolpath traveled by the robot torch.

In this study, various configurations of the existing commands were tested, as well as various values for each of them.

The originality of this study was to better understand the complex interaction between CMT equipment and robot controllers. Another objective was to propose a model to calculate the manufacturing time of any layer area from a preliminary identification for a single area.

The main purpose of these experiments was to answer the following questions: ➢ Are robots' movements repeatable in terms of time and trajectory? ➢ How accurate are they? ➢ Is accuracy dependent on the angles to be performed, or on the speed of the nozzle? ➢ Is it possible to predict the deposition time required for each type of strategy for a given part? ➢ Can switching the command Arc to ON and OFF in specific positions help to reduce waste without affecting the deposition time and consequently the performance of the process? ➢ Is it possible to find a compromise between time and material waste associated with the transitions? ➢ If there is a lack of accuracy in the trajectory, is it possible to introduce programming measures (such as using a large number of programmed points) to avoid this problem?

The importance of extracting one or several indicator(s) for the robot's movements is linked to a direct correlation between the productivity of the process and the associated cost of operations. The dissemination of this technology to other types of industry is also dependent on the standardization of the process. A large part of this standardization is linked to the adaptation of the robot and its ability to perform the required movements accurately.

Although the topic of kinematics is already the subject of research by others, an in-depth study where the strategies are compared in their productivity and geometric accuracy is lacking. This also gives an overview of the accuracy of each toolpath strategy, and the amount of material deposited. In my understanding and vision about the indicators, a big percentage of the cost of the process for a specific part is linked to his production time. To create a quantifiable indicator that would allow us to calculate the cost for the part, there is the need to define a formula to calculate the deposition time.

The studies were conducted on the following subjects:

➢ ACC.CP -Variable that defines the Cartesian acceleration for the toolpath in [m/s2] (here tested), the swivel acceleration in [°/s2] (not tested) and the Rotational acceleration in [°/s2] (not tested). ➢ VEL.CP -Variable that defines the continuous path velocity in [mm/s] ➢ Arc ON/OFF Transition -General definition for the instruction introduced in the robot that allows it to make transitions between zones with and without electric arc. ➢ Strategies -Strategies are different possible approaches to toolpaths used to cover the same area with material. ➢ Angles -Angles are curves or transitions made between straight sections with different orientations. ➢ Spatial repeatability -Spatial repeatability is a concept that intends to define the existence or not of repeatability in deposition times and trajectories when performed in different zones of a given volume.

Objectives

To make an in-depth study of the robot's behavior and its influence on the deposition process, several test campaigns were defined with different objectives. They are separated by topics as follows and with the following objectives respectively: ➢ The first campaign was dedicated to evaluating how the deposition times and the lengths of acceleration, deceleration and constant velocity evolve and were distributed when straight trajectories were made using different values in the ACC.CP command. ➢ The second test campaign was dedicated to studying the impact of the parameter VEL.CP. The parameter VEL.CP was set in the toolpath program and was set in accordance with the desired speed to perform the programmed toolpath. Assuming that the robot meets the speed placed in the program, the question remains whether when the % value of VEL.CP was changed in the button of the Kuka Robot Control Pad (KRCP) which variables change. Specifically, we want to understand if accelerations and decelerations change their behavior, affecting their distance, and therefore the length of the straight line between them. From a production analysis perspective, the goal was to understand if the deposition times change and how they change according with the percentage of VEL.CP in the Kuka Robot Control Pad (KRCP). ➢ The third campaign was dedicated to testing various programs to verify if the transition between the arc ON and OFF or Arc OFF to ON was possible to make without ceasing the robot's movement. It was also an objective to measure the time associated with this transition (if it takes place), and to verify if was there any unprogrammed robot movement. ➢ The fourth test campaign was based on several deposition strategies implemented in the manufacturing of parts by the WAAM process. The objective of this test campaign was to verify which transition between straight sections allows the ratio between WFS and TS to be as constant as possible, in order to check whether it was possible to achieve a uniform material deposit along the toolpath. It was also an objective to collect and compare the total deposition times, length traveled, speeds achieved in each one of the sections, and the amount of material that would be deposited in each strategy. Also in test campaign four, we aimed to test the arc transition whenever the robot left the OR area and re-entered. The goal was to verify whether it was possible to optimize the amount of material used in each of these strategies by reducing the material to be deposited in the areas that were only intended for transition between straight sections (where material was supposed to be deposited).

It was also important to evaluate if this transition was feasible, whether it induced precision defects, and what impact it had on productivity. ➢ In the fifth test campaign, the goal was to understand what exactly the accuracy and performance with which the robot performed different angles used in the strategies of the previous campaign, and in a specific range of defined angles. The goal was to collect results that would provide a spectrum of the accuracy, time, and lengths evolution from the lower angle to the higher angle. ➢ The sixth test campaign was dedicated to determining if by the simple fact of a part made at different points of the inert chamber and therefore working the robot with completely different angles between axes, there was repeatability of the total deposition time, and of the precision of the trajectory.

Experimental process

The following is a full description of all the parameters studied for each test campaign: In some strategies, a "virtual" arc transition is tested. The strategies where it was tested are those where there were transitions outside the OR between straight sections, and are described below:

ACC
The specific toolpath for testing the angles was made at speeds of 0.167 mm/s (10 mm/min) and 0.667 mm/s (40 mm/min) and for two quantities of programmed points, control points and 30 points distributed along the path.

Figure 13 shows some images of the experimental device. A six-axes KUKA robot (KR 100-2 HA 2000 model) and a KRC2 controller were used to control and perform the movement of the nozzle of a CMT device (Fronius). The spatial configuration of the robot allowed free and unobstructed movement of the equipment within the inert chamber that defines the robot's workspace. The latter was such that no kinematic singularity was possible. Most of the results in this study were obtained at a nozzle altitude Z = 50 mm from the platform, in the middle of the chamber. However, other locations in the chamber were also considered for comparison purposes.

In the framework of this study, the nozzle movement was studied without activating the torch (trajectory definition only).

Figure 13 -Photos of the system. In the framework of this study, the nozzle movement was studied without activating the torch (trajectory definition only).

ACC.CP

The first experiment is dedicated to the measure of the influence of the ACC.CP (1, 5 and 10 m/s²), parameter on the length and acceleration times. The expected behavior is represented in Figure 14 where the time and distance needed to reach the programmed speed should be different for different ACC.CP values, but the deceleration time would be the same. This hypothesis was formulated based on the understanding that the ACC.CP command affects only and exclusively acceleration, keeping the distance and deceleration time constant for the same programmed speed.

Vel.cp

The goal of the test is to analyze the behavior of the robot according to the variation of Vel.cp. The command will modify the form of the tool path to maintain the level of speed. It is also expected that only the constant speed represented in green in Figure 15 would be affected.

For the tests, the percentage of speed is changed in the robot Kuka control panel (KCP).

Arc ON/OFF

This test is intended to understand the robot's behavior at the arc transition locations (Figure 16). The goal is to test different programs (Figure 17) and aim to acquire the times required for the arc transition. At the same time aims to test various programming functions to identify the best solution without the robot stopping. The additional "continuous" command is also tested.

Angles

The goal is to understand the influence of the angles between successive elementary paths on the speed and accuracy of the trajectory while the programmed nominal speed of the nozzle is constant.

It is expected that the command computes smooth connect curves and introduces decelerations and accelerations at the corner.

The tests were done in two different sub-campaigns. The first sub-campaign tests the 8 proposed strategies. These angles were tested using two speeds of 10 and 40 mm/s, and for each speed two quantities of programmed points (control points and 30 points along the trajectory). 32 tests were performed.

In the second campaign all angles between 20° and 160° were tested with a 20° interval between each tested angle plus the 90° angle that was tested again. For the experiments with these angles only control points and 10 different speeds were used, starting the sequence with the lowest speed of 5 mm/s and increasing 5 mm/s in each test, up to the highest of 50 mm/s. 90 tests were performed.

Figure 18 shows four example trajectories for different angles of 20°, 45°, 90° and 160°, and the expected behavior of the robot during the displacement. As can be seen in the Figure, we expected initial acceleration (blue in Figure 18) and final deceleration (red in Figure 18) sections to be identical regardless of the angle of the trajectory. Two sections with constant velocities (green) are also expected, and finally, near the area where the angle is made, a deceleration before and an acceleration after performing the curve were also expected. The acceleration and deceleration time and length near the location where the curve is made should vary, increasing for closer angles and higher speeds.

Objective Rectangle (OR)

Two different manufacturing areas, named Objective Rectangle (O.R.) are proposed for the test. The O.R. defines a rectangular area ("small OR": 21.5×43 mm 2 and "large OR": 43×86 mm 2 ), to be theoretically filled by material deposit. Figure 19 represents the 8 considered strategies: raster-pass, semi-circular, spiral, rectangular, swiping, as well as three triangular strategies differing in the angle of the triangles (45°, 60° and 90°). The blue lines represent the theoretical toolpaths, whit the indication of the travel direction. According to the strategy, portions of the toolpath can be located outside the O.R (raster-pass, semi-circular and triangular strategies). That can imply a stop of the electric arc (Arc.OFF command). Other strategies (spiral, rectangular and swiping strategies) require Arc.ON command on the whole toolpath. The Material Deposition Rate is assumed equal to 94.25 mm 3 /s previously defined under similar conditions, using a WFS of 83.335 mm/s and a wire diameter of 1.2 mm. Two nominal travel speeds were considered in the study: 10 mm/s and 40 mm/s. The distance 𝑊 WB between the linear sections of adjacent paths (see Figure 19) is set to 4.43 mm, according to precedents experiments on 2209 stainless steel. Thus, the number of horizontal weld beads 𝑛 WB is equal to the ratio between 𝑊 WB and the width 𝑊 of the OR, where floor(𝑥) means the nearest integer lower than 𝑥:

𝑛 WB = floor ( 𝑊 𝑊 WB ) (1)
The remaining distance 𝑊 bound between the OR boundary and external depositions (see Figure 19) is equal to:

𝑊 bound = 𝑊-(𝑛 WB -1)×𝑊 WB 2 (2)
𝑛 WB is increased by 1, if 𝑊 bound ≤ 0.4 𝑊 WB in order to deposit enough material at the boundary of the OR. The numerical application gives 𝑛 wb equal to 5 and 10 for the small and large OR, respectively, and 𝑊 bound equal to 1.89 mm and 1.57 mm, respectively.

Spatial repeatability

As usual, it's clear that robot behavior is not isotropic in the workspace. It is therefore necessary to study its repeatability in the workspace. Several areas of the workspace are identified, and the swiping strategy is tested, as it offers the longest path (Figure 20). This strategy is initially executed at the center of the inerting chamber (position A in Figure 21), then at the 15 positions shown, to cover the total volume of the inerting chamber. The coordinates of each starting point are:

Collected data

The software ADAONE® (from ADAXIS®) is used to collect data of the robot's effector positions at variable intervals (IPOC) and transcribes them into an excel file.

Method used for processing the data

The data collected are the coordinates of the position of the torch tip every 12 milliseconds (IPOC). This interval was the minimum possible interval. Figure 22 shows the format of the collected data. For this study, only the timestamp and the orthogonal coordinates must be collected. In order to estimate: ➢ Length of wire (necessary). ➢ Incremental length of the wire. ➢ Volume of material (mm³). ➢ Incremental volume of material (mm³) (cm³).

Figure 23 shows in red programmed and in blue the collected points. Thereafter the theoretical distances between the different programmed points in the different axes in space, and the total distance traveled are calculated. Then several speed graphs are computed, either in each axis, or in space, or even focusing on important transition zones to make the necessary measurements and check the error between trajectories (theoretical and real). Thus, a sheet summarizes all the information calculated, namely: Thus, it was possible to obtain for each toolpath the values corresponding to: ➢ Average speed in straight sections. ➢ Average speed in curves. ➢ Total average speed.

➢
Finally, a page dedicated to the calculation of the amount of material is introduced. Using as input the time between each point collected, and the theoretical WFS, a calculation is made, allowing the association of each section with the amount of material that would be deposited.

Experimental results

Due to the volume of data collected, only the most representative results are presented below.

ACC.cp

Figure 24 shows the coordinates (X,Y) collected of the movement of the torch tip along the programmed toolpath from point (0,0) to point (100,0). Figure 25 shows the variation of the speed calculated using the real IPOC. The speed is equal to 10 mm/s and the acceleration (ACC.cp) equal to 1 m/s². Speed graphs show the variation of the speed along the toolpath. The programmed speed is the average of the speed values reached between the end of acceleration and the beginning of deceleration. The ACC.cp values changed the acceleration in a non-linear pattern. The backlash movements appear in the calculated velocities resulting in some peaks outside the normal range of values.

Table 1 presents the manufacturing times for each section, namely acceleration, constant speed, and deceleration that were collected for all robot motion tests performed with different ACC.cp. Table 2 shows that the decrease in acceleration time does not vary linearly with increasing ACC.cp. Acceleration time is also a function of rated speed. Tests show that ACC.cp = 10 reduces acceleration time. Acceleration times should be between 0.132 and 0.204 seconds for an ACC.cp of 10. As might be expected, deceleration times have also increased between speeds of 0.01 and 0.025 m/s, whereas with the difference between speeds of 0.025 and 0.04 m/s, times don't seem to change significantly. Backlash also affects acceleration time. Distances covered during acceleration increase non-linearly with programmed speed. Distances covered during deceleration are always longer than during acceleration. Figure 28 to Figure 33 show the proportion of distances covered in each phase for a 100 mm straight path.

At a speed of 10 mm/s, acceleration and deceleration phases account for a maximum of 3.3% of travel time (Figure 28). The results show predictable robot behavior with ACC.cp and programmed speed influencing acceleration and deceleration times. and the constant speed reached. Backlash always appears at the same coordinates, but the amplitude varies with speed and acceleration. Measured speed is very noisy, making identification of values only approximate.

Vel.cp

This sub-section presents results obtained for different imposed effector speeds (Vel.cp). The trajectory of the nozzle for a speed of 10mm/s (i.e. Vel.cp = 1% of 1000mm/s) placed in the KCP was: At a speed of 10 mm/s, acceleration lasted around 9.372 seconds and deceleration 9.828 seconds.

During the acceleration and deceleration phases, peaks of up to 5.43 and 5.67 mm/s respectively occurred, these speeds being related to the play in the Y axis.

Figure 36 shows the nozzle trajectory for a velocity of 50 mm/s (i.e. 5% Vel.cp of 1000 mm/s).

When the speed increased to 5% of 1000 mm/s, the initial backlash increased to 0.19 mm along Y+, over a length of around 25 mm in the X axis. At x = 0, initial backlash increased to 0.19 mm along Y+. At x = 90 mm, the robot began to oscillate towards the Y+ side, until the end of the trajectory at X = 200 mm, with an amplitude of 0.07 mm along Y+. The speeds recorded during the trajectory are presented in Figure 37. The speed achieved was 50 mm/s. The acceleration and deceleration had precisely the same duration of about 1.98 seconds. The rest of the distance was performed at constant speed in 2.03 seconds.

The trajectory of the nozzle for a speed of 100 mm/s (i.e. 10% of Vel.cp of 1000 mm/s) is presented in Figure 38. The tendency to drift towards the Y+ side already observed increases, reaching a value of 0.09 mm in the final section, whereas the initial clearance has a value of 0.1 mm, lower than with 5% (0.19 mm).

The speeds recorded during the trajectory are presented in Figure 39. The speed achieved was 100mm/s over a period of 0.92 seconds. Acceleration and deceleration had a value of 1.06 and 1.10 seconds respectively. As expected, the nominal speeds are affected according to the percentage set on the remote control.

It should be noted that accelerations and decelerations are also affected by this percentage, and for this reason for depositions it should always be used 100% of the defined speed.

Arc ON/OFF influence

This section presents the impact of flare management on trajectory at arc transitions. The programmed trajectory was a 100 mm straight line, travelled at a constant speed, except for acceleration and deceleration. Note that the scales of the X-and Y-axes are different for readability. The speeds reached by the torch nozzle during the motion of the robot with programs 3, 4 and 5 were identical. Only the graph corresponding to program 3 is shown here in Figure 43. The graph shows two speed peaks of 12.4 and 13 mm/s which, as mentioned above, are related to the fast backlash movements of the robot, when it undergoes decelerations and accelerations. After reaching the speed of 10 mm/s at second 5.124 there are small accelerations and decelerations with a maximum amplitude of 1.18 mm/s. These accelerations may be due to vibration in the robot arm, or to errors induced by the coordinate measuring system. It is important to note that with this programming the robot stopped to perform the arc transition. Table 5 gathers all the times collected for each section of the simulated trajectories. For all programs, the robot reaches the programmed speed regardless of whether the arc was in ON or OFF mode.

Program 5 with the "CONTINUE" command did not guarantee continuous movement of the robot. The position error is limited to ±0.03 mm, except in the transient sections of the trajectory (beginning, end and middle when switching from arc ON to arc OFF). Whatever the arc ON/OFF choice, a transverse error in position ("backlash") was visible at the beginning and at the end of the toolpath: Y  0.2 mm and Y  -0.1 mm respectively. A similar transverse error is observed at the transition between arc ON and arc OFF, and reverse. In all cases, this transverse error (along Y) is associated with an acceleration/deceleration of the robot. The robot stopped (zero speed) when switching from arc ON to arc OFF and reverse. The total travel time is therefore longer when changing the status of the arc ON/OFF command due to the associated stops. Consequently, an inhomogeneous deposition of material should be expected, due to the variation in speed while the WFS is constant. Indeed, an arc transition induces necessarily a robot stopping.

Angles

The complete analysis of the angle tests is presented in Table 6. Only the most characteristic graphs are shown. A backlash movement is located at the beginning of the trajectory. The rest of the toolpath follows the programmed points, except for the curve section. The graph A2 zooms on the curve section.

The section starts at the coordinate (42.13, 0) and presents the center of curvature at (42.55, -0.31). The trajectory error is 0.546 mm, expressed in the graph by the precision error PE. After passing the curve section, the error is equal to 0.1 mm.

Figure 49 shows that the curve section induces a slowdown of up to 3.73 mm/s during a period of around 0.288 seconds. The study of the speed produces the same conclusion (Figure 51). Thus, we can conclude that the number of programmed points does not change the trajectory. The following example is dedicated to the 90° angle. Figure 52 shows four graphs, C1 and C2 referring to the planned toolpath using 30 points along the toolpath, and D1 and D2 referring to the planned toolpath using only control points. Graphs C2 and D2 are zooms of the curve sections of the respective graphs of C1 and D1. The different numbers of points did not influence the robot's trajectory. PE are similar and located in the same sections of the trajectory. Figure 53 shows the speeds achieved by the torch nozzle during the motion of the robot using a speed of 10 mm/s and 30 programmed points. Speed profiles C1 and D1 are very similar (Figure 53). That confirms that the number of programmed points does not change the trajectory. Table 7 shows a summary of the results obtained for the angles used for trajectories with a speed of 40 mm/s. The Comparison of Table 6 and Table 7 shows the influence of the speed on the actual velocities achieved, times in each section and length of dislocation. The orange color identifies the lowest value of each column, while the green color identifies the highest. The values written in red appear abnormal that may have come from a software glitch or error when collecting the data. 12 present an overview of the results for the eight strategies illustrated in Figure 19 and the two nominal speeds (10 mm/s and 40 mm/s), for the small (21.5×43 mm2) and large (43×86 mm2) Objective Rectangle (OR), respectively. The total time, the total length and the total volume of deposited material (i.e. when arc ON is activated) are presented. Two experimental protocols are applied: with arc ON activated over the whole toolpath; with arc ON and OFF inside and outside the OR respectively. The raster-pass strategy is a special case because arc ON and arc OFF are both applied inside the OR, leading to "non-applicable" (N/A) indicated in certain cells of the table. Furthermore, for the rectangular, spiral, and swiping strategies, cells in the column "With arc ON and OFF" are indicated N/A because the whole toolpath remains in the OR. Analysis of the results is presented in the following sub-chapters. This section compares different strategies at the nominal speed of 40 mm/s for the small OR with arc ON activated over the whole trajectory. Only one of the triangular strategies (namely 60°) is presented in the illustrations for comparison, but other angles are also discussed. Firstly, Figure 57 presents the toolpaths and speeds for the semi-circular, rectangular, spiral strategies as well as for one of the triangular strategies (namely 60°). The nominal speed is set to 40 mm/s for an OR of 21.5×43 mm² and arc ON was activated over the whole of each trajectory. The red dots are the programmed points, whereas the blue curves correspond to the measured trajectories. The following comments can be expressed: ➢ As expected, trajectory errors appeared for all the changes in direction. This fact is significant for the quality of the WAAM process when the whole trajectory remains inside the OR (here for the rectangular and spiral strategies), because a local lack of material derives from the trajectory error. The problem is less crucial when trajectory errors occurred outside the OR (here for the semi-circular and 60° triangular strategies), but it can be observed that small, curved sections of the toolpath also exist inside the OR, at boundaries (when entering and leaving the OR). The comparison between the three triangular strategies (not illustrated here) shows that this problem increased with the angle from 45° to 90°. ➢ The speed variations are presented in the Figure 57. As expected, the speed decreased with each change in direction. The speed dropped about 30% and 50% for the semi-circular and 60° triangular strategies respectively. The comparison between the three triangular strategies (reported later) shows that the lower the angle was, the greater the speed drop suffered. These drops are not a priori a problem as they occur mainly outside the OR (see below for considerations about the travel time). For the rectangular and spiral strategies for which the toolpath remains inside the OR, the speed drop was of about 25% at the direction changes, which is a problem for the uniformity of the metal deposition. For all the small straight sections of the rectangular strategy as well as for the short section A-B of the spiral strategy, the robot had insufficient time to reach to the nominal speed (40 mm/s). Decreasing the nominal speed reduced these problems. ➢ Table 13 allows a comparison of the four strategies presented in Figure 57 in terms of total time, total length, and average speed. By construction, the total time is shorter for the spiral and rectangular strategies than for the semi-circular and triangular strategies due to the additional toolpath sections, outside the OR. The spiral strategy presented the lowest total time (5.628 s), due to the shortest total length. The rectangular strategy featured a slightly longer total time (5.664 s) due to the slightly longer overall length. The accuracy of the toolpath can be defined by the ratio of the total length over the programmed length. The best accuracy is obtained for the semi-circular strategy (97%), due to the absence of sharp changes in direction, because the programmed toolpath contains smooth and curved transitions between the horizontal straight sections. However, the accuracies of all four strategies can be considered as being quite similar (between 95% and 97%). Secondly, Figure 58 compares the raster-pass and swiping strategies, still for a nominal speed of 40 mm/s and an OR of 21.5×43 mm 2 . In addition to the trajectories and speeds, the figure also provides the variation in volume of deposited material (assuming a constant wire feed rate of 94.25 mm 3 /s) as a function of time and distance travelled.

The following observations can be expressed regarding this figure :   ➢ The sharp changes in direction have led to a significant speed drop of 100% and about 80% for the raster-pass and swiping strategies respectively (see Figure 58 were obviously present when arc OFF is activated; however, when plotting the volume of material as a function of the distance travelled, negative consequences of the speed drops were visible: see zooms in Figure 58-a-4 and -b-4. The order of magnitude of the volume "jumps" was the same for the two strategies (about 7 mm3). ➢ Table 14 enables a global comparison of the swiping and raster-pass strategies. The programmed and actual lengths as well as the volume of deposited material were higher for the swiping strategy than for the raster-pass strategy. This is due to the numerous weld bead overlap zones in the former case. The raster-pass strategy presents an accuracy (defined above as the ratio between total actual length and total programmed length) of 0.998. This good ratio was due to the fact that this strategy involves switches between arc ON and arc OFF at the beginning and end of each straight section, that imposes a stop at the beginning and at the end of each straight section. On the contrary, for the swiping strategy, accuracy can be considered as low (length ratio of 0.89). This was due to an accumulation of trajectory errors at each change in direction. Although over a much longer programmed length (464.246 mm compared to 387.910 mm), the total time for the swiping strategy was only slightly longer than that of the raster-pass strategy (12.036 s compared with 11.580 s). This was due to the time "lost" when switching between arc ON and arc OFF in the latter case. The following observations can be expressed regarding this figure: ➢ In Figure 59 a-1) and b-1) the toolpath (in blue) did not follow the planned toolpath in the change of direction sections. Since all angles are 90°, the error between planned and actual toolpath is similar for both strategies: 1.178 mm for rectangular, and 1.074 mm for the spiral strategy. The robot adapts the trajectory to maintain the programmed speed, but that implies the possibility of lack of material in these areas (points marked A, B, C, D for the rectangular and A, B, C, D, E, F, G, H for the spiral). ➢ A speed reduction occurs at the 90° angles (curves) locations (points A, B, C, D, E, F, G, H in graphics a-2) and b-2)). For the rectangular strategy a minimum velocity of 26.37 mm/s (average of 8 curves) is reached, while for the spiral strategy the velocity is 27.48 mm/s (average of 8 curves). The speed varies constantly when performing straight sections in a range of 2.5 mm/s in most cases. Even with this variation, the robot scrupulously complied with an average speed of 40 mm/s between all acceleration, deceleration, and cornering points. ➢ Table 15 enables a global comparison of the strategies rectangular and spiral. The amount of material "virtually" deposited is similar for both toolpaths, with a difference in favor of the rectangular strategy of 3.393 mm³ more material than the spiral. The small difference in the amount of material deposited between the rectangular and spiral toolpaths can be explained by the difference in the speeds achieved resulting in different deposition times. ➢ As we can see in graphs from the Figure 59 a-4) and b-4) (in the zoomed areas) the material deposition per unit of length increases in the curved sections, due to the fact that the WFS was considered constant regardless of the robot speed.

Influence of the arc OFF outside the OR

The arc transition usually takes place in transition zones and has the function of switching off the electric arc that enables the melting of the metal, while the transition path between deposition zones is ensured. This section discusses the difference depending on whether or not arc OFF should be applied outside the OR. Figure 60 illustrates the differences for the 45° triangular strategy at a nominal speed of 40 mm/s for an OR of 21.5×43 mm2. Figure 60 -a-1 and -b-1 show the toolpath in the two cases. The red and black dots correspond to the programmed points with arc ON and arc OFF respectively. The blue curves are the measured toolpaths. Some comments can be expressed: ➢ The trajectory error is much higher outside the OR when arc OFF is activated (Figure 60-a-1).

When switching from arc ON to arc OFF, the speed drops to zero at times A, C, E and G (Figure 60-a-2). Just after A, C, E and G, the speed is increased without reaching the nominal speed of 40 mm/s due to the transition from arc OFF to arc ON at times B, D, F and H. The robot stops were already observed and reported in section 2.5.3. The question arises as to whether the stop induced by arc ON or arc OFF might not have caused a subsequent catch-up movement, which would produce such a transition trajectory. In this case, the speed law is the result of interaction between the robot controller and the CMT equipment. The delays (acceleration and deceleration times) due to arc ON/OFF switching appear to have been compensated for by a shorter toolpath outside the OR. ➢ The speed reductions when arc ON was activated over the whole trajectory (Figure 60 ➢ When arc ON was activated over the whole trajectory, the time of the whole toolpath is shorter (6.732 s to be compared with 7.932 s), which is advantageous for productivity. Moreover, the total time at constant speed inside the OR is longer (4.632 s compared to 4.380 s), which is a priori better in terms of deposition quality inside the OR. ➢ The same conclusions can be expressed about the lengths. On the other hand, the arc ON / OFF command induces significant differences in the length of trips in and out of the OR. (19.474 mm, compared to 34.920 mm). ➢ The total time with "arc OFF inside the OR" was 0.156 s, which corresponds to about 2% of the whole toolpath time (7.932 s). This cannot be considered as a negligible parasitic effect in the case of large mechanical parts. Table 17 shows the influence of the arc ON / OFF function on robot motion for the triangular strategy with a 60° angle. Times and lengths are measured on different phases of the trajectory: constant speed in OR, acceleration in OR, deceleration in OR, inside OR, outside OR and on the whole tool trajectory.

The "total time with arc OFF inside the OR" indicator counts little time shifts observed in the application of the arc ON/OFF command. The following comments can be expressed from the table: ➢ When arc ON is activated over the whole trajectory, the time of the whole toolpath is shorter (6.456 s to be compared with 8.172 s), which is advantageous for productivity. Moreover, the total time at constant speed inside the OR was longer (4.632s compared to 4.272 s) similar to the 45° angle times, which is a priori better in terms of deposition quality inside the OR. ➢ Arc OFF produces a longer trajectory of 3.266 mm, because the robot marks the last point on the boundary of OR and does not cut the toolpath inside OR. ➢ The total time with "arc OFF inside the OR" is 0.192 s, which corresponds to about 2,4% of the duration of the whole toolpath (8.172 s). This cannot be considered as a negligible parasitic effect in the case of large mechanical parts. Table 18 provides the same results as Table 17, but here for 90° triangular strategy. The following comments can be expressed: ➢ Arc ON function activated over the whole trajectory reduces the time 7.932 s from to 6.180 s. But the total time at constant speed inside the OR is shorter (4.332 s compared to 4.380 s), which is a priori worse in terms of deposition quality inside the OR. ➢ Arc OFF activation induced a longer trajectory in contrast to results obtained with arc ON only.

Which means that the toolpath with arc ON only, had worse accuracy. ➢ The total time with "arc OFF inside the OR" is 0.216 s, which corresponds to about 2,7% of the total time (7.932 s). This also cannot be considered as a negligible parasitic effect in the case of large mechanical parts. Using table 19, following comments can be expressed for semi-circular strategy :

➢ Arc ON activation reduces the time (6.264 s to be compared with 7.908 s), which is advantageous for productivity. But the total time at constant speed inside the OR was shorter (5.628 s compared to 6.372 s), which is a priori worse in terms of deposition quality inside the OR. ➢ The length outside the OR implies a longer trajectory in contrast with some results obtained before. Which means that the toolpath with arc ON only has worse accuracy. ➢ The total time with "arc OFF inside the OR" is 0.492 s, which corresponds to about 6,2% of the time (7.908 s). This also cannot be considered as a negligible parasitic effect in the case of large mechanical parts. Table 20 shows the results obtained for all toolpaths with arc transition and the partial deposition times inside the OR and outside the OR, for two speeds 10 and 40 mm/s and for the two OR sizes.

Assuming that the accelerations were identical, the differences in deposition time within the OR is related to the length of deceleration within the OR, and to the accuracy of the toolpath. For this reason, the shortest time should indicate the strategy with the shortest deceleration length but also the shortest precision error. The toolpath with the longest deposition time should have the longest deceleration within the OR and/or the largest precision error. A few observations can be expressed: ➢ For the 10 mm/s speed and the small OR two toolpaths the triangular 45° and 60°are presented. The shortest deposition time is 22.152 s inside the OR. The shortest time outside the OR is the 45° triangular toolpath with 1.644 s, with an error of 0.458 mm.

➢ For the speed of 10 mm/s and the large OR the 45° triangular toolpath presented the shortest time of 87.456 s inside the OR, with an off-OR time of 12.912 s and an error of 0.43 mm. ➢ For the 40 mm/s speed and the small OR the shortest time inside the OR of 6.216 s is done in the 60° triangular toolpath, the transition time outside the OR was 1.956 s with an error of 0.12 mm. ➢ For the 40 mm/s speed and the large OR the shortest time inside the OR is 23.172 s obtained by the 45° triangular toolpath, and the time outside the OR was 4.956 s with an error of 1.64 mm.

As identified above, the 45° triangular toolpath presents satisfying deposition times for almost all scenarios. At transitions, the behavior of this strategy is different, as the reduced angle induces a strong slowdown that combines with the stop imposed by Arc OFF. As a result, the robot restarts in the right direction.

For strategies with arc ON only the quality evaluation has the same principle as for strategies with arc transition. Assuming identical acceleration for the same velocity, the trajectory with the shortest deposition time inside the OR has the shortest deceleration length inside the OR. Consequently, there will be less accumulation of material because the ratio between WFS and TS will be constant over a longer period of time.

➢ For the small OR, with a continuous arc ON and a speed of 10 mm/s, the semi-circular is the strategy with the shortest time within the OR with 21.552 s, while the time is increased of 2.832 s, for arc transition. ➢ The large OR at a speed of 10 mm/s, the 60° triangular presents the lowest time of 86.124 s.

Outside the OR this strategy has a time of 8.016 s. ➢ For the small OR at a speed of 40 mm/s, the 45° triangular strategy produces the lowest time of 5.580 s inside the OR, and 1.152 s outside the O.R. ➢ For the large OR made at 40 mm/s the 60° triangular strategy presents the shortest time with 21.708 s inside the OR, and a time of 2.004 s outside the OR.

Thus, the higher the average speed achieved during the entire trajectory is, the more constant the ratio between WFS and TS will be, which is an interesting indicator of the quality of the material. A long transition time is not necessarily negative for the quality, but negative for the productivity. A comparison between the two nominal speeds and the two OR sizes is therefore necessary to consider an extrapolation in a generic linear pattern. Table 21 compares the results between the two nominal speeds (10 mm/s and 40 mm/s) and between the two OR areas (21.5×43 mm 2 and 43×86 mm 2 ). The comparison concerns the 45° triangular strategy with arc ON activated over the whole trajectory. Some comments can be expressed about the ratios of results between the two nominal speeds and between the two areas: ➢ At a nominal speed of 10 mm/s, the ratio of total times is equal to 3.68 between the two sizes of OR, and to 3.70 for the total length, as the ratio of the area is equal to 4. The difference can be due to the computation of the distance between adjacent paths. Thus, a time 3.68 times longer is necessary to cover a 3.70 times longer toolpath, which shows a nearly linear response. On the other hand, at a nominal speed of 40 mm/s, a time 3.61 times longer is necessary to cover a 3.76 times longer toolpath, highlighting a loss of proportionality, due to a more longer period for the acceleration and for the deceleration. ➢ Concerning this difference ratio of 0.25 between the two nominal speeds, it can be noted that proportionality was clearly respected: the measured time ratio is 0.26 and 0.25 for small and large OR respectively. When multiplying the nominal speed by four, the travel length was lower: a decrease of 3% and 2% for the small and large OR respectively, which is not negligible. 21). Indeed, a serial robot features a priori variable structural stiffness within its workspace [32], and the magnitudes of trajectory errors may vary inside the workspace. The results described in the previous sections corresponded to location "A". Let us mention that the robot is not placed symmetrically with respect to the workspace, justifying the choice of testing symmetrical locations in the chamber. At each location, a trajectory is performed using the swiping strategy and a nominal speed of 20 mm/min. As in the previous sections, two OR areas are considered: 21.5×43 mm2 and 43×86 mm2 and two quantities of programmed points (control points and 200 points along the trajectory). For the small OR, the deposition time varied between 23.840 s and 23.890 s depending on the location in the workspace. For the large one, it varied between 92.964 s and 92.988 s. Deposition times can be considered as homogeneous within the workspace. The same conclusion can be expressed from the values of the lengths: there was no significant variation between the locations.

These results are positive, as they do not reveal any heterogeneity in the workspace of the robot. Table 22 shows some results of the robot motion tests performed at the most extreme points of the inerting chamber.

Definitions:

➢ 𝑇 init accel and 𝐿 init accel are the time and the length, respectively, of the initial acceleration.

➢ 𝐿 accel and 𝐿 decel are the lengths of acceleration and deceleration (respectively) at the beginning and end (respectively) of a horizontal straight section of the toolpath excluding the first and last ones. It can be noted in Table 23 that some values are equal to zero, meaning that acceleration or deceleration phases do not occur in the horizontal straight sections (they are in transitions in between). ➢ 𝑇 trans : time of the transition between two successive straight sections of toolpath, whether these are on the x axis or the y axis; (there is a variable for each curve and needs to be calculated in accordance with the formula given further in the manuscript). ➢ 𝑇 Tconst (𝑇𝑆): Transition time at constant speed (movement time between acceleration and deceleration relative to the arc transitions). ➢ 𝑇 final decel and 𝐿 final decel are the time and the length, respectively, of the final deceleration. ➢

Raster-pass strategy

The formula (3) is dedicated to calculating the total time for the raster-pass strategy as a function of the 𝑊× 𝐿 area of the OR, the nominal speed (𝑇𝑆) and the number of horizontal weld beads 𝑛 WB calculated from Eqs (1) and (2) (in section2.5.5): I would recall the relation you mention between the width W and the number of weld beads necessary to cover this width nWB . Then, only use 𝑛 WB and don't mention W in the input arguments anymore. 𝑇 total ( 𝐿, 𝑇𝑆, 𝑛 WB ) = 𝑇 init accel (𝑇𝑆) + 𝑇 init const (𝐿, 𝑇𝑆) + (𝑛 WB -1) × 𝑇 trans (𝑇𝑆) +(𝑛 WB -2) × 𝑇 straight const (𝐿, 𝑇𝑆) + 𝑇 final const (𝐿, 𝑇𝑆) + 𝑇 final decel (𝑇𝑆)

where:

➢ 𝑇 init const is the duration of the first horizontal straight section at constant speed:

𝑇 init const = 𝐿 -𝐿 init accel (𝑇𝑆) -𝐿 curve decel (𝑇𝑆)) 𝑇𝑆 (4)
➢ 𝑇 trans (𝑇𝑆) -Time of transition between horizontal straight sections at constant speed:

𝑇 trans (𝑇𝑆) = 2 [𝑇 decel (𝑇𝑆) + 𝑇 Arc transition (𝑇𝑆) + 𝑇 accel (𝑇𝑆)] + 𝑇 Tconst (𝑇𝑆) (5)
➢ 𝑇 straight const is the duration of any horizontal straight section at constant speed, excluding the first and final ones:

𝑇 straight const = 𝐿 -𝐿 accel (𝑇𝑆) -𝐿 decel (𝑇𝑆) 𝑇𝑆 (6)
➢ 𝑇 final_const is the duration of the final horizontal straight section at constant speed:

𝑇 final const = 𝐿 -𝐿 curve accel (𝑇𝑆) -𝐿 final decel (𝑇𝑆) 𝑇𝑆 (7)
2.8.2. Triangular and Semi-circle strategies

The formula (3) is also dedicated to calculating the total time for the triangular and semi-circular strategies as a function of the 𝑊× 𝐿 area of the OR, the nominal speed (𝑇𝑆) and the number of horizontal weld beads 𝑛 WB calculated from Eqs (1) and ( 2). Also, the parameters 𝑇 init const , 𝑇 straight const , and 𝑇 final_const are calculated using formulas ( 4), ( 6) and ( 7) respectively. For these trajectories, the 𝑇 trans (𝑇𝑆) must be calculated with a different method, as shown in the formula (8).

➢ 𝑇 trans (𝑇𝑆) -Time of transition between horizontal straight sections at constant speed:

𝑇 trans (𝑇𝑆) = 𝑇 decel (𝑇𝑆) + 𝑇 Arc transition (𝑇𝑆) + 𝑇 accel (𝑇𝑆) (8) 2.8
Where 𝑊 WB is the distance between the linear sections of adjacent paths as presented in the section 2.5.5.

Rectangular strategy

The formula ( 9) is dedicated to calculating the total time for the rectangular strategy as a function of the 𝑊× 𝐿 area of the OR, the nominal speed (𝑇𝑆) and the number of horizontal weld beads 𝑛 WB calculated from Eqs (1) and ( 2

where:

➢ 𝑇 init const is the duration of the first horizontal straight section at constant speed (4)

➢ 𝑇 straight const (𝐿, 𝑇𝑆) is the time of transition between horizontal straight sections at constant speed (6)

➢ 𝑇 final_const is the duration of the final horizontal straight section at constant speed (7) It should also be taken into account that 𝑇 trans (𝑇𝑆) is:

𝑇 trans ( 𝑇𝑆, ) = 𝑇 decel (𝑇𝑆) + 𝑇 ec ( 𝑇𝑆) + 𝑇 accel ( 𝑇𝑆)

𝑇 decel (𝑇𝑆) -Time for deceleration before the curve 𝑇 ec ( 𝑇𝑆) -Time necessary to do the effective curve 𝑇 accel ( 𝑇𝑆) -Time for acceleration after the curve until it reaches the nominal speed

The method is illustrated for the 45° triangular strategy, but the principle is the same for the other strategies. Based on the results of the experiments at 10 mm/s and 40 mm/s, Table 23 provides the parameters initially identified for the small OR (21.5×43 mm2), distinguishing whether arc OFF is applied outside the OR or not. The same approach was adopted to calculate the total times for the small OR from the parameters identified for the large OR. This gives 0.24%, 3.5%, 0.33% and 9.3% of error respectively. Thus, we consider that the formula is precise for all the cases with arc ON activated over the whole trajectory: the errors are less than 0.4%. The error is higher with arc OFF activated outside the OR: up to 16.3%. This is mainly due to the assessment of 𝐿 accel , 𝐿 decel and 𝑇 trans which was performed from one experiment, as noted above. This highlights the importance of the preliminary assessment of these parameters when using the manufacturing time model.

Conclusions

In the WAAM process, the accuracy of the toolpath is of prime importance for the mechanical properties of the final part because of the material defects that could be generated. This accuracy depends on the kinematic behavior of the robot, as well as the interaction between CMT equipment and robot controllers. The tests presented here show that a rigorous study of the robot's behavior and programming mode is required to obtain compliant parts.

A motion analysis of the nozzle using a KUKA KR 100-2 HA 2000 robot with a KRC2 controller is performed in this study. The movement of the robot is analyzed without depositing material (trajectory definition only) using various strategies, nozzle speeds and layer areas for continuous and discontinuous "virtual" depositions. The analysis also enabled us to identify various problems associated with acceleration and deceleration phases, in particular for discontinuous depositions. Several points can be highlighted: ➢ Discontinuous deposition leads to additional travel time, due to deceleration and acceleration at each deposition stop and restart respectively. However, it has the advantage of saving material (in transitional sections). ➢ Planning toolpaths on transitions sections outside the nominal deposition area can be useful to push away inaccuracy problems out of the functional area. Discontinuous deposition would be relevant when adding extra lengths outside the nominal deposition area, leading in practice to a larger deposition zone. These extra lengths should correspond to acceleration and deceleration phases measured on straight trajectory sections. That implies additional conventional machining time and tooling. ➢ The swiping strategy, the most commonly used, is not applicable to all cases. the semi-circular strategy (G1 continuous) can be a potential candidate, that enables accuracy problem due to sharp changes in direction in the programmed toolpath. ➢ It is possible to define manufacturing time estimation models considering acceleration and deceleration phases. However, stopping deposition outside the nominal deposition area requires precise parameter identification for a correct calculation of the manufacturing time. As a general comment from the above points, compromises must therefore be found. Note that the trajectories must be adapted to the part geometry to be built, allowing the correct filling of the entire part volume. The parameters ACC.cp and C_VEL should be kept at maximum values to minimize acceleration sections and keep the speed as constant as possible. The semi-circular strategy appears to be the most relevant in the case of continuous deposition over the whole toolpath. In general, the arc transitions within the geometry should be avoided by programming this transition outside the part geometry. Transitions can also be made depositing material, thereby increasing the cost of the process in terms of material but reducing the deposition time. As for the curves they should be programmed with angles as open as possible so that the ratio between WFS and TS remains constant.

Based on the results of the kinematic measurement, various models of manufacturing time estimation were finally proposed. They were used to calculate the manufacturing time of any W× L area from a limited number of previously identified parameters for a single area. Results showed that the formula is precise for all the cases with arc ON activated over the whole trajectory (the errors are less than 0.4%). The errors were higher with arc OFF activated outside the OR (more than 10%).

Chapter 3-Thermal impact of toolpath strategy

Introduction A reliable estimation of manufacturing time is a key point and must be addressed from both a kinematic point of view but also from a thermal point of view. Indeed, the introduction of interlayer times directly affects productivity. These interlayer times are actually the time required for the temperature of the deposited material to decrease to a target value. The purpose of the interlayer time is to make sure that the deposition of each layer is done under similar thermal conditions, thus achieving the same microstructures and mechanical properties throughout the part. The interlayer time dependent on the trajectory used since it strongly affects the distribution of heat during the construction of the part. This chapter intends to address the thermal signature/impact of a given toolpath through the evaluation of two indicators: a pre-heating indicator enabling the evaluation of the thermal homogeneity within a layer, and an interlayer time indicator providing an evaluation of the necessary cooling time in between layers.

Chapter three outline

Chapter 3 is organized as follows:

➢ Section 3.1 is dedicated to a literature review specifically on the problematics of thermal research and its relevant developments. ➢ In section 3.2 the thermal research problematics relevant to the context of this thesis is presented. ➢ In section 3.3 the objectives we intend to achieve with this thermal study are presented ➢ In section 3.4 the methodology used to assess thermal indicators is detailed. ➢ In section 3.5 the assumptions made, the analytical model, as well as the pre-heating indicator and the thermal field behavior for various layers is presented here. ➢ In section 3.6 presents the frame and methodology for the evaluation of the cooling behavior for a reduced set of layers. ➢ Section 3.7 presents a study case, the division of the study, as well as the pre-heating indicator, evaluation of interlayer time, comparison of the cooling behavior for different groups, a comparison of kinematic and thermos-kinematic times and advanced cooling rate analysis. ➢ Section 3.8 presents the conclusions achieved.

Thermal Bibliography

The WAAM process is characterized by having a heat source that describes a toolpath needed to deposit material on the entire part geometry [1]. The trajectories today are planned with the aim of obtaining a completely filled designed part volume [2]. But this criterion is not sufficient and the thermal behavior of the material when deposited must be considered during the planning of the part construction [3]. Each material deposition strategy has a direct influence on how the heat is distributed over the workpiece leading it to necessarily suffer a thermal gradient, in which heat concentration points can appear along the toolpath [4]. The thermal gradient suffered by the part during its construction is extremely important for its final mechanical properties and geometric dimensions [5].

Also the heat concentration points might lead to locally different cooling kinetics and therefore to potentially different material microstructure and properties [6]. But, the fact that the part is cooled differently throughout its length means that different phase transformations can occur at different locations on the part, even if no hot spots are identified [7]. Indeed, specific phase transformations may occur when the material is subjected to specific ranges of temperatures during certain periods of time (depending on the material used) [8]. The simple fact that the material is exposed to different heating and cooling cycles during the construction of a part leads to an accumulation of temperature within it [9]. It is therefore of great interest the prediction and anticipation of the thermal gradient across the part [10]. It is also of great relevance to understand what criteria should be taken into account in the design of an optimized toolpath from the thermal point of view.

The fact that the first layers are deposited on top of a substrate leads to a predominance of conduction in the heat transfer mechanism. But with the evolution of the construction, the conduction loses efficiency due to the increase of the distance from the deposited layer to the substrate, as well as the increase of the temperature of the part [11]. So, with the increase in the number of layers deposited, the heat transfer is mostly done through radiation and convection [12]. However, because the efficiency of conduction in metals is much higher than that achieved by radiation and convection, the temperature accumulates as the part is built [13]. Moreover, thermal gradient to which the workpiece under construction is subjected is known to be one of the driving causes for stress, plastic strain, and distortion [14], [15]. Heat dissipation during the WAAM process plays an important role, since this is intrinsically related to productivity. The appearance of heat concentration points in the toolpath, is the result of the deposition strategy adopted [9]. These points with very lower cooling speeds, negatively affect the productivity of the process when it is intended to comply with the interlayer temperatures designated by the manufacturer of the metallic material to be deposited [16]. The toolpath of each layer must then be programmed considering the heat conduction between the various points on the part, thus achieving a lower thermal gradient across the part [17].

Thermal simulation based on Finite Element Method (FEM) is one of the most natural approaches for studying the thermal impact of a given toolpath [18]. The thermal simulation of the WAAM process aims to provide information about the thermal behavior, such as the temperatures reached, the cooling, or the existence of hot spots on the part according to its geometry [19]. Nevertheless, due to the complexity of these models, programming and parameterization require specialized human resources. In addition, the calculation time associated with FEM simulation may limit its use to reduced size components [20], causing it not to be suited to an optimization loop where several deposition strategies need to be simulated [21].

This method is used frequently due to accurate results. Researchers have been using it for modeling strategies based on a heat source that considers the power distribution between the filler and the base materials [22], to perform thermo-mechanical analysis of the WAAM process [23], to study the thermal stresses [24] and also angular deformation [25]. The advantage of FEM simulation is that despite the cost of calculation, this option is reliable. Simulation avoids the costs associated with experimental metal deposition, where the method used is trial and error. Thermal monitoring equipment is normally used in these experiments. The function of this equipment is to extract information that allows to know the thermal behavior of the piece during its construction. However, this process is costly in terms of material and inaccurate since the data collected by this equipment requires emissivity calibration [16].

The search for an alternative to standard FEM simulation is at the core of several developments, often prioritizing the calculation speed and focusing only on heat conduction, neglecting other factors such as convection, radiation, and phase change [26], [27]. The use of analytical or semi-analytical models is one possible option. Rosenthal's model enables to derive the temperature field in the cross section of a weld and is particularly well adapted to the estimation of the melt-pool size, and the heat affected zone [28]. Other approaches based on superposition of instant point sources, or flash method are presented in [29].

Research problematics

The thermal phenomena occurring during the WAAM process raise several production problems/constraints. Some of these problems are related to the stress and potentially the distortion induced in the final part. A heat source, when depositing material, generates a thermal field around it, and a thermal gradient, this results in stresses generated in the material because of inhomogeneous expansion and contraction of the material. From a material microstructure point of view, a change in cooling rates may be crucial, since for specific materials like duplex stainless steel, the different cooling rates can have an influence on the microstructure achieved in different places of the part. The different microstructures can lead to different mechanical properties across the part. The thermal cycles experienced by the material are also the cause for material integrity issues like porosity.

The fact that a specific geometry can be achieved using several strategies in terms of toolpath, introduces another level of complexity to the research problematic.

Nowadays the method used to simulate how the part is going to be affected by the heat input whether it is mechanically or thermally, is in most cases the finite element model (FEM). Nevertheless, this approach can become heavy in computation terms. The simulation of a complete part using FEM can take a week or more, leading to time restrictions for part iteration. This ends up being a limitation for the application of FEM based process simulation to big and complex parts.

Objectives

The objective of the thermal assessment is to establish a procedure of analysis of the thermal impact of the trajectories of deposition and its influence on the productivity of a final part. For that it is necessary to develop a model with the goal of allowing for rapid iterations over possible strategies.

The developed model must be enriched with real kinematic information previously collected to simulate with a high fidelity how the strategy and the actual speeds attended by the robot affect the temperature field in the part.

The model should also deliver two types of information in separate, the first type would be the kinematic information, delivering graphics of speeds reached along the toolpath, the second type would be the thermal information, delivered through graphics allowing to analyze the indicator for one strategy, and for several strategies at the same time. Finally, a careful analysis and comparison of the cooling curves of the material should be made for different interlayer-temperatures. In particular, it is important to identify how the temperature evolves with increasing layers deposited. It is also important to understand whether the locations identified as critical in the thermal level by the indicators developed, are the same ones to be controlled in the later layers due to their location in the geometry, or whether the thermal dynamics change.

In summary the questions we want to answer with this analysis are: ➢ What are the hottest points on the trajectory for each simulated layer? ➢ How long does it take for the hottest point of each layer to reach a given interlayer temperature and restart deposition? ➢ Is the hottest point in the trajectory the same whatever the layer?

• If the hottest point is not always the same, what changes to make it vary?

• Is there a relationship with the type of form it was exposed to the heat source (Start/Start; Pass/Start; Pass/Start; Pass/Start)?

To understand if there is a relationship between the hottest points and: ➢ Configuration of the point where they are located, ➢ If there are 1 or 2 heat source passages, ➢ If there are 2 passes of the heat source at the hottest point, is the high temperature reached due to the fact that there is a short time variation between the first and second pass?

• Is this high temperature the reason why this point is the hottest point in the layer?

And lastly, when it comes to the quality of the material, we are interested to understand: ➢ What is the exposure time of the hottest points of the trajectory to temperatures that generate detrimental phases? ➢ How does the exposure time at high temperatures evolve with the increasing number of layers? ➢ How does the exposure time evolve for higher interlayer temperatures? Is it possible to parameterize the results obtained, and define laws that can be extrapolated to other geometries? 3.4.

Methodology followed

The developed thermal analysis involves two stages. First the question of thermal homogeneity is assessed through the evaluation of a pre-heating indicator. Two variants of this indicator are proposed, depending on whether the aim is to assess the thermal homogeneity of a single strategy or to compare several strategies. A score that combines kinematic aspects and pre-heating aspects is proposed, focusing only on the deposition of the first layer (see section 3.7.5.3). This score is then used as a reference for selecting the deposition strategy to be used for the subsequent layers, Figure 64.

The second stage involves the analysis of the cooling behavior of the part. It uses a grouping of points according to geometry, position, and thermal cycle characteristics. The cooling time required to reach a target temperature as well as the cooling rates are analyzed. The evaluation of the pre-heating indicator relies on an analytical model fast to compute and thus well suited to the comparison of several deposition strategies (section 3.5). However, the use of realistic boundary conditions (convection, radiation) is difficult to implement in such a model and would require specific developments that were not carried out during this research work. As a result, the analytical approach lacks accuracy for a detailed analysis of the cooling rates experienced by the material and the cooling times.

We have therefore chosen to use a more traditional approach, based on the finite element method, to assess the thermal behavior of the part more accurately, particularly during the cooling phases, Figure 65Figure 65 -The two models used for the thermal .The general idea is to use the FEM for a specific analysis of the most problematic points of the previously chosen strategy.

Figure 65 -The two models used for the thermal analysis.

Analytical thermo-kinematic model and definition of a preheating indicator

This section presents the analytical thermo-kinematic model developed for a fast comparison of several toolpath strategies. This model serves as a basis for the evaluation of a first thermal indicator, called pre-heating indicator, whose objective is to quantify the thermal homogeneity of a given deposition strategy. The model is fed with real kinematic data that was collected and presented in the previous chapter: characteristic times for acceleration and deceleration as well as speed variations at angles.

Assumptions made for the thermo-kinematic model

The proposed model had in consideration the following assumptions:

➢ Heat conduction was considered to be the driving cause for temperature rise in the part.

Convection and radiation at the boundaries were omitted. ➢ Thermal properties of material were considered uniform. ➢ The analytical model was based on semi-infinite domain approximation, meaning that the substrate was supposed to be infinitely thick and without boundaries in X and Y axis. ➢ Mirror boundary conditions were applied at all edges to account for finite domain boundaries (i.e., to transform the model into a simulation closer to reality)

Analytical model for transient heat equation

Given the aforementioned assumptions, the solution to the transient heat equation that describes the evolution in time and space of the temperature in the manufactured part, was analytically derived using a Green's function [30] denoted as G and written as:

𝐺(𝒙, 𝑡) = 1 (4𝜋𝐷𝑡) 3 2 𝑒𝑥𝑝(- ‖𝒙‖ 𝟐 4𝐷𝑡 ) (16)
where x = (x, y, z) is a position in the 3D computational domain, t is the time and D is the thermal diffusivity of the material. By integrating G over a short period of time ∆𝑡, one can evaluate the temperature rise generated by an instant point source (Dirac) of amplitude 1, located at position (0, 0, 0), that would be active (and not moving) during that period ∆𝑡. Considering a more generic source term Q, moving along a trajectory at a speed defined according to the kinematic rules identified experimentally (see Table 4, Table 5, Table 6, Table 7), and making use of the superposition principle, the temperature field was obtained with the following relation:

𝑇(𝒙, 𝑡) = ∫ ∫ 𝐺(𝒙 -𝑿, 𝑡 -𝜏) • 𝑄(𝑿, 𝜏)𝑑𝑿𝑑𝜏 + ∫ 𝐺(𝒙 -𝑿, 𝑡) • 𝑇(𝑿, 0) Ω Ω 𝑡 0 𝑑𝑿 (17)
where X = (X, Y, Z) is again a position in the computational domain. Two contributions are summed up, the first one is associated to heat input and is denoted as Tinp. The second one is associated to heat diffusion in the absence of a heat source and is denoted Tdif.

By considering a discretization of the time interval into time steps (ti)i=1,n, the evolution of temperature is computed incrementally using the relation:

𝑇(𝒙, 𝑡 𝑖 ) = ∫ ∫ 𝐺(𝒙 -𝑿, 𝑡 𝑖 -𝜏) • 𝑄(𝑿, 𝜏)𝑑𝑿𝑑𝜏 + ∫ 𝐺(𝒙 -𝑿, 𝑡 𝑖 -𝑡 𝑖-1 ) • 𝑇(𝑿, 𝑡 𝑖-1 )

Ω Ω 𝑡 𝑖 𝑡 𝑖-1 𝑑𝑿 (18) This relation remains valid for any kind of source term, i.e., acting on surface only or in the volume. In the case of a double ellipsoid/Goldak heat source (see Figure 66), more suited to the description of heat input in WAAM process, the heat input contribution simplifies to the following integral over time:

where ρ and cp are the density and the specific heat of the material, Q is the power, 𝐴(𝒙, 𝑡 𝑖 ) and 𝐵(𝒙, 𝑡 𝑖 ) are functions defined as follows: The interested reader can refer to [28] for details about the calculation. The heat source contribution is relatively fast to compute and only needs to be evaluated in the vicinity of the source path. Indeed, one can notice that the relation ( 20) can be split into two integrals over time with the integrand being a product of 1D Gaussian functions. The standard deviation of each Gaussian function is an indication about the size of the zone affected by the heat source. As a result, considering a distance of 3 to 4 times the standard deviation in each direction around the heat source path is enough to evaluate its impact on temperature rise. The evaluation of the diffusion term is more time consuming since it requires several 3D integrations.

𝐴(𝒙, 𝑡 𝑖 ) = 𝑟 𝑓 * exp (- 3(𝑥 -𝑉(𝜏 -𝑡 𝑖 )) 2 12𝐷(𝑡 𝑖 -𝜏) + 𝑎 𝑓 2 - 3𝑦 2 12𝐷(𝑡 𝑖 -𝜏) + 𝑏 2 - 3𝑧 2 12𝐷(𝑡 𝑖 -𝜏) + 𝑐 2 ) (20)
In order to reduce the computation time associated to the evaluation of the diffusion term, one can benefit from the parallelepipedal shape of the substrate. Indeed, the substrate can be seen as a 2D domain that is extruded along a 3 rd dimension. Such a spatial decomposition can thus be applied to the temperature field in the substrate. It was performed using a Singular Value Decomposition (SVD) algorithm, allowing to approximate the temperature field by a sum of modes, where each mode is the product of a 2D function and a 1D function:

𝑇(𝑋, 𝑌, 𝑍, 𝑡 𝑖-1 ) ≈ ∑ 𝛼 𝑗 𝑃 𝑗 𝑡 𝑖-1 (𝑋, 𝑍) 𝑄 𝑗 𝑡 𝑖-1 (𝑌) 𝑁 𝑗=1 (22)
The number of modes, denoted N, depends on the complexity of the temperature field. It was defined according to the singular values computed by the SVD algorithm. Only the modes associated to "large" singular values were kept: a decrease by 6 or 7 orders of magnitude with respect to the highest singular value is often considered as cut-off criterion. Less than 10 modes are usually necessary to approximate the temperature field.

The modal decomposition allows to transform the 3D integral involved in the calculation of the diffusion term into a sum of 2D integrals and 1D integrals, much faster to compute.

𝑇 𝑑𝑖𝑓 = ∫ 𝐺(𝒙 -𝑿, 𝑡 𝑖 -𝑡 𝑖-1 ) • 𝑇(𝑿, 𝑡 𝑖-1 ) Ω 𝑑𝑿 = 1 (4𝜋𝐷(𝑡 𝑖 -𝑡 𝑖-1 )) )

Ω 𝑦 𝑄 𝑗 𝑡 𝑖-1 (𝑌)𝑑𝑌 (25)
A further optimization is even possible by computing a decomposition into modes that are the product of X, Y and Z 1D functions. This requires the use of canonical decomposition algorithm, which was not carried out in this work.

Pre-heating Indicator

The analytical model presented in the previous section provides a fast estimation of the temperature field induced by the motion of a heat source along a given toolpath. An indicator is derived from the predicted temperature field and addresses the question of thermal homogeneity of a toolpath.

The proposed indicator is only focused on the first layer deposed over the substrate. The objective is to identify potential "hot points" along toolpath where the temperature is already high before reaching it with the heat source. The indicator, denoted Ipreheat was defined as follows:

𝐼 𝑝𝑟𝑒ℎ𝑒𝑎𝑡 (𝑥) = ( 𝑇(𝑥, 𝑡 * ) -𝑇 0 𝑇 𝑚𝑎𝑥 -𝑇 0 ) ( 26
)
The term pre-heating refers to the situation just before material is deposited. The value of T used in the indicator formula ( 26) is thus extracted from the analytical model at an appropriate time, denoted t*, that corresponds to a heat source located at a distance of 5mm from the point which is analyzed. 𝑇 𝑚𝑎𝑥 is the maximum pre-heating temperature identified along the toolpath. T0 is the initial temperature of substrate.

From this definition it follows that 𝐼 𝑝𝑟𝑒ℎ𝑒𝑎𝑡 ranges from 0 to 1. The zones where 𝐼 𝑝𝑟𝑒ℎ𝑒𝑎𝑡 is close to 1 are regions that are already hot before being heated up by the energy source, they're preheated regions.

Pre-heating affects both the maximum temperature reached during material deposition as well as the cooling kinetics since a smaller temperature gradient induces smaller conduction losses and hence a slower cooling.

The same indicator is used to compare several deposition strategies. In that case, 𝑇 𝑚𝑎𝑥 is the maximum pre-heating temperature identified on all the strategies to be compared. By doing so, the "thermal homogeneity" of each toolpath can be analyzed and an ideal strategy (from this indicator point of view) can be derived.

Cooling time indicator

To build a part the process relies on deposing several layers on top of each other. This deposition in height affects how the dissipation of the heat is done. Due to variations according to the geometry of the part, the material available to conduct heat also varies. This leads to different thermal dynamics between the first few layers and the following ones.

For a given geometry of typical parts in the aeronautical market it is necessary to study the thermal behavior in specific points of the trajectories that can be problematic for their construction. This type of part consists of a base (substrate) that is subsequently reinforced/stiffened with walls that are deposited perpendicular to the substrate. The path geometry of these parts usually consists of straight sections that intersect each other. Thus, several possibilities exist for the type of toolpath, such as continuous or discontinuous. In both types, the toolpaths are composed of straight sections with transitions as right-angle curves, intersections, and transition movements (TM) between sections. So, one characteristic taken into account when doing a thermal study was the type of configuration of the different points of the toolpath, and the influence they may have on the thermal behavior of the part.

The following are the 4 types of configurations considered.

Figure 68 -Top view of the first type of configuration. Figure 68 is a top view where the heat source is symbolized as an ellipsoid (in red), the section boundaries are defined in gray, and in orange is a heat expansion circle and finally the intersection between the heat expansion circle area and the lateral material boundaries, defined with a red pattern. The color pattern and respective designations defined in Figure 68 are also valid for Figure 69, Figure 70 and Figure 71. Figure 69 shows the second type of configuration. Here a third branch is in place and gives one more direction to conduct heat. A higher volume of material is "available" in the surrounding of the point for heat conduction. Taking this into account, faster cooling should be achieved when compared to the first type configuration. Figure 70 illustrates the third type of configuration. Here a fourth branch is in place, and this adds a fourth sense for heat conduction, as more material quantity. Again, it should then be considered that one more direction (perpendicular to the others) and a higher volume will affect the heat conduction. Taking this into account, faster cooling should be achieved when compared to the second type of configuration. A fourth configuration should also be considered (Figure 71) due to differences in the geometry and possibly in the cooling rate achieved.

In this configuration the heat conduction should have a different behavior than the configurations presented above. More area on the outside is available to evacuate heat: radiation and convection should be enhanced, resulting in a faster cooling rate than in configuration 1. The cooling of a point in the toolpath was not only conditioned by the amount of adjacent material available to evacuate/conduct heat, but also by the number of passes of the heat source at this point and the time Δt between these passes. Thus, a new grouping of the points along the trajectory was made considering both factors, the amount of material available to conduct heat, the amount of heat source passages and the duration between passages. Such a grouping is presented in section 3.7.6.

The presented approach intends to be generic and applicable to any component of the "stiffened plate" kind. Other configurations involving, for instance, more branches could also be considered if the studied part requires to do so. In this work, the approach was applied to the reference studied case presented in the following section.

Material properties

The material used as a reference for this study was the duplex 2205 stainless steel, see Table 24 for the material properties. The heat source was a double ellipsoid with an effective power (theorical power × efficiency) of 2000 W (Q parameter in equation 19). For the sake of simplicity, the heat source in our model and its geometrical parameters were kept constant over time and are given in Table 25. Thus, not taking into account the variation of power and wire feed speed (WFS) at arc ignition and extinction. where there was a transition from arc on to off (half marked with black). The black lines are the simulated toolpaths, and the red discontinuous lines represent the TM. As far as the analytical model is concerned, the temperature field was evaluated on a grid made of a total of 23,104 points (76×76×4).

For comparison and validation purposes, the same grid was considered for building a 3D mesh necessary for the FEM reference simulations.

Interlayer temperatures

The analysis of the cooling time indicator uses target interlayer temperatures. In the presented study case, three interlayer temperatures were considered: 150°C, 350°C and 550°C.

The first temperature is the one recommended by the duplex 2205 wire manufacturer. It is intended to avoid the creation of detrimental phase (sigma phase), that can occur for slow cooling rates (see TTT diagram in section 3.7.9). The other two temperatures were deliberately chosen to be much higher than the recommended temperature, in order to enhance the repercussion of such a choice in terms of cooling time and productivity. Figure 74 illustrates the speed profiles for the four different strategies simulated. It allows the identification of places in the toolpath, where due to the reduction of torch speed, there may be accumulation of molten metal and heat. The Z-axis represents the speed whereas X and Y axes correspond to positions. This graphic also allows us to identify if at the beginning and end of the toolpath the acceleration and deceleration respectively are being done within the part geometry. In Figure 74 four types of transition/behavior that can happen at each section join point are highlighted. These four types of transition/behavior are represented in Figure 75, viewed from a top perspective. Type A is where there were two movements with a variation of 12 mm/s (the stipulated speed), one due to the start of the toolpath (horizontal gradient), and the second due to a transition movement (TM3) in the sequence of the chosen toolpath (vertical gradient). Type B represents the speed reduction achieved during 90° turns.

Type C-a) existed at points where there were speed variations between 0 and 12 mm/s (in this case), but which were additionally crossed by a toolpath passage where a 90° curve was made type C-b). Finally, we have type D, in which there is only one velocity variation (in this case vertical).

Figure 75 -Zoom of the marked points in figure 3 and their classification by type. Initially, the pre-heating indicator 𝐼 𝑝𝑟𝑒ℎ𝑒𝑎𝑡 was evaluated for each strategy. In that context, the prefix local is used to refer to the indicator. We recall that 𝐼 𝑝𝑟𝑒ℎ𝑒𝑎𝑡 is computed as

Thermal analysis

𝐼 𝑝𝑟𝑒ℎ𝑒𝑎𝑡 (𝑥) = ( 𝑇(𝑥, 𝑡 * ) -𝑇 0 𝑇 𝑚𝑎𝑥 -𝑇 0 )
Figure 76 A) depicts the variation of this indicator along the deposition strategy Run 1. Here 𝑇 𝑚𝑎𝑥 corresponds to the maximum pre-heating temperature obtained over the entire Run 1. Also Figure 76 represents the comparison of results obtained between the analytical model presented here (Figure 76 A) and the FEM simulation (Figure 76 B), showing that the results obtained are consistent. The same trend was observed with both analytical and finite element model, as it can be seen by the identification of two "hot spots" in the vertical segments (top left side). We can also see that the lower value of Dt (81 s) in Run 4 with the shorter toolpath length (1011.8 mm) did not give a higher thermal gradient across the part. When comparing Run 4 with Run 2 it is possible to identify that Run 2 reached higher global pre-heating indicator (GI) values at two points in its trajectory, and its cause was simply the trajectory chosen.

The evaluation of pre-heating indicator required a computation time of around 10 to 12 min for each strategy when using the thermo-kinematic model. This time rose to almost one hour per strategy studied using FEM simulation. The use of the analytical model is thus of great interest as soon as the number of combinations to be tested is large.

Classification of toolpaths and hierarchization

As it is shown in Table 26, strategies with the same effective deposition length (EDL) can have very different total lengths (TL). This means that for the same quantity of deposition length the robot can travel a longer toolpath, wasting time and resources. Between Run 1 and Run 4, the total length can vary more than 20%. For Run 2, 3 and 4 the difference in deposition times was very small, only 1.66% and 1.62%, which corresponds to 1.35 and 1.31 seconds, and can be considered as negligible. The deposition time is also affected by the number of arc transitions (NAT). Table 26 displays the number of arc transitions with exception of the initial start and final stop. Arc transition imposes speed variations with the programmed speed range, and a short stop period, which leads directly to a reduction in productivity. Another disadvantage is that these areas are associated with defects in the quality of the material deposited.

A classification was then necessary to understand how a deposition strategy should be evaluated. The strategies were classified in a qualitative and in a quantitative way. A qualitative classification is given in Table 26. For this classification, the kinematic behavior was evaluated by the Dt; the smallest Dt was given the higher grade (A) and the largest Dt the lower grade (D). The thermal qualitative classification relies on the pre-heating indicator and more precisely on its gradient along the toolpath. Similar preheating conditions along the toolpath (small gradient of 𝐼 𝑝𝑟𝑒ℎ𝑒𝑎𝑡 ) was given the higher grade (A) and uneven pre-heating conditions (large gradient obtained for 𝐼 𝑝𝑟𝑒ℎ𝑒𝑎𝑡 ) was given the lower grade (D).

For a more quantitative classification, a score was established. It involves three contributions: the ratio between effective deposition length and total length, the number of arc transitions and the preheating indicator, in its global form (GI). The score, designated as kinematic score (𝐾 𝑆𝑐 ) is calculated using a summative formula:

𝐾 𝑆𝑐 = ( 𝐸𝐷𝐿 𝑇𝐿 × 1 3 + min (𝑁 𝐴𝑡 ) 𝑁 𝐴𝑡 × 1 3 + (1 -𝛥𝐺𝐼) × 1 3 ) × 10 ( 27
)
𝑁 𝐴𝑇 is the number of arc transitions necessary every time a transition movement exists inside the trajectory. min (𝑁 𝐴𝑡 ) is the minimum number of arc transitions given the topology of the first layer (2 in our study case) Moreover, ∆𝐺𝐼 = max(𝐺𝐼) -min (𝐺𝐼) is the maximum variation obtained along the analyzed toolpath for the pre-heating indicator. The value of the 𝐾 𝑆𝑐 score will thus range between 0 and 10. Having a 𝐾 𝑆𝑐 of 10 would mean that this chosen strategy has perfect accuracy, minimum number of arc transitions, and that the pre-heating indicator is constant along the toolpath. For the toolpaths tested, we can see from Table 27 that the 𝐾 𝑆𝑐 value for Run 3 (6.97) was the highest of all, indicating that this was the toolpath to use. This 𝐾 𝑆𝑐 value is due to the fact that strategy 3 exhibits small variations of the pre-heating indicator, the fewest possible arc transitions for this geometry, and one of the lowest deposition times. This analysis was only focused on the first layer, this was not sufficient for a correct assessment of the deposition time of the part. It was necessary to estimate the evolution of interlayer time/cooling time required to reach a target interlayer temperature.

Evaluation of interlayer time

After ranking the strategies based on the pre-heating indicator and other important criteria, Strategy 3 (Figure 78) proved to be a good compromise and was conserved for the study of a larger number of layers. FEM was then used to simulate and obtain temperature values for different layers. Indeed, FEM enables the use of complex boundary conditions (convection, radiation) corresponding to more realistic heat losses. This is a key point for assessing cooling kinetics within the part. As can be easily identified in Figure 78 C), the points that presented the highest pre-heating values were the points P11, P17, P24, P19, P13, P8, P2, P26, P20, P15, P9 and P4. For this reason, these points corresponded to the places that accumulated the most heat. These and other points were analyzed because of expected changes in heat conduction behavior with increasing number of layers. The methodology employed to analyze the cooling conditions obtained in the part is based on a grouping of points. This grouping is defined according to the following criteria:

• Type of configuration (see section 3.7.6.1)

• Number of heat source passages • Distance from the edge of the substrate The groups are detailed in Table 28. The first type of configuration is characterized by heat conduction in two directions, in the XY plane (top view of the part) Figure 68 shown in sub-section 3.6. These and other points were divided in groups in sub-section 3.7.6. according to other important characteristics. Here is detailed only the analysis of group C for this configuration, leaving the analysis of the remaining groups A-1, A-2, B, D, E and F in attachments A, B, C, D, E, and F respectively.

Detailed analysis of group C

The cooling curves of the points belonging to group C (points P8, P9, P19 and P20) resulting from the 3rd layer simulation for interlayer temperatures of 150°C and 550°C are shown in Figure 91 The graphs in Figure 80 show that the cooling curves for points P8, P9, P19 and P20 for 150°C are almost identical. For ITe of 550°C we have a small division in two groups with identical behavior the point P8 and P19 with a faster cooling, and the point P9 and P20 with a slower cooling. The same happens with the increase of the number of layers for the ITe of 550°C in the 20 th layer there was also the same division between the curves of points P8 and P19 and P9 and P20 varying between the two groups about 2 to 4 seconds approximately the time to reach 550°C. Table 29 shows the time required for the material to cool down to the different studied interlayer temperatures (ITe). In orange are marked the points and layers for which waiting times are required between each deposition. Of the four points in this group C, the point that accumulates the most heat was point P8 (even if by a marginal difference), and this would be the point to observe from the 7th layer onwards. It means that, for these points and layers, the cooling time exceeds the time in between two passes at this point (evaluated to 82.4s from the kinematic model). The non-productive waiting time is given in parenthesis and reaches almost 100 s (being thus larger than the deposition time itself) when the part comprises 20 layers.

Configuration of type 2

Detailed analysis of group G

The cooling curves of the points belonging to group G (points P2, P4, P24 and P26) during the deposition of the 3rd layer for interlayer temperatures of 150°C and 550°C are shown in Figure 82. Two distinct sub-groups with very similar curves clearly appear: P2 /P4 and P24 / P26. These cooling curves reflect for all points in this group the two passes of the heat source at different times. The difference between the peak temperatures of the two sub-groups of points, relative to the second passage of the heat source, was due to the fact that at points P24 and P26 (starting points) the point of analysis was exposed to the heat source for a slightly longer period. For points P2 and P4 (endpoints) this exposure to the heat source was lower, therefore the temperature peaks are lower. The differences that can be observed between peaks of the same sub-group are related to the different temperatures of the material when the energy source reached each of these points (pre-heating temperature). When increasing the Ite to 550°C (Figure 82 B) we logically obtain a temperature buildup as seen earlier in the other groups of points, leading to the temperature peaks being higher. This behavior was maintained for the following layers, where there was a gradual increase in the temperature peaks as the cooling times of the material got longer and longer. As shown in Table 29 the point to watch out for was P26, because this was the point that had the lowest cooling rate. It can be seen that both points P24 and P26 required an interlayer time (Iti)between each layer from the 3rd layer on, if the target ITe was 150°C. According to the interpolation made for an ITe of 350°C a cooling time would be introduced from the 8th layer on, since the 10th layer already should have had an ITi of 8.29 s. As far as the ITe of 550°C is concerned, it was necessary to introduce an ITi from layer 18 included (layer 20th requiring already an ITi of 3.43 s).

Detailed analysis of group H

The cooling curves of the points belonging to group H (points P11 and P17) during the construction of the 3rd layer for interlayer temperatures of 150°C and 550°C are shown in Figure 83.

In Figure 83 A) for a temperature of 150°C we can see that the cooling curves were different, with point P11 cooling faster after the first passage of the heat source. This difference was due to the fact that for point P11 the first temperature peak was relative to the start of deposition, while for point P16 it was relative to a passage. For the second heat source passage, the difference in the temperature peaks reached was due not only to the temperature at the time of the heat source passage, but also to the fact that P11 is an intermediate point p, while P17 is the end of deposition, where there is less exposure to the heat source. Increasing the ITe to 350°C and finally to 550°C, the graphs show that there was an accumulation of heat in the material, leading to higher temperature peaks and slower cooling. This behavior was also observed for both points with increasing number of layers. Table 31 shows the times required for the material in each layer to cool down to the target interlayer temperatures, and also the ITi (inside the parenthesis) for the layers and points at which they were to be applied. The point P11, was the one to observe, as it had the slowest cooling curve. For an ITe of 150°C it would be necessary to apply ITi at point P11 from the 3rd layer (included) as shown in Table 31. For a temperature of 350°C it would be necessary to start applying ITi from the 10th layer also at point P11.

Configuration of type 3

Figure 95 presents all the points that fit in the third type of configuration. This configuration is characterized by heat conduction in four directions, in the XY plane (top view of the part). A detailed analysis of group I for this configuration is presented in the following paragraph.

Detailed analysis of group I

The cooling curves of the points belonging to group I (points P13 and P15) during deposition of layer 3 for interlayer temperatures of 150°C and 550°C are shown in Figure 85.

In Figure 85 A) for a temperature of 150°C It can be seen that the cooling curves of both points were almost identical after the first passage of the heat source. For the second passage of the heat source there was a time gap of approximately 15.34s between these two points. This difference in "initial" material temperature resulted in different temperature peaks, and therefore different cooling curves.

Increasing the ITe to 350°C and finally to 550°C, the graphs show that there was an accumulation of heat in the material, leading to higher temperature peaks and slower cooling. This behavior was also observed for both points with increasing number of layers. Table 32 shows the times required for the material in each layer to cool down for the different ITe, and also the ITi (inside the parenthesis) for the layers and points at which they were to be applied. The P15 point was the one to observe, as it had the lowest cooling rate. For an ITe of 150°C it was necessary to apply ITi at point P15 from the 1st layer (including) according to the interpolation done. For a temperature of 350°C it would be necessary to start applying ITi from the 9th layer also at point P15.

Detailed analyses of other groups of points are given in the attachments section.

Crossed comparison of cooling behavior of each group

After analyzing all the points and making their comparison it was possible to obtain from each group a point with the slowest cooling. These points were P25 from group A, P18 from group B, P8 from group C, P16 from group D, P14 from group E, P22 from group F, P26 from group G, P11 from group H, and P15 from group I. These zones where these points are located are of particular interest since they drive the interlayer time to be considered in between each layer deposition and they hence have a direct impact on process productivity. Point P15 was identified as the hottest point for an ITe of 150°C, and the second hottest for temperatures of 350°C and 550°C. Point P26 was the second hottest at an ITe of 150°C and the hottest at temperatures of 350°C and 550°C. Of the 9 points chosen, the point with the best cooling for the 3 simulated temperatures and for all their layers was point P8 (Figure 86).

Figure 87 shows the cooling curves for the mentioned points. The following comments can be done from these cooling curves: ➢ The points P26, P15 and P11 were the three points with the longest cooling time in our study case. ➢ The points adjacent to point P26, namely points P25 and P27 had lower temperatures when the heat source passes through the second time. ➢ The lower temperatures of points P25 and P27 show that the material around point 26 had a higher heat absorption capacity when compared to points P14 and P16 surrounding P15. ➢ P14, P15 and P16 due to their location end up suffering (in the first layers) a concentration of heat that decreases with the number of layers deposited, as well as with the increase of ITe to 550°C (Figure 98 B)). ➢ This reversal in thermal behavior occurs because with the increment in deposited layers there was no longer any influence from the larger amount of available material in the substrate. The distance to the substrate is therefore a key point when estimating the cooling time. ➢ When increasing the number of layers, P26 with a 3 rd type of configuration lost the advantage in its cooling to point P15 with the 4 th type of configuration. This confirms that the material available for heat conduction in the close surroundings plays a major role in the cooling kinetics. The type of configuration (number of branches) is thus a central feature in the cooling analysis. Figure 88 illustrates the evolution of required cooling time according to the target ITe and the layer number. The use of response surface graphs enabled us to clearly visualize where ITi times were needed. This allows the prediction of the cooling times, to identify which point should be monitored, and also at which layer it needed to be implemented. The larger the area of the colored surface, the more critical the point was in terms of cooling.

These results confirm the choices made with regard to the criteria for grouping points: type of configuration, number of heat source passages, distance to substrate. They allow a clearer analysis of the cooling behavior of the part. These features form the basis of a generic cooling time estimator, based on an artificial neural network, presented in chapter 5.

Kinematic time vs thermo-kinematic time(s)

This detailed analysis enabled us to evaluate the manufacturing time necessary to construct/depose a given number of layers. It is limited to the study case (see chapter 5 for a more generic approach) but it clearly demonstrated the importance of considering thermal aspects in addition to the kinematic considerations.

Considering the deposition of 20 layers, a purely kinematic estimation would approximate the manufacturing time to about 28min (20 x 82.4s). When including the thermal considerations this time rises to:

• 51 min with an ITe of 150°C (+86%).

• 32 min with an ITe of 350°C (+17%).

• ~28 min with an ITe of 550°C (+0.4%).

The use of a low interpass temperature (ITe) must have a significant contribution in terms of "material quality" because it is very penalizing in terms of productivity.

As shown above, to achieve thermal stability/homogeneity of the thermal conditions during the whole deposition process of the metallic material, is not possible cooling speeds will vary. Depending on the material used, different cooling rates at different locations in the part can lead to different microstructures and therefore different mechanical characteristics. It is also important to take into account that as the number of layers increases (and therefore the distance to the substrate increases) the ITi will increase for the same ITe until a stabilization plateau is reached. The ITi stabilization plateau depends on several important factors, namely the substrate size, the deposition parameters, and also the part geometry.

Advanced cooling rate analysis at critical positions

Depending on the material deposed, it can be necessary either to avoid exposing the material to certain ranges of temperature during certain periods of time, or to avoid reaching certain cooling rates in certain ranges of temperature. The reason for that is their association with the formation of detrimental phases.

Figure 89 shows the time temperature transformation (TTT) graph for the 2205 stainless steel used in this study, superimposed to the continuous cooling transformation (CCT) curve (in blue) for the same material (Data collected in [31]). The formation of the sigma phase is to be avoided because of its lower ductility and lower toughness. We can see from the graph that an exposure of the material to 900°C during about 134 s can induce the formation of that phase. We can also see that a cooling rate of less than 9°C/min must be avoided.

Figure 89 -Representation of an approximation between the time temperature transformation (TTT) graphic and CCT curve for stainless steel 2205 using one known point (adapted from [START_REF] Martina | Welding Engineering and Laser Processing Centre[END_REF]).

From these considerations, it was then of great importance to understand if a higher ITe could expose the material to these temperatures conditions and cooling rates conditions, and by consequence enable the appearance of the sigma phase.

The following analysis concerns point 26 since it's the point exhibiting the slowest cooling. Figure 90 shows the cooling curve of point 26 for the 20th layer with an ITe of 150°C, and we can clearly distinguish the two passages of the heat source at this location.

Since the second temperature peak reaches the melting temperature of the material (considered to erase the previous "metallurgical" history), only exposure time at temperatures between 950°C and 600°C after this peak was considered. Figure 91 A) shows the cooling rates after both temperature peaks. After the second passage of the heat source (orange curve on Figure 91) the cooling speed at 950°C is around 10700°C/min and it reduces to about 1800°C/min when the material temperature reaches 600°C. The material only spends 5 s in the studied temperature range. Neither the exposure time nor the cooling rate conditions are therefore met for the material deposed.

The graph in Figure 91B) shows, the cooling rate curves (in blue), and cumulated time spent by the material in the studied temperature range (in orange).

The graph in Figure 91 C) makes a direct comparison between the cooling curve of point 26 and the limit cooling curve of the material, corresponding to the minimum acceptable cooling rate (i.e. for staying out of the sigma phase formation domain). Here it can be seen that the limit cooling curve made from literature data does not intersect at any point with the cooling curve at point in the 20th layer for an ITe of 150°C.: sigma phase formation is thus not induced in the deposited material. Finally, Figure 91D) shows the evolution of the time periods during which the just deposited material was exposed to temperatures between 950°C and 600°C.

3.7.9.2. Analysis of point 26 for an ITe of 350°C Figure 92 shows the cooling curve of point 26 in the 20th layer for ITe of 350°C. Only the cooling curve after the second passage of the heat source will be analyzed since fusion occurs at the second passage of the heat source (resetting the microstructure). Figure 93 A) shows the cooling rate after both temperature peaks.

After the second passage of the heat source (orange curve on Figure 93 A) the cooling speed at 950°C is around 7100°C/min and it reduces to about 760°C/min when the material temperature reaches 600°C.

Figure 93 B) shows two graphics in one, the cooling rate curves (in blue), and time cumulated in the studied temperature range (orange curve). This time was around 10s, twice the time estimated for an ITe =150°C. The graph in Figure 93 C) makes a direct comparison between the cooling curve of point 26 and the limit cooling curve of the material, also here can be seen that the limit cooling curve made from literature data does not intersect at any point the cooling curve of point P26 in the 20th layer for an ITe of 350°C. This means that also for the hottest point with an ITe of 350°C up to the 20th layer, the exposure of the deposited material to temperatures where detrimental phases can be formed in the microstructure of the material was not sufficient for their formation. Finally, Figure 93 D) shows the evolution of the time periods during which the just deposited material was exposed to temperatures between 950°C and 600°C: this time period increases almost linearly until layer 20.

3.7.9.3. Analysis of point 26 for an ITe of 550°C Figure 95 A) shows the cooling rate after both temperature peaks.

After the second passage of the heat source (orange curve on Figure 95 A) the cooling speed at 950°C is around 4500°C/min and it reduces to about 420°C/min when the material temperature reaches 600°C.

Figure 95 B) illustrates the time spent in the defined range of temperatures after the last peak that crossed the limit of 950°C.This time was of about 18 s thus almost doubled again compared to what was estimated for an ITe = 350°C. The graph in Figure 95 C) makes a direct comparison between the cooling curve of point 26 and the limit cooling curve of the material, and it can be seen that the limit cooling curve made from literature data does not intersect at any point with the cooling curve at point P26. This means that also for an ITe of 550°C up to the 20th layer, the exposure of the just deposited material to temperatures where detrimental phases are formed in the microstructure of the material was not sufficient for their formation. Finally, Figure 95 D) shows the evolution of the exposure time versus the number of layers. It exhibits an almost linear behavior until layer 20.

It was then verified that, for the three analyzed interpass temperatures the conditions to generate the sigma phase are never reached for the layer being deposited. It still remained to be verified what occurred during the following thermal cycles the material was exposed to (i.e. during the deposition of the following layers).

To that end, the thermal history of the lower layers was analyzed to verify if the material suffered prolonged exposure to the range of temperatures between 950°C and 600°C for a period of time sufficient to result in the appearance of the detrimental phase (sigma).

Analysis of thermal cycles at point 26

To analyze what thermal exposure the previously deposited layers were subjected to during the deposition of the following layers, an analysis of the temperature evolution at point 26 in layers 15 to 19 during the deposition of layer 20 was performed.

Figure 96 A (resp B, C, D, E) shows the temperature graphs (left column) and the cooling rate graphs (right column) estimated in layer 19 (resp. 18, 17, 16, 15) when deposition material on layer 20 (Data was collected at point 26 for an ITe of 550°C. In these graphs, the crossing between the temperature curves and the bounds of the studied temperature range are marked with red dots. When observing the temperature curves on graphs A), B), C), D and E) it can be seen that in each layer the material was exposed to the range [600°C, 950°C]. The total time spent in this interval could thus reach the threshold of about 135 s where the sigma phase formation would be initiated. This would be true if cumulative behavior is considered. Otherwise, the model seems to demonstrate that the material is never exposed continuously to this range of temperature for a sufficient period of time. The minimum cooling rate obtained in this analysis is 10°C/min ( Figure 96 D-1), is similar to the minimum allowed cooling rate before entering the sigma phase formation domain (see Figure 89).

Figure 96 -Graphs A), B), C), D) and E) represent the intersection between the cooling curves of layers 19, 18, 17, 16, 15 (respectively) and the Iso lines for temperatures of 600°C and 950°C collected during the deposition of layer 20th. Graphs A-1), B-1), C-1) D-1) and E-1

) represent the cooling rates of layers 19, 18, 17, 16, 15 (respectively) in order of time corresponding to A), B), C), D) and E) respectively.

Figure 97 -Graphs A-2), B-2), C-2), D-2) and E-2) represent two graphs, in blue the cooling lines corresponding to layers 19, 18, 17, 16 and 15 (respectively), and in orange we have the accumulated time between temperatures of 600°C and 950°C after reaching the last 950°C during the deposition of layer 20th. Graphs A-3), B-3), C-3) D-3) and E-3) represent the comparison between the cooling curves of layers 19,18,17,16,15 (respectively) and the cooling limit curve of the material, in order of time.

In Figure 97 A-2) and Figure 97 B-2) the exposure time to the range of temperatures from 950°C to 600°C was relatively short due to the high cooling rates. The exposure time increases linearly from layer n-5 (46 s) to layer n-3 (58 s) Then a small reduction of exposure time is observed from layer n-3 to n-1. This is due to the fact that temperature peaks exceed 950°C for the layers located close to the deposited layer. With the graphs A-3), B-3), C-3), D-3) and E-3) it can be seen that between layer 19 and 15 and taking into account the accumulated exposure times for the temperature range from 950°C to 600°C, there wasn't even a proximity between the continuous cooling transformation curves and the limit cooling curve of the material. By cumulating the exposure time evaluated on layers n-5 (i.e. layer 15) to layer n-1 (i.e. layer 19), a total of 235.91 s is obtained, more than the time indicated above in Figure 89 (134 s) necessary for the formation of sigma phase. As a consequence, we might expect, if cumulative time considerations apply, the formation of detrimental phase when working at an interpass temperature of 550°C. This a key information here because it illustrates how productivity optimization can impact material quality. An interpass temperature of 350°C might be the good compromise for the geometry considered in that study case.

Conclusions

Two thermal indicators have been presented: a pre-heating indicator aiming at the identification of hot spots and the optimization of the deposition strategy, and a cooling time indicator aiming at a more accurate estimation of manufacturing time.

Pre-heating indicator is evaluated via a thermo-kinematic model which proved to be faster and cheaper to compute compared to a full FEM simulation. It provides a simple indicator for evaluating the homogeneity of the thermal conditions encountered along a given toolpath. Its reduced computation cost makes it a good candidate for the optimization of toolpaths. A good strategy from the thermal point of view does not necessarily correspond to a good strategy from a productivity point of view. Therefore, the developed model can help selecting (for a given geometry) a toolpath that offers the best compromise A multi criteria formula is also proposed enabling to have a quantitative evaluation of each toolpath and providing a useful indicator for decision making. However, the implementation of complex boundary conditions (convection and radiation) remains a challenge in this kind of model, making its use to an accurate evaluation of thermal history still limited. The cooling time indicator, requiring a precise evaluation of the cooling rates, is based on the FEM simulation of some well-chosen layers and helps understanding the influence of interlayer temperature value (ITe) on the cooling rates in the part. Its application to a study case demonstrated the significative influence of ITeon the total manufacturing time. An increase of the manufacturing time by more than 80% was identified for an ITe of 150°C compared to an ITe of 550°C. However, a high ITe may have harmful effects on the material quality. In the case of the 2205 duplex stainless steel, the use of a high ITe promotes the development of the detrimental sigma phase and may also affect the resulting mechanical properties of the produced material. This key point is addressed in the next chapter.

Chapter 4 -Study of the material quality

Introduction

In metallic additive manufacturing, specifically for the WAAM process, mastering the properties of the deposited material is of prime importance. This chapter is thus dedicated to the study of important aspects of the material quality achieved by the WAAM process, in the particular case of the subprocess Cold Metal Transfer (CMT). Note that the construction of walls in duplex stainless steel 2209 (that allowed to obtain samples for mechanical characterizations) also permitted to understand some physical and digital constrains of the manufacturing process (e.g., movement restrictions and real time monitoring, respectively). It is essential to understand the impact of the interlayer temperature (ITe) on the mechanical properties, this parameter ITe also has a role on the productivity of the process (like the parameter ITi). So, this chapter aims at analyzing the influence of the ITe on the mechanical characteristics of the deposited material, having the other manufacturing parameters unchanged (constant deposition conditions and same input parameters for all the wall constructions). Three types of mechanical characterization were performed for that purpose: hardness measurement, quasi-static tensile tests (until failure) and accelerated fatigue tests (based on the self-heating measurements).

Chapter four outline

Chapter 4 is organized as follows: ➢ Section 4.1 is devoted to a literature review on the mechanical characterization of 3D printed 2209 stainless steels. In addition, the reference values obtained by the WAAM and standard manufacturing processes are indicated. ➢ Section 4.2 presents the research problematic regarding material quality in the context of this thesis, in relation to industrial problematics. ➢ In section 4.3, the experimental approach is described. ➢ In section 4.4, the objectives to be reached for the construction of the walls are presented, as well as the objectives to be reached with the different mechanical tests. ➢ In section 4.5, the method used to perform the walls construction and mechanical tests is described, as well as the sequence of parameters tested in the building of the wall. ➢ Section 4.6 presents all the set-up and equipment used during the wall construction and for the mechanical tests. ➢ Section 4.7 presents the results of the construction of the walls. ➢ Section 4.8 presents the results of the mechanical characterizations. ➢ Section 4.9 presents the conclusions of the chapter.

4.1.

Literature review

The additive manufacturing of metals is aimed at building topologically optimized parts or adding new functions as well as reducing the number of parts in a given assembly. These goals are directly linked to, or depend directly on, the mechanical characteristics of the parts achieved during their production. Thus, the introduction into the market of parts manufactured by additive manufacturing depends on the mechanical characteristics required for these parts. The WAAM process is known for producing parts with anisotropic characteristics, in contrast to the so-called standard production process [1].

Several works have been done on various materials to relate the input parameters to the various mechanical properties and microstructures achieved [2]. Duplex stainless steels are a family of stainless steels with a two-phase microstructure consisting of both austenitic and ferritic phases in roughly equal proportions [3]. The combination of these two phases provides duplex stainless steels with a unique set of properties, including: corrosion resistance, high strength, good toughness and ductility, good weldability, and a low coefficient of thermal expansion [4], [5]. Several works have been done regarding the microstructure and the corrosion resistance of the stainless steels [6], [7]. In the case of Stainless 2209 steel, a literature review by [8] shows that the mechanical properties of the material such as microhardness, hardness, as well as tensile strength depend on the deposition conditions and the input parameters [9], [10]. Also, the geometry of the part and the thermal history have an influence on the final result, since they affect the way the solidification phenomena happen. [11]. A study [12] suggests that, for super duplex stainless steels, internal defects affect fatigue performance in addition the other mechanical properties. In [13], the authors stated that the martensite content in each layer varied with the difference in cooling rate between each layer, and that the microstructure changes based on the height of the deposit in the CMT-WAAM process employing 2Cr13 stainless steel. In [14], the temperature history during WAAM was measured using Inconel 718, and the microstructure variation with respect to the height of the deposit was studied. This work showed that the lower and middle portions of the deposit remained within the agingtemperature range of Inconel 718 during deposition for a longer period than the upper part. As a result, increased precipitation occurred, hardening in the microstructure, and leading to enhanced mechanical properties. Comparisons have been made in welding joints using ER 2209 where this material performed better than other stainless steels [6]. However, there are not many wellestablished pieces of literature on the creation and characterization of duplex stainless steels elaborated by WAAM using ER2209. As a consequence, it is necessary to assess the mechanical properties of this material in as-built specimens. A few studies on the mechanical behavior have been carried out with the ER2209 material. The mechanical results of these works are presented in Table 33 where YS, UTS and EL are the yield stress, ultimate tensile stress, and the maximum elongation respectively. Reference values from two suppliers are also indicated. It should be noted that the reference values of UTS and EL in the table greatly vary between suppliers. This variation can be due to several factors, including the chemical composition of the wire. Also, it should be observed that all the YS values in the literature are lower than the reference values. Moreover, most of the achieved UTS values are between the two reference values.

Research problematics

The research problematic faced here concerns the quality of the material that is obtained through CMT deposition process. For most materials elaborated by additive manufacturing, the relationship between deposition conditions and the quality of the material attained is yet undefined. Besides this relationship is very complex, since there are several parameters outside the process that are not controlled but could have an influence on the process. For the material used in the present work (duplex stainless steel 2209), there is a strong relationship between cooling speed and microstructure obtained. For this reason, it is necessary to understand if the production parameter "interlayer temperature" (ITe) has an influence on the quality of the material achieved (measured here through its mechanical properties) and what is its impact on the productivity.

Experimental approach

Several walls made of duplex stainless steel (2209) with a minimum height of 160 mm were built using specific monitoring equipment to ensure that the pre-defined ITe is respected. Three values of ITe were considered: 150°C 350°C and 550°C. For each one, three walls were made for repeatability purposes. Nine walls were thus built. The walls were then cut, allowing tests to be performed on material samples for mechanical characterizations: hardness, tensile and fatigue tests. Usually, an ITi is defined and used during the entire construction of a wall. Here, an ITe is used in order to be precise in the repeatability of the thermal cycle to which the material is subjected. Thus, every layer was monitored in real time during and after its deposition, until its temperature reached the defined ITe.

From the point of view of the thermal reproducibility of the process, it was important to always monitor the last layer deposited. The reason for this is that this interface (between the previously deposited material and the material being deposited) is located where the largest temperature variation occurs. The temperature at this interface also affects the size of the melt pool and as a consequence the cooling time and mechanical properties. During the construction of the walls, various information was gathered such as averages and variations of the input parameters used, travel speeds, and temperatures throughout the wall.

Objectives 4.4.1. Objectives for the construction of the walls

Nine walls in duplex stainless steel 2209 (three per interlayer temperatures, namely 150°C, 350°C and 550°C) were built by: ➢ Depositing weld beads (WBs), 160 mm long, alternating the starting point with the finishing point; ➢ Obtaining straight (in their length) and vertically aligned walls with a thickness greater than 4 mm allowing it to be machined and cut to draw samples for the subsequent mechanical tests.

The objectives for the analysis during the construction of the walls were: ➢ Identify possible problems or limitations during the building; ➢ Record the production and interlayer times (ITi), allowing the comparison between the walls of the same ITe and between different ITe; ➢ Verify if the wall thickness varies as a function of ITe, and consequently if the height also varies for the same number of layers deposited; ➢ Verify if the roughness increased when the ITe increased (due to a higher fluidity of the metal). ➢

Objectives for the hardness tests

Performing the hardness tests in the two clamping areas of the samples (for quasi-static and accelerated fatigue tests) had the aim of:

➢ Verify if, in the vertical samples, the range of hardness values was within a small range over the increment in height. ➢ If there is a repeatability between walls made at same ITe.

Objectives for the quasi-static tensile tests

The objective of the quasi-static tensile tests was to measure for each sample:

➢ The material's conventional yield stress Rp0.2 (the stress at which it starts to deform plastically); ➢ The material's ultimate tensile strength Rm; ➢ The material's ductility (measured here through the maximum uniform elongation and the maximum strain reached during the test).

It was aimed at comparing the results between the two orientations (horizontal and vertical samples) and the three ITe (150°C, 350°C and 550°C). A comparison was also made with the reference values (standard manufacturing process).

Objective of the accelerated fatigue tests

The objective of the cyclic tests performed was to compare the fatigue performances, in an accelerated manner, of the different samples. For that purpose, cyclic tests with linearly increasing stress amplitude were performed while measuring the temperature change of the material ("self-heating", expressed in °C). The heat (in kJ/m3/cycle) associated with fatigue damage was then calculated. The data processing was based on the heat diffusion equation. We aimed at comparing the results between the two orientations (horizontal and vertical samples) and the three ITe (150°C, 350°C and 550°C).

Note that the tests do not enabled us to identify the Wöhler's curves of the materials (which would need months of tests and much more samples), but to compare quickly their fatigue performances.

4.5. Methods

Method for the construction of the walls

Prior to the construction of these walls, the input parameters were tested (WFS, TS, P) to understand if with different values of these input parameters, but maintaining the same lineic energy resulted, the WB maintained same geometric characteristics. From these preliminary experiments various WB geometries were obtained (not here reported). Using the results of these preliminary experiments, the input parameters were chosen:

For the first layer: ➢ WFS = 5 m/min, ➢ TS = 9 mm/s, ➢ P = 2574.8 W, ➢ Synergic law =1093. For the next layers:

➢ WFS = 4 m/min, ➢ TS = 8 mm/s, ➢ P = 1850 W, ➢ Synergic law = 1093. The first set of input parameters was chosen to obtain a good dilution on the substrate, whereas the second set was chosen taking as criteria the contact angles between WBs. These angles are important due to the relationship with the fluidity of the material, leading to higher roughness that could affect the growth of the wall in height (Z-axis) [17].

The construction plan of the walls also considered the use of various monitoring equipment. The equipment considered important for controlling the material deposit and for collecting data was:

➢ Pyrometer, ➢ FLIR thermal camera, ➢ Fronius Xplorer, ➢ 4 thermocouples, ➢ ADAONE.

The function of the pyrometer was to monitor the temperature in the last deposited layer during the deposition sequence. For this, the pyrometer was positioned pointing to the middle of the wall and was moved on the Z axis in between depositions. This increment in Z axis had the same height as the previous layer incremented wall growth, ensuring that the collected temperature was on the last layer. The Flir thermal camera had the objective to collect thermal images of the wall while it was being built.

As the thermal emissivity can change with the angles between the wall and the camera, it was necessary to make sure that the height of the camera accompanies the increasing height of the wall, by moving its position in Z axis.

Fronius Xplorer was dedicated to collecting the information from the Fronius equipment, namely real power and WFS, start and stop times for each WB among other data. Four thermocouples were welded in the side of the wall during its construction (in between depositions), to collect the thermal behavior of the wall in several points of its height and would serve later as a reference for the Flir calibration.

The ADAONE software collected the movements of the robot. Since the movement was straight with only 160 mm, the data collected would have been used only in case there was a trajectory deviation or defects indicating uncontrolled speeds during manufacturing.

The time necessary to build the walls increased conversely to the ITe used. For the construction of three walls with an ITe of 150°C, it took about 10 hours of effective deposition. It was about 4 hours for ITe = 350°C, and one hour and half for ITe =550°C.

The strategy used for all the constructions was a straight bi-directional line of 160 mm alternating the start and stop points, made on a substrate with 170 mm x 30 mm and 5 mm of thickness in duplex stainless steel 2205. This strategy had a first objective to deliver a leveled wall in all its length, with respect to its growth in the Z axis, avoiding problems which may derive directly from considerable height differences between the two sides of the same wall.

Locations of the hardness measurements

Measurements were done in the clamping areas on the samples cut for quasi-static tensile tests and accelerated fatigue tests (see Figure 98). After machining and electro discharge machining (EDM), the samples were subjected to hardness tests in these areas that would later be dedicated to fixing them in the jaws of the testing machine (red points in Figure 98 B). The orientation for hardness tests was not in the longitudinal direction of the material deposition but is transverse in plane to it.

Figure 98 -A) Image of wall after trimming B) scheme for all the samples to be taken from each wall. The red dotes indicate the locations where the hardness tests will be performed.

Samples for the quasi-static and fatigue tests

The samples cut from the different walls for the quasi static and accelerated fatigue tests met all the requirements for the dimensions defined in the ASTM E8/E8M standard.

Figure 99 presents a picture of the samples obtained after cutting and machining. Five samples (three vertical and two horizontal) of each wall were used for the quasi-static tests. The same number of samples per wall was used for the fatigue tests. Thus, a total of 10 quasi-static tests and 10 fatigue tests were performed for each ITe.

Data processing for the accelerated fatigue tests

Accelerated fatigue tests are based on temperature measurements, with subsequent calculation of the density of heat produced per mechanical cycle (in kJ/m3/cycle) due to mechanical irreversibility (in particular here fatigue damage). The density of total heat produced/absorbed by the material due to mechanical loading can be estimated by the following version of the heat diffusion equation [18], [19]:

𝑠 = 𝜌𝐶 ( d𝜃 d𝑡 + 𝜃 𝜏 ) (28)
where: ➢ 𝑠 is the "heat source", in kJ/m 3 . This quantity is composed of two parts: the thermo-elastic coupling (associated to the thermos-elastic behavior of the material) and the mechanical dissipation (associated to the irreversible mechanical behavior of the material, e.g., fatigue damage, plasticity, viscosity, cracking, depending on the material and the loading conditions); ➢ 𝜌 is the density of the material. Here 𝜌 = 7800 kg/m 3 ; ➢ 𝐶 is the specific heat of the material. Here 𝐶 = 418 J/kg/K; ➢ 𝜏 is the time decay characterizing the heat exchanges with the sample's environment. Here 𝜏 = 41 s (see below for the measurement of this value); ➢ 𝜃 is the temperature change with respect to the temperature of the "environment". In practice, the variation of the sample temperature was measured using a thermocouple placed in the middle of the useful length. The temperature change 𝜃 is then obtained by subtracting the initial temperature of the sample measured just before starting the mechanical loading.

For the data calorimetric processing, a preliminary characterization of the time decay 𝜏 is thus required. It consists in evaluating the ability of the sample to exchange heat with its environment (ambient air and jaws of the testing machine). This preliminary test consists in a mere natural cooling (while the sample is clamped in the jaws) after a homogeneous heating for a short time. The latter can be done with an air drier or by contact with a "hot" object. Figure 101 shows two tests corresponding to different pre-heating levels. The solid curves correspond to the data collected during the tests (using a thermocouple), while the dashed curves correspond to the theoretical exponential decrease. The decay of the exponentials was identified to 𝜏 = 41 s for the two tests. This value was used in the data processing of the temperature evolution to calculate the heat produced by the sample due to fatigue damage. During a cyclic loading at constant stress amplitude, the heat associated to the thermo-elastic coupling vanished over a mechanical cycle, see Ref [20]. This property can be used to extract heat due to mechanical dissipation (associated to fatigue damage) only. It consists in averaging thermal data over entire numbers of cycles. In the case of a linearly increasing stress amplitude, adaptation of the data processing must be done, see Ref [21] for details. For the analysis of the fatigue performance, the heat source associated with mechanical dissipation was expressed in kJ/m 3 /cycle.

4.6.

Experimental set-up 4.6.1. Set-up for the construction of the walls

The set-up used to build the walls is shown in Figure 102. All the equipment used in the metal deposition is visible, except the Fronius equipment and the Kuka robot. On the left can be seen the device for the welding of the thermocouples on the side of the wall facing the camera Flir, during the interlayer times. The pyrometer and the FLIR thermal camera were placed perpendicularly to the wall's plane according to the manufacturer's instructions. The control of the construction and the data collection were done from the Kuka control panel (KCP) of the robot and two computers, located in the safety zone, outside the robot's working area. All the safety equipment mandatory for this process was also used, namely: mask, appropriate clothing, protective footwear and thermal protection gloves.

Set-up for the hardness tests

The hardness tests were performed using Controlab equipment (Figure 103 A) and B)) using a load of 1471 N (Figure 103 C)). To ensure an accurate measurement, after the chemical etching of the samples (to be able to identify the different layers), all indentations were made as close as possible to the center of the sample at equal distances from its edges, as well as in the center of the WBs. The values were collected in Rockwell C (HRC) unit, and then converted to Vickers (HV) unit using a conversion table.

Results obtained about the construction of the walls

The construction of the walls went smoothly. However, some problems were identified. Figure 117 shows one of the problems that can directly affect the productivity of the process. The wire getting welded at the end of some layer depositions added rough defects in the beginning and end zones. The area in the red rectangle in Figure 117 shows an example. These defects are due to instability at the beginning of the deposition, and to the difference in height that starts to be accumulated from the first layer. Even though the same wire length was always guaranteed at the end of the torch, defects appear. All walls had similar defects, regardless of the ITe. After building the walls, it was necessary to process them to obtain a simple wall ready for sampling. The first step was to clean the walls with a steel brush for drilling of all the metal dross that was deposited around the wall during construction (attachment G). Then the walls were cut into four pieces: substrate, left and right side, and central zone, as explained in attachment H.

Figure 106 shows the average ITi used over the deposited layers for each temperature during the wall construction. The different colors represent the average ITi times for the different ITe calculated from the data collected from the Fronius Xplorer equipment. The following comments can be done from this figure: ➢ It was possible to identify different dwell times (ITi) between the different ITe right from the first layers. ➢ The ITi difference was much larger between the 150°C (blue line) and 350°C (black line) than between 350°C and 550°C (red line) even though the temperature variation was the same. ➢ For an ITe of 150°C, there was a significant increase in time between layer 6 and 20, where there was a rapid heat evacuation allowing low ITi. ➢ After layer 20, there was a continuation of the ITi increase, but in a much more gradual and slower way. ➢ For ITe = 550°C, the ITi practically did not change, whereas for ITe 350°C there was a noticeable increase between layers 6 and 40. ➢ The increase in ITi for ITe = 350°C between layers 6 and 40 was due to the accumulation of heat in the material, which reduces its cooling capacity. ➢ There was also a phenomenon that happened in layer 20 for ITe = 150°C and in layer 30 for ITe = 350°C: a reduction of the influence of heat conduction and an increase of radiation and convection.

As a final note, the area from which the substrate no longer affected the cooling of the wall, the cooling became slower. The reason was because here the cooling of the wall was done through heat exchange between the wall surfaces and the surrounding environment. During the experiments, it was possible to observe several relevant aspects, which may introduce some variability in the results. Some of these aspects are described below: ➢ The height of each layer varies with its position in the wall, increasing its height gradually with the increase of the wall. Recorded variations show that a single layer height can vary between 1.53 mm (minimum recorded value) and 2.21 mm (maximum recorded value) both for an ITe of 150°C. The variation of layer height is higher for an ITe = 150°C and decreases with the increase of ITe. We can therefore realize that it is necessary to adapt the programming to this variation of height in order to obtain a more stable process. ➢ The thicknesses achieved in the walls vary, between 6.25 mm and 7 mm and increased with ITe (values measured only for ITe of 150°C and 350°C). ➢ The distortions in the deposition length varied between 5.35 mm for an ITe of 150°C and 9.8 mm for an ITe of 350°C. (measured values only for ITe of 150°C and 350°C), see example in Figure 120 B). ➢ The spent material (coil wire) varied by 245 g between 1094 g (for an ITe of 150°C) and 1339 g (for an ITe of 550°C). ➢ The deposited material (including the imperfections at the beginning and end of the wall) varied between 1052 g (for an ITe of 150°C) and 1290 g (for an ITe of 550°C), see example in Figure 119 A) and C). ➢ The material lost during deposition thus varied between 34 g and 51 g. It corresponds to metal projections that occurred during the deposition process and were not "welded/glued" to the substrate. Also, the wire tips necessary to cut to maintain the tip size on torch constant are included here. The higher loss of material occurs for higher ITe (Figure 119 D).

Figure 107 shows an example of a wall after cleaning its surface, made with ITe = 550°C. The images in A), B) and C) show some of the different defects caused by the beginning and end of the deposition on this wall. In Figure 107 B), it is also possible to see the longitudinal distortion of the wall. On Figure 119 D), it can be seen the metal projections and the wire ends that had to be cut, either because they were welded or to keep the wire in the torch with quality (not thermally affected) and at a constant distance from the surface. If we compare the walls made with ITe of 150C° and 550°C, we can see that the wall made at ITe = 150°C had a more stable deposition allowing it to be straighter and with the difference between layers being practically constant. The walls made with ITe = 150°C also allow a greater amount of material to be used, since the wall is more horizontal in its length. It is also worth noting that the constructions with the three different ITe had completely different durations as shown in Table 34. Following comments can be done from this table: ➢ The total construction times for each ITe vary due to the number of layers deposited to reach the defined height. It is therefore very important to take into account that very different times per layer plus ITi were obtained. ➢ For a 150°C ITe, the average time per layer (including ITi) until it was possible to re-start deposition of the next layer was 7 minutes and 1 second. For a 350°C ITe, it was 1 minute and 58 seconds; and for a 550°C ITe, it was 58 seconds. The different times between different ITe have a direct impact on the cost of manufacturing, once all equipment needs to be turned on, increasing energy consumption costs, as well as the cost of having a dedicated operator to build the wall who will spend periods of time just monitoring the temperature. The work dynamics, with no intervals longer than ITi, means that normally two employees are needed for manufacturing, or relatively short shifts allowing no downtime during manufacturing. It is therefore necessary to increase the level of automation and monitoring of the process, in order to be able to plan it taking into account the thermal history associated with different part geometries, and also allowing to plan the management of human resources in an efficient way. Note that the results show a clear pattern regarding the influence of the different ITe used, whether the measurement were done on the samples with vertical or horizontal orientation.

Results of the quasi-static tensile tests

Figure 110 shows the stress-strain curves obtained with the samples taken from the built walls. All tests were displacement-controlled at a rate of 0.15 mm/s. Graphs A), B) and C) shows the results for an ITe of 150°C (in blue), 350°C (in black) and 550°C (in red) respectively. The continuous lines correspond to the vertical samples while the dashed lines correspond to the horizontal ones. As a general comment, it can be noted that, at fixed ITe, the horizontal samples had a higher tensile strength (Rm), a higher yield strength (Rp0.2) but lower maximum and uniform elongations compared to the vertical ones. Additional comments can be done from Figure 110 A): ➢ In graph A), it is possible to see that among the vertical samples there was a small variability (29.5 MPa) in the Rm values, ➢ Also, in graph A), the variation of the uniform elongation was 4.9% for the vertical samples, while the maximum elongation of the horizontal samples varied approximately twice as much (10%) between the smallest and the biggest. ➢ The horizontal specimens with the same ITe of 150°C, had a highest Rm variation (of 60 MPa) and a variation of uniform elongation of 4.2% while the variation of maximum elongation was 5.3%. Also, Rp0.2 had a larger variation among the vertical samples (24 MPa) than among the horizontal samples where the variation was about twice as large (47.7 MPa). Some comments can be done from Figure 110 B):

➢ The vertical samples had a small variability in the Rm values of 26.6 MPa, as for the uniform elongation the variation was 6.5%, while the maximum elongation had a much larger variation of 28% between the lowest and the highest values. ➢ The horizontal samples with the ITe = 350°C, had a larger Rm variation (43.3 MPa) and a uniform elongation variation (5.1%), while the variation of maximum elongation was 10.2%. ➢ The Rp0.2 had a variation among the vertical samples of 15.8 MPa, while among the horizontal samples the variation was about twice as large (29.3 MPa).

Final comments can be done from Figure 110 C): ➢ The vertical samples had a minor variability in the Rm values (5.8 MPa), as well as in the uniform elongation and maximum elongation with 5.1% and 5.8% respectively between the lowest and the highest values. ➢ The horizontal samples with ITe 550°C had a larger Rm variation (55.9 MPa), a small variation of uniform elongation (3.7%), while the variation of maximum elongation was 7.2%. ➢ The Rp0.2 values varied of 16.8 MPa among the vertical samples, similarly to the variation between horizontal samples with 15.6 MPa. Figure 111 shows all the curves of the vertical samples. Some comments can be made: ➢ All the samples with ITe = 550°C had a higher maximum elongation than all other samples. ➢ The samples with ITe = 550°C had the most repeatable response until almost 40% elongation. ➢ The majority of the samples with ITe = 150°C had a higher Rm than the other samples. ➢ The elastic limit decreased when ITe increased. Table 35 gives the median values of Rp0.2, Rm, maximum elongation, and uniform elongation for the vertical samples. The following comments can be done: ➢ Rp0.2 decreases with the increase of ITe.

➢ The maximum and uniform elongations increase with ITe. ➢ The values of Rm are very similar for the three ITe. Figure 124 shows the stress-strain curves of the horizontal samples. Several observations can be made: ➢ The values of Rp0.2 were maximum for ITe = 150°C and decreased with the increase of ITe, similarly to the vertical samples. ➢ There was great variability in maximum elongation. ➢ It is not possible to obtain a trend for the maximum elongation values as a function of ITe. ➢ In opposition to the Rp0.2 values, the maximum elongation increased with the increasing ITe. ➢ The samples with ITe = 150°C had the highest values of Rm, and those with an ITe = 550°C had the lowest ones.

➢ The strength Rm, as well as the average uniform elongations, had values very close to each other but it does not allow any trend to be recognized due to the variability between the results. Table 36 shows the median values of Rp0.2, Rm, max elongation, and uniform elongation for the horizontal samples. Figure 114 shows the values of the maximum elongation (gray) and uniform elongation (yellow) obtained for the vertical and horizontal samples with the different ITe. Following comments can be done from the figure: ➢ The vertical specimens gave maximum elongation and uniform elongation values, that were all superior to the horizontal samples. ➢ The difference in maximum elongation between the vertical and horizontal samples with ITe of 150°C was 12.6%, and for the ITe of 550°C, it was 23.4%. ➢ The maximum elongation of the two types of samples increased with increasing ITe, evidencing a significant increase of 12.7% for the vertical samples between ITe of 150°C and 550°C. ➢ The uniform elongation of the two types of samples also increased with increasing ITe, evidencing an increase of 8.1% and only 2.6% in the vertical and horizontal samples respectively. ➢ The horizontal specimens were much more stable having smaller variations in both the maximum and uniform elongations as can be compared between Table 35 and Table 36.

Results of the accelerated fatigue tests

Figure 115 shows an example of minimum and maximum stress evolution during a fatigue test. Let us indicate that a loading frequency of 20 Hz was imposed, with a ratio of 0.1 between the maximum and minimum forces applied. Thus, the mean stress σ mean was equal to 0.55 times the maximum stress σ max . And the stress amplitude σ a was equal to 0.45 σ max . Let us indicate also that the maximum force was increased by 1 N per cycle, up to sample failure. This led to a rate of stress amplitude of 0.768 MPa/s. However, a loss of linearity was observed for the highest force amplitudes, after nearly 400 s for all the tests. This was due to the setting of the machine, which was made for the "mean" force level of the test. It is difficult to have a setting that is good for both small and large forces. In practice, analysis will be limited to σ a < 290 MPa for all the tests, which is sufficient for the analysis. Figure 116 shows the evolution of the heat density per cycle associated with mechanical dissipation (in kJ/m 3 /cycle) as a function of the stress amplitude 𝜎 a . This heat is by definition associated with irreversible mechanical phenomena, i.e. fatigue damage, micro-plasticity or plasticity. Graphs A), B) and C) show the evolution for the samples elaborated with an ITe of 150°C, 350°C and 550°C respectively. The curves for the horizontal and vertical samples are in solid and dashed lines respectively. Note that the curves are limited to 𝜎 a < 290 MPa, corresponding to the correctly linear evolution of 𝜎 a during the tests. The following comments can be made: ➢ For all the curves, the heat generated by fatigue damage was almost zero at low loading levels. This is expected to be below the fatigue limit of the material (the stress amplitude below which the life duration is a priori infinite). ➢ Above a certain stress amplitude (which can be associated to the fatigue limit of the material), a self-heating occurred. The heat produced per cycle logically increased with the stress amplitude. ➢ At fixed ITe, it can be seen that the vertical samples produced more heat than the horizontal ones: at same level of mechanical loading, it can be said that the life duration will be lower for the vertical specimens.

➢ A strong repeatability was observed for the samples of the same category (same Ite, same orientation). In particular for ITe =550°C, the repeatability was very strong. This must be considered with the understanding that "classical" fatigue tests are generally subject to high statistical variability. This is an advantage of the experimental approach used here. ➢ The comparison between the different categories of samples is made on the following figure. ➢ Whatever the ITe value, the heat generated by fatigue damage was greater for the vertical samples. From a fatigue performance point of view, it is thus preferable to have the horizontal specimens. ➢ For both specimen orientations (horizontal or vertical), the heat increased with the value of ITe. From a fatigue performance point of view, it is therefore preferable to have an ITe of 150°C rather than 350°C, or 550°C. ➢ These trends are confirmed in Table 36, which extracts the values for 𝜎 a = 250 MPa. Figure 118 and Figure 119 show the zoom of the previous figures to determine the stress amplitude corresponding to the onset of fatigue damage, for the vertical and horizontal specimens respectively. This stress amplitude is noted as 𝜎 a onset in the following. Table 37 gives the values obtained. It can be noted that the identified values are quite close to each other. Note that the presence of noise makes the identification rather difficult. However, it appears that the higher the ITe, the slightly greater the value of 𝜎 a onset . In addition, it can be noted that the tests were very short (about 400 s per specimen), compared to classical fatigue tests. Considering 30 minutes per sample (including the placement of sample in the jaws, the waiting time to reach a steady thermal state, the removing of the sample and saving the data), all the accelerated fatigue tests were performed in two days.

Conclusions

The hardness tests show that the interlayer temperature has an influence on the hardness obtained. The difference is actually minimal. It can even be said that the median values for walls built at same interlayer temperature (ITe) end up in the same range of values. However, it can be identified that there is a superior hardness for the walls made with ITe = 150°C and a lower hardness for the walls made with ITe =550°C. The average hardness value for ITe = 350°C is between the two mentioned above. This result is consistent with the results obtained from the quasi-static tests.

The quasi-static tensile tests show that a lower ITe allows higher Rp0.2 values to be obtained, and a higher ITe in turn results in lower values. When compared to the reference (values of the supplier), the elastic limits achieved for the different ITe tested are all lower, with the smallest difference being for an ITe of 150°C and the largest for an ITe of 550°C for the samples of both orientations. The Rm values are also lower than the reference values, but there are no significant variations between the different ITe tested. The elongations in the case of the vertical samples vary by 10% between the different ITe, and have a minimum difference of 11% with the reference. The lowest elongation is obtained for an ITe = 150°C, and the highest for an ITe = 550°C. For the horizontal specimens, the elongations achieved not only vary little, but are identical to the reference. The reason for these results is directly related to the fact that, with a higher ITe, there is a greater accumulation of temperature in the wall. This temperature rise effect is minimized when using an ITe of 150°C, because at this ITe the material has time to evacuate the heat, allowing for repeatability in deposition conditions. Thus, it can be seen that with an ITe of 150°C, there is actually a thermal stability from a certain distance from the substrate. The accelerated fatigue tests enabled us to compare the expected long-term mechanical durability of the different materials differing in sample orientation (horizontal and vertical) and interlayer time (ITe of 150°C, 350°C and 550°C). The results obtained with the different ITe also show that there is a clear difference between the samples orientations: horizontal samples have better fatigue performance whatever the ITe value. When comparing samples with same orientation, it appeared that ITe plays a role in the fatigue performance: 1) the stress amplitude corresponding to fatigue onset very slightly increased when the ITe value decreased; 2) above this "onset" amplitude, the fatigue performance appears to be much better when decreasing the ITe value. Note that this latter conclusion was defined from a calorific point of view (the heat produced by the fatigue damage). Classical (and long and costly) fatigue tests would be necessary to express it in terms of life duration.

Chapter -KPI Overview

Introduction

The key performance indicators (KPI) for production are metrics, used to measure the effectiveness and efficiency of production processes. KPIs are generally applied in key sectors of the production process and provide insight into how well a production system is performing allowing the identification of the sectors that need improvement. For the WAAM process, two key sectors were identified, the robot kinematics and the thermal behavior during part construction. These two key sectors are directly linked to a third: the final quality of the part, and a fourth: the cost of manufacturing. Thus, the purpose of this chapter is to show how to evaluate the kinematic contribution and how to apply the evaluation method. For the thermal contribution, an Artificial neural network (ANN) model is presented here that was built to predict the interlayer dwell times. Also presented here is the relationship between these indicators and the quality of the material deposited as well as the cost of the process. The cost indicator is presented here and subjected to several considerations.

Chapter five outline

Chapter 5 is organized as follows: ➢ Section 5.1 presents the research problematics regarding KPI for WAAM process. ➢ Section 5.2 presents the introduction, the method, and the generic kinematic model to achieve the kinematic KPI. ➢ Section 5.3 introduces the artificial neural network (ANN) model developed for interlayer dwell time prediction, as well as a case study for the thermal indicator. ➢ Section 5.4 presents the relationship between the two indicators cinematic and thermal, and the expected quality of the material deposited (quality indicator). ➢ Section 5.5 presents the conclusions and the overall score.

5.1.

Research problematics regarding KPI for WAAM process

The development of performance indicators for the WAAM process and associated sub-processes requires a detailed analysis. Assuming that the WAAM process works in closed cells, the analysis is focused on the aspects that limit the production process without including the post-processing of the part. As the WAAM process is dedicated to short series and exclusive parts, the most important KPI are related to process constraining factors during material deposition The short series implies difficulties to measure, and therefore to obtain reliable indicators applicable to the many different methods that can be used.

Figure 120 presents the stages of the WAAM production process, as their dependencies and the resulting KPIs. As presented in Chapter 2, there are two products of kinematic evaluation. The first is the kinematic time for a given deposition strategy. The second concerns all the kinematic information necessary for the thermal model. This model then provides indicators that evaluate the pre-heating temperature, the deposition time with different ITe and also evaluates the influence of the trajectory on the thermal history. Thus, as shown in the figure there is a direct correlation between robot kinematics, thermal behavior, and production time, and thus the cost of the part. But if on the contrary the robot's kinematics and thermal behavior are regulated with the aim of obtaining a specific material quality, then the quality dictates the cost of the process.

Kinematic indicator

For the WAAM process, monitoring and controlling robot movements during part construction is critical to ensure consistent, high-quality "printed" parts. Indeed, any deviating movement outside the programmed toolpath can lead to defects in the built part.

So, if the robot moves too quickly or too slowly, the resulting deviating movements can induce uneven or incomplete deposition, with material gaps in the deposed layers. If the layer is not even or if material accumulates unevenly, this can cause the built part to deform or deviate from the original geometry during the build process.

Thus, the evaluation method and kinematic tests developed in chapter two allow us to identify and correct before the deposition of material the errors that may arise from deviations of the programmed trajectory. This evaluation method also allows to collect the times of each section, necessary to feed into the developed formulas and thus obtain a prediction of the deposition time. Identifying and addressing problems with robot motion prior to deposition will also help minimize the need for reprints or other time-consuming and costly corrections. This will lead to a more reliable and efficient process, while it allows the quality improvement of printed parts, increase productivity, and reduce waste. The importance of performing the developed evaluation method for robot motion prior to the deposition process cannot be overstated. By performing a global pre-evaluation of sections and of complete trajectories, situations can be identified that lack precision in the movement or that will be subject to the appearance of defects related to the variation of the WFS/TS ratio. This allows the programmer to make the necessary programming changes to correct the toolpath and achieve more reliable, efficient, and high-quality results.

The application of the WAAM process should be based on a battery of tests using different robot configurations and testing different robot parameters that directly influence the process accuracy and deposition time. The goal of the different test campaigns is to collect the necessary information to build a kinematic indicator. Some of the considerations that should be kept in mind before performing the tests are described below:

1. The kinematic indicator developed based on real tests is unique to the equipment chosen to build the cell. It is possible that the kinematic indicator will provide very close manufacturing time predictions (for a very similar accuracy) if two robots are of the same brand, with the same model, and both are new. 2. For the construction of the kinematic indicator, it is relevant to consider several types of geometries close to those that are intended to be built, to restrict the number of tests to be performed. 3. It is then necessary to consider all the trajectories that are considered the most suitable from the point of view of quality for filling the part volume. 4. Initially, each geometry must be analyzed separately, to develop the best possible trajectory, always bearing in mind that there must be continuity in the deposition (avoiding arc transitions) within the same layer. 5. Finally, there is the work of sectioning each of the trajectories into smaller sections that can be carefully measured separately. 6. The two types of sections that exist in the plane are straight and curved. In a straight section the variables can be acceleration length/time, the "constant" velocity length/time, and the deceleration length/time. 7. The straight sections with deposition start and end must be analyzed separately from the intermediate straight sections because their initial and final velocity is zero.

Figure 121 shows a scheme summarizing the kinematic data collection procedure and the resulting indicators. As can be seen in the diagram on the left are the specific programming parameters of each type of robot/equipment that must be tested. The designations in the scheme are specific to Kuka robots, but other brands of robots have equivalent parameters with only the designations changing.

In the yellow rectangle we can see the factors independent of the type of equipment/robot used. In orange we have the general components of the trajectories, from which the times should be collected.

All the collected information is then compiled into a database that is processed through the kinematic model to provide an estimate of: time and kinematic graphical model. Initial acceleration and final deceleration behavior have been proved to be speed dependent in the case of the robot studied in this work. They are based on the settings of the robot in terms of maximum jerk and maximum acceleration. Intermediate acceleration and deceleration as well as minimum curve speed have been demonstrated to be both speed dependent and angle dependent, with a larger reduction in speed observed for high speed and "closed angle" configurations, as logically expected. However, this behavior is determined by the setting of the robot, in particular by the "CVEL" parameter. This parameter results in a constant speed favored to the detriment of the fidelity of the trajectory to the theoretical path. Another setting, "CDIS" aims to provide the opposite behavior with an accurate fitting of crossing points, but a lot of fluctuations in the speed profile. Since, from a process point of view, a constant speed is more important than an accurate fitting of crossing points, "CVEL" is preferred. It is also affected by the look ahead parameter which plays a key role here, since the robot's behavior is affected by how many lines of code it is reading in advance. This parameter affects the precision of the robot in translations, but also the speed profile and therefore the ratio between wire speed and travel speed.

The generic kinematic model is programmed on Matlab®. In addition to the previously described kinematic rules, the model takes as an input the toolpath described as a sequence of crossing points.

Process parameters, such as the target deposition speed, the transition speed (speed during transition movements in between beads/layers, ARC OFF) and offset (systematic vertical offset used for transition) must also be provided. The toolpath is analyzed segment wise, and the appropriate kinematic rules are picked from the provided "rules catalog". The speed profile on each segment is evaluated first, taking into account the angle formed with the previous and with the following segment.

The calculated speed evolution along the segment is then used to estimate the travel time. The procedure is repeated on the next segment until the final point is reached. The code runs within a few seconds, which makes its use very convenient for iterating over several toolpath strategies.

Figure 122 presents the general scheme of the kinematic model, their inputs and output. The kinematic model contributes to a good visualization of the impact that each trajectory has on the robot's speed during the deposition of material. This format with visual results allows a quick iteration between trajectories allowing to understand which best fits the geometry desired. This model also provides the programmer with information to define the length of each section. This feature of the model allows the transition areas where there are significant TS variations and which are likely to introduce defects into the part, to be outside the desired areas that belong to the part geometry. The total calculation of the deposition time combined with the material cost defines a production cost for the part. The calculation of the production time is also very important from the perspective that it allows the production to be planned in an efficient way.

In resume as seen in chapter 3 the kinematic score (𝐾 𝑆𝑐 ) for a given toolpath can be calculated using the formula:

𝐾 𝑆𝑐 = ( 𝐸𝐷𝐿 𝑇𝐿 × 1 3 + min (𝑁 𝐴𝑡 ) 𝑁 𝐴𝑡 × 1 3 + (1 -𝛥𝐺𝐼) × 1 3 ) × 10 (27)
Where:

𝐸𝐷𝐿 -Is the effective deposition length 𝑇𝐿 -Is the total length (performed) 𝑁 𝐴𝑇 -Is the number of arc transitions necessary ∆𝐺𝐼 = max(𝐺𝐼) -min (𝐺𝐼) -Is the maximum variation obtained along the analyzed toolpath for the pre-heating indicator.

Thermal indicator

The estimation performed in chapter 3 is based on a numerical simulation reproducing the construction of the part to be analyzed. The model aggregates information from kinematics and thermal simulation (analytical model and FEM modeling). On the one hand, the analytical model is used to iterate over several toolpath/strategies and chose the trajectory with the most favorable score; including pre-heating indicator and other process-oriented considerations. On the other hand, the FEM model predicts accurately the thermal history occurring in the part during its fabrication. This approach showed that the developed thermo-kinematic model is interesting for estimating the two main thermal indicators: cooling time and cooling rate. It has also been proven that the model is accurate (once the model is correctly calibrated). However, the use of that procedure/methodology still has several drawbacks: ➢ Pre-processing: the setup of the simulation can be tricky and requires expertise in the field of numerical simulation. ➢ Computation: computation time reaches several hours, even for relatively small size components ➢ Post-processing: the extraction of cooling time is not straightforward and requires a particular development/and expertise.

The objective of this research work is to provide "relevant" KPIs as well as models, to evaluate them in an accurate and potentially in a fast way. It is also necessary to make the utilization and comprehension of these indicators accessible to low technical skilled persons. For those reasons, a specific methodology for assessing thermal KPI's is proposed. It is based on the use of an Artificial Neural Network (ANN).

« Generic » cooling time estimation by means of an Artificial Neural Network (ANN)

The estimation of cooling time necessary to reach a given target ITe has been demonstrated crucial for a proper evaluation of the manufacturing time. Indeed, as detailed in chapter 3 on a particular study case, the amount of time to be added in between the deposition of two successive layers can increase dramatically the actual manufacturing time. Regarding the cooling time KPI, a model based on a full numerical simulation is not completely satisfactory for the reasons mentioned above: it cannot be easily handled, and it might not provide a result in a reasonable amount of time.

One attempt is here made to derive a generic model and relies on the use of a particular regression model obtained by training an Artificial Neural Network (ANN). To improve the accuracy and quality of AM processes, several research studies have explored the use of ANNs and machine learning (ML) techniques. One area of focus has been on compensating for thermal deformation during the printing process. In this work the authors propose using ANNs to learn the relationships between process parameters (such as wire feed rate and welding speed) and the resulting geometry and distortion. They trained their ANN using a dataset of simulated WAAM processes and achieved good accuracy in predicting the geometry and distortion of test parts [1]. Another area of research has been on bidirectional modeling of robotic WAAM aiming for a leveled part. In this interesting approach the authors note that a hybridized ANN bi-directional model is important for accurately predicting the behavior of the material during the additive manufacturing process, particularly when working with complex geometries and multi-layer structures. This model also provides other advantages regarding the ability to predict the effects of changes in process parameters such as wire feed rate and welding speed [2]. A different approach for WAAM was made using adaptive motion analysis and trajectory (MAT) path planning. Here the authors propose an approach, which involves modelling the welding bead with ANN model, and using MAT to plan the trajectory of the welding tool. The results from their experiments show that their approach is able to improve the accuracy and consistency of the welding process, leading to higher-quality parts [3]. Other research studies have explored the use of machine learning for predicting and controlling the quality of WAAM processes. In [4] the authors train a machine learning model to predict layer roughness based on a range of process parameters. Other works regarding the prediction of the microstructure and hardness for low carbon steel components [5], quality control of WAAM process and the prediction of the weld bead geometry for the CMT process having the interlayer temperatures in consideration have also been carried out in the same subjects. [6] In the same problematic here approached others propose a methodology to predict the interpass temperature of a wire arc additive manufactured wall using finite element method (FEM) simulations and artificial neural networks (ANNs). The authors, Francisco Werley et al, suggest that the use of ANNs can improve the accuracy of the FEM simulations in predicting the interpass temperature [7].

Overall, these research studies demonstrate the potential of ANNs and machine learning techniques for improving the accuracy, quality, and optimization of AM processes, particularly in compensating for thermal deformation, bi-directional modeling, bead modeling, quality prediction and control, and hybrid manufacturing processes.

Two ANN's were built. A first ANN (ANN 1) is dedicated to the estimation of the cooling time, and second ANN (ANN 2) is dedicated to the estimation of the cooling rate. The output of ANN 1 is a single scalar value whereas the output of ANN 2 regards four scalar values that are necessary to parametrize the cooling curve (detailed in section 5.4.10).

The steps followed in the elaboration of both ANN can be summarized as follows:

➢ Definition of relevant predictors (geometrical and temporal features), ➢ Simulation of additional study cases to construct and enrich a database, ➢ Training of the ANN on database predictors and responses, ➢ Validation of the ANN on a test case.

Definition of relevant predictors

The definition of predictors is partially based on the features established in chapter 3 when comparing several configurations encountered on a given part. Five predictors are used and described hereafter.

Energy (this input can be divided in two contributions):

o Stored energy: amount of energy already in the part before starting the deposition of a given layer, o Added energy: the added energy is proportional to the time laps between the starting of the layer construction and the reaching of the studied point on the layer.

Diffusion time:

this input is defined as the ratio between the time available for heat diffusion and a characteristic time for diffusion evaluated from the distance between the studied point and the previously travelled points (anterior points on the toolpath). This input intends to quantify how much heat may reach the studied zone and affect the cooling behavior. The evaluation of "distance" between points is described d in attachment R.

Simulation of additional study cases

The robustness of the ANN regression model strongly depends on the training stage and thus on the available data. If the database covers a large range of configurations, the model might be able to provide a reliable estimate also in a large number of situations. As all "training-based approaches", the enrichment of the database can be done on the fly, by focusing during training on the configurations where the model is more prone to error. To enrich the database used for training the ANN model, two case studies were used:

• Reduced pattern size: the size of the deposition pattern is reduced, i.e., the length of the segments in between vertices is reduced to 30mm (against 50mm in the original study case), keeping the substrate size unchanged. • Increased substrate size: the pattern is kept the same as in the original study case, but the length and the width of the substrate are doubled (400mm against 200mm). In order to enrich the ANN model presented here, many more case studies could be considered, covering a wide variety of settings. Thus, it would be necessary to plan a design of experiments (DOE) in order to deepen the study of the information provided and the impact it had on the result. This ANN model is not intended to cover all possibilities, but it aims to prove the possibilities offered by this type of model.

Training of the ANN on database predictors and responses

Structure

The ANN is built using the "Deep Learning toolbox" available on Matlab® and is based on a structure made of 3 hidden layers. The first layer (Hidden 1) is composed of 6 neurons, the second layer (Hidden 2) comprises 4 neurons and the 3 rd layer (Hidden 3) is made of 2 neurons. This choice is purely arbitrary since it was not possible to find a reliable and specific methodology to define the architecture of the network. Another option could have been to reduce the number of layers and to increase the width of the network, that is to say the number of neurons on each layer. The deepness of the network has been preferred over the width. The transfer function is kept as sigmoid function for the hidden layers. The output layer is made of a single neuron and uses a linear transfer function as it is recommended for regression problems involving one output. Figure 132 shows the geometry used in this test case. In gray is represented the substrate, and in orange the vertex, which are the points where all the straight deposition segments begin and end (represented in green). The trajectory can be divided into three branches in which each branch includes several straight sections and vertex. In between branches of the same trajectory there are transition movements that have been considered in the model as well as their times. The toolpath is made of three distinct branches:

-First branch -4 -8-9-10-7-3-2-1-4 -Second branch -8-5-2-6-10 -Third branch -1-5-9-6-3

The segments oriented along the X-direction are of length a=50mm whereas the other segments are of length b = 56mm. With the objective of getting a reference, a thermal simulation was performed on this geometry. As a result, the cooling time necessary to reach an ITe = 150°C was extracted at the ten vertices shown and numbered on Figure 132. Figure 133 shows the FEM simulation of the presented test case. The cooling time estimation is of utmost importance for the evaluation of the manufacturing time. However, assessment of part quality requires an evaluation of cooling rate as discussed in chapter 3 and chapter 4. An approach based on a regression model is possible, but it faces more challenges than cooling time estimation as we will discuss in this section.

Parameterization of a cooling curve / multi-response output

The first step in the construction of a regression model consists in representing the model output by a set of numbers. In the case of the cooling curve, the use of exponential functions seems to be the most logical candidate. To illustrate this point, several cooling curves extracted from the study case FEM simulation (cf. chap 3) are fitted with a function f defined as:

𝑓(𝑡) = 𝑎𝑒 𝑏𝑡 + 𝑐𝑒 𝑑𝑡 (29)
This function involves 4 parameters, denoted a, b, c, and d. This kind of function provides an accurate fitting on most of the cooling curves analyzed as detailed in Table 40, where the last column details the regression coefficient R².: the closer R² is to 1, the better the quality of the regression. The inverse of the coefficients b and d can be interpreted as characteristic times associated to cooling, whereas the sum of the coefficients a and c is the peak temperature. In relation ( 29) the time t is relative to the time where the (last) peak temperature is reached, corresponding to the time when the heat source passes by the point for the last time.

Training metrics of ANN 2

As for ANN1 model the training of ANN2 is done with 80% of the data provided while the remaining 20% are used for testing. 420 instances are spread over the entire trajectory sequence and were used to train the data. Figure 135 A) shows the error evaluated on the whole dataset. The histogram on Figure 135 B) shows the error evaluated on the test data only.

Conclusions

The evaluation of thermal KPI's based on ANN is proposed to make the overall approach faster and much easier to employ, compared to advanced numerical simulations. The cooling time estimation based on an ANN is an interesting tool for quickly evaluating the need for cooling periods and for deriving a more accurate estimation of manufacturing time. A more advanced training of the second ANN dedicated to cooling rate estimation is required to improve its accuracy and make it a tool that can be trusted for metallurgical evaluation. The prediction of four outputs (the four parameters describing the cooling curve) instead of a single output (cooling time) logically requires a much larger set of training data. The challenge is to define on which geometry the training would be the most efficient. Thus, we can conclude that it is possible to use an ANN model to preview the interlayer times for different interlayer temperatures. It is therefore necessary for the model to be fed with data based on geometries from the same type to achieve accurate interlayer times.

From the estimation of the necessary cooling time between each layer, a deposition time can be evaluated and quantifies the time required to actually build the part. A thermal score (𝑇 𝑆𝑐 ) is defined and is evaluated for any strategy using the following formula:

𝑇 𝑆𝑐 = 𝐾𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑡𝑖𝑚𝑒 𝐷𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒 × 10 (29)
Being the deposition time calculated by: 𝐷𝑒𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒 = 𝐾𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑡𝑖𝑚𝑒 + 𝐼𝑛𝑡𝑒𝑟𝑙𝑎𝑦𝑒𝑟 𝑡𝑖𝑚𝑒 (30) For a given layer:

➢ Kinematic time is the necessary time to travel all the toolpath. ➢ Interlayer time is the necessary time to cooldown to a specific temperature, before starting the deposition of the next layer. It is worth noting that the interlayer time may vary from one layer to the next one. It will then be necessary to consider the sum of all interlayer times and add the kinematic time to obtain the total building time. The values for the 𝑇 𝑆𝑐 will range between 0 and 10. Having a 𝑇 𝑆𝑐 of 10, would mean that there is no interlayer time. This situation can happen in two completely different scenarios:

1. The first corresponds to the ideal situation from the thermal point of view, meaning that the toolpath is sufficiently long to allow the material to cool down to an interlayer temperature of reference given by the wire manufacturer.

2. The second corresponds to a production where thermal behavior is not considered, and the objective is only to have the lowest time of deposition. If, on the contrary the 𝑇 𝑆𝑐 is closer to 0, it means that there is a big impact of the interlayer time on the deposition time. This is due to poor cooling conditions during manufacturing, a low required interpass temperature, or a short kinematic time.

Quality indicator

The results of the quality indicator developed are specific to duplex 2209 stainless steel. As confirmed by the results in chapter 4 the quality of the material changes when different ITe are used. Figure 139 shows that the quality of the material depends on several factors. Some comments can be made on these factors: ➢ Some factors already mentioned above, such as the input parameters, could not be left out. This factor can affect the quality in many ways, as well as the geometry of the weld bead. ➢ Substrate size is a factor that contributes directly and indirectly to the quality of the material.

The fact that during the WAAM process it is attempted to include the substrate in the construction of the parts means that in a direct way the properties of the substrate are as important as the properties of the material that is deposited on it. The indirect way in which the substrate affects the quality of the part is related to how the volume of the substrate affects the cooling of the layers deposited on it. ➢ The material used (duplex stainless steel 2209) has well defined prerequisites (as shown in chapter 3) regarding deposition and cooling conditions. If the characteristics of the material are not considered, then production conditions (trajectories or ITe) can promote in the extreme the appearance of detrimental phases. As proved in chapter 4 the mechanical properties of the material change for different ITe. Thus, the relationship between material characteristics and material quality is clear. ➢ As proved in chapters 3 and 4, the temperature between layers is directly related to the microstructure of the material and has a big impact on the quality of the material as built.

Thus the quality of the piece produced can be, for the same material deposited in the same conditions but with different ITe, an indicator of the performance of the process. This means that the performance of the part with regards to its mechanical characteristics (hardness, quasi static and fatigue), is in itself an KPI of the process exclusive to each material. ➢ Trajectory is a key factor of DED processes and affects the quality of the part in different aspects. As proved in chapter 3 the optimal trajectory from a kinematical point of view, may not be the best from a quality point of view. The quality of the part depends on its cooling, and the gradient achieved through the part. A good toolpath is characterized by the most uniform possible heat distribution throughout the part, as well as the absence of hot spots.

Because the WAAM process has a moving heat source, the part will be subjected to cyclic heating and cooling across its geometry. These cycles and their variation across the part will lead to different thermal histories at different locations in the part, resulting in a different possible microstructure and therefore different mechanical properties. So, with uniform cooling throughout the part and with repeatability of cooling in all layers, the microstructure achieved as well as the mechanical properties will be similar (excluding the zone affected by the substrate). A quality indicator can then be computed for the material produced, taking into account the ITe used. This indicator is here called Quality score (𝑄 𝑆𝑐 ) and it is calculated by:

𝑄 𝑆𝑐 = 𝑅𝑝0.2 𝑊𝐴𝐴𝑀 𝑅𝑝0.2 𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 × 10 (31)
The quality score will also range between 0 and 10. Having a 𝑄 𝑆𝑐 of 10 would mean that the deposited material managed to achieve values (of Rp0.2 in this case) equal to the reference values, which is here considered the best scenario. In contrast, if 𝑄 𝑆𝑐 is close to 0, this means that the Rp0.2 is low and this value it is very different from reference (forging, casting, etc), meaning the quality is considered bad.

The 𝑄 𝑆𝑐 calculation is based on the methodology and material behavior observed during the realization of this work. For other materials it would be necessary to assess the material behavior for different Interlayer temperatures and possibly use different material characteristics other than Rp0.2 (Rm, fatigue resistance or elongation). The criteria to be chosen depends on the application and the most critical characteristics for that application. For this reason, the parameters to be computed in the formula have to be chosen by the user in accordance with the performance to attain.

Conclusions

Kinematic, thermal, and quality indicators have been developed. In order to make a direct comparison with other production processes, it is necessary to group the information from all the indicators developed. To obtain an overall indicator for the production process, considering all the parameters previously mentioned, one last formula needs to be implemented.

The overall score has the aim to aggregate all the three indicators:

𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝑠𝑐𝑜𝑟𝑒 = 𝐾 𝑆𝑐 +𝑇 𝑆𝑐 n° layers + 𝑄 𝑆𝑐 (32)
The overall score values should range between 1 and 30 for each layer. Having an overall score close to 30 means that the process is kinematically fast, no interlayer time is needed and the quality of the material for a given parameter is close to the reference value. Resuming, the higher the value, faster will be the production process, and the quality of the resulting part. If on the other hand the overall score is close to 0, it means that the process is kinematically slow, with long cooling periods, and the material achieved has properties very low compared to the reference. Using the study case presented in chapter 3 to test these formulas, the calculation of all the indicators were done for the 3rd layer with an ITe = 150°C, and are provided following:

The kinematic score is:

𝐾 𝑆𝑐 = 850 1682 × 1 3 + 4 4 × 1 3 + (1 -0.7) × 1 3 𝐾 𝑆𝑐 = 6.01
The kinematic score is the same for all the layers since there are no changes in the trajectory and its characteristics.

The thermal score (using interlayer time of the 3 rd layer for an ITe = 150°C) is: To allow a comparison, the 3 different overall scores were then calculated for the same part geometry. Considering the 3 ITe, 150°C, 350°C and 550°C the calculation is here made for the eighteen layers (from 3 rd layer to 20 th ). The first and second layers usually have rapid cooling and as a consequence they were not considered for this calculation. The kinematic score for the 18 layers is: For 550°C 𝑄 𝑆𝑐(550°𝐶) = 6.69

𝑇 𝑆𝑐 = 82
𝐾 𝑆𝑐(
The result for the overall scores for the sum of the 18 layers was then calculated and are shown following.

The overall score is for the ITe = 150°C: The formulas developed are able to translate a quantitative grade for the material result of the use of different ITe.

𝑂𝑣𝑒𝑟𝑎𝑙𝑙
It was thus possible to develop a performance indicator for the WAAM process. The kinematic indicator can however be calculated for several different trajectories for the same part geometry. This will require the calculation of the kinematic score for the different layers. The thermal/productivity score must always be calculated for all the layers that the part covers. As for the quality score, this is the only score that is always the same for all layers, since it concerns the quality of the whole part.

The results achieved here between the scores for 150°C and 350°C could also be more expressive. This means that in order to show the differences between different ITe (kinematic, thermal/productivity and quality) more expressively, it is necessary to input a multiplication factor in each variable to correctly define the weight that each factor has on the final result. This variable would also allow us to refine the formula for different materials that would necessarily have different behaviors. This is greatly due to the impact that the thermal/productivity factor has on the overall score. This factor can achieve big variations influencing this way (incorrectly) the balance between factors that the formula aims to deliver, and by consequence the evaluation of the process.

General conclusions and perspectives

Key performance indicators (KPIs) can be used to measure the effectiveness and efficiency of production processes. The present thesis work focused on the Wire Arc Additive Manufacturing (WAAM) process. Two first-order KPIs were identified and studied: i) the kinematics of the robot used to deposit layers of material, with potentially an interaction between the cold metal transfer (CMT) equipment and the robot controllers; ii) the thermal response during the construction of a part (need for a cooling time between layers). These two aspects play a role in the final quality of the part (geometrical accuracy, mechanical properties). They also impact the manufacturing cost, especially in terms of process productivity through the material deposition time and the interlayer time. After conducting specific literature reviews on the WAAM process, CMT and the materials elaborated by these techniques, the research work was divided into 3 studies (kinematic analysis, thermal analysis, and measurements of mechanical properties) and 1 last part (development of score formulas to evaluate the performance of each indicator, as well as proposal of an overall score aggregating the different contributions).

In the WAAM process, the accuracy of the toolpath is of prime importance. A lack of accuracy causes defects in the part, such as voids or unfilled volumes. It also impacts the quality of the final part and its mechanical properties. In the case of a robotized process, this accuracy depends on the kinematic behavior of the robot, as well as the interaction between CMT equipment and robot controllers. In chapter 2, a motion analysis of the nozzle using a KUKA KR 100-2 HA 2000 robot with a KRC2 controller was performed, without material deposition ("virtual" deposition including transitions between arc on and arc off). Several results were found, highlighting that compromises should generally be found: ➢ Discontinuous deposition leads to additional travel time, due to decelerations, pauses and accelerations between nominal and zero speed associated with arc transition. However, it has the advantage of saving material (in sections intended to be transient) when compared to continuous depositions over the whole trajectory. ➢ Planning sections of the toolpath outside the nominal deposition area can be useful to "move" inaccuracy problems to where they are not critical from a geometrical and material quality perspective. Deposition outside the nominal deposition area may also be relevant, but it requires additional material, conventional machining time and tooling. ➢ For fully dense parts, the swiping strategy is the most commonly-used but it has limits and is not applicable to all sizes or geometries. It is important to understand the limitations of the different possible strategies in order to choose which one to use and how to adapt it to the needs. Sharp changes in direction in the programmed toolpath led to a trajectory error. The analysis showed that the continuous semicircular strategy mitigates the accuracy problem, nearly achieving a constant ratio between travel speed (TS) and wire feed speed (WFS). ➢ It is possible to define deposition time models taking into account acceleration, constant speed, and deceleration phases. One important indicator is the total manufacturing duration including the interlayer time (ITi). The latter is the time required for the material to cool down to a given temperature, called "interlayer temperature" (ITe), between two consecutive layers. The interlayer temperature is defined by using time-temperature-transformation (TTT) diagrams. The objective is to avoid the appearance of detrimental phases that could lead to a decrease in the material's mechanical properties. The difficulty of predicting the cooling time comes from the complex correlation between part geometry, deposition strategy and substrate dimensions. This correlation needs to be understood in order to minimize the thermal gradient across the part while using the lowest deposition time (Dt) possible and at the same time ensuring an acceptable material quality. In Chapter 3, two different models are proposed. One is based on an analytical formulation and proves to be faster and cheaper to compute compared to a full FEM simulation. Its reduced computation cost makes it a good candidate for the iterative process that allows to identify the trajectories with the best kinematic (more efficient solution in terms of manufacturing time) or thermal strategies (more thermally efficient, allowing to obtain the lowest temperature variation across the part). The second model is related to the cooling behavior and was trained with information obtained from FEM modeling. This ANN based model aims to deliver predictions of the cooling times and the cooling rates across the part geometry. This is achieved by having in consideration kinematic and thermal criteria for WAAM. This model allows to have a fast estimation of the cooling time necessary in each point of the strategy. The estimation obtained is valid for geometries that remained similar to the geometries used has a reference to train the model. In what regards the cooling rate a deeper training is necessary. A good strategy from the thermal point of view does not necessarily correspond to a good strategy from a productivity point of view. Therefore, the developed models can help selecting (for a given geometry) a toolpath, that offers the best kinematic or thermal option, or even a compromise between both. A multi criteria formula was also proposed, enabling to have a quantitative thermal evaluation of each toolpath and providing a useful score for decision making.

Mastering the mechanical properties of the deposited material is of prime importance for the WAAM process. In Chapter 4, walls made with 2209 duplex stainless steel were built using three interlayer temperatures (150°C, 350°C and 550°C). Samples were then taken horizontally and vertically. Three types of mechanical characterization were performed for that purpose: hardness measurement, quasistatic tensile tests (until failure) and accelerated fatigue tests (based on the self-heating measurements). The accelerated fatigue tests enabled us to compare the expected long-term mechanical durability of the different materials differing in sample orientation and interlayer time. Results showed that decreasing the interlayer temperature led to higher hardness and yield strength, lower ductility, almost similar strength and better fatigue performance. It was also shown that samples taken horizontally have better mechanical performance than those taken vertically. The results showed that compromises have to be made regarding the quality of the material (in this case a 2209 duplex stainless steel) and the productivity of the WAAM process. In order to allow a correct evaluation of the contribution of each indicator, formulas were proposed in Chapter 5 to define a global score embedding kinematic, thermal and material quality aspects. The developed formulas enabled us to compare the impact of the three interlayer temperatures tested (150°C, 350°C and 550°C). The results showed that the lowest score is achieved with the interlayer temperature of 550°C despite the fact that it is the fastest process. The interlayer temperature of 150°C gave the best quality of material. The score achieved with the interlayer temperature 350°C showed that a compromise can be made advantageously achieved between productivity and quality. Different directions of perspectives to this work can be proposed:

➢ It is necessary to structure two important indicators for production: a geometric indicator, and a cost indicator. The geometric indicator is necessary because of the different types of part geometry that can be achieved through the WAAM process. The cost indicator is mentioned several times throughout this thesis, where several relationships affecting it have been revealed. In the calculation of the cost indicator, the performance indicators obtained here must be taken into account. ➢ Given the latest developments in WAAM technology with implementation of positioners, it is now possible to produce parts using all six axes of the robot plus two axes of the positioner. This means that the kinematic model must be improved by considering the movements of this new type of equipment. Also, regarding the construction of the kinematic model, it is possible to improve the resolution of the measurements used to feed the model thanks to sensors external to the robot. ➢ In the thermal domain, it would be interesting to test the developed models on parts with other configurations, in order to verify their applicability and the veracity of the results. It would also be interesting to clearly identify the context in which the detrimental phases are formed, and whether consecutive exposure for short time periods to the temperatures identified in the TTT diagram are sufficient for their formation. It is also in perspective the improvement of the ANN model, providing more information for the model training allowing a more accurate prediction of the necessary waiting times. From the material's point of view, it would also be interesting to study in depth the metallographic characteristics of the material, the percentages of each phase (ferrite, austenite and eventually sigma), and try to relate the results of this analysis to the interlayer temperatures that the samples were subjected to.

Attachments

A -Detailed analysis of group A-1

The representation of the cooling curves for the points in group A had to be split into two different graphs and consequently two distinct analyses due to differences between the curves that were not expected.

The cooling curves of the points belonging to the sub-group A-1 (points P1, P3 and P5) resulting from the 3rd layer simulation with ITe = 150°C and Ite = 550°C, are shown in Figure 140. The cooling curves of points P1, P3 and P5 are very similar, being the curve of point 1 (blue) and the curve of point 5 (yellow) identical. Point 3 has a cooling similar to points P1 and P5, but at some point, it crosses the curves of these points because it receives heat from the adjacent deposition -V2 and -V3, and its cooling ends up being slower when compared to the other two points. The behavior of the cooling curves when using an ITe of 550°C can be seen in Figure 54 B). Here we can see that the influence of the high temperatures of the previous layers starts to be noticeable, as more time is needed to reach the same temperatures compared to the graph in Figure 140 A). The Figure 141 show the 20th layer cooling curve for points P1, P3 and P5 (configuration type 1) with 150°C (A)) and 550°C (B)) of ITe. As can be seen the cooling curve changes its shape due to heat accumulation. When we compare the curves with an ITe of 150°C A) and 550°C B) we can identify that the time needed to reach the same temperature is much longer when we have an ITe of 550°C. At the productivity level we can make a comparison between the different ITe and the different analyzed points, using the time required to reach the predefined ITe shown in the Table 41. As we can see for an ITe of 150°C the point that we should take into consideration to restart the deposition would be P3. Of the three points presented here, this is the one with the highest heat build-up, as we can see from the cooling times for the ITe that are always the longest for each layer. Table 41 also shows in orange the times which are longer than the kinematic time, meaning that a cooling time (nonproductive time) is necessary and can reach almost 2 min (117 s). Such a cooling time will thus strongly affect the total manufacturing time as it represents 142% of the deposition (i.e. kinematic) time. For an ITe of 150°C there is a necessary waiting time from the 6th layer onwards, whereas for an ITe of 350°C this waiting time is only necessary from the 20th layer onwards, while for the ITe of 550°C there is no loss of productivity. B -Detailed analysis of group A-2

The cooling curves of the points belonging to the sub-group A-2 (points P23, P25 and P27) resulting from the 3rd layer simulation for interlayer temperatures of 150°C and 550°C are shown in Figure 142. The cooling curves of points P23, P25 and P27 are very similar, being the curve of point 23 (blue) and the curve of point 27 (yellow) identical. Point 25 has a cooling similar to points P23 and P27, but at some point (around second 66 and 62 respectively), it crosses the curves of these points because it receives heat from the adjacent deposition -V6 and -V7, and its cooling ends up being slower when compared to the other two points. The behavior of the cooling curves when using an ITe of 550°C can be seen in Figure 142 B). Here we can see that the influence of the high temperatures of the previous layers starts to be noticeable, as more time is needed to reach the same temperatures compared to the graph in Figure 142 A). The Figure 143 show the 20th layer cooling curve for points P23, P25 and P27 (configuration type 1) with 150°C (A)) and 550°C (B)) of ITe. As can be seen the cooling curve changes its shape due to heat accumulation. When comparing the graph in Figure 142 A) with the graph in Figure 143 A) we can identify that the time needed to reach the same temperature is much longer when we have an ITe of 550°C. noticeably that because the surrounding material has already absorbed heat from the previous layers, the cooling is slower in the 20th layer. When we compare the curves with an ITe of 150°C A) and 550°C At the productivity level we can make a comparison between the different ITe and the different analyzed points, using the time required to reach the predefined ITe shown in the Table 42. As we can see for all ITe the point that we should take into consideration to restart the deposition is P25. Of the three points presented here, this is the one with the highest heat build-up, as can be seen from the cooling times for the interlayer temperature that are always the longest for each layer. Table 42 also shows in orange the times which are longer than the kinematic time. For an interlayer temperature of 150°C there is a necessary waiting time from the 6th layer onwards, whereas for an interlayer temperature of 350°C this waiting time is only necessary from the 15th layer onwards, while for the interlayer temperature of 550°C there is no loss of productivity. As mentioned before the analysis was done separately because there are differences between the cooling curves between the points P1, P3, P5 and P23, P25 P27. Figure 144 represents the cooling curves for the referred points for the 3rd and 20th layer for an ITe of 150°C Figures A) and C), and for a temperature of 550°C Figures B) and D). For an ITe of 150°C the differences between the cooling curves in these point groups are relatively small, but when the ITe is 550°C the curves show that in the 3rd layer to reach the same temperature will take very different times. But if we see the 20th layer at 550°C IT the asymmetries of the curves decrease leading to smaller time differences. The hottest group of points is P23, P25 and P27.

C -Detailed analysis of group B

The cooling curves of the points belonging to group B (points P7, P10, P18 and P21) resulting from the 3rd layer simulation for interlayer temperatures of 150°C and 550°C are shown in Figure 145 At the productivity level we can make a comparison between the different ITe and the different analyzed points, for group B the point to take into observation is P18 which has the slowest cooling curve. Table 43 shows the necessary cooling times (of the 4 points) to reach the different temperatures between layers. It is possible to see that from the 6th layer on (including) the interlayer waiting times are necessary, so that the material cools down to the target temperature of 150°C. For ITe of 350°C the same point (P18) is to be observed and after the 14th layer waiting times are to be taken. The cooling curves of the points belonging to group D (points P12 and P16) resulting from the 3rd layer simulation for interlayer temperatures of 150°C and 550°C are shown in Figure 147. In the Figure 147 A) we can see that the cooling curves of points P12 and P16 are relatively close, starting to diverge slightly for temperatures below 750°C in the 3rd layer to an ITe of 150°C. The cooling curve of point P16, which is initially more efficient, eventually converges with the curve of P12, around 162°C and even crosses it around 154°C. Below 154°C point P12 ends up having a more efficient cooling Figure 147 A). The same happens in the 3rd layer, with an It 550°C Figure 147 B), here the divergence starts at 1400°C increasing slightly until the temperature of 550° where there is a difference of about 1s between P12 and P16 with P12 being more efficient. The behavior of the cooling curves shown in Figure 147 A) for the 3rd layer, can be seen in the 20th layer with an ITe of 150°C Figure 147 C) taking into account that the temperatures are higher due to heat buildup in the material from the 20 depositions made previously. For the graph of the cooling curve of the 20th layer (Figure 147 D)) we can see that until the ITe we have a divergence of 1s in the curves. This graph Figure 147 D) clearly shows compared to the other graphs Figure 147 A), B), C) the high temperatures of the material caused by consecutive heat deposition due to a high ITe.

In the Table 44 we can see that for points P12 and P16 using an IT of 150°C from the 6th layer onwards it is already necessary to make stops between each layer, because the cooling time is longer than the deposition kinematic time. For the It of 350°C we can see that the point to be observed is point P16 where the cooling is less efficient, so after the 15th layer it is necessary to stop to allow the material to cool down to IT of 350°C. For the temperature of 550°C up to the 20th layer we can obtain maximum productivity since the cooling time required is always shorter than the kinematic time.

E -Detailed analysis of groups E

The cooling curves of the points belonging to group E (point P14) resulting from the 3 rd , 6 th , 10 th , 15 th and 20 th layer simulation for IT of 150°C and 550°C are shown in Figure 148. In the figure we can see the (simulated) cooling curves of point P14 for an IT of 150°C A) and for an IT of 550°C. On Figure 148 A) it can be seen that as the number of layers increases the cooling curve becomes less efficient, with the cooling time varying from 110s to 250s approximately. In the graph of Figure 148 B) it can be seen that the cooling curves become less efficient gradually with height growth. The cooling times vary between 42.5 s and 81 s (approximate values) The Table 45 shows the times needed for the material at the point P14 to cool down to the different defined ITe. For an IT of 150°C we can verify that all the layers after the 3rd one it is necessary to make stops (being marked in orange in the table from the 6th and after). For an IT of 350°C these stops must start at 14 th layer, increasing the IT until the 20th. The interpolation calculation of cooling times was done for all values between the 3rd layer and the 20th.Figure 149 shows the interpolation graph made based on the simulation of layers 3, 6, 10, 15 and 20 for the IT of 150°C. In blue we have the interpolation line with the values of time needed for cooling of the material for each layer, resulting from the simulation. The red horizontal dashed line corresponds to the kinematic time.

In the case of point 14 represented here, we can see that the amount of time required increases consequently with the number of layers, showing no signs of stabilization until the 20th layer. This behavior predicts that in the subsequent layers the amount of heat will continue to increase, leading to the need for longer and longer time intervals for each added layer, resulting in a loss of productivity of the process.

F -Detailed analysis of group F

The presents all the points that fit in the fourth type of configuration. The points shown in Figure 150 are all the points that have the fourth type of configuration in this case study. The fourth type of configuration is characterized by heat conduction in four directions, in the XY plane (top view of the part). Following is presented a detailed analysis of group F for this configuration. The Table 46 shows the cooling times needed for the simulated layers taking into account the different ITe. The point to watch is P22, because it has the slowest cooling curves of the group even if by a relatively small difference. For an ITe of 150°C it is necessary to introduce stopping times from the 7th layer on. At the 10th layer there is already a difference to the kinematic time of 36.7s. For an ITe of 350°C point P22 already needs 1.32 s of stopping time at layer 15, a time which increases with each layer deposited.

G -Wall-cleaning protocol

The walls were cleaned using a pneumatic drill, and a circular steel brush. Figure 152 shows the difference between a cleaned wall B) and an uncleaned wall A). Due to the metal soot, this work was done with a mask, specific gloves for the effect and a vacuum cleaner positioned so that the soot/powder were vacuumed directly.

H -Wall-cutting protocol

In order to obtain samples of the walls made, after cleaning them, it was necessary to cut them. Figure 153 is a schematic view of how the cuts were planned before machining. The schematic shows the areas to be cut to obtain the side sections for microhardness and hardness tests, and the cutting place of the substrate, in order to obtain a plate to be machined later. The process of cutting the walls consisted in a first phase of cutting the ends of the wall, where the beginning and the end of each layer is made. This area was cut on the 150°C and 350°C interlayer walls using a metal saw (Figure 154), as for the walls made with an interlayer temperature of 550°C this was for logistical reasons cut using wire EDM technology. After cutting the sides of the walls, it was necessary to get rid of the substrate area by making a cut as close as possible to the substrate between layers 1 and 3. The final result can be seen in Figure 155.

Figure 1 -Figure 3 -Figure 4 -Figure 6 -Figure 7 -Figure 8 -Figure 9 -Figure 12 -Figure 14 -Figure 16 -Figure 19 -Figure 26 -

 13467891214161926 Figure 1 -Decorative part produced by WAAM and draw in Baker R. [11] patent. .............................. Figure 2-classification of metal transfer depicted in an arc voltage and welding current diagram [21]. ............................................................................................................................................................... Figure 3 -Gas metal arc (GMA) welding natural metal transfer modes [22][23]. ................................ Figure 4 -Graph of wire speed cycle, current cycle, and voltage cycle [26]. ....................................... Figure 5 -WAAM cell in "Addimadour" research platform. ................................................................. Figure 6 -Schematic diagram of all equipment and connections in the CMT process. ........................ Figure 7 -Block Diagram of a CMT system [32]. ................................................................................... Figure 8-Example of different spools of wires used in WAAM process [33]. ......................................Figure 9 -Example of a table comparing mechanical results [36]. ....................................................... Figure 10 -WAAM pre-and post-process steps scheme. ..................................................................... Figure 11 -Scheme of process indicators and their dependencies. ...................................................... Figure 12 -Strategy for achieving the indicators. ................................................................................. Figure 13 -Photos of the system. In the framework of this study, the nozzle movement was studied without activating the torch (trajectory definition only). ..................................................................... Figure 14 -Representation of the three linear depositions made for the ACC_CP assessment. The acceleration (represented in blue) and deceleration (represented in red) lengths are not correctly dimensioned in accordance with reality. .............................................................................................. Figure 15-Representation of the expected behavior of the robot with the 3 different sections, acceleration (in blue), constant speed (green), deceleration (red). ..................................................... Figure 16 -Representation of part of the expected robot behavior when "simulated" using an arc transition at the X=50 mm coordinate. ................................................................................................. Figure 17 -Part of program 1 and 3 where the trajectory instructions (without and with arc transition) are described. ...................................................................................................................... Figure 18 -Example trajectories for different angles of 20°, 45°, 90° and 160°, and the expected behavior of the robot during the displacement. ................................................................................... Figure 19 -Different strategies considered in the study. ...................................................................... Figure 20 -Top view of the inerting chamber and the five different locations within it where measurements are taken. ..................................................................................................................... Figure 21 -Schematic view of the inert chamber with the locations of the different zones in which the same swiping deposition was measured. .............................................................................................. Figure 22 -Example of information gathered from the ADAONE program. ......................................... Figure 23 -Example of the trajectory traced on page two of the excel file of the results analysis. ..... Figure 24 -Positions collected from the trajectory done by the nozzle during the movement with an acceleration of 1m/s². ........................................................................................................................... Figure 25 -Speed calculated for the nozzle displacement with an ACC.cp value of 1m/s². .................Figure 26 -Position and Speed calculated with an ACC.cp value of 5m/s². .........................................Figure 27 -Position and Speed calculated for the nozzle displacement with an ACC.cp value of 10m/s². ..................................................................................................................................................Figure 28 -Distribution of acceleration time (in green), constant speed (in blue) and deceleration time (in yellow) for the different ACC.cp values with and imposed speed of 10 mm/s. ......................Figure 29 -Distribution of acceleration (in green), constant speed (in blue) and deceleration lengths (in yellow) for the different ACC.cp values using an imposed speed of 10 mm/s. ...............................Figure 30 -Distribution of acceleration time (in green), constant speed (in blue) and deceleration time (in yellow) for the different ACC.cp values with and imposed speed of 25 mm/s. ......................

Figure 31 -

 31 Figure 31 -Distribution of acceleration (in green), constant speed (in blue) and deceleration lengths (in yellow) for the different ACC.cp values using an imposed speed of 25 mm/s. ............................... Figure 32 -Distribution of acceleration time (in green), constant speed (in blue) and deceleration time (in yellow) for the different ACC.cp values with and imposed speed of 40 mm/s. ...................... Figure 33 -Distribution of acceleration (in green), constant speed (in blue) and deceleration lengths (in yellow) for the different ACC.cp values using an imposed speed of 40 mm/s. ............................... Figure 34 -Trajectory of the nozzle for a speed of 1000 mm/s with and 1% of Vel.cp. ....................... Figure 35 -Speed achieved by the robot during toolpath robot movement with 1% Vel.cp. .............. Figure 36 -Trajectory of the nozzle for a speed of 1000 mm/s with and 5% of Vel.cp. .......................Figure 37 -Speed achieved by the robot motion test with 5% Vel.cp. ................................................. Figure 38 -Trajectory of the nozzle for a speed of 1000 mm/s with and 10% of Vel.cp. ..................... Figure 39 -Speed achieved by the robot motion test with 10% Vel.cp. ............................................... Figure 40 -Illustration of the linear trajectory using program 2 at a nominal speed of 10 mm/s. ...... Figure 41-Illustration of the speeds using program 1 for a linear trajectory at a nominal speed of 10 mm/s. .................................................................................................................................................... Figure 42 -Illustration of the influence of the arc ON/OFF command on the linear trajectory using program 3 at a nominal speed of 10 mm/s. .......................................................................................... Figure 43 -Illustration of the speeds using program 2 for a linear trajectory at a nominal speed of 10 mm/s . ................................................................................................................................................... Figure 44 -Illustration of the linear trajectory using program 1 at a nominal speed of 40 mm/s. ...... Figure 45-Illustration of the speeds attended using program 1 for a linear trajectory at a nominal speed of 40 mm/s. ................................................................................................................................. Figure 46 -Illustration of the influence of the arc ON/OFF command on the linear trajectory using program 4 at a nominal speed of 40 mm/s. .......................................................................................... Figure 47 -Illustration of the influence of the arc ON/OFF command on the speeds using program for a linear trajectory at a nominal speed of 40 mm/s. ........................................................................ Figure 48 -A1) Trajectory graph of the 45° curve traveled by the robot for a speed of 10 mm/s -A2) Zoomed graph of the curve section of graph A1. .................................................................................. Figure 49 -Speeds achieved during toolpath for the 45° angle and a programmed speed of 10 mm/s with 30 points. ....................................................................................................................................... Figure 50 -B1) Trajectory graph of the 45° curve traveled by the robot for a speed of 10 mm/s -B2) Zoomed graph of the curve section of graph B1. .................................................................................. Figure 51 -Speeds achieved during robot motion test" for the 45° angle using an imposed speed of 10 mm/s and control points. ................................................................................................................. Figure 52 -C1) Trajectory graph of the 90° curve traveled by the robot for a speed of 10 mm/s programmed with 30 points -C2) Zoomed graph of the curve section of graph C1 -D1) Trajectory graph of the 90° curve traveled by the robot for a speed of 10 mm/s programmed with control points -D2) Zoomed graph of the curve section of graph D1. ......................................................................... Figure 53 -Speeds achieved during robot motion test for the 90° angle using an imposed speed of 10 mm/s and 30 points along the trajectory. ............................................................................................. Figure 54 -E1) Trajectory graph of the 160° curve traveled by the robot for a speed of 10 mm/s programmed with control points -E2) Zoomed graph of the curve section of graph E1 -F1) Trajectory graph of the 160° curve traveled by the robot for a speed of 40 mm/s programmed with control points -F2) Zoomed graph of the curve section of graph F1. ............................................................... Figure 55-Speeds achieved during robot motion test for the 160° angle using an imposed speed of mm/s defined with 3 control points in the trajectory. ..........................................................................

Figure 44 -

 44 Figure 31 -Distribution of acceleration (in green), constant speed (in blue) and deceleration lengths (in yellow) for the different ACC.cp values using an imposed speed of 25 mm/s. ............................... Figure 32 -Distribution of acceleration time (in green), constant speed (in blue) and deceleration time (in yellow) for the different ACC.cp values with and imposed speed of 40 mm/s. ...................... Figure 33 -Distribution of acceleration (in green), constant speed (in blue) and deceleration lengths (in yellow) for the different ACC.cp values using an imposed speed of 40 mm/s. ............................... Figure 34 -Trajectory of the nozzle for a speed of 1000 mm/s with and 1% of Vel.cp. ....................... Figure 35 -Speed achieved by the robot during toolpath robot movement with 1% Vel.cp. .............. Figure 36 -Trajectory of the nozzle for a speed of 1000 mm/s with and 5% of Vel.cp. .......................Figure 37 -Speed achieved by the robot motion test with 5% Vel.cp. ................................................. Figure 38 -Trajectory of the nozzle for a speed of 1000 mm/s with and 10% of Vel.cp. ..................... Figure 39 -Speed achieved by the robot motion test with 10% Vel.cp. ............................................... Figure 40 -Illustration of the linear trajectory using program 2 at a nominal speed of 10 mm/s. ...... Figure 41-Illustration of the speeds using program 1 for a linear trajectory at a nominal speed of 10 mm/s. .................................................................................................................................................... Figure 42 -Illustration of the influence of the arc ON/OFF command on the linear trajectory using program 3 at a nominal speed of 10 mm/s. .......................................................................................... Figure 43 -Illustration of the speeds using program 2 for a linear trajectory at a nominal speed of 10 mm/s . ................................................................................................................................................... Figure 44 -Illustration of the linear trajectory using program 1 at a nominal speed of 40 mm/s. ...... Figure 45-Illustration of the speeds attended using program 1 for a linear trajectory at a nominal speed of 40 mm/s. ................................................................................................................................. Figure 46 -Illustration of the influence of the arc ON/OFF command on the linear trajectory using program 4 at a nominal speed of 40 mm/s. .......................................................................................... Figure 47 -Illustration of the influence of the arc ON/OFF command on the speeds using program for a linear trajectory at a nominal speed of 40 mm/s. ........................................................................ Figure 48 -A1) Trajectory graph of the 45° curve traveled by the robot for a speed of 10 mm/s -A2) Zoomed graph of the curve section of graph A1. .................................................................................. Figure 49 -Speeds achieved during toolpath for the 45° angle and a programmed speed of 10 mm/s with 30 points. ....................................................................................................................................... Figure 50 -B1) Trajectory graph of the 45° curve traveled by the robot for a speed of 10 mm/s -B2) Zoomed graph of the curve section of graph B1. .................................................................................. Figure 51 -Speeds achieved during robot motion test" for the 45° angle using an imposed speed of 10 mm/s and control points. ................................................................................................................. Figure 52 -C1) Trajectory graph of the 90° curve traveled by the robot for a speed of 10 mm/s programmed with 30 points -C2) Zoomed graph of the curve section of graph C1 -D1) Trajectory graph of the 90° curve traveled by the robot for a speed of 10 mm/s programmed with control points -D2) Zoomed graph of the curve section of graph D1. ......................................................................... Figure 53 -Speeds achieved during robot motion test for the 90° angle using an imposed speed of 10 mm/s and 30 points along the trajectory. ............................................................................................. Figure 54 -E1) Trajectory graph of the 160° curve traveled by the robot for a speed of 10 mm/s programmed with control points -E2) Zoomed graph of the curve section of graph E1 -F1) Trajectory graph of the 160° curve traveled by the robot for a speed of 40 mm/s programmed with control points -F2) Zoomed graph of the curve section of graph F1. ............................................................... Figure 55-Speeds achieved during robot motion test for the 160° angle using an imposed speed of mm/s defined with 3 control points in the trajectory. ..........................................................................

Figure 56 -

 56 Figure 56 -Speeds achieved during robot motion test for the 160° angle using an imposed speed of 40 mm/s defined with 3 control points in the trajectory. ..................................................................... Figure 57 -Toolpath and speed for the semi-circular, rectangular, and spiral strategies, as well as for one of the triangular strategies (namely 60°). The nominal speed was set to 40 mm/s and arc ON was activated over the whole of each trajectory. ........................................................................................ Figure 58 -Trajectory, speed, and volume of material for the raster-pass and swiping strategies, with a nominal speed of 40 mm/s. ................................................................................................................ Figure 59 -Trajectory, speed and volume of material for the rectangular and spiral strategies, with a nominal speed of 40 mm/s.................................................................................................................... Figure 60 -Influence of the arc ON/OFF command on the trajectory for the 45° triangular and a nominal speed of 40 mm/s: a) with arc ON and OFF inside and outside the objective rectangle respectively, b) with arc ON activated over the whole toolpath. ......................................................... Figure 61 -Influence of the arc ON/OFF command on the trajectory for the 60° triangular and a nominal speed of 40 mm/s: a) with arc ON and OFF inside and outside the objective rectangle respectively, b) with arc ON activated over the whole toolpath. ......................................................... Figure 62 -Influence of the arc ON/OFF command on the trajectory for the 90° triangular and a nominal speed of 40 mm/s: a) with arc ON and OFF inside and outside the objective rectangle respectively, b) with arc ON activated over the whole toolpath. ......................................................... Figure 63 -Influence of the arc ON/OFF command on the Semi-circle trajectory and a nominal speed of 40 mm/s: a) with arc ON and OFF inside and outside the objective rectangle respectively, b) with arc ON activated over the whole toolpath. ........................................................................................... Figure 64 -Schematic of the methodology for simplifying the use of FEM using the pre-heating indicator. ............................................................................................................................................. Figure 65 -The two models used for the thermal analysis. ............................................................... Figure 66 -Double ellipsoid heat source [21]. .................................................................................... Figure 67 -Schema showing the distance of the heat source to the point of interest used. ............ Figure 68 -Top view of the first type of configuration. ...................................................................... Figure 69 -Top view of the second type of configuration.................................................................. Figure 70 -Top view of third type of configuration............................................................................ Figure 71 -Fourth type of configuration where some data collection points are found in the studied trajectory. ............................................................................................................................................ Figure 72 -A) Developed geometry with the main data collection points marked B) Conventional positive directions for geometry. ........................................................................................................ Figure 73 -Representation of the four strategies considered in this study: Run 1, 2, 3, and 4, each one is separated into A) and B) two phases of the same deposition strategy. .......................................... Figure 74 -Representation of the speeds reached during the four strategies considered in this study: Run 1, 2, 3, and 4. ................................................................................................................................ Figure 75 -Zoom of the marked points in figure 3 and their classification by type. .......................... Figure 76 -Comparison of pre-heating indicator for strategy #1 evaluated with analytical model (A)) and FEM simulation (B)). ..................................................................................................................... Figure 77 -Comparison of global pre-heating indicator (GI) for all strategies evaluated. ................. Figure 78 -A) and B) Trajectory used for Run 3; C) LI indicators obtained with the thermal-kinematic for the strategy 3. ................................................................................................................................ Figure 79 -Top view of part geometry for study case showing all the points with the first type of configuration. ...................................................................................................................................... Figure 80 -3 rd layer cooling curve for points P8, P9, P19 and P20 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature. .........................................................................

Figure 81 -

 81 Figure 81 -Top view of part geometry for study case showing all the points with the second type of configuration. ...................................................................................................................................... Figure 82 -3 rd layer cooling curve for points P2, P4, P24 and P26 with configuration type 2, with 150°C (A)) and 550°C (B)) of interlayer temperature. ......................................................................... Figure 83 -3 rd layer cooling curve for points P2, P4, P24 and P26 with configuration type 2, with 150°C (A)) and 550°C (B)) of interlayer temperature. ......................................................................... Figure 84 -Top view of part geometry for study case showing all the points with the third type of configuration. ...................................................................................................................................... Figure 85 -3 rd layer cooling curve for points P13 and P15 with configuration type 3, with 150°C (A)) and 550°C (B)) of interlayer temperature. .......................................................................................... Figure 86 -Location of point 15, 26 and 8 in the geometry of the part considered. ......................... Figure 87 -Cooling curves of points P25, P18, P8, P16, P14, P22, P26, P11 and P15 for the 3 rd layer with 150°C (A)) and for the 20 th layer with 550°C (B)) of interlayer temperature. ............................. Figure 88 -Response surface graphs of Interpass temperature Vs layer from the points 25, 18, 8, 16, 14, 22, 26, 11, 15 from the groups A, B, C, D, E, F, G, H, and I respectively. ....................................... Figure 89 -Representation of an approximation between the time temperature transformation (TTT) graphic and CCT curve for stainless steel 2205 using one known point (adapted from [34]). ........... Figure 90 -Intersection between cooling curve of the 20 th Layer of the point 26 using an ITe of 150°C and ISO lines for temperatures of 600°C and 950°C. .......................................................................... Figure 91 -Analysis of point 26 for 150°C temperature -A) Cooling rate in temperature range = [600°C, 950°C]; B) Cooling rate in temperature range = [600°c to 950°C] and cumulative time in temperature range and not exceeded; (C) Comparison of continuous cooling curve diagram of the Limit and actual (Point P26); D) Evolution of time spent in temperature range of [600,950] °C. ......Figure 92 -Intersection between cooling curve of the 20 th Layer of the point 26 using an ITe of 350°C and Iso lines for temperatures of 600°C and 950°C. ........................................................................... Figure 93 -Analysis of point 26 for 350°C temperature -A) Cooling rate in temperature range = [600°C, 950°C]; B) Cooling rate in temperature range = [600°c to 950°C] and cumulative time in temperature range and not exceeded; (C) Comparison of continuous cooling curve diagram of the Limit and actual (Point P26); D) Evolution of time spent in temperature range of [600,950] °C. ...... Figure 94 -Intersection between cooling curve of the 20 th Layer of the point 26 using an ITe of 550°C and Iso lines for temperatures of 600°C and 950°C. ........................................................................... Figure 95 -Analysis of point 26 for 350°C temperature -A) Cooling rate in temperature range = [600°C, 950°C]; B) Cooling rate in temperature range = [600°c to 950°C] and cumulative time in temperature range and not exceeded; (C) Comparison of continuous cooling curve diagram of the Limit and actual (Point P26); D) Evolution of time spent in temperature range of [600°C, 950°C] .... Figure 96 -Graphs A), B), C), D) and E) represent the intersection between the cooling curves of layers 19, 18, 17, 16, 15 (respectively) and the Iso lines for temperatures of 600°C and 950°C collected during the deposition of layer 20th. Graphs A-1), B-1), C-1) D-1) and E-1) represent the cooling rates of layers 19, 18, 17, 16, 15 (respectively) in order of time corresponding to A), B), C), D) and E) respectively. ............................................................................................................................. Figure 97 -Graphs A-2), B-2), C-2), D-2) and E-2) represent two graphs, in blue the cooling lines corresponding to layers 19, 18, 17, 16 and 15 (respectively), and in orange we have the accumulated time between temperatures of 600°C and 950°C after reaching the last 950°C during the deposition of layer 20th. Graphs A-3), B-3), C-3) D-3) and E-3) represent the comparison between the cooling curves of layers 19, 18, 17, 16, 15 (respectively) and the cooling limit curve of the material, in order of time. ................................................................................................................................................

Figure 91 -

 91 Figure 81 -Top view of part geometry for study case showing all the points with the second type of configuration. ...................................................................................................................................... Figure 82 -3 rd layer cooling curve for points P2, P4, P24 and P26 with configuration type 2, with 150°C (A)) and 550°C (B)) of interlayer temperature. ......................................................................... Figure 83 -3 rd layer cooling curve for points P2, P4, P24 and P26 with configuration type 2, with 150°C (A)) and 550°C (B)) of interlayer temperature. ......................................................................... Figure 84 -Top view of part geometry for study case showing all the points with the third type of configuration. ...................................................................................................................................... Figure 85 -3 rd layer cooling curve for points P13 and P15 with configuration type 3, with 150°C (A)) and 550°C (B)) of interlayer temperature. .......................................................................................... Figure 86 -Location of point 15, 26 and 8 in the geometry of the part considered. ......................... Figure 87 -Cooling curves of points P25, P18, P8, P16, P14, P22, P26, P11 and P15 for the 3 rd layer with 150°C (A)) and for the 20 th layer with 550°C (B)) of interlayer temperature. ............................. Figure 88 -Response surface graphs of Interpass temperature Vs layer from the points 25, 18, 8, 16, 14, 22, 26, 11, 15 from the groups A, B, C, D, E, F, G, H, and I respectively. ....................................... Figure 89 -Representation of an approximation between the time temperature transformation (TTT) graphic and CCT curve for stainless steel 2205 using one known point (adapted from [34]). ........... Figure 90 -Intersection between cooling curve of the 20 th Layer of the point 26 using an ITe of 150°C and ISO lines for temperatures of 600°C and 950°C. .......................................................................... Figure 91 -Analysis of point 26 for 150°C temperature -A) Cooling rate in temperature range = [600°C, 950°C]; B) Cooling rate in temperature range = [600°c to 950°C] and cumulative time in temperature range and not exceeded; (C) Comparison of continuous cooling curve diagram of the Limit and actual (Point P26); D) Evolution of time spent in temperature range of [600,950] °C. ......Figure 92 -Intersection between cooling curve of the 20 th Layer of the point 26 using an ITe of 350°C and Iso lines for temperatures of 600°C and 950°C. ........................................................................... Figure 93 -Analysis of point 26 for 350°C temperature -A) Cooling rate in temperature range = [600°C, 950°C]; B) Cooling rate in temperature range = [600°c to 950°C] and cumulative time in temperature range and not exceeded; (C) Comparison of continuous cooling curve diagram of the Limit and actual (Point P26); D) Evolution of time spent in temperature range of [600,950] °C. ...... Figure 94 -Intersection between cooling curve of the 20 th Layer of the point 26 using an ITe of 550°C and Iso lines for temperatures of 600°C and 950°C. ........................................................................... Figure 95 -Analysis of point 26 for 350°C temperature -A) Cooling rate in temperature range = [600°C, 950°C]; B) Cooling rate in temperature range = [600°c to 950°C] and cumulative time in temperature range and not exceeded; (C) Comparison of continuous cooling curve diagram of the Limit and actual (Point P26); D) Evolution of time spent in temperature range of [600°C, 950°C] .... Figure 96 -Graphs A), B), C), D) and E) represent the intersection between the cooling curves of layers 19, 18, 17, 16, 15 (respectively) and the Iso lines for temperatures of 600°C and 950°C collected during the deposition of layer 20th. Graphs A-1), B-1), C-1) D-1) and E-1) represent the cooling rates of layers 19, 18, 17, 16, 15 (respectively) in order of time corresponding to A), B), C), D) and E) respectively. ............................................................................................................................. Figure 97 -Graphs A-2), B-2), C-2), D-2) and E-2) represent two graphs, in blue the cooling lines corresponding to layers 19, 18, 17, 16 and 15 (respectively), and in orange we have the accumulated time between temperatures of 600°C and 950°C after reaching the last 950°C during the deposition of layer 20th. Graphs A-3), B-3), C-3) D-3) and E-3) represent the comparison between the cooling curves of layers 19, 18, 17, 16, 15 (respectively) and the cooling limit curve of the material, in order of time. ................................................................................................................................................

Figure 98 -

 98 Figure 98 -A) Image of wall after trimming B) scheme for all the samples to be taken from each wall. The red dotes indicate the locations where the hardness tests will be performed. .......................... 151 Figure 99 -Sample sizes. ..................................................................................................................... 152 Figure 100 -Cutting scheme of the samples taken from the walls. .................................................... 152 Figure 101-Identification of the time constant characterizing the heat exchange of the sample with its environment. Two tests with different levels of pre-heating are presented. The dashed curves correspond to a theoretical exponential decrease with a time decay of 41 s. ................................ 154 Figure 102 -Picture of the setup used for the construction of the walls. .......................................... 155 Figure 103 -Machine used for the hardness tests. ............................................................................ 155 Figure 104 -A) Machine used for quasi-static and accelerated fatigue tests, B) sample in the jaws of the testing machine, C) sample in the grips of the testing machine. .................................................. 156 Figure 105 -Defects at the start/end of several layers. ...................................................................... 157 Figure 106 -Interlayer time (ITi) evolution during wall construction (blue line ITe = 150°C, black line ITe = 350°C, red line ITe = 550°C). ....................................................................................................... 158 Figure 107 -Example of a wall after construction; A) B) and C) construction defects in the start and stop phases; D) non-deposited material from the process. ................................................................ 159 Figure 108 -Comparison between results of the hardness tests done on the vertical samples for the 3 different ITe. ..................................................................................................................................... 161 Figure 109 -Comparison between results of the hardness tests done on the Horizontal samples for the 3 different ITe. ............................................................................................................................... 162 Figure 110 -Stress-strain curves: A) for ITe = 150°C, B) for ITe = 350°C, C) for ITe = 550°C). ............ 164 Figure 111 -Stress-strain curves of the vertical samples. .................................................................. 165 Figure 112 -Stress-strain curves of the horizontal samples............................................................... 166 Figure 113 -Mean yield strength (Rp0.2) and ultimate tensile strength (Rm). ................................. 167 Figure 114 -Mean maximum elongation (in %) and uniform elongation (in %). ................................ 167 Figure 115 -Evolution of the stress during the accelerated fatigue tests. ......................................... 168 Figure 116 -Heat generated by mechanical dissipation per cycle during the accelerated mechanical fatigue tests. ........................................................................................................................................ 169 Figure 117 -Heat generated by mechanical dissipation per cycle during the accelerated mechanical fatigue tests for the different categories of samples. ......................................................................... 170 Figure 118 -Heat generated by mechanical dissipation per cycle during the accelerated mechanical fatigue tests for the vertical samples: zoom for the identification of the onset of fatigue damage. . 171 Figure 119-Heat generated by mechanical dissipation per cycle during the accelerated mechanical fatigue tests for the vertical samples: zoom for the identification of the onset of fatigue damage. . 171 Figure 120 -Scheme representative of the dependencies between first degree indicators ............. 176 Figure 121 -Kinematic indicator scheme ........................................................................................... 178 Figure 122 -General scheme of the kinematic model ....................................................................... 179 Figure 123 -Examples of kinematic profiles for the rectangular and spiral strategy for two robot speeds. ................................................................................................................................................. 179 Figure 124 -Inputs and outputs of the thermo-kinematic model ...................................................... 181 Figure 125 -Illustration of the number of branches represented here by the third type of configuration. ...................................................................................................................................... 183 Figure 126 -Illustration of point 13, its location in a third configuration type, and the correspondent cooling graph. ...................................................................................................................................... 184 Figure 127 -(Left) Reduced pattern of the geometry shown in chapter 3; (Right) pattern of the geometry shown in chapter 3 on a larger substrate. .......................................................................... 185 Figure 128 -Structure of cooling time ANN (ANN1). .......................................................................... 185

Figure 1 -

 1 Figure 1 -Decorative part produced by WAAM and draw inBaker R. [11] patent.

Figure 2 -

 2 Figure 2-classification of metal transfer depicted in an arc voltage and welding current diagram [21].

Figure 3 -

 3 Figure 3 -Gas metal arc (GMA) welding natural metal transfer modes [22][23].

Figure 4 -

 4 Figure 4 -Graph of wire speed cycle, current cycle, and voltage cycle[26].

Figure 5 -

 5 Figure 5 -WAAM cell in "Addimadour" research platform.

Figure 6 -

 6 Figure 6 -Schematic diagram of all equipment and connections in the CMT process.

Figure 7 -

 7 Figure 7 -Block Diagram of a CMT system [32].

Figure 8 -

 8 Figure 8-Example of different spools of wires used in WAAM process [33].

Figure 10 -

 10 Figure 10 -WAAM pre-and post-process steps scheme.

Figure 11 -

 11 Figure 11 -Scheme of process indicators and their dependencies.

Figure 12 -

 12 Figure 12 -Strategy for achieving the indicators.

Figure 14 -

 14 Figure 14 -Representation of the three linear depositions made for the ACC_CP assessment. The acceleration (represented in blue) and deceleration (represented in red) lengths are not correctly dimensioned in accordance with reality.

Figure 15 -

 15 Figure 15-Representation of the expected behavior of the robot with the 3 different sections, acceleration (in blue), constant speed (green), deceleration (red).

Figure 16 -

 16 Figure16 -Representation of part of the expected robot behavior when "simulated" using an arc transition at the X=50 mm coordinate.

Figure 17 -

 17 Figure 17 -Part of program 1 and 3 where the trajectory instructions (without and with arc transition) are described.

Figure 18 -

 18 Figure 18 -Example trajectories for different angles of 20°, 45°, 90° and 160°, and the expected behavior of the robot during the displacement.

Figure 19 -

 19 Figure 19 -Different strategies considered in the study.

Figure 20 -

 20 Figure 20 -Top view of the inerting chamber and the five different locations within it where measurements are taken.

Figure 21 -

 21 Figure 21 -Schematic view of the inert chamber with the locations of the different zones in which the same swiping deposition was measured.

Figure 22 -

 22 Figure 22 -Example of information gathered from the ADAONE program.2.6.2. Data processing files

Figure 23 -

 23 Figure 23 -Example of the trajectory traced on page two of the excel file of the results analysis.

  Total deposition time and displacement (real). ➢ Time and displacement under acceleration. ➢ Time and displacement under deceleration. ➢ Time and displacement at constant speed. ➢ Total deposition time and displacement (programmed). ➢ Total deposition time and displacement (theorical). ➢ Total time with the arc on. ➢ Total time and displacement with the arc on within the O.R. rectangle. ➢ Amount of material deposited (theoretical value).

Figure 24 -

 24 Figure 24 -Positions collected from the trajectory done by the nozzle during the movement with an acceleration of 1m/s².

Figure 25 -

 25 Figure 25 -Speed calculated for the nozzle displacement with an ACC.cp value of 1m/s².All tests produce similar position graphs for the different values of ACC.cp. At the start of the movement, there is a backlash movement in the Y+ direction, which can vary up to 0.19 mm. The trajectory also made further backlash movement of 0.14 mm in the Y-direction, passing through the (79,0) coordinate. This deviation remains below the maximum value of 0.2 mm indicated by the manufacturer.

Figure 26 present

 26 Figure 26 present the results for a programmed speed equal to 10 mm/s and an acceleration equal to 5 ms².

Figure 26 -

 26 Figure 26 -Position and Speed calculated with an ACC.cp value of 5m/s².

Figure 27

 27 Figure 27 present the results for a speed equal to 10 mm/s and an acceleration equal to 10 ms²:

Figure 27 -

 27 Figure 27 -Position and Speed calculated for the nozzle displacement with an ACC.cp value of 10m/s².

Figure 28 -

 28 Figure 28 -Distribution of acceleration time (in green), constant speed (in blue) and deceleration time (in yellow) for the different ACC.cp values with and imposed speed of 10 mm/s.

Figure 29

 29 Figure29shows the distribution of the lengths of the acceleration, constant speed and deceleration for different values of ACC.cp with an imposed speed of 10 mm/s. The acceleration and deceleration length values correspond to a small percentage of at most 1.61% of the total deposition.

Figure 29 -

 29 Figure 29 -Distribution of acceleration (in green), constant speed (in blue) and deceleration lengths (in yellow) for the different ACC.cp values using an imposed speed of 10 mm/s.

Figure 30

 30 Figure 30 shows the distribution of the times of the acceleration, constant speeds, and deceleration for different values of ACC.cp with an imposed speed of 25 mm/s. The values of acceleration and deceleration time already correspond to a value to be taken into consideration, 6.18% the lowest value and 10.57% the highest for a 100 mm WB at a speed of 25 mm/s.

Figure 30 -

 30 Figure 30 -Distribution of acceleration time (in green), constant speed (in blue) and deceleration time (in yellow) for the different ACC.cp values with and imposed speed of 25 mm/s.

Figure 31 shows

 31 Figure 31 shows the distribution of the lengths of the acceleration, constant speed, and deceleration for different values of ACC.cp with an imposed speed of 25 mm/s. The values of acceleration and deceleration length correspond to a value ranging from 3.3% to 5.9% of the total deposition length of 100 mm and a speed of 25 mm/s. Such zones can induce material accumulation.

Figure 31 -

 31 Figure 31 -Distribution of acceleration (in green), constant speed (in blue) and deceleration lengths (in yellow) for the different ACC.cp values using an imposed speed of 25 mm/s.

Figure 32

 32 Figure 32 shows the distribution of the times of the acceleration, constant speed, and deceleration for different values of ACC.cp with an imposed speed of 40 mm/s. The values of acceleration and deceleration time already correspond to a value to be taken into consideration 13.30% the lowest value and 16% the highest for a 100 mm WB at a TS 40 mm/s.

Figure 32 -

 32 Figure 32 -Distribution of acceleration time (in green), constant speed (in blue) and deceleration time (in yellow) for the different ACC.cp values with and imposed speed of 40 mm/s.shows the distribution graph of the acceleration, constant speed, and deceleration lengths for different values of ACC.cp with an imposed speed of 40 mm/s. The acceleration and deceleration length values correspond to a value ranging from 7.7% to 9.15% approximately of the total deposition length. In this case too, such zones can induce material accumulation.

Figure 33 -

 33 Figure 33 -Distribution of acceleration (in green), constant speed (in blue) and deceleration lengths (in yellow) for the different ACC.cp values using an imposed speed of 40 mm/s.

Figure 34 -

 34 Figure 34 -Trajectory of the nozzle for a speed of 1000 mm/s with and 1% of Vel.cp.

Figure 34

 34 Figure 34 represents oscillations of the Y axis, during the movement of the robots along a 200 mm X programmed movement. Except the amplitude of the first oscillation equal to 0.13 mm due to the initiation of the movement, all backlash presents a maximum variation between 0.05 Y+ and 0.01 Ywhich is negligible. The speeds recorded during the trajectory are presented in Figure 35.

Figure 35 -

 35 Figure 35 -Speed achieved by the robot during toolpath robot movement with 1% Vel.cp.

Figure 36 -

 36 Figure 36 -Trajectory of the nozzle for a speed of 1000 mm/s with and 5% of Vel.cp.

Figure 37 -

 37 Figure 37 -Speed achieved by the robot motion test with 5% Vel.cp.

Figure 38 -

 38 Figure 38 -Trajectory of the nozzle for a speed of 1000 mm/s with and 10% of Vel.cp.

Figure 39 -

 39 Figure 39 -Speed achieved by the robot motion test with 10% Vel.cp.

2. 7 . 3 . 1 .

 731 Figure 40 show the movement of the torch usinge program 1. Two unexpected movements appear at Y+ (0.19 mm) at the beginning and at Y-(0.14 mm) near X = 79 mm.

Figure 40 -

 40 Figure 40 -Illustration of the linear trajectory using program 2 at a nominal speed of 10 mm/s.

Figure 41

 41 Figure41shows the speed evolution. A velocity peak of 12.5 mm/s appears at second 7.944. This velocity peak is due to the backlash motion occurring between coordinates x = 78.68 and x = 78.8 which can be seen in the graph of Figure40. The average velocity between initial acceleration and final deceleration rest equal to the nominal speed of 10 mm/s.

Figure 41 -

 41 Figure 41-Illustration of the speeds using program 1 for a linear trajectory at a nominal speed of 10 mm/s.The trajectory described by the torch nozzle using program 2 was an exact replication of the trajectory shown in Figure40with the same backlash movements shown previously. With a similar trajectory the speed profile was also exactly the same.The trajectories made by the robot for programs 3, 4 and 5 were exactly the same, and are represented here by the graph of program 3 in Figure42. With the introduction of the Arc transition at X = 50 mm, the robot made two new backlash movements first at Y-(0.15 mm) and then at Y+ (0.21 mm). These movements are associated with the deceleration and acceleration that the robot made during the arc transition.

Figure 42 -

 42 Figure 42 -Illustration of the influence of the arc ON/OFF command on the linear trajectory using program 3 at a nominal speed of 10 mm/s.

Figure 43 -

 43 Figure 43 -Illustration of the speeds using program 2 for a linear trajectory at a nominal speed of 10 mm/s .

2. 7 . 3 . 2 .

 732 Strategies "nominal speed of 40 mm/s" Program 1, 2, 3 and 4 are tested with a programmed speed of 40 mms/s. Both programs 1 and two had similar results, here are only shown the results of program 1 with Figure 44, representing the trajectory for the speed of 40 mm/s. Like for 10 mm/s tests, a backlash movement of 0.21 mm in Y+ appear at the beginning, and of 0.11 mm in Y-at the end of the toolpath. The accuracy of the robot was between 0.02 in Y+ and 0.03 in Y-.

Figure 44 -

 44 Figure 44 -Illustration of the linear trajectory using program 1 at a nominal speed of 40 mm/s.

Figure 45 -

 45 Figure 45-Illustration of the speeds attended using program 1 for a linear trajectory at a nominal speed of 40 mm/s. Programs 3 and 4 with arc transition resulted in identical trajectories, as well as the velocity profiles achieved in each zone of the trajectory. Thus, only the results for program 4 are presented here. Figure 46 represents the trajectory made by the robot nozzle using program 4 for a speed of 40 mm/s. The trajectories obtained with program 3 and 4 for a speed of 10 mm/s are identical to those obtained here for a speed of 40 mm/s.

Figure 46 -

 46 Figure 46 -Illustration of the influence of the arc ON/OFF command on the linear trajectory using program 4 at a nominal speed of 40 mm/s.

Figure 47 -

 47 Figure 47 -Illustration of the influence of the arc ON/OFF command on the speeds using program 4 for a linear trajectory at a nominal speed of 40 mm/s.

Figure 48 -

 48 Figure 48 -A1) Trajectory graph of the 45° curve traveled by the robot for a speed of 10 mm/s -A2) Zoomed graph of the curve section of graph A1.

Figure 48

 48 Figure48shows the trajectory, based on a program with 30 points and an imposed speed of 10 mm/s.

Figure 49 -

 49 Figure 49 -Speeds achieved during toolpath for the 45° angle and a programmed speed of 10 mm/s with 30 points.

Figure 50

 50 Figure50shows the toolpath programmed with CP (3 points) positioned at critical locations. Although the program is different, the movement is the same. The PE error is equal to 0.546 mm.

Figure 50 -

 50 Figure 50 -B1) Trajectory graph of the 45° curve traveled by the robot for a speed of 10 mm/s -B2) Zoomed graph of the curve section of graph B1.

Figure 51 -

 51 Figure 51 -Speeds achieved during robot motion test" for the 45° angle using an imposed speed of 10 mm/s and control points.

Figure 52 -

 52 Figure 52 -C1) Trajectory graph of the 90° curve traveled by the robot for a speed of 10 mm/s programmed with 30 points -C2) Zoomed graph of the curve section of graph C1 -D1) Trajectory graph of the 90° curve traveled by the robot for a speed of 10 mm/s programmed with control points -D2) Zoomed graph of the curve section of graph D1.

Figure 53 -

 53 Figure 53 -Speeds achieved during robot motion test for the 90° angle using an imposed speed of 10 mm/s and 30 points along the trajectory.

Figure 54

 54 Figure54shows the results for the 160° angle test, programmed with control points at a speed of 10 (E1 and E2) and 40 mm/s (F1 and F2) respectively. The robot toolpath followed for the 10 mm/s speed presents an error of 0.1304 mm, compared to an error of 0.6054 mm for a speed of 40 mm/s.

Figure 54 -

 54 Figure 54 -E1) Trajectory graph of the 160° curve traveled by the robot for a speed of 10 mm/s programmed with control points -E2) Zoomed graph of the curve section of graph E1 -F1) Trajectory graph of the 160° curve traveled by the robot for a speed of 40 mm/s programmed with control points -F2) Zoomed graph of the curve section of graph F1.

Figure 55 -

 55 Figure 55-Speeds achieved during robot motion test for the 160° angle using an imposed speed of 10 mm/s defined with 3 control points in the trajectory.

Figure 56 -

 56 Figure 56 -Speeds achieved during robot motion test for the 160° angle using an imposed speed of 40 mm/s defined with 3 control points in the trajectory.

Figure 55 and

 55 Figure55and Figure56show that no reduction in speed occurred for an angle of 160°C.

Figure 57 -

 57 Figure 57 -Toolpath and speed for the semi-circular, rectangular, and spiral strategies, as well as for one of the triangular strategies (namely 60°). The nominal speed was set to 40 mm/s and arc ON was activated over the whole of each trajectory.

  -a-2 and -b-2). Arc transitions of the swiping strategy induces trajectory errors of 1.8 mm: see Figure 58-b-1. ➢ Figure 58-a-3 and -b-3 show the variation in time of the volume of deposited material. Plateaus

Figure 58 -

 58 Figure 58 -Trajectory, speed, and volume of material for the raster-pass and swiping strategies, with a nominal speed of 40 mm/s.

Figure 59

 59 Figure59compares the rectangular and spiral strategies, for a nominal speed of 40 mm/s and for an OR of 21.5×43 mm2. As in Figure58in addition to the trajectories and speeds, the figure also provides the variation in volume of deposited material (assuming a constant wire feed rate of 94.25 mm3/s) as a function of time and distance travelled.

Figure 59 -

 59 Figure 59 -Trajectory, speed, and volume of material for the rectangular and spiral strategies, with a nominal speed of 40 mm/s.

  -b-2) are of higher amplitudes than those observed for the 60° triangular strategy in Figure58: the smaller the angle is, the greater the speed drop is. ➢ Variations in the volume of deposited material assuming a constant WFS are displayed in Figure60-a-3 and -b-3 as a function of time, and in Figure60-a-4 and -b-4 as a function of the distance travelled. The order of magnitude of the volume "jumps" are the same for the two strategies (about 7 mm3), but it is less problematic when arc ON is activated over the whole trajectory because it occurred outside the OR (see Figure59-b-1 and -b-4).

Figure 60 -

 60 Figure 60 -Influence of the arc ON/OFF command on the trajectory for the 45° triangular and a nominal speed of 40 mm/s: a) with arc ON and OFF inside and outside the objective rectangle respectively, b) with arc ON activated over the whole toolpath.

Figure 61

 61 Figure61illustrates the differences for the 60° triangular strategy at a nominal speed of 40 mm/s for an OR of 21.5×43 mm2. As in Figure60, Figure61-a-1 and -b-1 show the toolpath in the two cases. The red and black dots correspond to the programmed points with arc ON and arc OFF respectively. Some comments can be expressed:➢ Both strategies produce very close trajectories on the transition arc outside the OR when arc OFF was activated (Figure61-a-1). The switching from arc ON to arc OFF implies a drop of the speed to zero at times A, C, E and G (Figure61-a-2). Just after A, C, E and G, the speed is increased without reaching the nominal speed of 40 mm/s due to the transition from arc OFF to arc ON at times B, D, F and H. ➢ Arc transitions do not change the total length of the whole toolpath, despite the toolpath with full arc ON, presents more symmetric transitions. The accuracy error of the toolpaths is 2.08 mm, including 0.636 mm outside OR. Also, the arc transition has a lower influence over the speeds attended during the toolpath than in the strategy with 45°, which was not expected due to the fact of having a sharper angle before performing the 60° angle. ➢ The arc ON induces a lower amplitude of slowdowns (Figure61-b-2), than for the 45° triangular strategy in Figure60. Thus, the higher the angle is, the smaller the speed drop is. ➢ Variations in the volume of deposited material assuming a constant WFS are displayed in Figure61-a-3 and -b-3 as a function of time, and in Figure61-a-4 and -b-4 as a function of the distance travelled. The order of magnitude of the volume "jumps" are the same for the two strategies (about 7 mm 3 ), but it is less problematic when arc ON is activated over the whole trajectory because it occurred outside the OR (see Figure61-b-1 and -b-4).

Figure 61 -

 61 Figure 61 -Influence of the arc ON/OFF command on the trajectory for the 60° triangular and a nominal speed of 40 mm/s: a) with arc ON and OFF inside and outside the objective rectangle respectively, b) with arc ON activated over the whole toolpath.

Figure 62 -

 62 Figure 62 -Influence of the arc ON/OFF command on the trajectory for the 90° triangular and a nominal speed of 40 mm/s: a) with arc ON and OFF inside and outside the objective rectangle respectively, b) with arc ON activated over the whole toolpath.

Figure 62

 62 Figure62illustrates the differences for the 90° triangular strategy at a nominal speed of 40 mm/s for an OR of 21.5×43 mm 2 . As in Figure60and Figure61, Figure62-a-1 and -b-1 show the toolpath in the two cases. The red and black dots correspond to the programmed points with arc ON and arc OFF respectively. The blue curves are the measured toolpaths as in the previous figures. Some comments can be expressed:➢ Arc OFF activated induces a higher trajectory error, outside the OR (Figure62-a-1). When switching from arc ON to arc OFF, the speed dropped to zero at times A, C, E and G (Figure62a-2). Just after A, C, E and G, the speed is increased without reaching the nominal speed of 40 mm/s due to the transition from arc OFF to arc ON at times B, D, F and H. Like in the 45° strategy, the robot seems to correct the delay by cutting the programmed toolpath according to the programmed tolerance. The delays (acceleration and deceleration times) due to arc ON/OFF switching appear to be compensated for by a shorter toolpath outside the OR. ➢ The speed reductions when arc ON is activated over the whole trajectory (Figure62-b-2) are of higher amplitudes than those observed for the 60° triangular strategy in Figure61: the smaller the angle, the greater the speed drop. ➢ Variations in the volume of deposited material assuming a constant WFS are displayed in Figure62-a-3 and -b-3 as a function of time, and in Figure62-a-4 and -b-4 as a function of the distance travelled. The order of magnitude of the volume "jumps" are the same for the two strategies (about 7 mm3), but it is less problematic when arc ON is activated over the whole trajectory because it occurs outside the OR (see Figure62-b-1 and -b-4).

Figure 63

 63 Figure63illustrates the differences for the semi-circular strategy at a nominal speed of 40 mm/s for an OR of 21.5×43 mm2. As in previous figures a-1 and -b-1 show the toolpath in the two cases. Some comments can be expressed:➢ The trajectory error is higher outside the OR when arc ON is activated (Figure63-b-1).➢ Arc ON activation produces a very close trajectory to the obtained for the triangular strategies 60° and 90°. The command computes shorter semi-circles, inducing accuracy errors. A difference of 3.766 mm is obtained. Strategies with arc transition impose more passage points at the transition and achieve a more precise toolpath. Just after times A, C, E and G, the speed is increased without reaching the nominal speed of 40 mm/s due to the transition from arc OFF to arc ON at times B, D, F and H. The robot seems to have corrected the delay by cutting the programmed toolpath according to the programmed tolerance as for the previous triangular strategies. ➢ In this case, arc ON induces a lower speed reduction (Figure63-b-2) than those observed for the triangular strategies. ➢ Variations in the volume of deposited material assuming a constant WFS are displayed in Figure 63-a-3 and -b-3 as a function of time, and in Figure 63-a-4 and -b-4 as a function of the distance travelled. The order of magnitude of the volume "jumps" were the same for the two strategies (about 7 mm 3 ), but it was less problematic when arc ON was activated over the whole trajectory because it occurred outside the OR (see Figure 63-b-1 and -b-4).

Figure 63 -

 63 Figure 63 -Influence of the arc ON/OFF command on the Semi-circle trajectory and a nominal speed of 40 mm/s: a) with arc ON and OFF inside and outside the objective rectangle respectively, b) with arc ON activated over the whole toolpath.

Figure 64 -

 64 Figure 64 -Schematic of the methodology for simplifying the use of FEM using the pre-heating indicator.

2 12𝐷

 2 𝐵(𝒙, 𝑡 𝑖 ) = 𝑟 𝑟 * exp (-3(𝑥 -𝑉(𝜏 -𝑡 𝑖 )) 𝑖 -𝜏) + 𝑐 2 ) (21) with b the half-width, c the depth, af (resp. ar) the length of the front (resp. rear) portion of the double ellipsoid, as shown on Figure 66. V is the travel speed of the heat source in the time interval (ti-1, ti), assuming a motion along the x-direction, rf (resp. rr) is the portion of power distributed in front (resp. rear) part of the double ellipsoid.

Figure 66 -

 66 Figure 66 -Double ellipsoid heat source [21].

Figure 67 -

 67 Figure 67 -Schema showing the distance of the heat source to the point of interest used.

Figure 68

 68 Figure 68 depicts the first type of configuration to have into account. It corresponds to a zone located in the middle of a bead. Heat conduction is made mainly in deposition direction and z direction.

Figure 68 -

 68 Figure 68 -Top view of the first type of configuration.

Figure 69 -

 69 Figure 69 -Top view of the second type of configuration.

Figure 70 -

 70 Figure 70 -Top view of third type of configuration.

Figure 71 -

 71 Figure 71 -Fourth type of configuration where some data collection points are found in the studied trajectory.

  usedThe size of substrate considered for this study was 200 × 200 × 5 (mm). The geometry studied consisted of a group of six squares of 50 x 50 mm together, key points and directions of deposition are detailed on Figure72. The analysis of the thermal behavior is based on the extraction of the thermal history at each one of the key points.

Figure 72

 72 Figure 72 -A) Developed geometry with the main data collection points marked B) Conventional positive directions for geometry.

Figure 73 -

 73 Figure 73 -Representation of the four strategies considered in this study: Run 1, 2, 3, and 4, each one is separated into A) and B) two phases of the same deposition strategy.

3. 7 . 5 .

 75 Evaluation of pre-heating indicator 3.7.5.1. Kinematic analysis The analytical thermo-kinematic model provides an estimation of the speed performance during toolpath.

Figure 74 -

 74 Figure 74 -Representation of the speeds reached during the four strategies considered in this study: Run 1, 2, 3, and 4.

Figure 76 -

 76 Figure 76 -Comparison of pre-heating indicator for strategy #1 evaluated with analytical model (A)) and FEM simulation (B)).

Figure 77

 77 Figure77shows a comparison of the pre-heating indicator evaluated with the analytical model for the four strategies. In this context, the suffix global is used to refer to the indicator. Here the value of 𝑇 𝑚𝑎𝑥 considered is the maximum pre-heating temperature reached on all four toolpaths. This guarantees an indicator in range (0, 1). The low indicator values are shown in dark blue, meaning no pre-heating occurs. High indicator values are shown in dark red, meaning that the points with this color had the higher pre-heating. Ranking in increasing order of the pre-heating magnitude, we have Run 1, Run 3, Run 4, and lastly Run 2. In Run 2 we can observe the existence of a hot point at the coordinate (x = 100, y = 75).

Figure 77 -

 77 Figure 77 -Comparison of global pre-heating indicator (GI) for all strategies evaluated.The fact of being the longest trajectory allowed the heat to be conducted through the substrate over a longer period, leading to lower indicator values for PhT in the vertical segments. Run 2 and 3 had the same value of deposition time Dt (82.3 s) for the same theoretical length. Although the Dt values for Run 2 and 3 were the same, the thermo-kinematic model clearly showed that Run 3 undergoes a smaller thermal gradient across the part. We can also see that the lower value of Dt (81 s) in Run 4 with the shorter toolpath length (1011.8 mm) did not give a higher thermal gradient across the part. When comparing Run 4 with Run 2 it is possible to identify that Run 2 reached higher global pre-heating indicator (GI) values at two points in its trajectory, and its cause was simply the trajectory chosen. The evaluation of pre-heating indicator required a computation time of around 10 to 12 min for each strategy when using the thermo-kinematic model. This time rose to almost one hour per strategy studied using FEM simulation. The use of the analytical model is thus of great interest as soon as the number of combinations to be tested is large.

Figure 78 -

 78 Figure 78 -A) and B) Trajectory used for Run 3; C) LI indicators obtained with the thermal-kinematic for the strategy 3.

Figure 79

 79 Figure 79 presents all the points that fit in the first type of configuration.

Figure 79 -

 79 Figure 79 -Top view of part geometry for study case showing all the points with the first type of configuration.

Figure 80 - 3

 3 Figure 80 -3 rd layer cooling curve for points P8, P9, P19 and P20 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature.

Figure 81 -

 81 Figure 81 -Top view of part geometry for study case showing all the points with the second type of configuration. The points shown in Figure 81 are all the points that had the second type of configuration in this case study. The second type of configuration was characterized by heat conduction in three directions, in the XY plane (top view of the part). A detailed analysis of group G (points 2/4/24/26) and H (points 11/17) is presented in the next paragraphs.

Figure 82 -

 82 Figure 82 -3 rd layer cooling curve for points P2, P4, P24 and P26 with configuration type 2, with 150°C (A)) and 550°C (B)) of interlayer temperature.

Figure 83 - 3

 3 Figure 83 -3 rd layer cooling curve for points P2, P4, P24 and P26 with configuration type 2, with 150°C (A)) and 550°C (B)) of interlayer temperature.

Figure 84 -

 84 Figure 84 -Top view of part geometry for study case showing all the points with the third type of configuration.

Figure 85

 85 Figure 85 -3 rd layer cooling curve for points P13 and P15 with configuration type 3, with 150°C (A)) and 550°C (B)) of interlayer temperature.

Figure 87 -

 87 Figure 87 -Cooling curves of points P25, P18, P8, P16, P14, P22, P26, P11 and P15 for the 3 rd layer with 150°C (A)) and for the 20 th layer with 550°C (B)) of interlayer temperature.

  Figure 90 -Intersection between cooling curve of the 20 th Layer of the point 26 using an ITe of 150°C and ISO lines for temperatures of 600°C and 950°C.

Figure 92 -

 92 Figure 92 -Intersection between cooling curve of the 20 th Layer of the point 26 using an ITe of 350°C and Iso lines for temperatures of 600°C and 950°C.

Figure 94 -

 94 Figure 94 -Intersection between cooling curve of the 20 th Layer of the point 26 using an ITe of 550°C and Iso lines for temperatures of 600°C and 950°C.

Figure 94

 94 Figure94shows the cooling curve of point 26 in the 20th layer for ITe of 550°C. The graph shows two points marked in red representing the intersection between the ISO 950°C and 600°C lines and the cooling curve after the last time this point reached the melting temperature.

Figure 99 -

 99 Figure 99 -Sample sizes. Dimensions are: A-32 mm (useful length), B-30.0 mm (length of the clamping section), C-100 mm (total length), D-6 mm (width of useful length), E-10.0 mm (width of clamping section), F-6.0 mm (chamfer radius), G-2 mm (thickness).

Figure 100 A

 100 Figure 100 A) shows the schematic used to cut the wall samples, Figure 100 B) presents a photograph of the samples cut from a wall.

Figure 100 -

 100 Figure 100 -Cutting scheme of the samples taken from the walls.

Figure 101 -

 101 Figure 101-Identification of the time constant characterizing the heat exchange of the sample with its environment. Two tests with different levels of pre-heating are presented. The dashed curves correspond to a theoretical exponential decrease with a time decay of 41 s.

Figure 102 -

 102 Figure 102 -Picture of the setup used for the construction of the walls.

Figure 103 -

 103 Figure 103 -Machine used for the hardness tests.

Figure 104 -

 104 Figure 104 -A) Machine used for quasi-static and accelerated fatigue tests, B) sample in the jaws of the testing machine, C) sample in the grips of the testing machine.

Figure 105 -

 105 Figure 105 -Defects at the start/end of several layers.

Figure 106 -

 106 Figure 106 -Interlayer time (ITi) evolution during wall construction (blue line ITe = 150°C, black line ITe = 350°C, red line ITe = 550°C).

Figure 107 -

 107 Figure 107 -Example of a wall after construction; A) B) and C) construction defects in the start and stop phases; D) nondeposited material from the process.

Figure 108 and

 108 Figure 108 and Figure 109 show the results of hardness tests. As indicated before, these hardness tests were done in the fixation area of the samples used for the quasi-static and accelerated fatigue tests. Figure 108 presents first the hardness values for the vertical samples. The purpose of the figure is to show how the hardness values for different ITe change with height on the side of the vertical samples. Following comments can be done: ➢ The hardness values are between 238 HV and 260 HV. A maximum variation of 22 HV exists between all vertical samples tested. ➢ The highest values were obtained for ITe = 150°C and the lowest for ITe = 550°C. ➢ For an ITe of 150°C, the values obtained are mostly concentrated between 251 HV and 259 HV. For an ITe of 350°C, the values are more dispersed, with the range of values extending between 246 and 257 HV. Finally, the hardness values for an ITe of 550°C range between 238 HV and 254 HV. So, the dispersion between the values of ITe = 550°C increases by 5 HV compared to the dispersion with ITe = 350°C. When comparing the dispersion of an ITe = 550°C and Ite = 150°C, the dispersion increases 8 HV. This means that the greater the ITe, the greater the variability of hardness was.

Figure 108 -

 108 Figure 108 -Comparison between results of the hardness tests done on the vertical samples for the 3 different ITe.

Figure 108

 108 Figure 108 presents the hardness values for the horizontal samples. Following comments can be done from this figure: ➢ When comparing values of different ITe, they show the same pattern of hardness as observed in the vertical samples: the higher the ITe value, the lower the hardness. ➢ The hardness values of the samples produced with an ITe of 150°C are concentrated between 252 HV and 260 HV (approximate values). ➢ As for the samples obtained from the walls built with an ITe of 350°C they have values ranging from 246 HV to 254 HV. ➢ The samples obtained from the walls built with an ITe of 550°C are spread between 231 HV and 248 HV. ➢ The dispersion between samples with an ITe of 150°C is the same as for an ITe of 350°C, with an 8 HV range. ➢ The scatter of the hardness values for an ITe of 550°C are spread over 16 HV, meaning that (as seen before for the vertical samples) also here the ITe of 550°c delivers a greater variability of hardness.

Figure 109 -

 109 Figure 109 -Comparison between results of the hardness tests done on the Horizontal samples for the 3 different ITe.

Figure 110 -

 110 Figure 110 -Stress-strain curves: A) for ITe = 150°C, B) for ITe = 350°C, C) for ITe = 550°C).

Figure 111 -

 111 Figure 111 -Stress-strain curves of the vertical samples.

Figure 112 -

 112 Figure 112 -Stress-strain curves of the horizontal samples.

Figure 113

 113 Figure113shows the average Rp0.2 and Rm values obtained for all the vertical and horizontal samples. Following comments can be done from the figure:➢ The blue bars (corresponding to the average Rp0.2) show a decreasing trend when increasing the ITe. This occurred for both sample orientations. ➢ The values of Rp0.2 for the horizontal samples with an ITe of 150°C and 350°C were approximately 100 MPa higher than those of the vertical ones. ➢ The horizontal samples with an ITe of 550°C had a difference (lower than ITe 150°c and 350°C) of approximately 60 MPa higher than the vertical ones. ➢ The average Rm values for different ITe were very close among the horizontal samples. Same for the vertical samples. ➢ The difference between the average Rm values obtained for the vertical specimens was generally approximately 70 MPa lower than for the horizontal samples.

Figure 113 -

 113 Figure 113 -Mean yield strength (Rp0.2) and ultimate tensile strength (Rm).

Figure 114 -

 114 Figure 114 -Mean maximum elongation (in %) and uniform elongation (in %).

Figure 115 -

 115 Figure 115 -Evolution of the stress during the accelerated fatigue tests.

Figure 116 -

 116 Figure 116 -Heat generated by mechanical dissipation per cycle during the accelerated mechanical fatigue tests.

Figure 117

 117 Figure117shows the average evolution of the heat generated by mechanical dissipation. The values have been averaged for each category for samples. It can be seen that:➢ Whatever the ITe value, the heat generated by fatigue damage was greater for the vertical samples. From a fatigue performance point of view, it is thus preferable to have the horizontal specimens. ➢ For both specimen orientations (horizontal or vertical), the heat increased with the value of ITe. From a fatigue performance point of view, it is therefore preferable to have an ITe of 150°C rather than 350°C, or 550°C. ➢ These trends are confirmed in Table36, which extracts the values for 𝜎 a = 250 MPa.

Figure 117 -

 117 Figure 117 -Heat generated by mechanical dissipation per cycle during the accelerated mechanical fatigue tests for the different categories of samples.

Figure 118 -

 118 Figure 118 -Heat generated by mechanical dissipation per cycle during the accelerated mechanical fatigue tests for the vertical samples: zoom for the identification of the onset of fatigue damage.

Figure 119 -

 119 Figure 119-Heat generated by mechanical dissipation per cycle during the accelerated mechanical fatigue tests for the vertical samples: zoom for the identification of the onset of fatigue damage.

Figure 120 -

 120 Figure 120 -Scheme representative of the dependencies between first degree indicators

Figure 121 -

 121 Figure 121 -Kinematic indicator scheme A generic model for an accurate evaluation of processing time is developed using the kinematic rules derived from experimental campaigns, as presented in detail in chapter 2 in the case of a KUKA KR100 -KRC2 robot. The kinematic rules are divided into five "categories": ➢ Initial acceleration behavior: quantifies the distance (time) required to accelerate from static to target speed, ➢ Deceleration at intermediate segments: quantifies the distance (time) required to reach the min curve speed (from an initial speed considered as the target speed), ➢ Minimum speed in curve: quantifies the distance (time) done at the minimum constant speed achieved (from the first point the minimum speed is reached I the end of deceleration until the first point of the re-acceleration), ➢ Re-acceleration at intermediate segment transitions: quantifies the distance (time) required to reach the target speed (from an initial speed considered as the min curve speed) ➢ Final deceleration behavior: quantifies the distance (time) required to decelerate from target speed until stop.

Figure 122 -Figure 123 -

 122123 Figure 122 -General scheme of the kinematic model Figure 123 presents the robot speed profiles for two types of strategies widely used in the WAAM process. The differences in the robot's kinematics between the nominal travel speed of 12 mm/s and 30 mm/s is highlighted. It is then possible to see if the variation in speed is within the desired geometry area, and thus test different strategies to minimize the travel speed variations.

Figure 124 -

 124 Figure 124 -Inputs and outputs of the thermo-kinematic model

1 .

 1 Number of branches/arms:This number reflects the amount of material available for diffusion of heat in the surrounding of the studied point. It is considered that this feature affects the cooling behavior at the studied position.

Figure 125 - 2 .

 1252 Figure 125 -Illustration of the number of branches represented here by the third type of configuration.

Figure 126 -

 126 Figure 126 -Illustration of point 13, its location in a third configuration type, and the correspondent cooling graph.

Figure 127 -

 127 Figure 127 -(Left) Reduced pattern of the geometry shown in chapter 3; (Right) pattern of the geometry shown in chapter 3 on a larger substrate.

Figure 128 -

 128 Figure 128 -Structure of cooling time ANN (ANN1).

Figure 129 -

 129 Figure 129 -Training methodology for both cooling time ANN (ANN 1) and cooling rate ANN (ANN 2).

Figure 130 -

 130 Figure 130 -Error graph obtained for 100% of the ANN 1 model data training.

Figure 131 -

 131 Figure131 -A) Regression Plot of ANN 1 training process for 100% of the data; B) Regression Plot of ANN 1 training processfor 20% of the data, using the remaining 80% to train the model.5.3.2. Validation of the cooling time ANN on a test case

Figure 132 -

 132 Figure 132 -Pattern used for the test case.

Figure 133 -

 133 Figure 133 -FEM simulation of the test pattern used.

Figure 134

 134 Figure 134 and Table39shows the comparison between cooling time prediction from ANN model and numerical simulation for all intersection points of trajectory for layers 3, 6, 10, 15, and 20 of the case study. The graph also shows a discontinuous blue line, which marks the kinematic time the robot takes to execute the trajectory. The following comments can be made:➢ Using the numerical simulation values as a reference, we can see the predictions made by the ANN model are close in the vast majority of cases. ➢ The largest errors occur in vertex 3 for layers 6, 10, 15 and 20. ➢ Due to the kinematic timing, the error only becomes important from the 6th layer onwards.

Figure 134 -

 134 Figure 134 -Comparison of results obtained through numerical simulation and ANN model.

Figure 135 -

 135 Figure 135 -Error graph obtained when compared to 100% A) and 20% B) after training the model 2.

Figure 136

 136 Figure 136 shows the regression plot of ANN 2, where the relationship between the predicted output values from the network and the actual target output values are compared. The predicted values are displayed on the x-axis, as for the y-axis it displays the actual target values. Each point on the plot represents a single instance in the training dataset.

Figure 136 A

 136 Figure136A) shows a significant dispersion in the results obtained from the ANN model for a specific range of instances. It is possible to see that many results are far from the target value. This distance between predicted and actual output means that a large error in the cooling curve will be obtained. Figure136 B) shows the regression plot of ANN 2 training process for the test data only. The quality of the regression is logically worse. It confirms that the worst points observed on Figure136 B) originate from test data. It is also possible to state a residual error or prediction error between the ideal diagonal, and the obtained diagonal. This residual error shows values with a more pronounced tendency to underestimate the target value.

Figure 136 -

 136 Figure 136 -Regression Plot of ANN 2 training process compared with 100% A) and 20% B) of the data. 5.3.3.2. Cooling curve prediction made by the ANN model for the test case

Figure 137 -

 137 Figure137-Cooling curves obtained in Vertex 5 using the numerical and ANN models for layers3, 6, 10, 15, and 20.

Figure 138 -

 138 Figure 138 -Schematic of the ANN analysis of the test case geometry.

Figure 139 -

 139 Figure 139 -Relationship between the various critical manufacturing factors and the mechanical quality of the material as built.

  The thermal score needs to be calculated for each layer, since for a given interlayer temperature, the cooling time required varies in each layer. The quality score (considering Rp0.2 of the horizontal samples with an ITe = 150°C) is:

Figure 140 -

 140 Figure 140 -3 rd layer cooling curve for points P1, P3 and P5 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature

Figure 141 -

 141 Figure 141 -20th layer cooling curve for points P1, P3 and P5 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature

Figure 142 -

 142 Figure 142 -3 rd layer cooling curve for points P23, P25 and P27 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature

Figure 143 -

 143 Figure 143 -20th layer cooling curve for points P23, P25 and P27 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature.

  . The cooling curves of points P7, P10, P18 and P21 are close to each other, but show a clear influence of the trajectory on the cooling of these points. It is noticeable that points P10 and P18 are negatively affected by the arrival of heat from the surrounding deposition at T = 35 s for P18 and T = 45 s for P10, increasing the time required for cooling these points to a temperature of 150°C. When we look at the graph in Figure145 B) for an ITe of 550°C we can clearly see that the thermal behavior of the different points starts to diverge significantly. Point P10 reaches 550°C in 11.5 s while P7 reaches it in 13.5, P21 in 17 s and P18 in 22.25 (approximate values). This means that just the influence of the tool path indicates a difference of 10.75 s between the most efficient and the least efficient cooling curve, for this set of points with the same configuration.

Figure 145 -

 145 Figure 145 -3 rd layer cooling curve for points P7, P10, P18 and P21 with configuration type 1, with 150°C (A)) and 550°C (B))of interlayer temperature.

Figure 146

 146 Figure146shows the cooling curves of points P7, P10, P18 and P21 for the 20th layer with ITe of 150°C Figure146 A) and 550°C Figure146 B). We can see that the graph of the 20th layer (Figure146 A)) when compared with that of Figure145 A) already reflects the accumulation of heat and therefore a lower capacity of its evacuation. In the graph of FigureB) it can be seen that the cooling curves after several layers diverge due to the different amount of heat received, coming from the deposition in the rest of the toolpath.

Figure 146 -

 146 Figure 146 -20th layer cooling curve for points P7, P10, P18 and P21 with configuration type 1, with 150°C (A)) and 550°C(B)) of interlayer temperature.

Figure 148 - 3

 3 Figure 148 -3 rd 6 th , 10 th , 15 th and 20 th layer cooling curves for point P14 with configuration type 1, with 150°C A) and 550°C B) of interlayer temperature

Figure 149 -

 149 Figure 149 -Cooling times required for each layer (blue line), and kinematic time (red dashed line).

Figure 150 -

 150 Figure 150 -Top view of part geometry for study case showing all the points with the fourth type of configuration.The cooling curves of the points belonging to group F (points P0, P6, P22 and P28) resulting from the 3rd layer simulation for interlayer temperatures of 150°C and 550°C are shown in Figure151. The graphs in Figure151 A) show that for 150°C of heat the cooling curves are identical. The cooling curves of Figure151 B) show that there are differences in the cooling of the different points. These differences are caused by the different temperatures of the material at the passage of the heat source. This leads to different temperature peaks which consequently have different cooling curves for points with the same configuration. The cooling curves for the following layers (namely up to the 20th) reflect the same pattern as described above for the 3rd layer, but already showing gradual heat build-up either for an ITe of 150°C, 350°C or 550°C.

Figure 151 - 3

 3 Figure 151 -3 rd layer cooling curve for points P0, P6, P22 and P28 with configuration type 4, with 150°C (A)) and 550°C (B))of interlayer temperature.

Figure 152 -

 152 Figure 152 -Set up for the walls cleaning after deposition; A) Wall still with residues and soot from its manufacture; B) Wall after cleaning with the pneumatic drill and steel brush.

Figure 153 -

 153 Figure 153 -Cutting scheme to obtain a plate.

Figure 154

 154 Figure 154 Cut execution using a hacksaw

Figure 155

 155 Figure 155 Walls after cutting with a hacksaw

Table des matières

 des Abstract ...........................................................................................................................................

  .............................. Figure 32 -Distribution of acceleration time (in green), constant speed (in blue) and deceleration time (in yellow) for the different ACC.cp values with and imposed speed of 40 mm/s. ...................... Figure 33 -Distribution of acceleration (in green), constant speed (in blue) and deceleration lengths (in yellow) for the different ACC.cp values using an imposed speed of 40 mm/s. ............................... Figure 34 -Trajectory of the nozzle for a speed of 1000 mm/s with and 1% of Vel.cp. ....................... Figure 35 -Speed achieved by the robot during toolpath robot movement with 1% Vel.cp. .............. Figure 36 -Trajectory of the nozzle for a speed of 1000 mm/s with and 5% of Vel.cp. ....................... Figure 37 -Speed achieved by the robot motion test with 5% Vel.cp. ................................................. Figure 38 -Trajectory of the nozzle for a speed of 1000 mm/s with and 10% of Vel.cp. ..................... Figure 39 -Speed achieved by the robot motion test with 10% Vel.cp. ............................................... Figure 40 -Illustration of the linear trajectory using program 2 at a nominal speed of 10 mm/s. ...... Figure 41-Illustration of the speeds using program 1 for a linear trajectory at a nominal speed of 10 mm/s. .................................................................................................................................................... Figure 42 -Illustration of the influence of the arc ON/OFF command on the linear trajectory using program 3 at a nominal speed of 10 mm/s. ..

........................................................................................ Figure 43 -Illustration of the speeds using program 2 for a linear trajectory at a nominal speed of 10 mm/s . ...................................................................................................................................................

  ................................................................................................................................... Figure 82 -3 rd layer cooling curve for points P2, P4, P24 and P26 with configuration type 2, with 150°C (A)) and 550°C (B)) of interlayer temperature. ......................................................................... Figure 83 -3 rd layer cooling curve for points P2, P4, P24 and P26 with configuration type 2, with 150°C (A)) and 550°C (B)) of interlayer temperature. ......................................................................... Figure 84 -Top view of part geometry for study case showing all the points with the third type of configuration. ...................................................................................................................................... Figure 85 -3 rd layer cooling curve for points P13 and P15 with configuration type 3, with 150°C (A)) and 550°C (B)) of interlayer temperature. .......................................................................................... Figure 86 -Location of point 15, 26 and 8 in the geometry of the part considered. ......................... Figure 87 -Cooling curves of points P25, P18, P8, P16, P14, P22, P26, P11 and P15 for the 3 rd layer with 150°C (A)) and for the 20 th layer with 550°C (B)) of interlayer temperature. ............................. Figure 88 -Response surface graphs of Interpass temperature Vs layer from the points 25, 18, 8, 16, 14, 22, 26, 11, 15 from the groups A, B, C, D, E, F, G, H, and I respectively. .......................................

Figure 89 -Representation of an approximation between the time temperature transformation (TTT) graphic and CCT curve for stainless steel 2205 using one known point (adapted from [34]). ........... Figure 90 -Intersection between cooling curve of the 20 th Layer of the point 26 using an ITe of 150°C and ISO lines for temperatures of 600°C and 950°C. ..........................................................................

  Training methodology for both cooling time ANN (ANN 1) and cooling rate ANN (ANN 2). ............................................................................................................................................................. Figure 130 -Error graph obtained for 100% of the ANN 1 model data training. ................................ Figure 131 -A) Regression Plot of ANN 1 training process for 100% of the data; B) Regression Plot of ANN 1 training process for 20% of the data, using the remaining 80% to train the model................ Figure 132 -Pattern used for the test case. ....................................................................................... Figure 133 -FEM simulation of the test pattern used. ....................................................................... Figure 134 -Comparison of results obtained through numerical simulation and ANN model. ......... Figure 135 -Error graph obtained when compared to 100% A) and 20% B) after training the model 2. ............................................................................................................................................................. Figure 136 -Regression Plot of ANN 2 training process compared with 100% A) and 20% B) of the data. ..................................................................................................................................................... Figure 137 -Cooling curves obtained in Vertex 5 using the numerical and ANN models for layers 3, 6, 10, 15, and 20. ..................................................................................................................................... Figure 138 -Schematic of the ANN analysis of the test case geometry. ............................................

	Figure 151 -3 rd layer cooling curve for points P0, P6, P22 and P28 with configuration type 4, with
	150°C (A)) and 550°C (B)) of interlayer temperature.

). .......................................................................... 185 Figure 129 -Figure 139 -Relationship between the various critical manufacturing factors and the mechanical quality of the material as built. ........................................................................................................... Figure 140 -3 rd layer cooling curve for points P1, P3 and P5 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature ........................................................................................... Figure 141 -20th layer cooling curve for points P1, P3 and P5 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature .................................................................................... Figure 142 -3 rd layer cooling curve for points P23, P25 and P27 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature .................................................................................... Figure 143 -20th layer cooling curve for points P23, P25 and P27 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature. .........................................................................

Figure 144 -3 rd and 20th layer cooling curves for points P1, P3, P5, P23, P25 and P27 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature ................................ Figure 145 -3 rd layer cooling curve for points P7, P10, P18 and P21 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature. ......................................................................... Figure 146 -20th layer cooling curve for points P7, P10, P18 and P21 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature. ......................................................................... Figure 147 -3 rd and 20 th layer cooling curve for points P12, P16 with configuration type 1, with 150°C (A) and C)) and 550°C (B) and D)) of interlayer temperature .............................................................. Figure 148 -3 rd 6 th , 10 th , 15 th and 20 th layer cooling curves for point P14 with configuration type 1, with 150°C A) and 550°C B) of interlayer temperature ....................................................................... Figure 149 -Cooling times required for each layer (blue line), and kinematic time (red dashed line). ............................................................................................................................................................. Figure 150 -Top view of part geometry for study case showing all the points with the fourth type of configuration. ...................................................................................................................................... ......................................................................... Figure 152 -Set up for the walls cleaning after deposition; A) Wall still with residues and soot from its manufacture; B) Wall after cleaning with the pneumatic drill and steel brush. .................................

Figure 153 -Cutting scheme to obtain a plate. ................................................................................... Figure 154 Cut execution using a hacksaw .......................................................................................... Figure 155 Walls after cutting with a hacksaw ................................................................................... Figure 156 -Diffusion path for the lower layers (in red) and for the upper layers (in blue). .............

Table 1 -

 1 Collected times for each section of the simulated toolpath for different ACC.cp values. .... 48

Table 2 -

 2 Measured lengths for each section of the simulated toolpath for different ACC.cp values. 49

Table 3 -

 3 Times and lengths collected from robot motion test performed for velocities of 1, 0.2 and 0.02 m/s in their different phases and for their respective backlash. .................................................. 55

Table 4 -

 4 Overview of the times obtained in each section using the 5 different program types.......... 57

Table 5 -

 5 Overview of the times obtained in each section using the 4 different program types.......... 59

Table 6 -

 6 Results obtained from all robot motion tests performed for all angles to be used in the eight strategies preceding this study for a speed of 10 m/s. ......................................................................... 64

Table 7 -

 7 Results obtained from all robot motion tests performed for all angles to be used in the eight strategies preceding this study for a speed of 40 m/s. ......................................................................... 65

Table 8 -

 8 Presents the results for the second campaign of experiments for the 20°, 40° and 60° angles, for all "simulated" speeds. .................................................................................................................... 66

Table 9 -

 9 Presents the results for the second campaign of experiments for the 80°, 90° and 100°

angles, for all "simulated" speeds. ........................................................................................................ 67 Table 10 -Presents the results for the second campaign of experiments for the 120°, 140° and 160° angles, for all "simulated" speeds. ........................................................................................................ 68 Table 11 -Comparison between different strategies and two nominal speeds for the small OR (21.5×43 mm2). Measured parameters are the total time and length over the whole toolpath, as well as the total volume of material deposited (i.e. when arc ON is activated). ......................................... 69 Table 12 -Comparison between different strategies and two nominal speeds for the large OR (43×86 mm2). Measured parameters are the total time and length over the whole toolpath, as well as the total volume of material deposited (i.e. when arc ON is activated). .................................................... 70 Table 13 -Comparison between the semi-circular, 60° triangular, rectangular, and spiral strategies for a nominal speed of 40 mm/s and small OR (21.5×43 mm2). For the triangular strategy, arc ON was activated over the whole toolpath. ....................................................................................................... 72 Table 14 -Comparison between raster-pass and swiping strategies for a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 ). ................................................................................................................ 74 Table 15 -Comparison between rectangular and spiral strategies for a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 . ........................................................................................................................ 76 Table 16 -Influence of the arc ON/OFF command for the 45° triangular strategy, with a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 ). .................................................................................. 80 Table 17 -Influence of the arc ON/OFF command for the 60° triangular strategy, with a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 ). .................................................................................. 83 Table 18 -Influence of the arc ON/OFF command for the 90° triangular strategy, with a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 ). .................................................................................. 85 Table 19 -Influence of the arc ON/OFF command for the semi-circular strategy, with a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 ). ............................................................................................ 88

Table 20 -

 20 Impact of switching between arc ON and arc OFF for the four strategies featuring a toolpath outside the OR. Comparison is made for two nominal speeds and two OR areas (21.5×43 mm2 and 43×86 mm2, simply written "small" and "large" respectively in the table). ........................ 89

Table 21 -

 21 Comparison between the length and time values obtained during the robot motion tests of the 45° triangular toolpath, on the two "objective rectangle" (O.R.) sizes 21.5×43 and 27.972 for two

nominal speeds 10 mm/s and 40 mm/s with "arc on" only. ................................................................. 91 Table 22 -Collected times from robot motion tests performed at some of the different positions shown in figure 21 for a small OR. ........................................................................................................ 92

Table 23 -

 23 Parameters identified for the 45° triangular strategy with the small OR (21.5×43 mm2), to be used in Equations (3-7) for time calculation. ...................................................................................

Table 24 -

 24 Material properties of 316L stainless steel (J.J. Valencia et al., 2008). ..............................

Table 25 -

 25 Goldak geometric heat source parameters collected in Addimadour. ..............................

Table 26 -

 26 Comparison of kinematic and thermal performances of each simulated strategy. ...........

Table 27 -

 27 KSc calculation results. .......................................................................................................

Table 28 -

 28 Group of points defined for cooling analysis. .....................................................................

Table 29 -

 29 Cooling time for the different simulated layers at points P8, P9, P19 and P20 for interlayer temperatures of 150°C, 350°C and 550°C. ..........................................................................................

Table 30 -

 30 Cooling time for the different simulated layers at the point P2, P4, P24 and P26 for interlayer temperatures of 150°C, 350°C and 550°C. .........................................................................

Table 31 -

 31 Cooling time for the different simulated layers at the point P11 and P17 for interlayer temperatures of 150°C, 350°C and 550°C. ..........................................................................................

Table 32 -

 32 Cooling time for the different simulated layers at the point P13 and P15 for interlayer temperatures of 150°C, 350°C and 550°C. ..........................................................................................

Table 33 -

 33

	Glossary
	-AM: Additive manufacturing
	-DED: Direct energy deposition
	-WAAM: Wire arc additive manufacturing
	-2D: Two-dimensional
	-WB: Weld bead
	-WFS: Wire feed speed
	-TS: Travel speed
	-GMA: Gaz metal arc
	-CMT: Cold Metal Transfer
	-MAM: Metal Additive Manufacturing
	-SP: Subtractive Process
	-KCP: Kuka control panel
	-OR: Objective rectangle
	-GMAW: Gas metal arc welding
	-MIG: Metal inert gas
	-KPI: Key performance indicator
	-DT: Deposition time
	-LI: Local indicator
	-GI: Global indicator
	-PhT: Pre-heating temperature
	-ITe: Interlayer temperature
	-ITi: Interlayer time

Mechanical properties indicated in the literature and reference values provided by manufacturers. ....................................................................................................................................

Table 34 -Production times for each of the walls made and their number of layers. ....................... Table 35 -Mechanical performances in quasi-static loading for the vertical samples. ...................... Table 36 -Mechanical performances in quasi-static loading for the horizontal sample. ................... Table 37 -Heat generated by mechanical dissipation per cycle for a stress amplitude of 250 MPa. Table 38

-Stress amplitude corresponding to fatigue damage onset. ............................................... Table 39 -Times predicted by numerical simulation and ANN model for all vertices of the test case geometry. ............................................................................................................................................ Table 40 -Fitting coefficients for the cooling curves extracted on several points of the study case (3 rd layer). ................................................................................................................................................... Table 41 -Cooling time for the different simulated layers at points P1, P3 and P5 for interlayer temperatures of 150°C, 350°C and 550°C ........................................................................................... Table 42 -Cooling time for the different simulated layers at points P23, P25 and P27 for interlayer temperatures of 150°C, 350°C and 550°C ........................................................................................... Table 43 -Cooling time for the different simulated layers at points P7, P10, P18 and P21 for interlayer temperatures of 150°C, 350°C and 550°C .......................................................................... Table 44 -Cooling time for the different simulated layers at points P12 and P16 for interlayer temperatures of 150°C, 350°C and 550°C ........................................................................................... Table 45 -Cooling time for the different simulated layers at the point P14 for interlayer temperatures of 150°C, 350°C and 550°C ........................................................................................... Table 46 -Cooling time for the different simulated layers at the point P14 for interlayer temperatures of 150°C, 350°C and 550°C ...........................................................................................

Table 1 -

 1 Collected times for each section of the simulated toolpath for different ACC.cp values.

						Time of
			0,01 m/s			0,025 m/s			0,04 m/s
	ACC.cp	Accel (s)	Constant speed (s)	Decel (s)	Accel (s)	Constant speed (s)	Decel (s)	Accel (s)	Constant speed (s)	Decel (s)
	1	0,108	9,852	0,18	0,228	3,756	0,216	0,216	2,28	0,216
	2	0,132	9,852	0,168	0,216	3,768	0,204	0,24	2,268	0,192
	3	0,156	9,828	0,168	0,132	3,864	0,18	0,216	2,268	0,204
	4	0,144	9,84	0,168	0,132	3,852	0,122	0,192	2,292	0,216
	5	0,156	9,84	0,18	0,132	3,852	0,192	0,216	2,268	0,192
	6	0,144	9,816	0,192	0,204	3,78	0,192	0,216	2,28	0,192
	7	0,144	9,84	0,168	0,204	3,78	0,192	0,216	2,268	0,204
	8	0,156	9,828	0,18	0,144	3,84	0,204	0,216	2,268	0,204
	9	0,168	9,84	0,168	0,168	3,804	0,192	0,18	2,292	0,192
	10	0,132	9,84	0,168	0,156	3,828	0,216	0,204	2,268	0,204

Table 2 -

 2 Measured lengths for each section of the simulated toolpath for different ACC.cp values.

						Length of
			0,01 m/s			0,025 m/s			0,04 m/s
	Acc.cp	Accel (mm)	Constant speed (mm)	Decel (mm)	Accel (mm)	Constant speed (mm)	Decel (mm)	Accel (mm)	Constant speed (mm)	Decel (mm)
	1	0,567	98,878	0,689	3,391	94,084	2,523	4,268	91,327	4,372
	2	0,575	98,891	0,665	3,263	94,386	2,383	5,129	90,858	3,976
	3	0,713	98,637	0,894	1,288	96,691	2,02	5,273	90,856	4,33
	4	0,715	98,749	0,654	1,301	96,413	2,3	3,904	91,817	4,25
	5	0,617	98,731	0,768	1,329	96,391	2,271	5,36	90,847	3,727
	6	0,705	98,538	0,883	3,061	94,671	2,266	4,904	91,356	3,708
	7	0,618	98,751	0,768	3,077	94,657	2,258	4,924	90,875	4,174
	8	0,62	98,6	0,885	1,346	96,11	2,553	4,936	90,866	4,16
	9	0,587	98,744	0,875	2,197	95,248	2,538	4,016	91,636	3,675
	10	0,595	98,741	0,758	1,657	95,777	2,855	4,958	90,896	4,109

Table 3 -

 3 Times

	Control pad % →	1%	5%	10%	1%	10%	10%	50%	100%
	Initial acceleration	9,372	1,98	1,152	1,068	0,24	0,168	0,132	0,18
	Constant speed time	10,704 2,028 0,876	98,64	9,756	99,936 19,872	9,84
	Final deceleration	9,828	1,98	1,164	1,848	0,312	0,096	0,168	0,18
	Total time of deposition	29,904 5,988 3,192 101,556 10,308	100,2	20,172	10,2
	Initial backlash length (mm)	0,13	0,19	0,1	0,14	0,18	0,18	0,21	0,16

and lengths collected from robot motion test performed for velocities of 1, 0.2 and 0.02 m/s in their different phases and for their respective backlash.

Vel.cp = 1m/s Vel.cp = 0,2m/s Velcp = 0,02m/s

Table 4 -

 4 Overview of the times obtained in each section using the 5 different program types.

			Program with 10 mm/s
		1	2	3	4	5
	Total virtual deposition	10,212	10,224	10,488	10,56	10,44
	Initial acceleration (Ia)	0,144	0,144	0,144	0,144	0,12
	Final deceleration (Fd)	0,252	0,276	0,228	0,276	0,216
	Ratio between (Fd/Ia)	1,75	1,917	1,583	1,917	1,8
	Behavior	No Stop	No Stop	Stops	Stops	Stops

Table 4

 4

summarizes the times for each program and the robot stops. Programs 3, 4 and 5 show a longer time of around 0.2 s, due to the stop at the arc transition. While accelerations are similar, decelerations are different, which affects the ratios.

Table 5 -

 5 Overview of the times obtained in each section using the 4 different program types.

			Program with 40 mm/s
		1	2	3	4
	Total virtual deposition	2,724	2,712	3,012	2,928
	Initial acceleration (Ia)	0,216	0,216	0,216	0,192
	Final deceleration (Fd)	0,228	0,228	0,288	0,228
	Ratio between (Fd/Ia)	1,056	1,056	1,333	1,188
	Behavior	No Stop	No Stop	Stops	Stops

Table -

 - Results obtained from all robot motion tests performed for all angles to be used in the eight strategies preceding this study for a speed of 10 m/s.

Table 6

 6 shows a summary of the results obtained for the angles used for trajectories with a speed of 10 mm/s. It can be seen in red abnormal values, which are probably the result of measurement errors. The highest values in each column are marked in orange, and the lowest values are marked in green. This color scheme is also valid for Table7.

	10 m/s

Table 7 -

 7 Results obtained from all robot motion tests performed for all angles to be used in the eight strategies preceding this study for a speed of 40 m/s.

	40 m/s

Table 8 -

 8 Presents the results for the second campaign of experiments for the 20°, 40° and 60° angles, for all "simulated" speeds.

	Speed (mm/s)

Table 9 -

 9 Presents the results for the second campaign of experiments for the 80°, 90° and 100° angles, for all "simulated" speeds.

	Speed (mm/s)

Table 10 -

 10 Presents the results for the second campaign of experiments for the 120°, 140° and 160° angles, for all "simulated" speeds.

	Speed (mm/s)

Table 11 and

 11 Table

Table 11 -

 11 Comparison between different strategies and two nominal speeds for the small OR(21.5×43 mm2). Measured parameters are the total time and length over the whole toolpath, as well as the total volume of material deposited (i.e. when arc ON is activated).

	Strategy	Nominal speed	Measured parameter	With arc ON over the whole toolpath	With arc OFF outside the OR Over the whole When arc is toolpath ON
			Time	N/A	40.644 s	22.38 s
	Raster-pass	10 mm/s	Length Volume	N/A N/A	387.900 mm 2118.353 mm 3	215.084 mm 2108.176 mm 3
			Time	N/A	11.580 s	6.408 s
		40 mm/s	Length	N/A	386.971 mm	214.712 mm
			Volume	N/A	615.133 mm 3	605.083 mm 3
			Time	26.280 s	27.972 s	22.152 s
	Triangular 45°	10 mm/s	Length Volume Time	258.896 mm 2476.881 mm 3 6.732 s	259.877 mm 2159.070 mm 3 7.932 s	215.642 mm 2085.557 mm 3 6.132 s
		40 mm/s	Length	249.857 mm	235.549 mm	215.870 mm
			Volume	634.489 mm 3	619.788 mm 3	577.939 mm 3
			Time	25.212 s	26.856 s	22.152 s
	Triangular 60°	10 mm/s	Length Volume Time	248.426 mm 2376.223 mm 3 6.456 s	249.427 mm 2165.724 mm 3 8.172 s	215.889 mm 2085.557 mm 3 6.096 s
		40 mm/s	Length	240.050 mm	242.118 mm	215.360 mm
			Volume	608.476 mm 3	615.264 mm 3	574.546 mm 3
			Time	24.156 s	25.848 s	22.068 s
	Triangular 90°	10 mm/s	Length Volume Time	238.759 mm 2276.695 mm 3 6.180 s	239.893 mm 2161.332 mm 3 7.932 s	215.354 mm 2082.164 mm 3 6.132 s
		40 mm/s	Length	230.613 mm	235.549 mm	215.870 mm
			Volume	582.463 mm 3	613.002 mm 3	577.939 mm 3
			Time	21.936 s	N/A	N/A
		10 mm/s	Length	215.997 mm	N/A	N/A
	Rectangular		Volume	2067.461 mm 3	N/A	N/A
		40 mm/s	Time Length	5.664 s 207.618 mm	N/A N/A	N/A N/A

Table 12 -

 12

	Strategy	Nominal speed	Measured parameter	With arc ON over the whole toolpath	With arc OFF outside the OR Over the whole toolpath When arc is ON
			Time	N/A	167.436 s	87.708 s
		10 mm/s	Length	N/A	1636.161 mm	860.635 mm
	Raster-pass		Volume Time	N/A N/A	8270.973 mm 3 44.880 s	8265.319 mm 3 23.436 s
		40 mm/s	Length	N/A	1634.200 mm	859;632 mm
			Volume	N/A	2220.143 mm 3	2206.573 mm 3
			Time	96.612 s	100.368 s	87.084 s
		10 mm/s	Length	959.644 mm	961.592 mm	861.657 mm
	Triangular		Volume	9105.649 mm 3	8346.780 mm 3	8204.245 mm 3
	45°		Time	24.312 s	28.128 s	22.812 s
		40 mm/s	Length	939.284 mm	941.410 mm	860.906 mm
			Volume	2291.398 mm 3	2220.143 mm 3	2151.154 mm 3
			Time	94.140 s	97.932 s	87.096 s
		10 mm/s	Length	936.174 mm	938.188 mm	861.729 mm
	Triangular		Volume	8872.663 mm 3	8376.156 mm 3	8204.245 mm 3
	60°		Time	23.712 s	27.600s	22.824 s
		40 mm/s	Length	917.451 mm	922.234 mm	862.392 mm
			Volume	2234.848 mm 3	2226.929 mm 3	2148.892 mm 3
	Triangular 90°	10 mm/s	Time Length	91.800 s 914.583 mm	95.616 s 916.983 mm	87.036 s 861.650 mm

Comparison between different strategies and two nominal speeds for the large OR (43×86 mm2). Measured parameters are the total time and length over the whole toolpath, as well as the total volume of material deposited (i.e.

when arc ON is activated).

2.7.5.1. Strategies "nominal speed of 40 mm/s -small OR"

Table 13 -

 13 Comparison

		Semi-circular	60° triangular	Rectangular	Spiral
	Total time	6.264 s	6.456 s	5.664 s	5.628 s
	Total length	234.201 mm	240.050 mm	207.618 mm	206.320 mm
	Average speed	38.573 mm/s	38.349 mm/s	37.800 mm/s	37.902 mm/s
	Total "programmed" length	242.603 mm	250.437 mm	217.600 mm	215.710 mm
	Ratio between actual and programmed lengths	0.97	0.96	0.95	0.96

between the semi-circular, 60° triangular, rectangular, and spiral strategies for a nominal speed of 40 mm/s and small OR

(21.5×43 mm2)

. For the triangular strategy, arc ON was activated over the whole toolpath.

Table 14 -

 14 Comparison between raster-pass and swiping strategies for a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 ).

	Raster-pass	Swiping

Table 15 -

 15 Comparison between rectangular and spiral strategies for a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 .

	Rectangular	Spiral

Table 16

 16 provides a quantitative comparison showing various output parameters. Times and lengths are measured over different phases of the trajectory: constant speed in the OR, acceleration in the OR; deceleration in the OR; inside the OR; outside the OR; and over the whole toolpath. The "total time with arc OFF inside the OR" indicator counts little time shifts observed in the application of the arc ON/OFF command. The following comments can be expressed from the table:

Table 16 -

 16 Influence of the arc ON/OFF command for the 45° triangular strategy, with a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 ).

	With arc OFF outside	With arc ON over the whole
	the OR	toolpath

Table 17 -

 17 Influence of the arc ON/OFF command for the 60° triangular strategy, with a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 ).

	With arc OFF outside	With arc ON over
	the OR	the whole toolpath

Table 18 -

 18 Influence of the arc ON/OFF command for the 90° triangular strategy, with a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 ).

	With arc OFF	With arc ON over the
	outside the OR	whole toolpath

Table 19 -

 19 Influence of the arc ON/OFF command for the semi-circular strategy, with a nominal speed of 40 mm/s and small OR (21.5×43 mm 2 ).

	With arc OFF	With arc ON over the
	outside the OR	whole toolpath

of the whole toolpath 237.967 mm 234.201 mm

	Total "programmed" length	242.603 mm	242.603 mm
	Total volume of material deposited	607.347 mm 3	590.380 mm 3

Table 20 -

 20 Impact of switching between arc ON and arc OFF for the four strategies featuring a toolpath outside the OR.Comparison is made for two nominal speeds and two OR areas (21.5×43 mm2 and 43×86 mm2, simply written "small" and "large" respectively in the table).

	Strategy	Nominal speed	OR size	Total time	With arc OFF outside the OR	With arc ON over the whole toolpath
				inside the OR	22.524 s	21.552 s
			Small
				outside the OR	3.612 s	2.832 s
		10 mm/s
				inside the O.R	87.708 s	86.184 s
	Semi-circular		Large
				outside the OR	8.316 s	6.12 s
				inside the OR	6.372 s	5.628 s
		40 mm/s	Small
				outside the OR	1.536 s	0.636 s

2.7.5.3. Comparison between the two speeds and the two OR areas

Table 21 -

 21 Comparison between the length and time values obtained during the robot motion tests of the 45° triangular toolpath, on the two "objective rectangle" (O.R.) sizes 21.5×43 and 27.972 for two nominal speeds 10 mm/s and 40 mm/s with "arc on" only.

	OR of	OR of	Time ratio	Length ratio
			between the	between the
	21.5×43 mm 2	43×86 mm 2	two sizes	two sizes

Finally, experiments were duplicated at 15 various locations in the workspace (see schematic view in Figure

Table 22 -

 22 Collected times from robot motion tests performed at some of the different positions shown in figure21for a small OR.Based on the results of the experiments, a manufacturing time estimation model is now proposed to calculate the manufacturing time of any 𝑊× 𝐿 area of OR from a limited number of previously identified parameters for a single area. The designations used are transversal to all the formulas.

	Small Area

  𝑇 init const is the duration of the first horizontal straight section at constant speed:

	+(𝑛 WB -2) × 𝑇 Horizontal straight const	straight const (𝐿, 𝑇𝑆) + (𝑛 WB -1) × 𝑇 Vertical	(𝐿, 𝑇𝑆)
	+ 𝑇 final const (𝐿, 𝑇𝑆) + 𝑇 final decel (𝑇𝑆)
	where:
	➢ 𝑇 init const =	𝑇𝑆 𝐿 -𝐿 init accel (𝑇𝑆) -𝐿 curve decel (𝑇𝑆) -( 𝑊 WB 2 )	(11)
	➢ 𝑇 Horizontalt straight const is the duration of any horizontal straight section at constant speed,
	excluding the first and final ones:
	𝑇 horizontal straight const =	𝐿 -𝐿 curve accel (𝑇𝑆) -𝐿 curve decel (𝑇𝑆) -𝑊 𝑇𝑆	(12)
	➢ 𝑇 final_const is the duration of the final horizontal straight section at constant speed:
	𝑇 final const =	𝐿 -𝐿 curve accel (𝑇𝑆) -𝐿 Final decel (𝑇𝑆) -( 𝑊 WB 2 ) 𝑇𝑆	(13)
				(10)

):

𝑇 total (𝑊, 𝐿, 𝑇𝑆, 𝑛 WB ) = 𝑇 init accel (𝑇𝑆) + 𝑇 init const (𝐿, 𝑇𝑆) + (𝑛 WB -1 × 2) × 𝑇 trans (𝑇𝑆) 𝐿 initial accel ( 𝑇𝑆) -Length of the initial acceleration until the robot reaches the nominal speed 𝐿 curve accel ( 𝑇𝑆) -Length for acceleration after the curve until it reaches the nominal speed 𝐿 curve decel (𝑇𝑆) -Length for deceleration before the curve 𝐿 final decel ( 𝑇𝑆) -Time needed to decelerate from nominal speed to 0 mm/s at the end of the path

2.8.5. Swiping Strategy

The formula (

13

) is dedicated to calculating the total time for the swiping strategy as a function of the 𝑊× 𝐿 area of the OR, the nominal speed (𝑇𝑆) and the number of horizontal weld beads 𝑛 WB calculated from Eqs (1) and (2): 𝑇 total (𝐿, 𝑇𝑆, 𝑛 WB ) = 𝑇 init accel (𝑇𝑆) + 𝑇 init const (𝐿, 𝑇𝑆) + (𝑛 WB -1) × 𝑇 trans (𝑇𝑆) +(𝑛 WB -2) × 𝑇 straight const (𝐿, 𝑇𝑆) + 𝑇 final const (𝐿, 𝑇𝑆) + 𝑇 final decel

(𝑇𝑆)

Table 23 -

 23 Parameters identified for the 45° triangular strategy with the small OR (21.5×43 mm2), to be used in Equations(3- 7) for time calculation.

			Nominal speed (TS)
		10 mm/s			40 mm/s
		With arc ON over the	With arc OFF	With arc ON over	With arc OFF outside the
		whole toolpath	outside the OR	the whole toolpath	OR
	Tinit accel	0.144 s	0.144 s	0.204 s	0.216 s
	Linit accel	0.617 mm	0.610 mm	4.212 mm	4.944 mm
	Ldecel	0 mm	0.876 mm	2.500 mm	3.670 mm
	Laccel	0 mm	0 mm	2.200 mm	4.387 mm
	Ttrans	1.200 s	1.410 s	0.426 s	0.408 s
	Lfinal decel	0.806 mm	0.807 mm	3.862 mm	3.807 mm
	Tfinal decel	0.180 s	0.180 s	0.192 s	0.192 s

Let us note that parameters 𝑇 init accel , 𝐿 init accel , 𝑇 final decel and 𝐿 final decel are measured from the median of several experiments with different strategies (they are not specific to the 45° triangular strategy). On the contrary, as 𝐿 accel , 𝐿 decel and 𝑇 trans are specific to the strategy considered, we measured them for the 45° triangular strategy (one experiment). As an evaluation of the accuracy of the formula, numerical applications were performed to calculate the total times for the large OR (𝑊 = 43 mm and 𝐿 = 86 mm) from the parameters identified for the small OR. They give:

➢ for 𝑇𝑆 = 10 mm/s and arc ON over the whole trajectory: 96.982 s, i.e. 0.38% of error with respect with measured value (96.612 s), see

Table 20 ;

 20 ➢ for 𝑇𝑆 = 10 mm/s and arc OFF outside the OR: 98.081 s, i.e. 2.28% of error with respect with measured value (100.368 s); ➢ for 𝑇𝑆 = 40 mm/s and arc ON over the whole trajectory: 24.304 s, i.e. 0.03% of error with respect with measured value (24.312 s); ➢ for 𝑇𝑆 = 40 mm/s and arc OFF outside the OR: 23.544 s, i.e. 16.3% of error with respect with measured value (28.128 s).

Table 24 -

 24 Material properties of 316L stainless steel (J.J.Valencia et al., 2008).

	k, thermal conductivity	15	[W.m -1 .K -1 ]
	cp, specific heat capacity	470	[J.kg -1 .K -1 ]
	ρ, density	7800	[kg.m -3 ]
	D, thermal diffusivity	4	[m².s -1 ]

Table 25 -

 25 Goldak geometric heat source parameters collected in Addimadour. Four different strategies among the possible options were studied. They are represented in Figure73with designations RUN 1, 2, 3 and 4. The green points mark the arc transition from extinction (arc OFF) to ignition (arc ON). The black points mark the opposite transition from arc ON to arc OFF. The red points are intermediate points during a continuous movement that might contain speed variations. The points divided into two halves with the colors red and black have a double meaning: they are intermediate points (half marked with red),

	af, front length	2	[mm]
	ar, rear length	4	[mm]
	b, half width	2	[mm]
	c, depth	2	[mm]
	3.7.3. Strategy

The travel speed was set to 12 mm/s during deposition and to 50 mm/s during transition movements (TM). This choice was based upon experimental campaigns previously performed on this material.

Table 26 -

 26 Comparison of kinematic and thermal performances of each simulated strategy.

	Strategy Classification

Table 27

 27 thus presents the result of the 𝐾 𝑆𝑐 calculation for the RUN 1, 2, 3 and 4 strategies presented above.

Table 27 -

 27 𝐾 𝑆𝑐 calculation results.

		Kinematic score (𝐾 𝑆𝑐 )
	Run 1	4.46
	Run 2	5.97
	Run 3	6.97
	Run 4	6.13

Table 28 -

 28 Group of points defined for cooling analysis.

	Group	Points	Type of config	Number heat source passages	Distance to closest substrate edge
	A	1/3/5/23/25/27	1	1	50
	B	7/10/18/21	1	1	25
	C	8/9/19/20	1	1	75
	D	12/16	1	1	50
	E	14	1	1	100
	F	0/6/22/28	4	1	25
	G	2/4/24/26	2	2	50
	H	11/17	2	2	25
	I	13/15	3	2	75
		3.7.6.1	Configuration of type 1

Table 29 -

 29 Cooling time for the different simulated layers at points P8, P9, P19 and P20 for interlayer temperatures of 150°C, 350°C and 550°C.

			Time to cool down to interlayer temperature (Dwell time) (s)
	Interlayer temperature (ITe)	Layer	Point P8	Point P9	Point P19	Point P20
		3rd	54,47	52,21	53,32	51,25
		6th	76,46	73,41	75,41	72,67
	150°C	10th	109,43 (27,03)	105,32 (22,92)	108,46 (26,06)	104,62 (22,22)
		15th	148,95 (66,55)	143,66 (61,26)	148,18 (65,78)	143,15 (60,75)
		20th	181,86 (99,46)	175,76 (93,36)	181,46 (99,06)	175,56 (93,16)
		3rd	22,58	21,91	22,08	21,27
		6th	34,32	32,82	34,26	32,66
	350°C	10th	49,65	46,87	49,85	47,07
		15th	66,10	62,20	66,57	62,73
		20th	78,94	74,36	79,63	75,16
		3rd	11,71	12,04	11,83	11,15
		6th	19,27	18,74	19,22	18,47
	550°C	10th	28,08	26,39	28,42	26,54
		15th	36,76	34,18	37,34	34,60
		20th	43,19	40,16	43,88	40,78

Table 30 -

 30 Cooling time for the different simulated layers at the point P2, P4, P24 and P26 for interlayer temperatures of 150°C, 350°C and 550°C.

			Time to cool down to interlayer temperature (dwell time) (s)
	Interlayer temperature (ITe)	Layer	Point P2	Point P4	Point P24	Point P26
		3rd	68,73	72,39	91,15 (8,75)	96,46 (14,06)
		6th	90,71 (8,31)	93,66 (11,26)	112,38 (29,99)	116,66 (34,26)
	150°C	10th	124,84 (42,44)	126,92 (44,52)	146,46 (64,06)	149,36 (66,96)
		15th	166,04 (83,44)	167,26 (84,86)	188,46 (106,06)	190,12 (107,72)
		20th	200,18 (117,78)	200,76 (118,36)	223,60 (141,2)	224,45 (142,046)
		3rd	36,84	42,23	62,57	68,24
		6th	47,51	51,41	71,92	77,05
	350°C	10th	63,28	65,69	87,07 (4,67)	90,69 (8,29)
		15th	81,08	82,69 (0,29)	105,16 (22,76)	107,70 (25,31)
		20th	95,02 (12,62)	96,23 (13,83)	119,65 (37,25)	121,63 (39,23)
		3rd	27,89	34,22	55,10	61,23
		6th	32,73	37,97	59,62	64,85
	550°C	10th	40,93	44,54	66,54	71,09
		15th	50,26	52,82	75,50	79,22
		20th	57,47	59,47	82,50 (0,1)	85,83 (3,43)

Table 31 -

 31 Cooling time for the different simulated layers at the point P11 and P17 for interlayer temperatures of 150°C, 350°C and 550°C.

			Time to cooldown to interlayer
			temperature (dwell time) (s)
	Interlayer temperature (ITe)	Layer	Point P11	Point P17
		3rd	87,80 (5,4)	74,34
		6th	111,02 (28,62)	96,48 (14,08)
	150°C	10th	146,83 (64,43)	131,34 (48,94)
		15th	189,75 (107,35)	173,45 (91,05)
		20th	225,20 (142,8)	208,26 (125,86)
		3rd	57,61	45,52
		6th	69,37	55,64
	350°C	10th	86,71 (4,31)	71,48
		15th	106,21 (23,81)	89,61 (7,21)
		20th	121,15 (38,75)	103,88 (21,48)
		3rd	46,52	37,92
		6th	54,18	42,65
	550°C	10th	64,38	50,29
		15th	74,71	59,45
		20th	82,05	66,40

Table 32 -

 32 Cooling time for the different simulated layers at the point P13 and P15 for interlayer temperatures of 150°C, 350°C and 550°C.

			Time to cooldown to interlayer
			temperature (dwell time) (s)
	Interlayer temperature (ITe)	Layer	Point P13	Point P15
		3rd	88,95 (6,55)	100,65 (18,25)
		6th	110,33 (27,93)	120,91 (38,51)
	150°C	10th	143,31 (60,91)	152,76 (70,36)
		15th	183,39 (100,99)	191,88 (109,49)
		20th	216,90 (134,5)	224,76 (142,36)
		3rd	53,18	65,74
		6th	63,22	74,66
	350°C	10th	78,50	88,60 (6,2)
		15th	96,16 (13,76)	105,25 (22,85)
		20th	110,21 (27,81)	118,80 (36,4)
		3rd	41,19	54,96
		6th	46,52	59,55
	550°C	10th	54,63	66,14
		15th	64,05	74,49
		20th	71,25	81,27

Table 33 -

 33 Mechanical properties indicated in the literature and reference values provided by manufacturers.

	Material Process	Sample orientation	Micro-hardness	Hardness	YS (MPa)	UTS (MPa)	EL (%)	Reported by
		CMT			235 -260 HV				[15]
	Duplex stainless steel (DSS) ER2209 wire	CMT	Vertical (Position 1) Vertical (Position 2) Horizontal		Average 266HV Average 270HV	455	717	28	[16]
		WAAM	Horizontal #1	293		510	743	35	[9]

Table 34 -

 34 Production times for each of the walls made and their number of layers.

		Ite	Wall number	Total time of experience	Number of layers
			1	09:31:48	81
		150°C	2	09:52:57	90
			7	10:03:24	91
			3	02:43:28	86
		350°C	5	02:43:03	85
			6	02:42:29	88
			8	01:41:37	96
		550°C	9	01:31:47	95
			10	01:30:32	95
	4.8.	Results of the mechanical tests
	4.8.1. Results of the hardness measurements

Table 35 -

 35 Mechanical performances in quasi-static loading for the vertical samples.

	Vertical samples	Rp0.2 (MPa)	Rm (MPa)	Max Elongation (%)	Uniform Elongation (%)
	Median for ITe = 150°C	452.8	685.1	39.0	24.1
	Median for ITe = 350°C	405.5	687.3	45.6	28.1
	Median for ITe = 550°C	384.9	681.6	51.8	32.2

Table 36 -

 36 Mechanical performances in quasi-static loading for the horizontal sample.

	Horizontal samples	Rp0.2 (MPa)	Rm (MPa)	Max Elongation (%)	Uniform Elongation (%)
	Median for ITe = 150°C	543.7	754.3	26.4	17.7
	Median for ITe = 350°C	500.0	757.1	27.4	17.4
	Median for ITe = 550°C	441.7	752.4	28.3	20.0

Table 37 -

 37 Heat generated by mechanical dissipation per cycle for a stress amplitude of 250 MPa.

	Samples	Ite	Heat (in kJ/m 3 /cycle) for 𝜎 a = 250 MPa
		150°C	13.4
	Vertical	350°C	25.3
		550°C	40.4
		150°C	8.6
	Horizontal	350°C	10.6
		550°C	19.3

Table 38 -

 38 Stress amplitude corresponding to fatigue damage onset.

	Samples	ITe	𝜎 a onset
	Vertical	150°C	159 MPa
		350°C	156 MPa
		550°C	137 MPa
	Horizontal	150°C	170 MPa
		350°C	163 MPa
		550°C

Table 39 -

 39 Times predicted by numerical simulation and ANN model for all vertices of the test case geometry.

			Layer 3	Layer 6	Layer 10	Layer 15	Layer 20
	Vertex 1	ANN N.Sim	42.1 49.8	63.3 73.2	96.9 108.1	137.7 149.1	171.0 182.1
	Vertex 2	ANN N.Sim	63.4 61.8	87.9 85.1	123.7 120.5	165.9 162.4	199.0 195.8
	Vertex 3	ANN N.Sim	41.6 49.7	108.5 62.5	95.5 141.7	135.6 181.7	169.2 214.1
	00Vertex 5	ANN N.Sim	56.7 62.6	78.7 84.2	111.9 117.2	152.0 156.2	185.4 187.8
	Vertex 6	ANN N.Sim	55.2 61.8	76.7 82.9	109.1 115.1	148.4 153.1	181.4 183.8
	Vertex 7	ANN N.Sim	50.5 49.8	73.9 73.7	114.7 111.9	163.4 156.7	197.1 191.9
	Vertex 8	ANN N.Sim	64.8 46.8	89.0 71.2	124.5 108.6	165.9 152.5	198.5 187.4
	Vertex 9	ANN N.Sim	54.7 53.6	75.8 74.4	107.8 106.8	147.1 146.1	180.4 178.2
	Vertex 10	ANN N.Sim	42.6 79.1	64.5 102.4	99.3 138.5	141.6 181.1	176.4 215.1

Table 40 -

 40 Fitting coefficients for the cooling curves extracted on several points of the study case (3 rd layer).

				Coefficient
	Point	a	b	c	d	R²
	0	905.8	-0.2892	552.8	-0.0272	0.9976
	2	421.7	-0.3170	409.4	-0.0204	0.9978
	4	433.4	-0.2920	365.9	-0.0196	0.9966
	6	918.9	-0.2786	524.4	-0.0253	0.9974
	11	786.2	-0.3297	549.6	-0.0252	0.9968
	13	694.1	-0.3974	527	-0.0216	0.9970
	15	710.5	-0.4208	488.8	-0.0213	0.9981
	17	506.5	-0.3090	362.9	-0.0195	0.9955
	22	915.9	-0.2697	563.6	-0.0242	0.9978
	24	756.6	-0.3663	418.1	-0.0225	0.9960
	26	735.5	-0.4307	447.7	-0.0243	0.9972
	28	913.6	-0.2775	557.6	-0.0255	0.9978

  𝑓𝑜𝑟 19 𝑙𝑎𝑦𝑒𝑟𝑠) = 𝐾 𝑆𝑐(𝑙𝑎𝑦𝑒𝑟 3) + 𝐾 𝑆𝑐(𝑙𝑎𝑦𝑒𝑟 4) + 𝐾 𝑆𝑐(𝑙𝑎𝑦𝑒𝑟 5) + ⋯ + 𝐾 𝑆𝑐(𝑙𝑎𝑦𝑒𝑟 18) (33) 𝐾 𝑆𝑐(𝑓𝑜𝑟 18 𝑙𝑎𝑦𝑒𝑟𝑠) = 108.18

	The quality scores is:
	For 150°C
	𝑄 𝑆𝑐(𝑓𝑜𝑟 18 𝑙𝑎𝑦𝑒𝑟𝑠) =	𝑅𝑝0.2 𝑊𝐴𝐴𝑀 𝑅𝑝0.2 𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒	× 10	(35)
	𝑄 𝑆𝑐(150°𝐶) = 8.24
	For 350°C
	𝑄 𝑆𝑐(350°𝐶) = 7.58
	The thermal score for the 18 layers is:
	For 150°C
	𝑇 𝑆𝑐150°𝐶 = 𝑇 𝑆𝑐(𝑙𝑎𝑦𝑒𝑟 3) + 𝑇 𝑆𝑐(𝑙𝑎𝑦𝑒𝑟 4) + 𝑇 𝑆𝑐(𝑙𝑎𝑦𝑒𝑟 5) + ⋯ + 𝑇 𝑆𝑐(𝑙𝑎𝑦𝑒𝑟 18)	(34)
	𝑇 𝑆𝑐150°𝐶 = 98.64
	For 350°C
	𝑇 𝑆𝑐350°𝐶 = 104.82
	For 550°C
	𝑇 𝑆𝑐550°𝐶 = 29.26

Table 41 -

 41 Cooling time for the different simulated layers at points P1, P3 and P5 for interlayer temperatures of 150°C, 350°C and 550°CTime to cool down to interlayer temperature (Dwell time) (s)

	Interlayer temperature	Layer	Point P1	Point P3	Point P5
		3rd	54,96	58,21	54,15
		6th	79,55	84,82 (2,42)	79,20
	150°C	10th	116,02 (33,62)	122,16 (39,76)	115,65 (33,25)
		15th	158,73 (76,33)	164,84 (82,4)	157,85 (75,45)
		20th	193,58 (110,18)	199,31 (116,91)	192,07 (109,67)
		3rd	21,44	20,04	20,24
		6th	34,64	32,75	32,66
	350°C	10th	54,37	54,49	52,24
		15th	74,28	75,73	72,02
		20th	89,00 (6,6)	91,04 (8,64)	86,63 (4,23)
		3rd	12,17	11,45	11,18
		6th	20,30	19,00	18,88
	550°C	10th	30,34	28,33	27,96
		15th	41,36	39,02	38,22
		20th	49,26	48,04	46,22

Table 42 -

 42 Cooling time for the different simulated layers at points P23, P25 and P27 for interlayer temperatures of 150°C, 350°C and 550°CTime to cool down to interlayer temperature (Dwell time) (s)

	Interlayer temperature (ITe)	Layer	Point P23	Point P25	Point P27
		3rd	56,37	73.45	52,87
		6th	90,74 (8,34)	103,17 (20,77)	89,61 (7,21)
	150°C	10th	129,52 (47,12)	142,80 (60,4)	128,85 (46,45)
		15th	174,26 (91,87)	187,18 (104,78)	173,15 (90,75)
		20th	210,93 (128,53)	222,98 (140,58)	209,18 (126,78)
		3rd	29,99	27,49	27,22
		6th	42,87	39,93	40,16
	350°C	10th	66,66	68,10	60,02
		15th	90,30 (7,9)	96,97 (14,57)	87,16 (4,76)
		20th	106,43 (24,03)	114,26 (31,86)	103,62 (21,22)
		3rd	20,87	18,75	17,82
		6th	30,07	27,68	27,07
	550°C	10th	41,30	38,18	38,11
		15th	51,56	47,59	48,16
		20th	62,86	57,84	54,66

Table 43 -

 43 Cooling time for the different simulated layers at points P7, P10, P18 and P21 for interlayer temperatures of 150°C, 350°C and 550°CTime to cool down to interlayer temperature (Dwell time) (s)

	Interlayer temperature (ITe)	Layer	Point P7	Point P10	Point P18	Point P21
		3rd	53,97	49,81	65,07	56,29
		6th	76,98	71,69	90,65 (8,25)	81,88
	150°C	10th	112,49 (30,09)	105,41 (23,01)	128,86 (46,47)	119,27 (36,87)
		15th	154,96 (72,57)	146,02 (63,62)	173,92 (91,53)	163,12 (80,73)
		20th	189,98 (107,58)	179,72 (97,32)	210,80 (128,40)	199,07 (116,67)
		3rd	23,86	20,84	30,99	26,66
		6th	36,85	32,97	47,31	39,41
	350°C	10th	54,97	49,31	69,53	59,52
		15th	74,13	66,62	91,23 (8,83)	80,52
		20th	88,43 (6,03)	79,82	106,90 (24,5)	95,59 (13,19)
		3rd	13,50	11,47	22,28	16,86
		6th	22,53	19,08	31,21	25,97
	550°C	10th	33,24	28,39	44,93	36,86
		15th	43,55	37,69	58,35	47,89
		20th	50,80	44,37	66,41	55,77
	D -Detailed analysis of group D

Table 44 -

 44 Cooling time for the different simulated layers at points P12 and P16 for interlayer temperatures of 150°C, 350°C and 550°C

			Time to cooldown to interlayer temperature (Dwell time) (s)
	Interlayer temperature (ITe)	Layer	Point P12	Point P16
		3rd	67,64	69,99
		6th	92,02 (9,62)	101,03 (18,63)
	150°C	10th	127,93 (45,53)	138,58 (56,18)
		15th	169,90 (87,5)	181,02 (98,62)
		20th	204,26 (121,86)	215,31 (132,91)
		3rd	24,53	24,64
		6th	38,97	36,92
	350°C	10th	61,04	60,22
		15th	81,89	87,53 (5,13)
		20th	97,11 (14,71)	104,29 (21,89)
		3rd	14,57	15,48
		6th	23,00	23,79
	550°C	10th	33,18	33,33
		15th	46,43	43,56
		20th	55,11	50,57

Table 45 -

 45 Cooling time for the different simulated layers at the point P14 for interlayer temperatures of 150°C, 350°C and 550°C

			Time to cooldown to
			interlayer temperature
			(Dwell time) (s)
	Interlayer temperature (ITe)	Layer	Point P14
		3rd	81,54
		6th	107,45 (25,05)
	150°C	10th	144,34 (61,94)
		15th	186,45 (104,05)
		20th	220,42 (138,02)
		3rd	22,92
		6th	34,25
	350°C	10th	64,37
		15th	90,18 (7,78)
		20th	106,98 (24,58)
		3rd	14,27
		6th	22,26
	550°C	10th	31,12
		15th	40,65
		20th	53,40

Table 46 -

 46 Cooling time for the different simulated layers at the point P14 for interlayer temperatures of 150°C, 350°C and 550°CTime to cool down to interlayer temperature (and dwell time) (s)

	Interlayer temperature (ITe)	Layer	Point P0	Point P6	Point P22	Point P28
		3rd	50,00	49,15	54,86	52,33
		6th	74,63	73,13	79,14	76,42
	150°C	10th	111,44 (29,04)	108,883 (26,48)	119,099 (36,7)	115,087 (32,687)
		15th	154,614 (72,21)	150,761 (68,36)	166,177 (83,78)	161,021 (78,62)
		20th	189,788 (107,39)	184,864 (102,46)	204,132 (121,732)	198,092 (115,69)
		3rd	22,34	20,52	31,04	26,92
		6th	35,54	33,48	44,67	40,56
	350°C	10th	53,63	50,80	63,27	58,73
		15th	72,84	68,97	83,72 (1.32)	78,40
		20th	87,235 (4,84)	82,7281 (0,33)	99,412 (17,012)	93,424 (11,02)
		3rd	12,72	11,16	21,84	17,32
		6th	21,43	19,12	31,48	26,87
	550°C	10th	31,88	28,68	43,19	38,33
		15th	41,96	38,42	53,89	48,83
		20th	49,12	45,41	60,52	55,53

19,8 20,1 20,2 20,1 20,1 20,1 20,2 20,1 20,1 20,1 Average speed for all transitions 13,6 13,5 13,5 13,1 13,4 12,3 12,8 13,1 12,7 12,3

Figure 86 -Location of point 15, 26 and 8 in the geometry of the part considered.

Figure 88 -Response surface graphs of Interpass temperature Vs layer from the points 25, 18, 8, 16, 14, 22, 26, 11, 15 from the groups A, B, C, D, E, F, G, H, and I respectively.

Figure 91 -Analysis of point 26 for 150°C temperature -A) Cooling rate in temperature range = [600°C, 950°C]; B) Cooling rate in temperature range = [600°c to 950°C] and cumulative time in temperature range and not exceeded; (C) Comparison of continuous cooling curve diagram of the Limit and actual (Point P26); D) Evolution of time spent in temperature range of [600,950] °C.

Figure 93 -Analysis of point 26 for 350°C temperature -A) Cooling rate in temperature range = [600°C, 950°C]; B) Cooling rate in temperature range = [600°c to 950°C] and cumulative time in temperature range and not exceeded; (C) Comparison of continuous cooling curve diagram of the Limit and actual (Point P26); D) Evolution of time spent in temperature range of [600,950] °C.

Figure 95 -Analysis of point 26 for 350°C temperature -A) Cooling rate in temperature range = [600°C, 950°C]; B) Cooling rate in temperature range = [600°c to 950°C] and cumulative time in temperature range and not exceeded; (C) Comparison of continuous cooling curve diagram of the Limit and actual (Point P26); D) Evolution of time spent in temperature range of [600°C, 950°C]

Figure 144 -3 rd and 20th layer cooling curves for points P1, P3, P5, P23, P25 and P27 with configuration type 1, with 150°C (A)) and 550°C (B)) of interlayer temperature

Figure 147 -3 rd and 20 th layer cooling curve for points P12, P16 with configuration type 1, with 150°C (A) and C)) and 550°C (B) and D)) of interlayer temperature

Acknowledgements

The relationship that translates this behavior is described by the formula: Thus, it can be concluded that if the result of this division is greater than 1 there is pre-heating of point 2 made by the passage of the heat source at point 1. If the result is less than 1 it means that the passage of the heat source through point 1 has no impact on the temperature of point 2.