Jerez Ramón

Mesa

J Antonio

Travieso-Rodr Íguez

Yann Landon

Jordi Llum

À-Fuentes Gilles

Gilles Dessein

Vincent Wagner

Vos

José Ramón Navarro

María Dolores Bermúdez

Ana Eva Jiménez

Giovanni

Eva David

Joan Silvia

Francesc Pozo

Maneles Y Los

Serge Tovar

Anis Hor

Abdallah Bouzid

Study and characterisation of surface integrity modi cation a er ultrasonic vibration-assisted ball burnishing

Keywords: vibration-assisted ball burnishing, surface integrity, surface texture, residual stress, hardness, steel, titanium Je voudrais

is dissertation is an experimental research project into the mechanical e ects of the ultrasonic vibration-assisted ball burnishing process on the surface integrity of surfaces machined through ball-end milling. First, a prototype able to perform the process is designed and characterised.

en, it is tested on AISI 1038 and Ti-6Al-4V surfaces, following an experimental campaign based on a Taguchi orthogonal array.

e preload, number of passes, feed velocity, strategy and initial surface texture are included as factors. Results are analysed in terms of topological characteristics, residual stress and hardness.

e original texture proves to be the most in uential parameter on all outcomes. Texture results show that the vibrations can enhance the roughness and texture results, as long as they have sucient low initial amplitude.

e main conclusion arising from the study are di erent parameter sets that can deliver the best results from the performance of the vibration-assisted ball burnishing process, accoding to a speci c desired optimisation target.

is thesis was wri en in L A T E X. Figures were drawn using Résumé Ce e thèse étudie les e ets du processus de brunissage à bille assisté par vibrations ultrasoniques sur l'intégrité surface des surfaces usinées par fraisage hémisphérique. Compte tenu de l'inexistence d'outils commerciaux capables de réaliser ce processus, l'étude débute par la conception et la caractérisation d'un prototype capable de l'exécuter. Par la suite, une analyse expérimentale est menée, en utilisant le procédé sur les surfaces de deux alliages d'intérêt industriel et aéronautique, AISI 1038 et Ti-6Al-4V. Pour cela, un plan d'expériences est elaboré à base d'une matrice orthogonale Taguchi. Cinq facteurs sont inclus dans le modèle : la précharge, le nombre de passes, la vitesse d'avance, la stratégie de brunissage et la texture initiale de la surface préalablement usinée. Les résultats sont évalués en termes de texturenale, de contrainte résiduelle et de dureté, pour identi er et comprendre l'impact de ce procédé et des paramètres opératoires sur l'intégrité de surface, pour dé nir les meilleurs paramètres à appliquer pour chaque matériau, et pour évaluer les e ets positifs provoqués par l'introduction de vibrations comme moyen d'assistance. Pour cela, la notion d'intégrité de surface est rappelée, voire redé nie dans le cas de la texture de surface. En e et, les critères classiquement utilisés se révèlent inaptes à caractériser les surfaces obtenues, et une nouvelle méthodologie d'analyse des topologies de surface est proposée. Les résultats obtenus suite à la réalisation du plan d'expériences révèlent que la texture initiale est le paramètre prépondérant. Les résultats de la topologie de surface montrent que les vibrations peuvent améliorer la rugosité et la texture des surfaces dans la mesure où létat de surface initial est su samment n. Ensuite, seule la précharge et le nombre de passes in uencent le résultat, avec, dans tous les cas, un couple de valeurs limites à partir desquelles les surfaces sont endommagées. Les résultats des contraintes résiduelles montrent que tous les paramètres in uent sur le résultat nal, en particulier la stratégie de brunissage, avec laquelle la direction préférentielle du tenseur de la contrainte super cielle peut être modi ée. En n, le brunissage montre une modi cation positive de la dureté à des couches d'environ 0,5 mm en appliquant le processus assisté avec vibrations. Nous concluons que les paramètres de processus optimaux sont di érents en fonction de l'objectif d'optimisation, et que certaines combinaisons peuvent être utiles en fonction de ces objectifs.

L

Resumen

Esta tesis es un estudio experimental que versa sobre los efectos del proceso de bru ˜nido con bola asistido por vibraciones ultrasónicas sobre la integridad supercial de super cies mecanizadas mediante fresa hemisférica. Dada la indisponibilidad de herramientas comerciales capaces de efectúar este proceso, el estudio incluye en primer lugar el dise ˜no y caracterización de un prototipo a tal efecto. Posteriormente, se realiza un análisis experimental aplicando el proceso sobre super cies de dos aleaciones de interés industrial y aeronáutico, AISI 1038 y Ti-6Al-4V, siguiendo un dise ˜no de experimentos parcial basado en una matriz ortogonal de Taguchi. Para ello, cinco factores son incluidos en el modelo, a saber: la precarga, el número de pasadas, la velocidad de avance, la estrategia de bru ˜nido, y la amplitud de textura inicial. Los resultados se evalúan en términos de textura, tensiones residuales y dureza, para de nir los mejores parámetros a aplicar para cada material, y con el n de evaluar los efectos positivos provocados por la introducción de las vibraciones como medio de asistencia. Los resultados revelan que la textura inicial es el parámetro que de ne en mayor medida el estado de las super cies nales. Los resultados de textura evidencian que las vibraciones pueden mejorar en mayor medida la textura de las super cies objetivo, siempre que éstas sean su cientemente nas. Además, sólo la precarga y el número de pasadas in uyen en el resultado, encontrando en todo caso un par de valores limítrofe a partir del cual las super cies se ven da ˜nadas. Los resultados de tensiones residuales muestran que todos los parámetros son in uyentes en el resultado nal, especialmente la estrategia de bru ˜nido, con la que puede modi carse la dirección preferencial del tensor de tensiones super cial. Finalmente, el bru ˜nido demuestra modi car la dureza positivamente hasta capas de aproximadamente 0,5 mm, aplicando el proceso asistido con vibraciones. Se concluye que los parámetros óptimos de proceso son diferentes en función del objetivo de optimización, y deben de nirse en base a dos variables de partida: el material objetivo y la textura que éste presenta antes del proceso. e introduction of new materials has been one of the major historical facilitators for the enhancement of industrial products. For instance, a big leap forward in the aerospace manufacturing industry has been the expansion of composites in crucial components and parts such as the fuselage or major control surfaces. However, metallic components shall never be totally replaced, as they provide unique a ributes difcult to be substituted by other materials.

M

List of Tables

Metallic parts are predominantly shaped from raw materials through machining routines. Although chip removal processes are nowadays highly reliable due to the expertise acquired during the last decades, innovation can always be achieved by developing alternative nishing methods to enhance the surface integrity of engineering parts. Indeed, today the term enhancement contemplates additional metrics other than adequate dimensioning or accurate material selection. In that respect, tailor-made surface integrity on workpieces is determinant to optimise product performance, and maximise the longevity and reliability of engineering parts. For in-stance, about 56% of catastrophic failure in turbine blades are caused by cracks initiated in positively stressed machined surfaces under high-frequency fatigue regimes, and can be prevented with adequate nishing treatments a er machining, according to Prevéy et al. (2002) [113]. In this eld, ball burnishing has proved to deliver better results in terms of surface roughness, residual stress and hardness of objective surfaces, when compared to other processes long integrated in the manufacturing industry such as laser shock peening (Altenberger et al., 2012) [2], electropolishing or shot peening (Shepard et al., 2004) [129]. us the necessity to increase the knowledge related to it. Surface integrity management is remarkably important when special alloys are used to manufacture relevant parts. Advanced materials such as titanium or nickel alloys pose a high di culty of surface integrity preservation a er machining, as note numerous authors such as Ulutan et al. (2011) [155]. Consequently, thorough postprocessing techniques are required to rectify the surface integrity. Manufacturing innovation through nishing processes development is not in contradiction with new material application. Much on the contrary, it can contribute to develop a mainstream of manufacturing technology enhancement.

One typical engineering surface that exempli es the importance of surface integrity control are typically found in the transportation industry, formed by complex forms, conformed by juxtaposed curved surfaces. We can think about turbine blades or landing gears, but also moulds and dies for upse ing operations. is kind of parts are o en manufactured through 3 or 5 axis machining with the aid of successive adjacent passes of hemispherical tools (Figure 1.1). Whereas this ball-end milling strategy allows to achieve complex surfaces by following the desired shape through NC interpolations generated by a CAM, it also has deep constraints. Guillemot (2010) [49] highlighted the importance of the tilt angle of the hemispherical tool during machining to guarantee a good surface integrity. However, these scienti c recommendations are not taken into account by many manufacturers, who o en use automatised CAM systems in which hemispherical milling is performed perpendicular to the surface, i.e. with tilt angle equal to zero. at type of machining execution is very o en forced by the context de ned by the only availability of 3-axis machines with no possibility of adjusting a speci c tilt angle for the tool, thus generating a detrimental surface integrity.

In this context, ball burnishing can contribute to improve the described surfaces in industrial parts. e process is known for a aining a comprehensive surface im- provement in terms of texture, residual stress and hardness, as well as for being easily manoeuvrable from a procedural point of view. Spring-based ball burnishing tools are easily a achable to NC machines through custom commercial holders, simplifying the whole manufacturing system and equipment. at means that ball burnishing tools can be used at the same NC machines were previous machining has been performed, hence the reduction of handling and processing times, as well as an increase in the automation easiness. Burnishing tools, on the other hand, could be likely to be implemented on advanced automated systems such as robotic arms.

e presented pros a ributed to ball burnishing makes it an interesting option to consider as an advanced nishing process for today's industry. On the other hand, the phenomenon of process assistance is today a highly extended strategy in manufacturing engineering innovation systems [14], since it allows to obtain emergent advantages from operations that are already totally integrated in manufacturing workshops. Taking this fact into account, it is worth questioning whether the ball burnishing operation can be enhanced by vibration-assistance, in search of emergent e ects on industrial materials. In this thesis, the incorporation of ultrasonic vibrations is proposed to improve the ball burnishing process. e evidence that this combination can lead to interesting results is based on the physical phenomenon of acoustoplasticity, that is, the reduction of the quasi-static stress required to deform a material by the simultaneous propagation of waves inside it, while causing a residual hardening e ect. Isolated results performed by other researchers have lead to think that this combina-tion can be positive, as shall be presented in the state-of-the-art chapter [START_REF]X-ray di raction spectrum showing a di raction peak at 2𝜃 𝜓 position, with regards to the spectrum registered for the reference material[END_REF]. As no comprehensive and consistent research has been developed previously, the following subsection presents the contributions expected to be delivered by this dissertation.

Research contributions

In this dissertation, a new nishing process resulting from modifying the ball burnishing process is executed on ball-end milled at surfaces. At sight of the previously described surfaces, applying experimental design on at surfaces means that we are dealing with surface states that are not necessarily realistic. However, they are obtained through a mastered machining strategy that allows to excerpt control on the surface topology by varying the peaks and amplitudes of the surface texture. On the other hand, they can be considered as preliminary results that shall eventually serve to characterise the process on curved more realistic surfaces. e modi cation of the ball burnishing process is to be carried out by overlapping an oscillating force on the static burnishing preload, which allows to transmit an ultrasonic wave inside the material that makes it easier to deform plastically. e combination of ball burnishing with the acoustoplastic e ect referred in this dissertation as vibration-assisted ball burnishing (VABB), in contrast to the non-vibration assisted process (NVABB), that is, conventional ball burnishing. e physical basis of the process enhancement is the acoustoplastic or Blaha e ect [7]. is e ect shows that acoustic and ultrasonic waves propagated inside a material while it is being deformed, reduce the quasi-static stress required to achieve a certain level of strain. is sort of metal so ening has a transient e ect, as is only present during the transmission of the wave inside the metal. In other words, when that irradiation stops, most materials show a residual hardening e ect. As a process based on plastic deformation, ball burnishing is expected to be a recipient of enhancement through acoustoplasticity, which leads to enunciate the main hypothesis posed for this thesis: e application of acoustoplasticity to enhance the ball burnishing operation leads to a technically feasible technology enabling the successful enhancement of the surface integrity of milled surfaces from topological, mechanical and metallurgical points of view.

To test that hypothesis, this dissertation must tackle with diverse scienti c issues, that are due to be answered by a set of well-se led and properly formulated questions, as follows:

1. To what extent can the surface integrity of ball-end milled surfaces be enhanced by the introduction of the acoustoplastic e ect in the ball burnishing operation?

2. Is surface texture essentially modi ed by the vibration-assisted ball burnishing process? Are 𝑅 𝑎 and 𝑅 𝑡 , as the classical surface roughness parameters, enough to describe that change?

3. What are the e ects of the vibration-assisted ball burnishing process on the surface and sub-surface layers of the material from a mechanical and metallurgical perspective?

4. What is the impact of the original surface state on the results? At sight of the described scienti c issues, and due to the lack of comprehensive results of the VABB process on surface integrity, this dissertation adopts fundamentally an experimental scope that shall allow to provide comprehensive data about its results.

Furthermore, to ful l the objectives of this dissertation, some technical issues can also be identi ed, and must be tackled to succeed in assessing the e ects of the VABB process, and compare it to the non-vibration-assisted one. ese technical issues can be described as follows:

1. No VABB tool is currently commercially available. For that reason, an innovative ultrasonic VABB prototype must be designed, protected by a patent, manufactured and characterised.

2. During the characterisation process, special instrumentation systems shall be required to sample and reconstruct the ultrasonic signals implicated in the process.

This dissertation in brief

e reader shall nd in this text an extensive analysis of bibliographical studies and theoretical approaches that justify the application of VABB, along with extensive ex-CHAPTER 1. INTRODUCTION perimental results obtained from the application of the process on steel and titanium surfaces. e chapters of which it is composed are structured as follows.

Chapter 2 presents a review of bibliographical references that tackle with the issues at stake in this dissertation. ree main parts can be di erentiated. e rst one presents a de nition of the ball burnishing process and di erent tooling con gurations. Secondly, the e ects of the ball burnishing process on the surface integrity of di erent materials is presented. e third section of this chapter focuses on explaining acoustoplasticity mechanisms as proposed by some authors, and the few references dealing with it to assist the ball burnishing process.

As no VABB prototype is available commercially, it must be designed, characterised and tested. Chapter 3 shows all activities undertaken to this aim. Piezoelectricity is presented as the driver of vibration transmission on which the functioning of the prototype is based. A mechanical construction composed of three units is proposed in this chapter, and materialised in a prototype which is tested by applying acoustic emission, dynamometric measurements and motion track. ese techniques ultimately deliver the characteristics of the vibratory force transmi ed by the piezoelectric module installed inside the tool casing.

e prototype is then tested on Ti-6Al-4V and AISI 1038 surfaces. ese materials have been chosen due to their industrial interest for applications on workpieces expected to function in highly demanding environments, such as fatigue regimes, thus requiring thorough nishing surface states. Speci cally, the rst one is known for its generalised presence in various aeronautical workpieces, whereas the AISI founds extended applications in gears, axes or power shovels. With that aim, an experimental design based on Taguchi orthogonal arrays is proposed, as explained in Chapter 4.

at chapter also includes the set of techniques which are deployed to evaluate the surface integrity results on both materials. Specially interesting is the proposal of texture measurement through a comprehensive set of three-dimensional parameters, which has no precedents in the analysis of ball burnishing results.

Finally, the experimental results are compiled and explained in chapter 5. First, topological results are shown for both materials. e incorporation of surface parameters, in contrast to the two-dimensional parameters traditionally used to characterise burnished surface, is introduced. en, the residual stress generated on the di erent VABB and NVABB patches is analysed. Finally, mechanical parameters describing the surface are presented to ful l a comprehensive surface integrity characterisation of the VABB e ects, including both metallography analysis and deep hardness measurement.

e knowledge developed along the referred chapters leads to formulate nal conclusions and expected future works at the end of the text, which also includes appendices with relevant data not included in the report.

2

State of the art is chapter includes the results emerging from an extensive bibliographical research which tackles with di erent burnishing references. Burnishing itself is a generic process that comprises innumerable versions de ned by the contextual conditions that govern its execution, such as the geometry and construction of the burnishing tool.

e rst section of this chapter is a descriptive one, exposing the di erent burnishing versions by analysing di erent burnishing tools and the parameters governing the operation.

e second section in this chapter establishes a de nition of surface integrity, and includes the results found by ball burnishing on di erent materials. e rst descriptive references found for the process were published in the 80's, and focus on steel, aluminium and copper alloys. e following years brought a breakthrough of the burnishing knowledge through the exploration of further similar alloys, and the incorporation of stainless steel to the system. Still today, the lack of results on the burnishing operation performed on titanium alloys or superalloys leaves a vast exploration territory for new research. e VABB operation is de ned and introduced in next section. e Blaha e ect, which justi es its e ectiveness, also known as acoustoplasticity, is presented along with a historical review of di erent explanations proposed by di erent authors. Last CHAPTER 2. STATE OF THE ART of all, the scarce references found related to the VABB process are presented.

General aspects of the burnishing operation

Burnishing is a general term that referes to a surface nishing operation based on local plastic deformation a ained through the action of an indenter with a cylindrical or spherical geometry, which rolls over the objective surface while transmi ing a preload [103]. Plastic deformation during the feed motion is successfully performed as a result of frictional engagement of the indenter and the surface irregularities. e process is performed along successive adjacent passes with the aim of covering the whole target surface, as shown schematically in Figure 2.1. During the movement of the tool, the indenter makes contact with the peaks of the texture irregularities. At rst, the peak material is deformed elastically, but the extended contact and deformation leads to the nal plasti cation of the material, and its residual strain that is translated into a holistic modi cation of the surface. Indeed, this process modies the surface integrity of the workpiece, as e ects on surface topography, hardness, and residual stresses of subsurface layers are signi cant [64]. Conceptually, the plasti cation process is gradual. e instantaneous contact area between the indenter and the surface can be described as a tear-shaped region, covering the wide range of strain states, starting from the elastic deformation in the engagement zone, until the super nishing zone at the points with longer contact with the indenter.

is mechanism provides the general roughness improvement along the burnishing direction [START_REF]E ects of ball burnishing parameters on surface nish-a literature survey and discussion[END_REF]. Surface roughness is a fundamental feature of the sur-2.1. GENERAL ASPECTS OF THE BURNISHING OPERATION face integrity of the part, not solely for outer aspect ma ers, but also for its general performance. Poor surface nish disables geometric tolerances, and it a ects wear resistance, fatigue life, and load-carrying capacity.

On the other hand, as the instantaneous application of the burnishing force is local, the topological changes are hardly larger than 10 µm, so that general geometry of the part is not changed. erefore, form errors and the general shape of the part are not signi cantly recti ed through burnishing.

is makes the process suitable for the nishing of parts manufactured until their nal dimensions, and is especially interesting in manufacturing contexts where high precision results are required. It is the case, for instance, of mould manufacturing, lleted bearing components, or curved surfaces.

Burnishing can be found in the bibliography a er diverse designations. Practically, the main di erence among the di erent processes based on di erent tools is the objective that justi es the execution of the process. Deep Rolling (DR) is used to refer to the execution of ball or roller burnishing with the aim of inducing high compressive residual stresses and increasing cold work on the part surface. When the sought objective is decreasing the surface roughness of the objective part, the process is generally denoted as Low Plasticity Burnishing (LPB) [2].

From a systemic point of view, burnishing can be de ned as a set of interrelated resources, whose function is to perform the nishing of an objective workpiece, and whose combination de ne a singular burnishing system. Under this perspective, Figure 2.2 shows a shbone diagram of the di erent aspects which de ne burnishing systems. Items belonging to the tooling system categories allow to establish a certain classi cation of di erent burnishing operations. at is, by varying the shape of the indenter, the force regulation method, or the mechanical composition of a tool to be a ached to di erent machines, diverse burnishing operations are feasible.

Burnishing tooling is therefore highly important when the implementation of a speci c burnishing operation must be carried out. It plays a fundamental role in the de nition of the burnishing system, as it enables the application of the process on one or several speci c machines, and allows to regulate and control most of the burnishing parameters governing the process, and that determine the burnishing results. e next subsections present di erent burnishing tooling con gurations, as a rst step to decide the general features of the design of the VABB tool.

An overview of burnishing tooling

e scienti c bibliography shows a great variety of burnishing tool designs. In general, a burnishing tool must be conceived to ful l the following requirements:

• It must be a achable to a speci c machine tool where the process must be developed. • It must guarantee mechanical engagement between the indenter and the material, allowing the free movement of the former while maintaining its mechanical integrity. • It must bring into play the whole of the desired burnishing parameters, especially preload, while ensuring accessibility to the target surface.

Basic tools utilised originally in general applications of the burnishing technique were applied on simple geometries such as bores and sha s, hydraulic cylinders, pistons for hydraulic systems, or llets. Classical burnishing tool-workpiece con gurations can be consulted at Figure 2.3.

e lack of automation and handling limitations presented by conventional machines made di cult to nish more complex parts. Later, the generalisation of NC machines in manufacturing workshops, and the emergence of more simple xation systems, enabled new designs. e technique was subsequently embraced for more complex geometries such as the nishing of free-form parts (e.g. moulds), and contributed to its expansion [START_REF]Computer-integrated ball burnishing of a plastic-injectionmould cavity insert[END_REF]132]. e geometry of the indenter is one of the main features de ning a burnishing tool. Roller tools have been classically more widespread, for its higher simplicity in terms of preparatory activities and force adjustment [32,33,90,92]. Regarding the roller geometry, dimensions and pro les are also diverse. Rollers with higher cylindrical land would allow the execution of the process by selecting higher feeds, as the contact surface between the tool and the part is higher. However, rollers lack of the versatility that balls o er to burnish, since they are ine cient to treat complex surfaces, extensively found in the advanced manufacturing industry.

However, roller burnishing tools are also known for their lower e ectiveness in hardness improvement, and require higher forces to obtain the same improvements as with sphere shape indenters. Consequently, ball burnishing can be presented as a CHAPTER 2. STATE OF THE ART more advantageous process in terms of absolute results. Comparative research has proved that ball burnishing is able to achieve signi cantly lower surface roughness and higher hardness with lower forces in materials such as AISI 1335 steel [50], and non-ferrous alloys [START_REF]e e ects of ball-and roller-burnishing on the surface roughness and hardness of some non-ferrous metals[END_REF]. For that reason, the tool that shall be designed in this dissertation shall be based on a ball-burnishing con guration.

Special burnishing tool configurations

e development of tools with speci c con gurations is one of the innovative approaches to burnishing development (Figure 2.4). Multi-roller tools can be found at several bibliographical references. amizhmanii et al. (2009) [START_REF]An experimental work on multi-roller burnishing process on di cult to cut material-titanium alloy[END_REF] tested a frontal multiroller tool on TA6V speciments, and Tadic et al. (2013) [START_REF]Using specially designed high-sti ness burnishing tool to achieve high-quality surface nish[END_REF] designed and successfully tested a multiroller tool on aluminium parts. Multi-ball tools can also be found at Gharbi et al. (2010) [START_REF]Adjustable roller tool[END_REF] and Tadic et al. (2016) [START_REF]Using a high-sti ness burnishing tool for increased dimensional and geometrical accuracies of openings[END_REF]. In general, multiindenter tools show a remarkable stability of the process due to higher surface contact of the burnishing indenters and the workpiece, although the range of objective geometries is not so wide. More complex con gurations have been also conceived and prototyped. El-Axir & Ibrahim (2005) [28] designed and mounted a multi-ball tool embedded in a centre rest, being able to burnish on a lathe through a steadier regime, and showing be er results in terms on nal roundness, compared to conventional burnishing. Okada et al. (2015) [107] designed a roller tool able to adapt at will the burnishing angle, and a er testing it on ASTM 2017 aluminium and ASTM 1055 carbon steel specimens, concluded that burnishing at a 45 degrees angle is the optimum process in terms of surface roughness. Integrating cu ing tools and nishing burnishing tools on one single piece has also been explored by Segawa et al. [START_REF]Development of a new tool to generate compressive residual stress within a machined surface[END_REF].

General description of ball burnishing parameters

In manufacturing engineering, controlling the parameters of any process is necessary to comply with design speci cations, guarantee the repeatability of results, and their reproducibility from a small-scale research context to a real manufacturing workshop. Burnishing is no exception, as proves the preponderance of bibliographical references which focus on testing di erent levels of burnishing parameters on a great variety of objective materials. is subsection explains the di erent parameters that govern the Center rest multi-ball tool [28] c. Multi-roller tool [START_REF]Using specially designed high-sti ness burnishing tool to achieve high-quality surface nish[END_REF] d. Multi-ball tool [START_REF]Adjustable roller tool[END_REF] e. Adjustable roller tool [107] f. Multi-ball tool [START_REF]Using a high-sti ness burnishing tool for increased dimensional and geometrical accuracies of openings[END_REF] operation.

2.1.2.1 Plastic strain parameters: burnishing force and number of passes e most in uential parameter on ball burnishing results is the burnishing force, that is, the normal force transmi ed by the burnishing tool to the workpiece surface in order to deform plastically its microtopology.

e speci c pressure applied on the workpiece to achieve that plastic deformation is the direct result of this force, and must exceed the yield point of the material to succeed in achieving good results. It can be therefore considered as the essential physical driver of plastic strain. e constructive con guration of the burnishing tool de nes the way through which the force is controlled and transmi ed to the workpiece. In other words, according to the technical solution adopted to apply the force on the surface through the ball on the surface, the force is controlled di erently. From this point of view, mainly three kind of tool can be distinguished, as can be observed in Figure 2.5. ese three solutions are explained below. Depth of penetration is solution appears to be the original force regulation method, as is found in all the oldest references (Figure 2.5.a).

e tools based on this force transmission principle are ended by a spherical shape in which the ball is housed, allowing its free rolling. In order to regulate the force, the tool tip is pressed onto the target surface. e force is exerted by screwing the supporting rod in which the burnishing ball is embedded. e linear length along which the screw is tightened along the supporting rod is called depth of penetration ℎ 𝑝 . e burnishing force or preload, 𝐹 𝑝 , derived from this mechanism can be therefore deduced from the approximate solution of slipping of a rigid sphere over a plastic semi-plane, as shown in Eq. 2. 1 [103].

𝐹 𝑝 = 𝜋 4 ℎ 𝑝 𝐻𝑉 𝑅 (2.1)
where 𝐻𝑉 is the Vickers hardness of the material,and 𝑅 is the indenter radius.

e fact that the preload is calculated through this indirect method does not allow its accurate regulation. erefore, the actual values of the burnishing force applied during the burnishing process can only be known if the machine is equipped with a force measuring device. Consequently, this solution is advisable to burnish complicated geometries, which do not allow the application of other pressing systems [START_REF]Improvements in out-ofroundness and microhardness of inner surfaces by internal ball burnishing process[END_REF].

Hydrostatic pressure

ese kind of tools o en use a ceramic or chrome-steel ball embedded inside a support piece at the tip, which is connected to an inner channel e tool is fed by an auxiliary pump of the burnishing machine, which propels lubricant uid through that channel.

e uid reaches the ball bed, and supports it due to the excerpted hydrostatic pressure. e lubricant acts therefore as a hydrostatic bearing, allowing the ball to roll freely. e burnishing pressure is regulated by adjusting the hydrostatic pressure of the lubricant, as a result of simple equilibrium of forces along the longitudinal axis of the tool. Due to the constructive solution, these tools cannot be applied on surfaces showing a degree higher than ±28 ○ . Celaya et al.

[16] estimated the burnishing force, 𝑃 𝑏 , by deducing it from the pressure delivered by the pump (Eq. 2.2), considering a 89% e ciency according to the results shown by a FEM.

𝑃 𝑏 = 0.89 𝜋 4 𝐷 2 𝑝 ℎ (2.2)
where 𝐷 is the ball diameter, and 𝑝 ℎ is the hydrostatic pressure delivered by the pump.

Calibrated spring A linear spring is lodged inside this kind of tools, and accounts for the normal force regulation (Figure 2.5.c). A er the ball contacts the target surface, the burnishing force increases as the spring is progressively compressed. e total axial force is ruled by Hooke's law (Eq. 2.3). e tool can be calibrated by knowing the sti ness of the spring, so that the burnishing force can be easily controlled by managing the 𝑧 coordinate with the NC programme managing the burnishing operation, provided that the origin o set on the workpiece surface has been accurately determined. For that reason, the force regulated in this kind of tools can speci cally be referred to as preload, 𝐹 𝑝 . rough these tools, the force regulation can be easily integrated in the process inside the NC code.

𝐹 𝑝 = 𝑘 𝛥𝑧 (2.3)
where 𝐹 𝑝 is the axial preload transmi ed by the spring, 𝑘 is the elastic constant of the tool due to the spring, 𝛥𝑧 is the compressed length of the spring, being the result of the total compression executed by the NC and the microvariation due to the translation of the ball along the roughness pro le.

Despite the capability of controlling the nominal force applied during the burnishing process, its actual value varies during its execution. is is mainly because of the friction present during the feed movement of the tool over the surface, as well as su ciently prominent surface irregularities that oppose that movement. e con-sequence is that tangential components of the burnishing force appear during the execution of the process, diminishing the strain e ect, as observed by Lye & Leong (1990) [91]. Figure 2.6 shows both tangential and normal burnishing forces, exemplifying the described e ect. e burnishing force is not the only parameter de ning the degree of plastic strain a er burnishing. It is also dependent on the number of passes, which quanti es the number of overlay passes performed over the burnished surface.

is parameter is also a productivity parameter, as more passes require more processing time, but its higher relevance on the strain is undeniable.

Generally, the increase of the burnishing force and number of passes derive in a higher level of plastic deformation, so that both parameters are equivalent in terms of burnishing e ectiveness. Both of them must be chosen correctly, as excessive cold hardening through plastic strain can also derive in detrimental results, as shall be further analysed in following sections of this chapter.

Productivity parameters: feed and lateral pass width

Productivity parameters a ect the total time required to burnish a surface. References dealing with burnishing from a productivity point of view are scarce. It can be justi ed by the fact that these productivity parameters have not proved to positively a ect the potential enhancement of burnishing as a nishing process. e feed parameter refers to the linear speed at which the tool is displaced, which is usually programmed inside the NC code implemented on the machine tool where the process is applied. A study by Rodríguez et al. (2012) [START_REF] L ´ C | Surface improvement of sha s by the deep ball-burnishing technique[END_REF] proved that no in uence is observed in terms of surface roughness, but the lack of further evidence leads to think that a certain in uence could eventually be detected.

e second productivity parameter is the lateral pass width, that is, the o set length between two adjacent burnishing passes. Most authors do not pay a ention to x a speci c value for this parameter, and take conservative values to guarantee the a ectation of the whole surface. Obviously, although this is a compromise solution to achieve uniform results, the use of a too small lateral pass width increases the number of passes required to treat a surface, thus increasing burnishing time and harnessing the overall productivity.

In this regards, the works of Gómez-Gras et al. (2015) [44] concluded that to minimise burnishing time without harnessing the burnishing results, a standard lateral pass width could be established in function of the burnishing force, the type of burnishing which is applied (vibration-assisted or not), and the objective material. e la er is introduced in the model through its self-hardening coe cient. In e ect, materials experiencing high strain hardening tend to form pile-ups at the limits of the plastically deformed area [START_REF]In uence of penetration depth and mechanical properties on contact radius determination for spherical indentation[END_REF].

ey conclude that the optimal lateral pass width should be included inside an interval (0.5 𝑙, 𝑙⌋, being 𝑙 the width of a burnishing line performed by a certain set of parameters.

e minimum limit of the interval was established by considering that smaller values would lead to redundant passes during the burnishing operation, with the consequent detrimental e ect on productivity. On the other hand, the maximum boundary was established as a means of limiting the o set between passes, which would leave non-deformed material on the surface, diminishing the burnishing e ects. Consequently, these values can be taken into account as a means of optimising the burnishing time without causing any harm on the surface nishing.

Experimental results on surface integrity a er

ball burnishing e e ect of ball burnishing a ects exclusively surface and near-surface layers of a workpiece, as the bulk material is not modi ed by it. Consequently, burnishing results should be studied and quanti ed from a comprehensive scope by considering di erent surface parameters. In this regard, the concept of surface integrity can be presented as an adequate contextual reference to characterise the e ects of the VABB process.

Surfaces confer unique properties to engineering parts besides their outward appearance.

e realisation that minor and catastrophic failures of engineering parts cannot always be explained by detrimental properties of the bulk material, but they are the consequence of the inadequacy of the surface integrity of the part itself, was late embraced by engineers. Until this statement was acknowledged, numerous mechanical failures were being erroneously identi ed as uncontrollable, and consequently unmanaged. For instance, fatigue failure identi ed and characterised experimentally by Wöhler in the end of the 19th century, was not modelled until Irwin succeeded in the 50's to relate it to surface roughness by means of a stress concentration factor, 𝐾 𝐼 , as follows:

𝐾 𝐼 = 𝜎 𝑛𝑜𝑚 𝑌 ⌋ 𝜋𝑎 (2.4)
where 𝜎 𝑛𝑜𝑚 is the maximum stress, 𝑌 is a geometrical factor, and 𝑎 is the crack's length.

As 𝑌 can be linked to surface roughness, Irwin acknowledged in publishing this model the link between surface integrity and fatigue failure. e same as fatigue, today, we know that, other phenomena such as corrosion, contact mechanics or wear depend upon the surface state of the part, and not on the bulk material. Surface engineering was born as an extended branch of surface science, to characterise the relation between the design of surfaces and their functionality and cost e ectiveness [20]. e ASTM Handbook de nes it as the treatment of surface and near-surface regions of a material to provide unique properties that enable it to perform functions that are distinct from the ones delivered by the bulk material [36]. In this context, surface integrity can be described as the group of parameters that describe the comprehensive state of a nished surface. is de nition exhibits that surface integrity can be described as an inherent consequence of materials processing techniques and parameters, as has been proved by numerous authors [35,110,155,156].

Following the same principle, ball burnishing has been treated in the bibliography as an e ective method to modify surface integrity. Historical ball burnishing references deal mainly with steel, aluminium and cuprous alloys.

is is logical if one thinks of the kind of applications for which burnishing was originally applied -the nishing of sha s, moulds, dies and tubes. e visual inspection of that table leads to the conclusion that the majority of ball burnishing references have focused on lathe burnishing. Although a certain correlation between lathe and milling burnishing can be found -for instance, lateral pass width in mill burnishing is the feed in lathe burnishing-, the kinematics of both processes are quite di erent, and should be treated as two independent processes. e tool to be designed in this thesis shall be used in a milling machine. erefore, this state of the art shall focus mainly on this type of setup conditions, whereas lathe burnishing is referred only in speci c cases where it is u erly necessary. Lathe references are also omi ed if possible due to the limitations of lathe burnishing to treat complex surface geometries, such as warped surfaces, un ed for the potential applications of the system which is being considered in this dissertation.

On the other hand, Table 2.2 gathers those references that focus on the study of ball burnishing on stainless steel, titanium and nickel-based alloys. ese are conspicuously scarcer than the ones represented above, for two main reasons. Firstly, the need of developing special nishing processes for advanced materials in the industry is a relatively recent topic. Secondly, these materials are applied in the manufacturing of special parts, expected to function in highly demanding environments. erefore, most of these studies tackle with the comparison of ball burnishing with other nishing processes that are already validated at an industrial level, such as shot peening, which exceeds the object of this dissertation.

At sight of the previous tables, it can be concluded that spring-based tools have been scarcely studied in the bibliography, and that there is an evident lack of information about ball burnishing of titanium alloys. Along the next subsections, results are classi ed in function of geometrical, mechanical and metallurgical parameters a er ball burnishing. All materials are included in the analysis.

Geometrical parameters: surface roughness and texture

e presence of irregularities on a surface is the inherent result of the transformation process to which any material is subjected a er a manufacturing operation. e DIN 4760 standard di erentiates between macrogeometric -high scale deviations and waviness-and microgeometric deviations -cracks, grooves, texture or roughness pro les-on a surface. Engineering applications require the limitation of macrogeometric topological irregularities to guarantee, for example, the interchangeability of parts and the assembly of di erent components. On the other hand, many authors [START_REF]Detailed surface roughness characterization of engineering surfaces undergoing tribological testing leading to scu ng[END_REF].

Controlling surface geometry means, in practice, quantifying its features through di erent descriptors. Texture and roughness measurement methods are based on the idea of modelling the surface as a mathematical function formed by height points, and the calculation of parameters based on this function to make that data pro table for decision making. One of the original methods based on this idea was proposed by Abbo & Firestone (1933) [1]. ey proposed transforming the heights of a surface into a bearing-area curve representing its as an accumulated function. On that representation, three parameters which described the bearing area and lubricant retention capabilities of the surface were calculated. e evolution of height registration equipments to devices based on high-sensitivity diamond styli, supposed a considerable evolution in texture assessment. In the second half of the 20th century, pro lometer diamond tips became actuated by a motor, through which they could automatically traverse the target surface along a line that shall represent the whole surface. is leap forward allowed the generalisation of an automatic surface characterisation method, and new standards de ning two-CHAPTER 2. STATE OF THE ART dimensional descriptors of the surface were published.

e pro le method de ned in ISO 4287 is the most generalised one. It establishes a methodology to lter and arranged the acquired height dataset with respect to a mean line obtained my least squares deviation. On that pro le, di erent two-dimensional R parameters can be calculated to de ne the surface features based on the registered dataset [START_REF]Characterization of surface roughness[END_REF]. ese parameters can also be associated to speci c processes [105], and are a good indicator to trace the manufacturing history of a surface [162]. e literature shows extensive work which interpret the roughness results through the R parameter set [130,138], and the interrelation among some of their parameters as skewness or kurtosis [46,99].

Despite the diversity of parameters in that R set, the average surface roughness, 𝑅 𝑎 , is the most extended one to represent surface texture, as it o ers an average indicator of the overall surface topological state. Originally, it could be easily calculated by primitive pro lometer devices with low computing capacity. It is established in the ISO 1302 as the reference value to represent roughness in technical drawings. As it happens, 𝑅 𝑎 has been the most extensively chosen parameter to evaluate ball burnishing results, as show, for instance, the works of Shiou et al. on di erent mould steels [131][132][133]. ey concluded that the force and the ball diameter had a high inuence on burnishing results. Other researchers, such as Loh et al. (1989) [START_REF]Optimisation of the surface nish produced by ball burnishing[END_REF], have evaluated the ball burnishing results on a AISI 1045 alloy in terms of 𝑅 𝑡 . In all cases, the inverse proportionality between burnishing force and roughness parameters is con rmed.

Adopting a di erent scope, the in uence of the target surface shape on the topological e ects of ball burnishing have also been studied. Travieso-Rodríguez et al. (2011) [START_REF] G ´ R | Improving the surface nish of concave and convex surfaces using a ball burnishing process[END_REF] compared the in uence of di erent curvature radius on concave and convex parts made of AISI 1038 and EN AW 2017 aluminium. Both the 𝑅 𝑎 and 𝑅 𝑡 improvement along and perpendicular to the burnishing direction were higher as the radius of curvature increased. Curved surfaces have also been burnished by López de la Calle et al (2011) [88]. A 5-axis machine was used, by following two di erent strategies: continuous burnishing and patch strategy. Both of them lead to 𝑅 𝑎 decrease, although the continuous proved to be more e ective while being less productive due to the limited feed of the rotary axes of the machine.

Studies have also proved that there is a threshold preload level for which roughness is actually harmed. Klocke et al. In uence of ball diameter [START_REF]Surface integrity of Inconel 718 by ball burnishing[END_REF] .

proved to be detrimental to surface roughness. Furthermore, the surface exhibited roughness increase when the ball diameter was increased from 6 to 13 mm. erefore, the burnishing force and the diameter of the ball are limited by threshold values that should not be surpassed to prevent harmful e ects on the surface. Sequera (2014) [START_REF]Surface integrity of Inconel 718 by ball burnishing[END_REF] rati ed the same results for the burnishing pressure, although did not nd a detrimental in uence of the ball diameter (Figures 2.7.c and 2.7.d).

In all the evaluated cases, the topological assessment of ball burnishing is based on the evaluation of a limited number of parameters calculated on linear pro les, especially 𝑅 𝑎 and 𝑅 𝑡 . However, the limitation of these 2D parameters to represent a 3D surface must not be neglected, as surfaces actually interact in the three directions of the space [START_REF]Comprehensive study of parameters for characterizing three-dimensional surface topography II: Statistical properties of parameter variation[END_REF]. Although nowadays the calculation potential of computers and equip-ment are highly advanced, the surface topology assessment methods are the heritage of old-fashioned two-dimensional height analysis marked by low computation capability which is no longer limiting factor in presently available systems. In fact, many authors have highlighted that the only reason why 𝑅 𝑎 parameter exists is because of the original computing limitations of roughness measurement devices [116], as it lacks of statistical meaning, and is insensitive to re ect changes in the shape of the pro le [130]. As an alternative, Sherrington et al. (1987) proposed 𝑅 𝑞 as an alternative to 𝑅 𝑎 . While still being a two-dimensional parameter, its statistical meaning as the root mean square of the height pro le, and its capability to describe any possible redistribution of material from one side of the mean line to the other. It is remarkable that no reference has been found considering other two-dimensional parameters, such as 𝑊 or 𝑃 , to analyse burnishing results. Nevertheless, could they provide further information about the e ects of the process? All these reasons lead to conclude that the parameters that have been traditionally used to describe surface topography can be upgraded to obtain further information about ball burnished surfaces. A new methodology shall be proposed to tackle with this objective in the following chapters.

Metallurgical parameters: hardness and metallography

e metallurgical state of a surface can be described by numerous factors, such as phase change a er a surface treatment, or the presence of a phase gradient towards deeper layers.

ese parameters are of high importance to de ne surface integrity, as they are the result of the combination of mechanical or thermal mechanisms. As ball burnishing is not a thermal process, microstructure change is not due to occur. Consequently, other metallurgical factors must be more adequate to describe the process e ects. at is the reason why the measurement of strain hardening is relevant to study the metallurgical state of the material, as it is the direct consequence of the plastic deformation caused by the ball.

Strain hardening is the phenomenon whereby ductile metals become harder and stronger as they are plastically deformed, whereas their ductility falls [15]. A practical way to de ne the degree of plastic deformation is by the calculation of the percent cold work experienced by the solid:

%𝐶𝑊 = 𝐴 0 -𝐴 𝑑 𝐴 0 × 100 (2.5)
where 𝐴 0 is the initial area of the cross section and 𝐴 𝑑 is the same section a er deformation.

e direct consequences of strain hardening on a material is the increase of its yield and tensile strengths, caused by dislocation propagation due to stress. at multiplication of la ice defects results in an increase of resistance to further dislocation motion, which is subsequently revealed at a macro scale as an increase of hardness.

erefore, the quanti cation of the hardness can describe the microstructural surface integrity of burnished surfaces. For instance, López de la Calle et al. (2007) [87] determined the depth of a ectation of burnishing in the order of 10 µm, in both Inconel 718 and AISI P20 preheated steel alloys.

e resulting hardness increased as more burnishing pressure was applied during the process. In all cases, the hardness obtained a er machining was improved (Figure 2.8). e direct relationship between burnishing force and surface hardness had already been reported by Loh et al. [START_REF]Statistical analyses of the e ects of ball burnishing parameters on surface hardness[END_REF][START_REF]Surface hardening by ball burnishing[END_REF], from experiments executed on AISI 1045 specimens.

Albeit the positive e ect of the burnishing force on the metallurgical integrity of the burnished surface, if the force is too high, severe strain hardening may occur due to overplasti cation. is was reported by Kuznetsov et al. (2015) [START_REF]Nanostructuring burnishing and subsurface shear instability[END_REF], who detected evident harm on the surface of a 20Cr4 steel alloy due to shear instability during burnishing as the burnishing force was increased (Figure 2.9). e extreme e ect of this excessive force is the aking of the surface material, which leads to a clear surface integrity degradation and unsuitability of the process. [115] observed that this aking phenomena due to excessive force has also detrimental e ects on the surface hardness, and proposes the application of lubricants to decrease the shear stress that appears during burnishing due to friction dynamics.

Rao et al. (2008)

Results also show that the maximum hardness improvement is not registered directly on the surface. Although their work is based on lathe burnishing, it is worth mentioning the results of Chomienne et al. (2016) [18] on 15-5PH stainless steel bars. Figure 2.10 shows not only a hardness improvement at the surface, but a substantial increase is conspicuous until a 0.3-mm depth. ey also nd that no recrystallisation takes place at the surface, probably because not enough thermomechanical energy is added in the system by burnishing.

Ball burnishing has proved its positive e ects for the improvement of corrosion resistance, not only on industrial parts [108], but also on biocompatible materials such as magnesium alloys used for implants, where it proves to be a very a ractive alternative to coatings or chemical alloys [START_REF]Process mechanics in ball burnishing biomedical magnesium-calcium alloy[END_REF]153].

Mechanical parameters: residual stress

Residual stress is what remains in a material volume which is stationary and at equilibrium with its surroundings [158]. e reason why this internal stress state appears, is to balance the various mis ts occurring between di erent regions of the body itself.

ey can have di erent physical origins, such as thermal gradients or mechanical disparities. e length or scale over which the equilibrium is achieved is usually taken as a reference to classify the di erent types of residual stress (Figure 2.11). Based on that classi cation, residual stress can be typi ed as follows:

• Type I or macrostresses vary continuously over large distance range, 𝑙 0,𝐼 , originated by non-uniform plastic deformation, or the presence of bending moments which subject bres at one side of the neutral plane to compression. • Type II act in an intergranular domain, and are usually present in materials which are formed by adjacent grains with heterogeneous mechanical and thermal properties. erefore, tend to be slightly higher in multiphase materials where that heterogeneity is much more abrupt. at is what origins an internal stress state to set the achieve the equilibrium of the volume.

• Type III have an atomic scale, 𝑙 0,𝐼𝐼𝐼 , typically due to lack of coherency at grain interface and dislocation stress elds.

From the perspective of manufacturing technology, all types are of interest, depending on the research focus. For instance, types II and III are interesting for composite materials designers, to learn how stress is transmi ed from the matrix to the reinforcement. For this dissertation, only type I shall be measured, as are the ones related to fatigue performance. In this sense, the e ect of residual stress on the mechanical behaviour of components is various depending on the stress distribution.Normally, compressive residual stress are associated to positive e ects, as they prevent the initiation and propagation of cracks, as stated Novovic et al. (2004) [106].

is observation can be extended to di erent materials. For instance, Koster & Field (1973) [71] found that the fatigue life shown by Ti-6Al-4V specimens was dependent on the residual stress provoked by the applied nishing operation, and not its surface roughness. El-Helieby et al. (1980) [START_REF]In uences of surface roughness and residual stress on fatigue life of ground steel components[END_REF] reached the same conclusion in AISI 52100 specimens.

e measuring technique used to quantify the residual stress of parts must usually be chosen according to the type which is desired to be measured. For instance, material removal techniques such as hole drilling tend to remove macroscopic layers of material, neglecting therefore types II and III, whereas other such as neutron strain gauges are sensitive enough to detect those residual stress types [157]. e assessment of residual stress is clearly oriented in the bibliography as a means of understanding its in uence on the fatigue behaviour of materials with regards to other nishing processes. Furthermore, results focusing on the in uence of burnishing parameters on the residual stress of materials are mainly focused on lathe bur- nished surfaces, and do not tackle with the process exclusively. Below these lines, the residual stress results are partially presented, whereas the ones related to comparison with other nishing processes are included in the following subsection.

Avilés et al. (2013) [4] observed remarkable higher values of compressive residual stress on hourglass ASI 1045 specimens (Figure 2.12.a), in line with previous essays performed by Rodríguez et al. (2012) [START_REF] L ´ C | Surface improvement of sha s by the deep ball-burnishing technique[END_REF]. e same burnished specimens were then tested to rotative bending tests, concluding that ball burnishing increases high cycle fatigue lifespan to a maximum of 21.25%. On the contrary, fatigue improvement at low cycle fatigue is not remarkable (Figure 2.12.b). e authors also alert of the risk of crack nucleation at the boundaries caused between two burnished paths, as they behave as stress concentration points.

Vibration-assisted ball burnishing

Innovation in the manufacturing industry o en comes from improving already existing processes, instead of developing brand new operations based on radically di erent working principles. One possible way to undertake this innovative approach is based on the assistance of processes by combining a conventional operation with an external power source which triggers additional e ects in the system, facilitating the cut or deformation of the objective material. is approach to manufacturing innovation is called process assistance.

e assistance source can be very varied, and includes laser beams [START_REF]Laser-assisted burnishing of metals[END_REF], electric currents [72], current pulses [159] or magnetic elds [100]. is thesis is based on the assistance of the ball burnishing process by overlapping ultrasonic vibrations on a force preloaded on the target surface by controlled spring compression. e hypothesis of improvement is based on the acoustoplasticity principle, which is explained below in this section, along with successful case studies and some isolated applications on ball burnishing that have been found in the bibliography.

Description of the acoustoplastic e ect

e hypothesis that the superposition of ultrasonic vibrations can improve the execution and results of the burnishing process is based on an physical phenomenon called acoustoplasticity, or Blaha e ect, a er the rst researcher who observed it on an experimental basis. It consists on the overall reduction of the quasi-static stress required to deform a material as a result of the superimposition of vibrations on the deforming agent. As a process based on plastic deformation, the ball burnishing process can be susceptible of improvement by this principle. Acoustoplasticity was rst observed by Blaha & Langenecker in 1955 [7]. It was reported at sight of the results undertaken on pure zinc crystal specimens submerged in a carbon tetrachloride solution, and subjected to a 800 kHz ultrasonic wave. e tests were performed in two ways, as shows Figure 2.15. On one hand, the intermi ent connection of the ultrasonic source proved to reduce the tensile stress by about 40%, whereas it returned to its value prior to insonation -curve A-. A second experimental development showed that continuous application of ultrasound from the beginning of the essay -curve B-lowered the stress to the same extent. Both strategies were declared equivalent, as they lead to the same approximate stress value at about 1.5% deformation with no signi cant increase of temperature of the liquid environment.

e acoustoplastic e ect can be universally observed in metals, but its a ectation depends on their physical characteristics. Izumi et al. (1966) [START_REF]E ects of superimposed ultrasonic vibration on compressive deformation of metals[END_REF] performed tests on annealed copper, brass, mild steel, Al-Al 2 O 3 alloy and magnesium specimens. ey observed a divergent behaviour according to the vibration amplitude, as shows Figure 2.16. Whereas mild steel showed a regular evolution of the stress as the amplitude increased, copper and aluminium alloy showed a higher sensitivity by the e ect. Especially for high amplitudes, they showed a change in the behaviour, with an abrupt fall of stress as strain grew higher. is amplitude dependency has been con rmed by other authors [START_REF]Peculiarities in the plastic deformation of crystals subjected to the acoustoplastic e ect[END_REF][START_REF]Kinetics of the acoustoplastic e ect[END_REF]. e di erent reaction of materials to acoustoplastic strain can be quanti ed. Izumi et al. (1966) [63] de ned the vibration sensitivity factor, 𝑘, that is, the material constant showing the decrease of ow stress per unit of the vibration amplitude, according to Eq. 2.6.

𝜎 = 𝜎 0 -𝑘 𝑠 𝑢 0 (2.6)
where 𝜎 is the ow stress a ected by the superimposed vibration, 𝜎 0 is the ow stress with no vibration, 𝑘 𝑠 is the vibration sensitivity, and 𝑢 0 is the vibration amplitude.

Furthermore, they found a correlation with some of the main physical characteristics of the alloys, such as the acoustic impedance, Young's modulus, melting point, work-hardening and stacking-fault energy. Materials with higher acoustic impedance and higher elastic modulus showed a higher sensitivity to strain through vibration superposition, and therefore, so ening by acoustoplasticity. A lower work-hardening coe cient also favours the process, as can be seen in Figure 2.17.

Acoustoplasticity is described in the literature to have dual e ect on materials, as it causes so ening during the application of the ultrasounds, but also residual hardening [START_REF]E ects of ultrasound on deformation characteristics of metals[END_REF]. is result is actually the most interesting one to justify the assistance of ball burnishing by this e ect, as it can eventually facilitate plastic deformation during the process, while causing a remnant hardness on the workpiece which can improve its wear during in-service functioning.

Brief insight into acoustoplasticity causality

Albeit the observation of acoustoplasticity on di erent materials, its actual physical causality is still controversial, due to the lack of agreement about whether it has an extrinsic or intrinsic nature. at is, whether it is caused by the reaction of the material microstructure to the external source of ultrasonic energy, or by the increase -by the e ect of ultrasounds-of the amount of input energy into the system, with no change in the intrinsic properties of the material.

In summary, it can be stated that the extrinsic approach based on an additive stress superposition, has been rejected by numerous authors due to the inconsistency of the proposed modes with experimental results [93,[START_REF]A theory of the blaha e ect[END_REF]. Another intrinsic approach, based on thermal causality, has already been rejected by Endo et al. (1979) [34] On the contrary, the intrinsic approach based on preferential absorption of the ultrasonic wave by la ice defects has had more continuity in time and acceptation among researchers. It is based on the hypothesis that ultrasonic energy is preferentially absorbed by dislocations and defects in the metal la ice. As la ice defects de ne the plastic deformation mechanisms of a material, this approach can easily explain the facilitation of the process. is idea was suggested by Blaha & Langenecker [7,8]. Mason (1955) [98] argued that the preferential absorption of ultrasonic energy by lattice defects derived in an increase in dislocation mobility which enabled the metal to deform at a lower load.

is theory allowed Gindin et al. (1972) [42] to justify the observed residual hardening a er acoustoplasticity, as a consequence of the newly formed stable vacancy accumulations and dislocation loops in the material la ice.

A steady discussion about the source of acoustoplasticity has been recently reactivated, enabled by the advances in technology for microstructure analysis. Siu et al. (2011) [137] used a vertical 30-kHz vibrating Vickers microindenter to perform hardness tests on pure aluminium. e so ening-residual hardening dual e ect of acoustoplasticity was observed on the resulting prints. SEM observations proved that indentation prints showed residual subgrain formation, an undetected e ect on specimens which were quasi-statically indented. ese e ects were later con rmed experimentally on copper, molybdenum and aluminium specimens [135]. e explanation for acoustoplasticity resulting from the combined extrinsic and intrinsic theories, seems to be the most complete approach. Neither is acoustoplasticity a mere stress addition e ect, nor a simple preferential absorption by la ice defects.

It also justi es the fact that no frequency dependence has been detected on the soening e ect [136]. On the contrary, Cheng et al. (2015) found that so ening during vibratory deformation and residual hardening depends on the amplitude, existing a threshold value which has to be surpassed to observe the e ect [17]. Recent results established that subgrain formation is not always observed, and, therefore, cannot be considered as the ultimate acoustoplasticity explanation [27].

Regardless of the lack of de nition of the actual source of the acoustoplastic effect, its experimental application has been long proved, and are to be incorporated to the ball burnishing operation to enhance its surface integrity results. e following subsection presents the results that have been already reported about the vibrationassisted process in the bibliography.

Experimental results of ultrasonic burnishing

e acoustoplasticity e ect as the basis for the assistance of processes has been tested on some traditional operations such as polishing [134] or impact peening [101,[START_REF]Fatigue resistance of welded details enhanced by ultrasonic impact treatment (UIT)[END_REF].

e VABB process was rst reported during the 70's under the designation of ultrasonic burnishing, assisted by vibrations characterised by 41.5 kHz frequency, and an amplitude ranging from 5 to 10 µm. Marakov (1973) [94] found a remarkable interaction between the amplitude of the oscillation and the surface roughness results, as the expected positive e ect of higher forces on surface roughness was only detected if the amplitude of the vibration was higher than 2 µm (Figure 2.18.a), at mild steel specimens. is result would be later contradicted by Pande & Patel (1984), as shows Figure 2.18.b. In this case, the process was assisted by vibrations with frequencies ranging from 10 to 70 Hz, and amplitudes from 0.2 to 2.5 µm. Accordingly, the process was called vibratory burnishing, in contrast to the high-frequency ultrasonic burnishing. Results revealed a reverted interaction between the force and the amplitudes, obtaining lower surface roughness for amplitudes lower than 0.5 µm [109].

Pande & Patel (1984) [109] also analysed the in uence of the frequency on the results, through an experimental design with other three parameters, namely: burnishing force, feed and spindle speed. Both result variables, surface roughness and hardness, showed a positive direct relation with the vibration frequency. However, that positive e ect was remarkable higher in terms hardness, as it can be enhanced e literature review undertaken for the composition of this state of the art has not evidenced any other research source about ultrasonic burnishing until the 2000, evidencing a long timespan since the results by Pande & Patel were published in 1984. Ti-6Al-4V specimens were subjected to ultrasonic burnishing by Bozdana et al. (2005Bozdana et al. ( ,2008) ) [12,[START_REF]X-ray di raction spectrum showing a di raction peak at 2𝜃 𝜓 position, with regards to the spectrum registered for the reference material[END_REF]. e experimental setup was composed of a hydrostatic tool a ached to a milling machine. It was excited by a piezoelectric transducer that transmi ed a 20 kHz and 6.75µm vibration.

According to the same author, surface roughness results are very modest and not especially promising for the ultrasonic burnishing process. e average surface roughness is improved to a higher extent through the non-assisted process, probably because in situ so ening caused by acoustoplasticity may act as a harming phenomena in this material [12]. Results in terms of hardness and residual stress are much more encouraging. Figure 2.20 exempli es that the ultrasonic process allows the result of higher surface hardness, whereas the deep residual stress pro le shows the positive e ects of ultrasonic burnishing, while applying half the force with respect to the conventional process. e major in uence of ultrasonic burnishing on work hardening and super cial residual stress was con rmed by Huuki et al. (2014) [START_REF]Integrity of surfaces nished with ultrasonic burnishing[END_REF] on AW 6082-T6 aluminium, 34CrNiMo6-M tempering steel and S355J2 structural steel.

e materials were prepared as cylindrical specimens mounted on a lathe. e experimental setup was constituted by using a spring-regulated tool, 3-mm ball and assisting the process with 20 kHz vibrations, the maximum static force level was 195 N. Ultrasonic burnishing re-2.4. OBJECTIVES ARISING FROM THE STATE OF THE ART vealed to be a highly repeatable process, and results on surface roughness and out-ofroundness improved, regardless of the initial super cial state of the workpieces [START_REF]In uence of ultrasonic burnishing technique on surface quality and change in the dimensions of metal sha s[END_REF].

Within the framework of this thesis, the most relevant results about vibrationsassisted ball burnishing are those published by Gómez-Gras (2014) [43], since they represent the direct antecedent of the work to be developed throughout the next chapters. e results presented at that thesis are based on the application of the process through 2.4 kHz vibrations transmi ed by a thin plate excited by a coil. When the coil was excited with a variable magnetic eld, it caused an alternative de ection in those plates, which was transmi ed to the burnishing ball [45].

is tool was tested on AISI 1038 and EN AW 7078, and results were compared to those derived from the conventional process. is characterisation was performed by analysing the surface roughness, hardness pro le and compressive residual stress. In this case, the average surface roughness was substantially enhanced by the introduction of vibrations on both materials, and the authors concluded that one pass of the assisted process delivered a similar surface roughness as ve passes of conventional burnishing. Nonetheless, although the improvement is also conspicuous in terms of residual stress and micro-hardness, results were not so determinant, especially in the steel specimens [150,151].

e authors explain this fact because of an unsatisfactory frequency or amplitude transmission of the vibration, which scarcely reaches the minimum threshold to activate acoustoplasticity mechanisms, and propose further work to improve the process, which can be at last ful lled with the development of this thesis.

Objectives arising from the state of the art

From the initial state of the art revision, the following conclusions can be drawn:

• ere is enough evidence to think that the superposition of an ultrasonic vibration signal on a conventional ball burnishing process can deliver positive results on the surface integrity of the target material, due to a generalised residual hardening e ect, and a lower quasi-static stress required to succeed in deforming metals plastically, on the basis of empirical works.

•

ere is no commercial tool able to apply the described process. In fact, although a few publications can be found by authors who claim to execute it, references about the tooling and working principle are vague due to the lack of information shared with the scienti c community. Consequently, a new tool should be design to apply the process successfully.

• e classical evaluation strategy followed by researchers with regards to the e ects of traditional ball burnishing does not tackle the issue through a comprehensive approach. Speci cally for the texture e ects of ball burnishing, only the 𝑅 𝑎 , and eventually 𝑅 𝑡 , have been used to quantify the e ects of the process. However, are these two-dimensional precise enough to characterise an operation that spans a whole surface? At sight of those observations, the following speci c objectives can be formulated. ey shall drive the activities undertaken inside the framework of this dissertation: 1. To design, manufacture, and test a burnishing tool capable to execute the vibrationassisted ball burnishing process, that is, to deform plastically a surface through a preload force on which a vibratory component is overlapped.

2. To test the prototype on di erent engineering surfaces nished through ballend milling.

3. To assess the e ects of the VABB process on the surface integrity of two workpieces made of AISI 1038 and Ti-6Al-4V alloys, including topological, metallurgical and mechanical parameters to describe it.

4. To propose an alternative set of parameters to describe the topological e ects of the VABB process, considering three-dimensional parameters and descriptors other than amplitude ones.

5.

To evaluate the improvement delivered by the vibration-assistance by comparing the results to those obtained by complementary tests using the non-assisted process.

3

Design and characterisation of the VABB tool e implementation and validation of innovative tool design for manufacturing is the basis for the development of this thesis. With that aim, the conception of a prototype enabling the execution of the VABB process plays a decisive role in the quanti cation and characterisation of its e ects on the surface integrity enhancement. is chapter presents the mechanical design of a VABB tool, structured in three di erent functional units which work together to execute the process. In this design, the role of piezoelectric transducers is fundamental to achieve the vibratory component of the burnishing force required for the VABB process.

A prototype manufactured based on the presented design is then validated through di erent techniques. However, the high frequency and low amplitude characteristic movement of the burnishing ball poses a remarkable technical challenge. Hence the need of deploying a set of di erent techniques to register and reconstruct the wave generated by the ultrasonic prototype.

ese tests include motion track with HD images, acoustic emission and dynamometric measurements with high sampling frequency to quantify the actual functioning of the tool when the piezoelectric are e prototype is based on spring compression to control the burnishing preload, and incorporates an innovative system of support of the burnishing ball. To successfully execute the burnishing process, the new prototype must comply with the following basic speci cations:

• Guarantee the constant rolling of the burnishing ball during the process.

• Control with a certain reliability the burnishing preload magnitude through a calibrated spring. • Enable the interchangeability of the tool on di erent machine tools.

Besides, to enable the tool to execute the VABB process, additional requirements must be demanded, as follows:

• Ensure that all electronic devices are separated from inside the humid machine tool environment. • Transmit the vibratory movement originated at the piezoelectric thickness alternative change to the burnishing ball.

Beyond the cited practical aspects, the actual key feature that must be satis ed by the conceived tool is to deliver an oscillating burnishing force 𝐹 𝑏 , product of a superposition of two main components: a preload, 𝐹 𝑝 , applied during the preliminary phase of the burnishing operation by means of the controlled spring compression, and an oscillatory force, 𝐹 𝑣 , delivered by the vibration of a piezoelectric stack. During the process, the actual burnishing force shall be the result of a composition of both, modi ed by an uncontrolled variation due to the interaction of the ball with surface irregularities, as follows:

𝐹 𝑏 = 𝐹 𝑝 + 𝐹 𝑣 + 𝜂 (3.1)
where 𝐹 𝑏 is the total burnishing force, 𝐹 𝑝 is the preload, 𝐹 𝑣 is the vibratory force originated from the piezoelectric vibration dynamics, and 𝜂 is the low-frequency force variations due to the topological irregularities found during the feed motion of the tool.

e force perturbation, 𝜂, shall be neglected for the analysis undertaken in this dissertation, as shall be justi ed in the next subsection. All technical requirements considered, the nal design consists of a tool composed of three di erent units (Figure 3.1). Conjointly, all three modules allow a feasible preload regulation, introduce the vibratory component in the system, and overlap and transmit both of them to the workpiece. Further explanation about them is presented along the subsequent subsections.

Force regulation unit

e force regulation unit is composed of the parts responsible for the selection and control of the preload, 𝐹 𝑝 , applied during a ball burnishing operation.

is force is the main driver of plastic strain during both the NVABB and VABB processes. e calibrated spring responsible for force control is housed inside a ø25 AISI 1045 cylindrical case, which glides freely along a rod, in turn coaxial to the central axis of the tool (Figure 3.2). e steel case also serves to perform the xation of the tool to the machine, by clamping it to the tool holder. e compression length experimented by the spring de nes the burnishing preload, as it is the Hooke's law (Eq.3.2) that governs the elastic force exerted by the spring inside the unit. e compression of the spring is possible due to the described free axial movement of its case, which pushes on it so that preload can be regulated during the burnishing operation as follows. Once the tool is a ached to the machine spindle, its head is approached to the workpiece until the ball makes contact with the surface. From that point on, further plunge of the tool head shall revert in compression of the spring. is force transmission is possible on account of the rigid connection between the rod base and the case of the central body of the tool (i.e. the vibration transmission unit).

𝐹 𝑝 = 𝐹 0 + 𝑘 𝛥𝑧 (3.2)
where 𝐹 0 is the precompression force, 𝑘 is the spring sti ness, 𝛥𝑧 is the compression For the realisation of the prototype, a drawn AISI 5160 die spring with rectangular section, according to ISO 10243, was mounted on the FRU. It has a nominal 100-N/mm sti ness. To accurately control the preload, a previous calibration phase was undertaken to de ne the actual sti ness and preload of the spring. e tool prototype used for the essays was tested through a universal testing machine equipped with a 2-kN load cell. e tool was supported on an auxiliary part which emulates the tool holder. e testing machine compressed then the spring at constant velocity, while the force was registered by a Spider8 data acquisition device, with a 60-Hz sampling rate (Figure 3 e recorded set of time data was translated into displacement, as the compression was performed at constant velocity. is calibration operation was performed at three di erent compression velocities: 1 mm/min, 10 mm/min and 100 mm/min. All dataset describe a rectilinear graph, as expected due to the nature of Hooke's Law. As an example, Figure 3.3.b shows the calibration curve for the 100 mm/min test. e respective resulting calibration lines were calculated using a Microso Excel worksheet and the INTERCEPT and SLOPE native functions (Table 3.1).

e 𝑦intercept coordinate corresponds to the precompression force, due to the initial compression caused by the pressure exerted by the case as a result of a top nut screwed on the base support. Parameters are similar, although slightly di erent due to the variation in the sample size introduced taken by the so ware to perform the calculation. Results also show that the actual elastic constant of the spring, 𝑘 , has an average value of 83.70 ± 0.61 N/m, inside the tolerance interval o ered by the manufacturer in its catalogue. Only this physical spring is used for the experimental procedures included in this thesis. On the other hand, due to the variability of the precompression force depending on the thread length of the nut, a calibration operation was performed before every experimental test to verify its value. However, it will not be speci ed in this memoir, as it is considered a trivial preliminary operation.

At this point, it is easy to justify the omission of 𝜂 in the quanti cation of the burnishing force, due to its negligible value with regards to the preload level. Indeed, the source of this variation is the absorption of the spring inside the tool of the surface topological features as the ball rolls over them during the process. Since they have units of µm, considering the sti ness of the spring used for this tool, 𝜂 shall have units of mN according to Hooke's law. Consequently, this perturbation can be ignored.

Vibration transmission unit

is module is composed of the elements necessary to generate the ultrasonic vibratory component of the burnishing force, 𝐹 𝑣 . e design speci cations describing the force that this unit must be able to deliver are shown in Table 3.2. ese piezoelectric transducers deform accordingly at the same frequency as the electrical eld which excites it. is is the principle on which this VTU is based, and is based on previous successful applications on vibration-assisted machining tools [14].

e design contemplates the installation of a piezoelectric transducer stack inside an enclosed case along with the corresponding counterweight, and xed on a thin surface extended at top of the sonotrode to ensure the connection with the FTU. Screwed at the top of that case is the spring support, and, therefore, the whole FRU described above.

e electrical excitation of the vibration transmission unit is achieved by a BNC external plug that connects the electrodes among the piezoelectric disks and the electronic circuit (Figure 3.4). e FRU explained above made reference to the static force supplied by the tool through spring compression. However, the di erential feature of the prototype is the ability to overlay a vibratory movement on the burnishing ball by means of a set of piezoelectric ceramic parts a ached conjointly to the burnishing ball. e principle of piezoelectricity justi es and explains the tool behaviour and its potential to implement the VABB process. Piezoelectricity describes the property of certain materials to transform mechanical energy in electrical energy -direct piezoelectric e ect-, and vice versa -inverse e ect-.

is property can be arti cially induced by polling in arti cial materials such as lead zirconate titanate (PZT) for engineering applications.

e constitutive model of a piezoelectric transducer, comprising both the inverse and the direct e ects, is composed of the electromechanical equations represented at Eq. 3.3. e second one models the inverse e ect, and explains the utilisation of piezoelectric ceramics as actuators. It shows that the deformation experienced by a piezoelectric is the result of an external electric eld forced on it and, eventually, the application of a stress on its surface.

⌊ D 𝜀 } = ⌊ 𝜉 𝜎 d d S E } ⌊ E 𝜎 } (3.3)
where D is the vector of electric displacement , 𝜀 is the strain vector, E is the vector of applied electric eld, 𝜎 is the stress vector, 𝜉 𝜎 is the permi ivity matrix measured at constant stress, d is the matrix of piezoelectric strain constants and S E is the matrix of compliance coe cients measured at constant electric eld.

is equation can be particularised for the case study. e vibratory displacement is desired along the longitudinal axis of the tool, that is, the direction 3 of the space, performed by an anisotropic piezoelectric polled along that same direction, with no external stress applied on it. Considering these requisites, Eq. 3.3 can be simpli ed to Eq. 3.4, which allows the calculation of the total elongation of the piezoelectric material.

𝛥𝑡 = 𝑑 33 𝑉 (3.4)
where 𝛥𝑡 is the piezoelectric thickness variation.

is equation calculates the displacement that any element a ached to the piezoelectric volume is due to experience when the la er is excited, and does not depend on the original thickness. e technical solution for the VTU was developed in collaboration with an industrial rm that manufactures and distributes piezoelectric sonotrodes. e resulting con guration inside the ball burnishing prototype consisted of four stacked hard PZT8 piezoelectric disks, whose properties are summarised in Table3.3.

e disks are separated by metallic electrodes connected alternatively to an oscillating voltage source. is distribution allows an axial actuation of the system, as long as they are excited by an electric eld aligned with the polarisation direction. is con guration is a classical engineering solution which presents a high e - 400 ⋅ 10 -12 m/V ciency in transforming electrical to mechanical energy, and successfully delivers the vertical vibration of the burnishing ball. It also allows high magnitude resonant frequencies of the system, which is suited for the desired ultrasonic excitation of the prototype. e stack was xed on the thin surface at the top of the sonotrode of the FTU, thus enabling the conjoint functioning of both units, as has been explained before. is VTU-FTU connection was already presented in Figure 3.4). e behaviour of this stacked con guration can be explained by extending the constitutive equation represented by Eq. 3.4 for single piezoelectric layers to a sequence of 𝑞 piezoelectric plates:

𝛥𝑡 = 𝑞 𝑑 33 𝑉 (3.5)
where 𝑞 is the number of stacked ceramic modules , 𝑑 33 is the longitudinal piezoelectric signal deformation coe cient along the axial direction, and 𝑉 is the applied voltage .

e piezoelectric stack is excited through a BNC connection to an external generator which transforms the electrical signal into a 40 kHz and 1.3 kV mono-phase AC voltage. As the AC source excites the piezoelectric, it shall change its width in unison with the exciting current, as polarity reverses alternatively the strain sense of the piezoelectric material, i.e. negative potential shall make the piezoelectric thinner, and the negative potential thicker.

According to Eq.3.5, and the described characteristics, the nominal displacement of the whole stack can be estimated in 1.5 µm. A model property of the manufacturer of the whole sonotrode, resulted in a maximum displacement at the tip of the sonotrode, that is, the tool itself, of 8.9 µm, which is the value established at rst at the design speci cations.

External power circuit: resonance at maximum impedance

e external power circuit plays a fundamental role in making the tool function according to the described speci cations, as it must be able to generate the correct electrical signal to make the piezoelectric vibrate at the desired frequency. For us, the generator is a black box whose composition is unknown for the purposes of this dissertation, and has been provided by the manufacturer of the piezoelectric actuator.

e electrical circuit has been tuned so that the actuator works always at resonant frequency, and at maximum impedance, 𝑍 . As the impedance is the measurement of the opposition that a circuit presents to a current when a voltage is applied, according to Ohm's Law, se ing the mentioned condition as a design requirement has two main consequences. First of all, it is an electronic means of guaranteeing that the piezoelectric is always working at resonance frequency of 40 kHz. Secondly, the circuit always work at minimum intensity, 𝐼 , and, therefore, with minimum power consumption.

To guarantee that this condition is invariable in time, the circuit of the external generator includes an electronic auto-tuning system which modi es the impedance automatically, through a feedback system reporting the value of the output signal to the input terminal of the ampli er. To check this condition, the prototype was connected to a Banry PV70A impedance analyser. is device enables the excitation the transducer of the prototype with a sequence of electrical signals of increasing frequency. Incremental steps of 100 Hz, from 30 kHz to 50 kHz, were taken to excite the transducer. Figure 3.5 represents the impedance value measured for each frequency. Maximum impedance can be found at around 42 kHz, as desired according to design speci cations. A second measurement was taken while the piezoelectric was manually loaded on a free surface.

e impedance presents a certain variability as a consequence of the circuit constant autotune, but the global maximum can be also seen at the same frequency level. e electrical circuit is also equipped with a potentiometer which allows the variation of the vibration amplitude. e maximum amplitude is coded as a 100%, and is the reference value. is amplitude can be changed continuously just by interacting with the power circuit potentiometer switch. e quanti cation of this change and its consequence in the VABB process application shall be assessed in the following tool characterisation activities.

Force transmission unit

e function assigned to this module is the execution of the burnishing force, 𝐹 𝑏 , by overlaying and transmi ing both the preload controlled through the FRU, and the oscillating force, 𝐹 𝑏 , enabled by the VTU. e ultimate mechanical transmi er of that force is the burnishing ball, which is supported on a set of bearing spheres inside a hemispherical slot machined on the tool head (Figure 3.6).

at head is actually the extension of the thin support surface on which the piezoelectric disks are xed. Its second function is acting as a sonotrode amplifying the piezoelectric vibration amplitude from its top, on which the piezoelectric is xed.

Frequency measurement through acoustic emission

An industrial rm holding the expertise in manufacturing and implementation of piezoelectric actuators executed the implementation of the design in a VABB prototype, which was used for the experiments described in this thesis. Before applying it on the materials of interest, a preliminary testing phase was performed to prove that vibrations were actually being transmi ed to the objective material.

In this ma er, the great technological challenge resided in the limitation of sensors to register ultrasonic frequency and micrometric displacements , in this case of the burnishing ball. For that reason, during this phase, the e orts were focused on the characterisation of the frequency of the signal transmi ed from the tool to the part through alternative technologies.

A second handicap was found in the fact that conventional accelerometers and other equipments such as laser vibrometers cannot sample an ultrasonic signal. 20 kHz is usually considered as a the threshold value to de ne the adequacy of this kind of systems. erefore, the reconstruction of the actual signal would not be representative of the actual one. As the Nyquist-Shannon sampling theorem states, the sampling frequency should be at least twice the expected measured frequency, so that the digitalised data is not aliased, and the real signal can be represented by the reconstructed signal. In this case, a frequency higher than 80 kHz would be necessary to succeed in the vibratory signal characterisation. At sight of the described situation, an acoustic emission (AE) experimental setup was proposed as a rst approach to the characterisation of the prototype dynamic behaviour. AE sensors are devices based on the inverse piezoelectric e ect described above, as they transform a mechanical stimulus into a measurable di erence of potential. e range of frequencies fully detected through AE goes from the acoustic to the ultrasonic frequency range, depending on the sensor and its resonant frequency, which ts the requirements for our needs.

However, an issue with this technique derives from the advantages it delivers in detecting high frequencies: it requires high sampling rates of a MHz magnitude, and, therefore, generates huge datasets di cult to postprocess [96]. Hence its usual application for non-continuous measurement, as a means to register transient highfrequency waves which do not require to be subjected to continuous sampling and acquisition. For instance, one of its applications is the detection and monitoring of elastic waves originated at subtle changes in materials la ice, such as underlayered breakdowns or microcrack nucleation [95, 97].

Acoustic emission experimental setup

In order to monitor the signal transmi ed by the vibrating tool, these AE experiments took an AISI 1038 block as the solid to allow ultrasonic transmission. Table3.4 summarises the di erent testing conditions which where nally registered. Two preload levels where applied on the target surface, to perform both burnishing lines and points, that is, by imposing a feed movement to the prototype or not, respectively.

is allows the evaluation of a possible in uence of the feed motion on the measurements. An initial set of experiments revealed sensor saturation when the highest amplitude allowed by the system was selected through the potentiometer at the power circuit.

erefore, 𝐴 = 100% measurements were discarded from the experimental plan. e complete experimental setup can be seen in Figure 3.7.

e steel block was mounted on the vise and face milled, to ensure perpendicularity of the objective surface with regards to the central axis of the prototype. e external circuit which excites the VTU was installed next to the machine, so that the vibrations amplitude could be easily changed. AE measures were made with the following equipment:

• Vallen VS-150M acoustic emission piezoelectric transducer, xed on the surface of the steel piece through a gel-type couplant. • Vallen EAP4 34 dB pre-ampli er for signal conditioning. • Vallen AMSY-5 acquisition system for signal recording.

All data was registered through the Vallen 32 Visual AE acquisition so ware. It was then processed through a Matlab script through which the signal was ltered and represented in the time domain. e power spectrum was calculated from the ltered signal. Results are presented in the next subsection.

Frequency of the ultrasonic signals recorded by AE

e signals recorded for the 0% amplitude case study did not reveal any data registration, as could be beforehand easily expected. On the other hand, all point and linear tests lead to similar conclusions. For instance, Figure shows the graph of the signal obtained for the 270 N and 50% amplitude test. results leads to think that the tool actually vibrates equally in frequency terms during the execution of the process, and its behaviour does not change essentially when it is loaded.

To quantify the value of the fundamental frequency visible in the spectrum, the Matlab script was prepared so that it could return the value for each signal in a results array. Table 3.5 represents all these results. Regardless of the preload level or the amplitude of the vibration, all signals transmi ed had the exact fundamental frequency of 39.1 kHz, very near from the 40 kHz de ned at the initial speci cations.

e amplitudes do not reveal any pro table information, as the measurements were not calibrated.

Dynamometric characterisation

During the previous subsection, handicaps and technical limitations were found to measure the actual ball displacement during piezoelectric excitation. Having succeeded in nding a value of the frequency through the AE experimental analysis, an alternative method was considered to quantify that displacement by direct determination of the sinusoidal force overlapped on the preload while the piezoelectric is being excited, that is, 𝐹 𝑣 .

e quanti cation of 𝐹 𝑣 during this phase is completed by a second layer of objectives, as it allows the assessment of the e ectiveness of the potentiometer installed in the external circuit for the piezoelectric excitation. On the other hand, it also delivers information about a possible dependence of this oscillating force on other process parameters.

Dynamometric experimental setup

e experimental application of the dynamometric measurements contemplated a total of 6 preload levels, which were tested at amplitudes 10%, 50% and 100%. Furthermore, the 𝐹 𝑣 was recorded at the highest preload level for amplitudes from 10% to 100% in steps of 10. A summary of all tested conditions are contained in Table 3.6. e press force sensor was mounted on the vise on the milling machine, with the help of a copper shell to protect it. e tool would be directly compressed on the sensor surface to a ain the di erent preload levels. With that aim, the following equipment was implemented:

• Kistler 9323A press force sensor, especially conceived for measuring dynamic and quasistatic forces (Natural frequency: 72 kHz). • Kistler 5015A charge meter.

• Hameg HM2008 oscilloscope A rst set of measurements were taken to construct a calibrating line by progressively compressing the spring inside the prototype, and monitoring the static force. Figure 3.10 shows the equivalent calibration line obtained my linear regression, Compared to the equation obtained by continuous compression. Both sti ness coe cients can be considered equivalent, although the precompression force is slightly di erent. As that precompression is caused manually by the operator by tighting the nut at top of the prototype, it can change from one situation to another. Consequently, this calibration should be performed before each application of the process. An alternative precompression method could be developed in future improvement activities. During the second phase, all preload levels and amplitudes were combined and registered. Preloads were managed by compressing according to the calibrating function deduced from the previous phase. For each preload level, the tool was compressed directly on the sensor, until the searched preload value was achieved. e measure-3.3. DYNAMOMETRIC CHARACTERISATION ment was then reset, and the piezoelectric was excited.

at way, the only force detected by the sensor was the additional vibrating force, 𝐹 𝑣 . By the inverse piezoelectric e ect, the sensor transformed that force acting on the quartz element inside the capsule into an analogue voltage signal, which was acquired and sampled by a Hameg HM2008 oscilloscope.

For a proper reconstruction of the signal, a 10-MHz sampling frequency was used to process the signal by the oscilloscope so ware. However, although the oscilloscope delivered the sampling and reconstruction of the signal at a satisfactory frequency, it also provided a technical limitation linked to the fact that only the portion of signal shown in the screen could be exported. In order to have a good representativeness of the force, each signal was acquired ten times, and processed by a Matlab routine to calculate a sine function t.

antification of the superimposed vibratory force

e arguments of the ed sine are the descriptors of the vibratory force, 𝐹 𝑣 , as represents Eq. 3.6.

𝐹 𝑣 = 𝛥𝐹 𝑣 sin (𝜔 𝑡 + 𝜑 0 ) (3.6)
where 𝛥𝐹 𝑣 is the force variation in one half cycle, 𝜔 is the angular frequency, and 𝜑 0 is the phase.

Figure 3.11 shows an example of the sine t calculated for one of the sampled signals for a 600-N preload at 100% amplitude. All ts have a Pearson 𝑅 2 parameter higher than 94%, thus con rming the reliability of the calculated parameters (Table 3.7). Only the ings for the measurements at 100 N of preload are around 85%, probably because the signal is more unstable at this preload level. Still, this ing can be considered as acceptable to quantify the level of force delivered by the vibrating s. Standard deviations have not been represented for the purposes of simplicity, as they are all below 0.01. e Matlab routine returned all descriptors of the sine curves, which are actually the descriptors of the vibratory force overlaid on the preload. Of all those descriptors, the frequency and the amplitude of a half cycle are the most interesting ones to characterise 𝐹 𝑣 . Table 3.8 gathers all those descriptors averaged from the ten samples taken for each measuring condition, along with their standard deviation. e divergence between the mean half-cycle amplitude arising from the sine ing and For a be er comprehension of the vibratory force scales, Figure 3.12 represents half cycle force amplitudes calculated from the sine ts, and both the maximum and minimum forces acquired through the dynamometer for the two highest tested amplitudes. All piezoelectric amplitudes regulated from the external power circuit generate a similar behaviour of the vibratory force, for all preload levels. e force variation in a half cycle is around ± 4 N, except for the case of 200 N preload force, where a slightly higher value of 5.5 N is observed. is non-linearity can be associated to the fact that the sti ness of the prototype, 𝑘 ′ , changes as the spring is compressed di erent compression lengths, i.e. as the preload is changed.

e most simple model to explain this is by assuming that the displacement of any mechanical system is directly proportional to the force causing it through its sti ness (Eq. 3.7). In the VABB prototype, this 𝑘 ′ sti ness is the result of the mechanical combinations of all its components, including the spring. erefore, it is unknown.

𝐹 ′ = 𝑘 ′ 𝛿 (3.7)
where 𝐹 ′ is the force acting on the mechanical system, 𝛿 is the displacement, and 𝑘 ′ is the system sti ness.

As the spring governing equation is linear, meaning that the variation of 𝑘 ′ must come from other uncontrolled factors related to the mechanical composition of the tool, and it introduces the non-linearity observed in the experimental results, which lead to conclude that sti ness is minimum at a preload of around 200 N. e direct consequence is that it enables the whole FTU to vibrate along a higher displacement. Nevertheless, this variation should not be in uential in the result, as the acoustoplas- 203 tic e ect is not a ma er of additive force, but the transmission of the ultrasonic wave inside the material, the source of which is con rmed for all preload levels. Furthermore, the reference values of 4 N and 5.5 N, over the di erent adopted preload levels provide a similar ratio, so that they can be considered at all e ects equivalent.

As 𝐹 𝑝 = 600 N was object of more measurements at di erent amplitudes, it has been represented in Figure 3.13 along with 300 N for comparison. at Figure shows the stability of the vibratory force descriptors, even for the more discretised 600 N measurements. is behaviour is common for all preload levels. As for the 𝐹 𝑣 frequencies, 𝜈, they can be obtained from the angular frequency of the sine ts, according to Eq. 3.8. e frequencies corresponding to all the studied cases were calculated and averaged. Table 3.9 shows the high stability of the frequency at 39.2 kHz, regardless of the preload and the amplitude.

𝜈 = 𝜔 2𝜋 (3.8)
In general, the dynamometric measurements have evidenced that the vibratory signal is stable for preloads lower and higher than 200 N, as this preload level shows a decrease in the sti ness of the system that slightly ampli es 𝐹 𝑣 . e next section tackles with the measurement of the mechanical integrity of all tool parts by the analysis of motion tracking.

Preliminary validation tests

Once the vibratory behaviour of the tool was measured, the next step was to con rm that the tool could actually modify the surface texture. With that aim, the prototype was tested on an AISI 1038 workpiece by performing a whole burnishing operation on a previously milled surface. Each burnishing cycle included precompression followed by successive parallel passes separated by a certain lateral o set were performed to obtain a whole burnishing patch. (Figure 3.14).

e initial surface was obtained by a surface milling operation with a ∅80 5-insert front mill, obtaining a surface characterised by 𝑅 𝑎 = 2.735±0.473 µm. e roughness was measured on the workpiece with a Mitutoyo S-210 Sur est pro lometer, ltering the signal with 𝜆 𝑐 = 0.8 mm cut-o length and 4 mm evaluation length, and by averaging 20 di erent measures along the burnishing direction. is rst test proved to improve the surface roughness by 56.17%, con rming the positive e ects of the tool. However, the prototype exhibited a slight bending e ect during its displacement on the surface as the feed movement was induced, by e ect of the friction. As an excessive geometric deviation between each pair of modules could prevent the tool to perform the process adequately, so it was decided to quantify it.

With that purpose, motion tracking was used to study the mechanical integrity of the burnishing tool, along with the relative movement and rotation of its constructive parts. e tool was a ached to a LAGUN 600 milling machine. An AISI 1038 block was xed on the vise and surfaced to clean the working surface. A CNC code was wri en to perform successive going and returning burnishing passes along one line.

e whole body of the tool was acquired with an HD video camera at 80 fps during 3 s, for two preload levels: 90 N and 270 N.

Each video was decomposed in 240 frames of 1280×720 pixels, which were processed through a Matlab routine that delivered the relative movement of speci c prede ned points throughout the di erent frames. ose marks were organised in a 237point array composed by four sub-meshes (Table 3.10). Each sub-mesh corresponded to one component of the tool, as shows Figure 3.15. rough the Matlab script, the 𝑥 and 𝑦 coordinates of all mesh points were located, and were followed along the next 239 frames, recalculating their 𝑥 and 𝑦 coordinates throughout the video sequence. e routine returns, for each of the four meshes, a matrix composed of those coordinates along the 240 frames. By coordinate subtraction, the slope of the lines composed by the points at each row with regards to the horizontal line were calculated. For instance, as mesh I is composed of 5 rows (points 1-3, 4-6, 7-9, 10-12 and 13-15) (Figure 3.16), the respective ve slopes were calculated for each of the 240 frames. Each frame is represented by one slope value calculated by the average of all points. For instance, Figure 3.17 shows the evolution of the slopes for the element I for each frame, along with a smoothed curve. Two clearly di erentiated slopes can be observed in the graph, each one associated with the displacement of the tool in the corresponding direction, namely 𝑚 𝑟 and 𝑚 𝑠 . e former is associated in the represented case by the points comprised between frames #40 and #150, For our 80-fps acquisition, 𝑚 𝑠 is present during 1.375 s, which corresponds to the time that the tool takes to go along the 7-mm path at the established 300-mm/min feed. For both registered preload forces, the presence of dual slope values is found at the four sub-meshes drawn on the tool geometry. Both 𝑚 𝑟 and 𝑚 𝑠 themselves are related to the rotation of the tool during the burnishing feed movement around a xed point -the tool-holder origin-and can be calculated according to Eqs. 3.9 and 3.10.

𝜃 𝑟 = 𝜋 -arctan 𝑚 𝑟 (3.9)
where 𝜃 𝑟 is the rotation of the tool when it moves in one sense.

𝜃 𝑠 = 𝜋 -arctan 𝑚 𝑠 (3.10)
where 𝜃 𝑠 is the rotation of the tool when it moves in the opposite sense.

e maximum angle that the 𝑖 component of the tool is pivoting when the feed direction changes, 𝜃 ′ 𝑖 , is obtained as half the di erence of angles 𝜃 𝑟 and 𝜃 𝑠 (Eq. 3.11). It can be seen in Figure 3.18. Although this calculation is based on the hypothesis that the tool swivels the same angle in both feed senses, this calculation method allows a good approximation to its value, and means that it is not necessary to take a vertical reference, which would be impossible to de ne properly due to the spherical deformation caused by the camera objective.

𝜃 ′ 𝑖 = 𝛿 2 = 𝜃 𝑟 -𝜃 𝑠 2 (3.11)
where 𝛿 is the di erence of the angles that the tool bends in both displacing directions. e relative pivoting angle of each part with regards to the part to which it is a ached, 𝜃 𝑖 , can be calculated by the di erence of the angles already deduced, as follows:

) ⌉ ⌉ ⌋ ⌉ ⌉ ]

𝜃 𝑖 = 𝜃 ′ 𝑖 -𝜃 𝑖-1 ∶ 𝑖 = 1, 2, 3 𝜃 𝑖 = 𝜃 ′ 𝑖 ∶ 𝑖 = 4 (3.12)
e absolute pivoting angles of the four distinguished parts of the tool change are higher as the preload grows, as expected, at sight of results contained in Table 3.11.

e ball, as the furthest element from the tool holder, experiences the highest pivoting, being 0.2970 ○ with the 90-N preload, and 0.4622 ○ if the tool is preloaded 270 N. When it comes to relative angles, the transition between parts II and III exhibits the largest rotation angle, namely, 0.1688 ○ and 0.3070 ○ for both preloads. at is, respectively, 59% and 66% of the absolute angle, which means that this part is experiencing the highest rotation during the preload and feed movement of the prototype. However, in both cases the rotation angles are small enough to state that they shall not a ect the application of the process through this prototype.

ese results show that the prototype design is a ected by friction force during the operation, which acts a shear interaction provoking the relative bending of the tool. It can be caused due to the fact that the piezoelectric actuator is supported on a 1-mm Ti-6Al-4V plate at the top of the sonotrode. is low thickness plate is highly 3.5. SYNTHESIS Table 3.11. Absolute and relative pivoting angles of each part of the prototype for both preload levels.

N

270 N I II III IV I II III IV 𝜃 𝑟 (rad) -0.0105 -0.0092 -0.0027 -0.0028 -0.0057 -0.0108 -0.0075 0.0094 𝜃 𝑠 (rad) -0.0004 -0.0002 0.0005 -0.0002 0.0102 0.0063 -0.0023 0.0130 𝛿 (rad) -0.0102 -0.0091 -0.0032 -0.0026 -0.0154 -0.0171 -0.0052 -0.0037 𝜃 ′ (deg) 0.2907 0.2601 0.0914 0.0734 0.4622 0.4560 0.1490 0.1048 𝜃 (deg) 0.0305 0.1688 0.0180 0.0734 0.0061 0.3070 0.0442 0.1048 a ected by the shear force provoked by friction during burnishing. However, this degree of rotation is not a problem for the execution of the process, and, therefore, the prototype shall not be modi ed and is ready to be tested in terms of dynamic behaviour.

is conclusion shall be useful in future activities to improve the tool conception.

Synthesis

As no VABB tool is commercially available, a new design is proposed and was manufactured to apply the process on the target workpieces. Along this chapter an innovative design has been proposed and executed to successfully apply the process.

e prototype was successfully tested on an AISI 1038 surface, con rming its feasibility for the application of the process. e main ndings arising from the di erent characterisation activities of the prototype can be summarised as follows:

1. A spring-based ball burnishing tool equipped with a piezoelectric stack has been successfully designed to succeed in applying the process by using a vibratory force on the target surface.

2. e vibratory system is resonant at nearly 40 kHz. It sticks to this frequency even when the piezoelectric is loaded, by means of an electronic auto-tune circuit that forces it to work at minimum impedance.

is frequency has been experimentally de ned as slightly lower, of 39.1 kHz, by acoustic emission measurements.

3.

e vibratory force introduced in the system follows a sine function, with minimum average half-cycle amplitude found for a 100-N preload, possibly due to the fact that this reduced force does not make the tool engage with the workpiece at the same extent as higher forces. For 200 N, a mean ± 5.5 N amplitude is found to be added in the system, but then it se les at a ± 4 N level for higher preloads. In all, this change should not be in uential, as acoustoplasticity is not an e ect based on stress addition. In all cases, the sine frequency is of 39.2 kHz, agreeing with the other performed measurements.

4. A slight relative pivoting of the sonotrode has been detected during the preliminary tests. However, it has been quanti ed to be of around 0.5 ○ , which is considered low enough to not be detrimental for the process.

4

Description of the experimental methodology is chapter presents the di erent issues and techniques related to the VABB characterisation process. e rst section tackles with the preparatory tasks developed to de ne the experimental plan. e di erent techniques and methods applied to assess the VABB results on surface integrity are then explained. A third section includes the characterisation of the materials on which ball burnishing tests are due to be applied. Finally, some aspects regarding the experimental execution are presented to report on the development of all VABB and NVABB tests.

It is important to note that no experimental results are included here, aside from some auxiliary tests that have been performed to assist design the whole experimental phase itself. e main results are included in the next chapter. is segregation has been done with the deliberate aim of not eclipsing the results assessment discussion with methodological data. Indeed, both contents could generate an excessively long chapter that could distract the a ention of the reader, and prevent it to focus on the results and conclusions drawn from their discussion.

Experimental design

Design of experiments (DOE) constitutes one of the most used techniques to perform an in-depth assessment of di erent engineering issues. e ultimate objective of DOE is to determine the most in uential factors in the case study, by performing an experimental campaign where those factors are tested at di erent levels. e de nition of the DOE is the result of a series of strategic decisions leading to decide the whole experimental procedure, taken as follows:

1. De nition of the factors of study and the response variables on which results shall be evaluated.

2. Layout of the experimental plan that shows the order of the di erent tests to be undertaken. is plan is usually represented in an array, in which each row corresponds to a "run", or a single experimental execution where the factors of study are combined conveniently.

3.

anti cation of the response variables and statistical data analysis.

e variety of methods to de ne the experimental campaign introduces a high variability in the second step. e most simple -and rudimentary-approach to DOE, delivering the biggest volume of data, is a factorial design. However, it is only materially feasible if the number of levels or factors are low, or, as unusual as it is, the available time and budget are enough to extend the experimental phase inde nitely. Complex studies, seeking comprehensive interpretations of the case study, such as the one tackled in this dissertation, do not allow the performance of factorial designs. For that reason, an alternative strategy, namely fractional experimental design, can be followed to reduce the number of experiments, as is presented below.

Fractional design of experiments

Given the described circumstance, an alternative fractional design of experiments (FDOE) can be proposed to reduce the number of tests without losing considerable amount of information. at reduction in evidence of the variation of the response variable a ects rst to high-order interactions between factors, then second order interactions, and, in an extreme case, to the factors itself. Meaning that, the risks of using a too restrictive FDOE are (1) losing the capability of explaining non-linearities present in the system, and, ( 2) not being able to de ne the model itself. at being the price to pay to reduce the number of experimental repetitions, FDOE are highly extended and are usually chosen to tackle with research activities, as the e ect of interactions is usually less relevant than the e ects of rst degree factors. Now the question is, what experiments are to be removed form the complete factorial array to generate a reduced experimental plan from which drawing valuable conclusions? One could intuitively think that the design of the experimental plan cannot be randomly performed. Indeed, it depends on the number and nature of the actions, understanding by action any factor -rst degree-or interactions -second and higher degrees-included in the model. To answer that question, it is necessary to consider that FDOE arrays must comply with two main properties, as explained below [111]:

• Condition 1. Su cient degrees of freedom.

e number of experiments composing the FDOE must be high enough to obtain all the coe cients taking part of the linear model associated to the system of study. erefore, as an action is introduced into the case study, the total number of tests required to evaluate the in uence of all actions on the response variable increases according to the degrees of freedom introduced by the new action. In practice, this condition establishes the minimum number of experiments to be executed to have enough information to complete the model.

• Condition 2. Orthogonality. e condition for the orthogonality of a FDOE as a whole is satis ed if each pair of uncoupled actions included in the model are also orthogonal. erefore, its assessment is reduced to a two-by-two analysis of actions that do not have factors in common. at condition is invariably ful lled for each pair of individual factors, but not so when interactions are included in the model. A pair of uncoupled actions are orthogonal if each level of the rst one is combined the same number of times with the levels of the other, along the whole experimental array. e orthogonality condition guarantees that the e ect of all actions can be analysed independently from the other ones.

e described conditions are necessary and su cient to validate a FDOE as a proper method to conduct an e ective study. Although their application and calculation might seem complicated, FDOE arrays are usually prede ned as a result of decades of experimentation with this kind of arrays, and can be chosen from a great variety of literary sources. In fact, the strategies to reduce experimental plan to fractional designs are numerous. For this thesis, a Taguchi DOE approach has been selected [START_REF]Taguchi's quality engineering handbook[END_REF]. Before detailing the construction and selection of the experimental array, the factors to be included in the model are de ned in the next subsection.

Factors included in the study

e de nition of the actions of interest, along with the levels that shall be object of study, is necessary to elaborate the experimental array, as the degrees of freedom to be covered by experimental results depend on them. Five di erent factors are established as object of study of this dissertation. ey have been chosen at sight of the analysis of previous ball burnishing results presented in the state of the art revision. e ve factors are explained along the following paragraphs.

Preload force -F p e burnishing force, 𝐹 𝑏 , is the physical driver that describes the interaction between the burnishing ball, and the target surface. As was described at the previous chapter, during ultrasonic burnishing, 𝐹 𝑏 is the result of overlapping an oscillating force 𝐹 𝑣 to the preload. According to the characterisation tasks explained in the precedent chapter, that preload, 𝐹 𝑝 can be changed through the spring compression length, whereas the value of 𝐹 𝑣 is constant regardless of the preload level. ese regulation operations are commanded by the NC programme, by selecting the appropriate negative 𝛥𝑧 coordinate to compress the spring to the desired value.

Number of passes -n p Total successive iterations performed during the burnishing operation on a speci c surface position. If the interaction of the burnishing ball with the surface was ideally imagined as a line, this parameter represents the number of times that this line is traced on that position. erefore, the higher its value, the more plastic deformation would be a ained through burnishing. It must not be mistaken with the number of lines necessary to cover the whole surface dimension, which would be also dependent on the lateral o set taken between passes. e trajectory through which these passes are executed is described through the Strategy parameter, which is explained below.

Feed -v f Linear velocity at which the tool is linearly translated over the surface. It is easily commanded through the NC code.

erefore, it corresponds to the conventional feed in a milling operation, with mm/min units.

Original surface topology -S 0 e in uence of the initial surface texture on the burnishing results is of high interest, to associate the e ectiveness of the process with a certain nishing degree achieved through machining. To that purpose, three di erent surfaces are to be tested. All of them shall be machined by ball-end milling operations with a hemispherical milling tool with a TiN coating. e ball-end strategy consists on following adjacent passes with the hemispherical milling tool. To vary the levels of this parameter, the o set distance between passes is increased from one strategy to the other, as shall be explained below.

Strategy -St.

is parameter describes the trajectory followed by the burnishing ball to cover the whole target surface 𝑛 𝑝 times. e resulting strategies have been developed by combining di erent burnishing directions and protocols to cover the previously burnished areas. ey are represented in Figure 4.1. First passes are in all cases performed perpendicular to the initial milling direction, hence its denomination as main burnishing direction. e "0" strategies are contemplated always along that direction, "0" denoting no angular change in the trajectory between passes. Alternatively, the "90/0" strategy is based on turning alternatively ±90 ○ the burnishing direction between one pass and the next one. As for the relative order between lateral o set and number of passes, the "bn" strategies cover 𝑛 𝑝 times the whole target patch, whereas the "nb" strategy is performed by passing 𝑛 𝑝 times one line, and then taking the lateral pass until covering the whole target patch. By choosing these three strategies, the eventual in uence of direction change during burnishing, as well as the e ects of passing repeatedly on the same burnishing path, must be detected.

All strategies are executed according to a succession of linear interpolations dened in di erent NC codes wri en with that aim, and coded through capital le ers as represented in Table 4.1. e combination of di erent 𝑛 𝑝 -St. pairs originates various burnishing pa erns in the experimental array. For instance, the pair 3passes-bn90/0 covers the target surface through two complete passes along direction I, and one along II between both of them, and corresponds to tests #6, #14 and #22 1 . All tests performed by 1 pass do not include further passes, and are therefore not a ected e response variables that are going to be considered to assess the e ects of these factors on the material are di erent parameters describing the surface topology and residual stress along the two main directions of the surface. ese variables shall be discussed in upcoming sections.

Taguchi array

To implement the experimental plan according to the factors of interest, an L27 (3 13 ) Taguchi orthogonal array was chosen. Appendix A shows the whole matrix and its particularisation to the materials on which it shall be applied.

is con guration allows the analysis of a maximum of 13 factors at 3 levels. However, as only 5 factors are to be included in the model, a large amount of degrees of freedom provided by the array are unused, making possible the inclusion of three di erent interactions among coupled factors in the model. e derived experimental design based is proposed as a linear graph in Figure 4.2, and shall be proved valid below. is L27 array is executed twice on both target materials, once with the VABB process, and the second one by executing the NVABB operation, to establish a comparative point. An overview of a standard workpiece, along with the reference directions considered in the dissertation, is represented at Figure 4.3. e con rmation of the orthogonality and su cient degrees of freedom conditions that were presented as necessary to validate the simpli cation of the experimental design provided by the L27 array is explained in Appendix A.

Particular DOE arrays for the studied materials

e methodology for experimental design exposed during the previous section was particularised for both chosen materials. As both of them exhibit di erent mechanical behaviour, the preload as main deforming source, was determined at sight of bibliographical review [117, 150] and a preliminary set of tests performed on both materials to con rm the deformation a er those preload levels.

e rest of the parameters were common for both the AISI 1038 and Ti-6Al-4V experimental execution. Table 4.3 shows the factors and levels which have been applied for the burnishing of the AISI 1038 surface. e 𝑆 0 must be object of further explanation. Although this factor is de ned in the DOE through three levels common to both materials, the respective three initial textures shall predictably di erent between both tested materials. Indeed, they shall be determined as a consequence of the machining process, by changing the lateral o set between every hemispherical tool passes. e whole experimental array for both materials can be consulted in Appendix A. According to the provided materials, and the required high number of repetitions, a

Unvaried process factors

e factors of study were varied along the di erent tests as the Taguchi array describes. However, there are some parameters that, while being eligible to be varied as process factors, were kept constant for all tests. ese factors, along with other unvaried process descriptors, are included in Table 4.4. e burnishing ball material and diameter have been chosen to give continuity to the experimental execution followed in previous studies of our research group [43,[START_REF] T R | Estudio para la mejora del acabado super cial de super cies complejas aplicando un proceso de deformación plástica (Bru ñido con Bola)[END_REF]. e determination of a xed lateral pass width was the result of a combination of di erent criteria, described as follows. As was described in the state of the art chapter, this value must be low small enough, not to leave any non-deformed material on the surface, regardless of the productivity loss that could be caused by taking a too low value. For that reason, a conservative value was chosen and kept constant for all tests, to discard it as a variability source. In the case of the AISI 1038 material, previous studies by Gómez-Gras et al. (2014) [45] recommended 0.36 mm as lateral pass width for 90 N of preload. Consequently, a conservative value of 0.3 was taken. On the other hand, as no bibliographical data was identi ed for the Ti-6Al-4V material, a preliminary experimental test was performed on a milled surface. Burnishing tracks applying di erent preloads and number of passes were performed, and the resulting pro les were acquired and measured through an ALICONA In nite Focus optical prolometer, as exempli es Figure 4.5. e lowest imprint width was 0.732 mm, obtained by applying 150 N, proving that 0.3 mm was also a valid lateral pass width for this material.

Results assessment through Analysis of Variance

e methodology associated to the analysis of the Taguchi experimental setup contemplates the calculation and analysis of the results through two di erent approaches:

• antifying the mean e ects that all actions (factors and interactions) have on the selected response variables.

• Evaluating the robustness of the actions associated to each response variable. e parameter used to evaluate the robustness of a factor used in the Taguchi system is the signal-to-noise ratio (S/N) . Robustness refers to the neutralisation of the e ect of noise e ects in the response, and is included in the Taguchi analysis because it is a fundamental aspect contained in its quality approach. e Taguchi experimental design focuses on achieving a desired response goal while minimising the variance of that response, that is, maximising its robustness. As S/N is an input-to-output relationship, it should be maximised. is perspective is based on the idea that a certain product or process should always respond the same way to an external signal. In our case, when a certain combination of burnishing parameters is applied on a workpiece, the process should always derive in the same result. Its calculation depends on the objective with regards to the response variable, according to the desired e ect on the response variable, as shows Table 4.5

S/N Goal Expression

Larger is be er Maximise response

-10 log ∑ 1 𝑌 2

𝑁

Smaller is be er Minimise response -10 log ∑ 𝑌 2 𝑠 2

𝑌 : responses for the given factor level combination, 𝑁 : number of responses in the factor level combination, 𝑠: standard deviation of the responses for a given factor combination.

To analyse the in uence of all factors on the response variables and the robustness associated to them, the results linked to a Taguchi experimental array can be assessed through an analysis of variance technique (ANOVA) . e purpose of ANOVA applied to experimental design analysis, is to compare the e ect of single factors and interactions which are applied simultaneously on the response variable. erefore, it allows the di erentiation of the e ects of the actions of interest from the residual variation, or noise. In other words, the ANOVA table delivers a hierarchy of the di erent sources of variation of the response variable. If all the observed means, i.e. the result for each run, are close together, then the di erences between them can be a ributed to residual variation. If, on the contrary, they are dispersed, then there is a reason

MEASUREMENT OF THE SURFACE INTEGRITY PARAMETERS

to believe that the e ects of di erent treatments are signi cantly di erent because of the application of di erent levels. e problem can be formulated as a hypothesis test:

) ⌉ ⌉ ⌋ ⌉ ⌉ ] 𝐻 0 ∶ 𝜇 1 = ... = 𝜇 𝑖 = ... = 𝜇 𝑐 𝐻 1 ∶ 𝜇 𝑖 ≠ 𝜇 𝑗 𝑓 𝑜𝑟 𝑠𝑜𝑚𝑒 𝑖 ≠ 𝑗 (4.1)
where 𝜇 𝑖 is the mean response for observation 𝑖.

e null hypothesis can be rejected if the p-value associated to it a er the test is higher than a pre xed level of signi cance, 𝛼, in which case the null hypothesis can be rejected, and one can assume that the variation of the response is not caused by a variation of the related action. All ANOVA calculations shall be performed with the so ware Minitab 18.

Measurement of the surface integrity parameters 4.2.1 Acquisition of topological data

As explained in chapter 2, the evaluation of surface texture using two-dimensional parameters can be a biased and incomplete approach to assess VABB results. With the advances in surface metrology measurement, a new set of 3D parameters was progressively introduced to describe mathematically the nature of engineering surfaces [START_REF]antitative characterisation of surface texture[END_REF]. Nowadays, optical systems allow the transformation of a surface into a mathematical function which assigns one height value to each sampled point (Figure 4.6). e publication of the ISO 25178 standard o ered a wide set of tools to convert that mathematical function into functional descriptors grouped in two main categories, namely the 12 S parameter and the 13 V parameter sets [67].

To perform the calculation of those parameters, the sampled surface must be initially processed by establishing a reference plane, obtained through least squares [START_REF]Comprehensive study of parameters for characterising three-dimensional surface topography III: Parameters for characterising amplitude and some functional properties[END_REF]. Let 𝑧(𝑥 𝑖 , 𝑦 𝑗 ) be a 3D equispaced sampled surface, formed by a set of points 𝑥 𝑖 = 𝑖𝛥𝑥 ∶ 𝑖 = 1, 2, ..., 𝑀 , and 𝑦 𝑗 = 𝑗𝛥𝑦 ∶ 𝑗 = 1, 2, ..., 𝑁 , being 𝛥𝑥 and 𝛥𝑦 the sampling intervals, and 𝑀 and 𝑁 the number of sampling points along the 𝑥 and 𝑦 axis, respectively. A least squares mean plane 𝑓 (𝑥, 𝑦) calculated on the aforementioned dataset is calculated, and shall serve as the reference datum, so that all parameters e rst descriptor set that allows the exploitation of the topological data delivered by the 𝜅(𝑥, 𝑦) dataset, is composed by the 12 S parameters. Table 4.6 summarises the mathematical expressions that lead to their calculation. e interpretation of each parameter is developed along the following paragraphs.

S amplitude parameters

ey represent statistical characteristics of the surface height distribution, the scale of the irregularities, and the extreme points it presents. Due to their de nition, all of them have a corresponding analogous parameter de ned in 2D, calculated from the linear height distribution. Both the average surface texture, 𝑆 𝑎 , and the RMS height, 𝑆 𝑞 , are related to the scale of the surface texture, as already presented above for their two-dimensional counterparts. 𝑆 10𝑧 represents the amplitude of maximum deviations.

e skewness and kurtosis are actually de ned in statistical analysis as the 3 𝑟𝑑 and 4 𝑡ℎ order central moments of the surface (Table 4.7). According to this de nition, the RMS parameter is actually the second central moment, hence the statistical relevance already a ributed to this parameter in detriment of 𝑆 𝑎 .

MEASUREMENT OF THE SURFACE INTEGRITY PARAMETERS

Table 4.6. 12 S parameter set for surface topography assessment, as de ned in the ISO 25178.

Amplitude

Root mean square height

𝑆 𝑞 = ⌉ 1 𝑀 𝑁 ∑ 𝑁 𝑗=1 ∑ 𝑀 𝑖=1 𝜂 2 (𝑥 𝑖 , 𝑦 𝑗 ) Skewness 𝑆 𝑠𝑘 = 1 𝑀 𝑁 𝑆 3 𝑞 ∑ 𝑁 𝑗=1 ∑ 𝑀 𝑖=1 𝜂 3 (𝑥 𝑖 , 𝑦 𝑗 ) Kurtosis 𝑆 𝑘𝑢 = 1 𝑀 𝑁 𝑆 4 𝑞 ∑ 𝑁 𝑗=1 ∑ 𝑀 𝑖=1 𝜂 4 (𝑥 𝑖 , 𝑦 𝑗 ) Arithmetical mean height 𝑆 𝑎 = 1 𝑀 𝑁 ∑ 𝑁 𝑗=1 ∑ 𝑀 𝑖=1 ⋃ 𝜂(𝑥 𝑖 , 𝑦 𝑗 ) ⋃ Ten-point height 𝑆 10𝑧 = 1 5 ∑ 5 𝑘=1 ⋃ 𝜂 𝑠𝑖 ⋃ + ∑ 5 𝑘=1 ⋃ 𝜂 𝑣𝑖 ⋃ Maximum peak height 𝑆 𝑝 = max {𝜂(𝑥 𝑖 , 𝑦 𝑗 )} Maximum pit height 𝑆 𝑣 = min {𝜂(𝑥 𝑖 , 𝑦 𝑗 )}

Spatial

Fastest decay autocorrelation length 𝑆 𝑎𝑙 = min

⌉ 𝑡 2 𝑥 + 𝑡 2 𝑦 ∶ 𝐴𝐴𝐶𝐹 (𝑡 𝑥 , 𝑡 𝑦 ≤ 0.2)
Texture aspect ratio

𝑆 𝑡𝑟 = min ⌉ 𝑡 2 𝑥 + 𝑡 2 𝑦 max ⌉ 𝑡 2 𝑥 + 𝑡 2

𝑦

Hybrid

Root mean square gradient

𝑆 𝑑𝑞 = ⟨ ⧸ ⧸ ⧸ ⟩ ∑ 𝑁 -3 𝑗=4 ∑ 𝑀 -3 𝑖=4 𝜅(𝑥 𝑖+1 ,𝑦 𝑗 )-𝜅(𝑥 𝑖 ,𝑦 𝑗 ) 𝛥𝑥 2 + 𝜅(𝑥 𝑖 ,𝑦 𝑗+1 )-𝜅(𝑥 𝑖 ,𝑦 𝑗 ) 𝛥𝑦 2 (𝑁 -6)(𝑀 -6)
Developed interfacial area ratio

𝑆 𝑑𝑟 = ∑ 𝑁 -1 𝑗=1 ∑ 𝑀 -1 𝑖=1 { 1 + 𝜅(𝑥 𝑖+1 ,𝑦 𝑗 )-𝜅(𝑥 𝑖 ,𝑦 𝑗 ) 𝛥𝑥 2 + 𝜅(𝑥 𝑖 ,𝑦 𝑗+1 )-𝜅(𝑥 𝑖 ,𝑦 𝑗 ) 𝛥𝑦 2 (𝑁 -1)(𝑀 -1)
-1

Miscellaneous

Texture direction 𝑆 𝑡𝑑 Angle of texture's main direction

𝜇 𝑛 = ∫ -∞ ∞ 𝑦 𝑛 𝑑𝑦 2 Root mean square 3 Skewness 4 Kurtosis
Figure 4.7 shows typical values of both parameters. e skewness value, 𝑆 𝑠𝑘 , represents the proportion of negative and positive points in the pro le, as it can take negative or positive values according to its de nition. Skewness = 0 is the reference value for equilibrated Gaussian distributions. Negatively skewed surfaces are predominantly peak biased. Many processes, such as lapping or plateau honing generate these kind of surfaces, whereas positively skewed ones are not so easily obtained. On the other hand, Kurtosis, 𝑆 𝑘𝑢 gives an idea of the abruptness of the surface. A Gaussian distribution is characterised by kurtosis value 3, which is its reference value. Higher values correspond to leptokurtic surfaces, typical of spiky surfaces, whereas kurtosis lower than 3 is typical of non-abrupt platykurtic surfaces. Skewness and Kurtosis can be easily interpreted and, according to Stout & Davis (1984) [138], used to relate the characteristics of a surface with its functional performance. For instance, medical, food and antifatigue components require low kurtosis surfaces, which are related to unscratched surfaces desired for those applications.

S spatial parameters

ese parameters represent a practical set to evaluate the texture of the surface, and they introduce the factor of directionality in topology characterisation. ey do not have a 2D correspondence, as the spatial factor is not present if a directionality is xed where 𝑚 and 𝑛 are the maximum numbers of the autocorrelation lengths in the 𝑥 and 𝑦 directions, respectively, and 𝑀 and 𝑁 are the number of sampled points along 𝑥 and 𝑦.

e parameter 𝑆 𝑎𝑙 represents the shortest distance in which the value of the AACF decays under a threshold, normally 0.2. Large values of this parameter represent surfaces dominated by low frequency components, that is, the surface features are repeated along longer distances, and, therefore, are characterised by high scale features and irregularities. On the other hand, the 𝑆 𝑡𝑟 parameter is useful to identify the existence of a preferential texture pa ern. is ratio ranges between 0 and 1, being 0 for surfaces who show strong anisotropy, that is, an outstanding preferential direction in the texture.

S hybrid and miscellaneous parameters

ese parameters combine spatial and amplitude features of the surface, by evaluating the degree of heterogeneity of the average slope shown by the surface features. 𝑆 𝑑𝑟 represents the ratio of the increment of interfacial area of a surface over the at sampling area. Large values of the developed interfacial area are related to rough surfaces. erefore, its value tends to 0 as the surface presents a state nearer from a nishing. Super nished surfaces usually show values smaller than 1%, which is the value usually taken as reference. Alternatively, 𝑆 𝑑𝑞 calculates the root mean square of the surface slope within the sampling area. Whereas 𝑆 𝑑𝑟 has an intuitive de nition, 𝑆 𝑑𝑞 has a strongest statistical meaning. However, both parameters provide similar information about the nishing state of the surface.

On the other hand, the 𝑆 𝑡𝑑 miscellaneous parameter is the value of the angle that indicates the main direction of the surface features with respect to the 𝑦 axis. ere-fore, it is useful in highly anisotropic surface that show a preferential texture direction.

4.2.1.5 V parameter set e complementary 13 V parameter set (Table 4.8) is actually an evolution of the calculations proposed by Abbo -Firestone [1], by expanding their de nition of bearingarea curve to a three-dimensional height dataset. e parametrisation of the bearing curve help to assess the topological features of a surface, while allowing the systematisation of the analysis of the curve by reducing it to a few parameters, which can be subsequently divided into two main groups. First, the amplitude descriptive parameters that represent the main geometrical features of the surface. Secondly, the volumetric parameters (void and material volumes), which are used to adopt a functional perspective of the height distribution of a surface, as the peak zone is associated to the material which shall eventually be the initial recipient of running-in wear, the core corresponds to the stationary bearing material, and the valley zone is related to the surface capability for lubricant retention and debris evacuation [67]. e approach of dividing the material into peak, core and valley zones requires a systematic method to establish the di erence. In this dissertation, the ISO 13565-2 method is used. It is based on tracing a line secant to the Abbo -Firestone (AF) curve with the lowest gradient, with the restriction that the points de ning the line must span 40% of bearing area percentage (𝑥 axis). Its intersection with the 𝑦 axis de nes the peak, core and valley areas, as is shown in e burnishing patches derived from all tests were registered by an ALICONA In nite Focus device. is device is able to register the topology of a surface by successive image acquisition along the vertical direction, without contact with the surface. Its functioning principle is focus variation achieved at di erent heights, assisted by a coaxial LED ring light, that assigns a height coordinate depending of the focal distance for each measured point.

MEASUREMENT OF THE SURFACE INTEGRITY PARAMETERS

e 10x objective was used to perform this acquisition, delivering to the system a 100 nm vertical resolution.

In order to homogenise the measurement and discarding edge e ects that could eventually distort the measurement, only the central areas of the burnishing patches were acquired. However, as standards do not de ne the exact area that guarantees an unambiguous characterisation of the target surface, a preliminary study was performed on the 𝑆 0 1 , 𝑆 0 2 and 𝑆 0 3 machined surfaces (Figure 4.3), to determine the optimal size of the target area to be acquired. is operation was necessary in order to minimise the acquisition time of all burnishing surfaces, while not losing valuable data or aliasing the measurements for ulterior topological analysis.

As all three machined topologies consist on a highly periodic pa ern formed by alternated peaks and valleys, it was decided to adjust the dimensions of each patch to include an integer value of coupled peak&valley pairs (henceforth P&V) . Due to the variation in the scale of topology features, this strategy involved capturing di erent sizes for each P&V set depending on the surface, as shows Figure 4.9.a. Whereas the 𝑆 𝑠𝑘 and 𝑆 𝑘𝑢 of the surfaces show stability for all sampling sizes, the evolution of 𝑆 𝑞 shows that the surfaces de ned by larger features require larger areas to be fully characterised (Figure 4.9.a). For instance, 𝑆 0 1 shows the same 𝑆 𝑞 value for all sizes, so that 2 P&V, -that is, a 1 × 1 mm 2 surface-represent su ciently the whole surface. On the contrary, a surface similar to type 𝑆 0 3 , more abrupt, must be at least described by 6 P&V, or a 6.8 × 6.8 mm 2 surface. at is the value from which 𝑆 𝑞 stabilises and shows no variation with the sampling size.

MEASUREMENT OF THE SURFACE INTEGRITY PARAMETERS

Unlike the second, third and fourth moments of the surface, the 𝑆 10𝑧 extreme value does not show any signal of stabilisation, as it increases as the surface size grows. is e ect is not atypical for this parameter, as explain Dong et al. (1994) [START_REF]Comprehensive study of parameters for characterising three-dimensional surface topography III: Parameters for characterising amplitude and some functional properties[END_REF]. Indeed, due to the fact that the summit heights are calculated by algorithms that depend on the evolution of the slope of the surface, so that atypical values can be discarded, they are sensitive to the sampling interval. erefore, as that interval increases, the threshold to de ne a characteristic peak point increases, and the value of 𝑆 10𝑧 grows naturally.

At sight of the results, it is decided to take patches containing 6 P&V sets for all surfaces. A second measuring phase was carried out, by registering the three initial topologies ve times at di erent positions of the whole machined surface. e descriptors measured at all patches were averaged, and the error associated to their repeatability was calculated (Table 4.9). For instance, the average value of 𝑆 𝑘𝑢 for 𝑆 0 1 is 1.6816 µm, with a standard deviation of 0.0494 µm. at represents an error of 2.94% in terms of repeatability.

is error is enclosed between 1.5% and 3% for all initial states. ere is not an increase of error as the surface present more abrupt features, thus allowing the validation of the selected approach to perform the measurements.

All amplitude parameters show acceptable low error values, while, on the con-trary, extreme parameters 𝑆 10𝑧 , 𝑆 𝑝 and 𝑆 𝑣 present a lower repeatability. is observed e ect can be understood from the way these values are de ned, their sensitivity with regards to the sampling area, and their higher dependence of extreme values which can be inconspicuously present as anomalous values in a certain acquired surface. Consequently, these extreme parameters must be taken carefully into consideration in the topological analysis to come.

Retained topological parameters from the S set

Given the high amount of 2D and 3D parameters available to describe the surface, it is worth reconsidering the possibility of discriminating parameters that might be redundant with regards to others, or that do not deliver any valuable information to the system of study. Table 4.10 shows the selected parameters for each surface feature.

Miscellaneous

𝑆 𝑡𝑑 e mean square surface texture 𝑆 𝑞 shall be preferred over the average one 𝑆 𝑎 as the general amplitude descriptor of the surface nishing. As already explained, it can be consistently framed in the statistical analysis to be performed. Furthermore, King & Spedding (1982) [69] proved that both parameters were proportional to one another. Skewness and Kurtosis shall also be considered in the results discussion, for their uniqueness in surface characterisation. As for the extreme value parameters, 𝑆 10𝑧 is preferred over the peak and valley extreme values 𝑆 𝑝 and 𝑆 𝑣 . e spatial and miscellaneous parameters, that is, 𝑆 𝑎𝑙 , 𝑆 𝑡𝑟 and 𝑆 𝑡𝑑 , are also kept for analysis. However, not both hybrid parameters are required, for they give similar information about the surface, that is, its proximity to a nishing state. As the error associated to repeatability of both parameters is similar, it is decided to keep 𝑆 𝑑𝑞 , due to its scale proximity to 𝑆 𝑡𝑟 , that facilitates further representation. All these parame-ters shall be completed by other descriptors belonging to the V parameter set, as shall be speci ed in the result discussion chapter.

Metallurgical characterisation of subsurface layers

Analysing the metallurgical state of the surface and subsurface layers is fundamental to characterise the e ects of VABB on surface integrity. Changes in metallography are usually explained through the hardness magnitude, as the phases that compose a certain metal have di erent structures, and consequently pose di erent behaviours towards indentation tests. For that reason, in addition to visual inspection of the microstructure of a metal, the mentioned tests are highly representative of this surface integrity descriptor. Specimen preparation is common for both techniques. e protocol includes material cu ing, so that the deep layers of the surface can be then studied. e next step consists on specimen encapsulation in resin (Figure 4.10) which is then polished. e result of the described process is a mirror-polished specimen encapsulated in a stable resin body. is kind of specimens can be used to assess the hardness of the specimen through microindentation testing. where 𝑝 is the load applied on the specimen in gf, and 𝑑 is the average diagonal of the indentation in µm.

Normally, the highest di culty facing hardness measurements is the selection of the load. Indeed, although the actual hardness results should be stable regardless of its value, numerous studies about microindentation techniques have shown that results are not stable at low loads due to a higher experimental error and the indentation size e ect. erefore, excessive reduction of the indentation load can lead to a high error.

e load selection is therefore an important factor to bear into account, especially for multiphase materials, which might show highly disperse hardness results if small loads are applied. If selective microstructural grains are spanned in the indentation, the average of all measurements could not be descriptive of the whole material.

Once hardness was measured, specimens were prepared for optical microscopy and SEM observation. An etching operation was performed to guarantee enough contrast between phases, and fully reveal the microstructure of the target specimen. Although etching techniques are varied, chemical a ack is o en selected for this aim because of its easiness of application. Chemical etching is based on the fact that metal phases react at di erent speeds with chemical reagents. erefore, by pu ing them in contact with di erent chemical inorganic substances, the most vulnerable phases shall dissolve, revealing grain boundaries that di erentiate them from the most stable ones that remain creating a nearly three-dimensional image of the material structure. As the AISI 1038 and Ti-6Al-4V are subjected to di erent etching operations, this stage is detailed in particular for each of them at subsequent subsections.

Error estimation for Vickers hardness measurements

For this dissertation, a minimum of 10 indentation tests are performed for each desired hardness measurement. As hardness is not an absolute measure, and depends on the point on which the indentation is performed, an error term must accompany the hardness value. In this case, the Student's t-distribution delivers the estimation the mean HV value for small size samples from which the mean and standard deviation of the population is unknown, as is the case. erefore, the statistical uncertainty, 𝐸 𝑠 , associated to the HV measurement, can be calculated as:

𝐸 𝑠 = 𝑠 ⌋ 𝑁 𝐻𝑉 𝑡 𝛼,𝑁 𝐻𝑉 -1 (4.5)
where 𝑠 is the standard deviation of the HV sample and 𝑁 𝐻𝑉 is the sample size, and 𝑡 𝛼,𝑁 𝑉 𝐻 -1 is the Student's t statistic at a 𝛼 con dence level.

A second term arising from experimental execution must be added. is term includes the error introduced by the limitation in optical resolution given by the microscope used to measure the indentation imprint diagonals, 𝐸 𝑜𝑝𝑡 , considering that the maximum resolution achievable by the system is restricted by the light wavelength, as establishes the Rayleigh principle (Eq. 4.6) [9]. is term is x for all measures, and depends on the equipment.

𝐸 𝑜𝑝𝑡 = 1.220 𝑓 𝜆 𝐷 𝑙 (4.6)
where 𝑓 is the focal length of the objective, 𝐷 𝑙 is the diameter of the light beam, and 𝜆 is the light wavelength.

A third term related to the bias in the diagonal measurement caused by the spherical deviation of the operator's eyeball, 𝐸 𝑒 , must be considered in the experimental error. is term is calculated with a previous calibration phase performed on a stan-dard block for hardness testing. e total error is, therefore, the addition of the three terms: 𝐸 = 𝐸 𝑠 + 𝐸 𝑜𝑝𝑡 + 𝐸 𝑒 (4.7)

Residual stress measurement

e methods to measure the residual stress (RS) state of a material are numerous, including both destructive and non-destructive techniques.

e decision of what method to use is conditioned by the technical constraints that each of them pose, as well as the type of residual stress to be measured, as explain Withers & Badeshia (2001) [157]. For instance, the deep hole drilling technique is an e ective method to assess type-I residual stress gradient along progressively deeper layers of the material, by the adhesion of strain rose es and gauges on the surface. In previous works, this method has been successfully used by the author of this dissertation to evaluate residual stress on AISI 1038 and AA2017-T4 surfaces [40]. However, specimen preparation is highly time consuming, comprising delicate gauge adhesion onto the target workpiece. Furthermore, the low repeatability of the method makes it infeasible for the purposes of this thesis, where 108 burnishing tests must be measured.

Alternatively, the X-ray di raction method has been selected to evaluate the super cial residual stress a er VABB. e technique is based on applying Bragg's law while quantifying the change of interplanar spacing inside crystals which conserve elastic strain con ned inside plastically deformed crystals due to VABB. As elastic strain results in a change of the la ice dimension, crystalline planes inside the grains are actually used as intrinsic strain gauges in this method. Albeit the major drawback of this di raction method is the low depth to which compressive residual stresses measurements can be performed, its technical availability and feasibility makes it proper to evaluate VABB results in this experimental plan.

Bragg's law states that when an X-ray beam with a certain wavelength is incident onto a crystal, it is di racted by the same angle. is is only true for certain waves that verify the analytical expression of the law (Eq. 4.8). Let us consider an X-ray beam irradiating a surface with incidence angle 𝜃, on a set of crystalline planes de ned by an interplanar distance, 𝑑, then all magnitudes are related as follows:

2 𝑑 sin 𝜃 = 𝑛 𝜆 (4.8)
where 𝑑 is the interplanar distance between planes, 𝜃 is the di raction angle, 𝜆 is the wavelength of the beam, and 𝑛 ∈ N is the order of di raction.

Let us consider a crystal in an non-deformed state, characterised by an interplanar spacing 𝑑 0 . In that case, the di raction angle shown by an X-ray beam is 𝜃 0 . A er experiencing a deformation, that distance has diminished due to plastic strain and compression to 𝑑 𝜓 , and re exes the X-ray wave a 𝜃 𝜓 angle (Figure 4.12). As in both states is Bragg's law true, the initial state and the state a er modication can be related as expressed in Eq. 4.9.

at initial state is characterised by reference interplanar distance 𝑑 0 , and di raction angle, 𝜃 0 , which are determined by applying the technique to reference standard specimens obtained by powder metallurgy, which are free of residual stress.

𝑑 0 = 𝑑 𝜓 sin 𝜃 0 sin 𝜃 𝜓 (4.9) e explained principle allows the calculation of deformation of crystals and link it to the stress state that generates that deformation, i.e. the residual stress, as follows.

e multiangle technique used in this dissertation consists on irradiating the surface with an X-ray collimator mounted on a goniometer. at device is equipped to adjust the azimuth angle, 𝜑 , in which the measure shall be performed. Once this angle has been xed, the collimator irradiates the surface with X-ray at di erent incidence angles, 𝜃. Of all those beams, only the one complying with Bragg's law shall be detected by a receiver coupled to the system. is operation is repeated for several negative and positive tilt angles, 𝜓, regulated through the motorised workpiece base. Once this operation has been completed, the goniometer is used to change the azimuth angle and take a subsequent measurement.

Along the described process, for each tilt angle at each azimuth position, the intensity registered by the receiver is saved for every explored angle 2𝜃 𝜓 is represented in a di raction spectrum. Each pair 𝜑-𝜓 has an associated di ractogram on which an intensity peak is present for the irradiation angle for which Bragg's law is satis ed, 2𝜃 𝜓 (Figure 4.13). e residual stress quanti cation is based on the analysis of a set of those spectra. e calculation of the interplanar distance for every tilt angle 𝜑 -𝜓, and its comparison with the reference non-deformed distance, delivers the deformation to which the crystal is being subjected, through the following equation:

𝜀 𝜑𝜓 = 𝑑 𝜓 -𝑑 0 𝑑 0 = sin 𝜃 0 sin 𝜃 𝜓 -1 (4.10)
If the strain state of the crystal is considered tridimensional, then that deformation can be related to the stress state that generates it, that is, the residual stress, through the elastic mechanics equations in a continuum:

𝜀 𝑖𝑗 = 1 + 𝜈 𝐸 𝜎 𝑖𝑗 - 𝜈 𝐸 𝛿 𝑖𝑗 𝜎 𝑖𝑗 (4.11)
where

𝛿 𝑖𝑗 = 1 if 𝑖 = 𝑗 and 𝛿 𝑖𝑗 = 0 if 𝑖 ≠ 𝑗
As this elastic strain in measured along the normal direction to the di racting planes at a certain tilt position of the collimator, . It can be quanti ed by projecting the strain tensor on the n direction, as follows:

𝜀 𝜑𝜓 = n 𝜀 n 𝑇 = 1 + 𝜈 𝐸 (𝜎 𝜑 -𝜎 𝑧𝑧 ) sin 2 𝜓 + 1 + 𝜈 𝐸 𝜎 𝑧𝑧 - 𝜈 𝐸 𝑇 𝑟 (𝜎) + 1 + 𝜈 𝐸 𝜏 𝜑 sin (2𝜑) (4.12) 4.

MEASUREMENT OF THE SURFACE INTEGRITY PARAMETERS

Eq. 4.12 actually represents a function, namely 𝜀 𝜑𝜓 = 𝑓 (sin 𝜓). erefore, if 𝜀 𝜑𝜓 , i.e. 2𝜃 by Eq. 4.10, is graphically represented against sin 2 𝜓), the characteristic parameters of the linear t (slope and intercept) can be compared to the graphical representation to deduce the values of the residual stress tensor (Figure 4.14). Specifically, normal stress 𝜎 can be calculated by determining the slope, whereas tangential stress 𝜏 are by the overture of the parabolic function ed on the measured points. A measure at 𝜑 = 0 𝑜 delivers 𝜎 𝑥 and 𝜏 𝑥𝑦 , whereas 𝜑 = 90 0 allows the calculation of 𝜎 𝑦 and 𝜏 𝑦𝑥 . erefore, in practice, normally only these two azimuth angles are irradiated for one measurement. e technological application of the X-ray di raction measurements changes according to the objective material. Table 4.11 shows the technological parameters used for both considered materials in this thesis. All tests were performed with a SET-X goniometer and the STRESSDIFF so ware was used to automatically register all di raction measurements and calculate the stress tensor associated to the analysed burnishing patch. However, the data postprocessing was di erent. As the AISI 1038 di ractometer spectres hardly showed noise, the approximative FWHM-peak height method was used to estimate the di raction angle. On the contrary, the spectres presented by Ti-6Al-4V spectres were postprocessed through polynomial ing, to overcome the high noise presented by the measurement. Consequently, the incertitude associated to Ti-6Al-4V was higher, as shall be presented in the next chapter. AISI 1038 is a medium-carbon steel alloy with medium-high machinability. It has been chosen for this experimental execution for two main reasons. e rst one is to give continuity to previous works [43]. Secondly, the 1038 alloy is used for an extensive range of industrial applications such as gears, axes, sha s, or moulds, as well as larger components such as power shovels, due to its high versatility. erefore, it is a steel prone to be found in numerous industrial workshops of di erent scale. Table 4.12 shows its composition according to the AISI standard.

Component

Fe Mn C S P Weight (%) 98.6-99.05 0.6-0.9 0.35-0.42 ≤0.05 ≤0.04 e material has been provided as laminated bars of 100 × 60 mm section. A 170mm long piece was cut from the bar to obtain the workpiece to be burnished, so that all planned essays could be carried out.

e mechanical properties of that material were characterised by Travieso-Rodríguez (2010) (Table 4.13). ey are considered as valid for this thesis, as the material was taken from the same bar.

To observe the metallurgical structure of the material, a sample from its core was extracted from the bar, and was cut along the lamination direction, coincidental with the milling direction, or direction II, according to the criterion established in Figure 4.3. A second specimen to observe the microstructure along direction I, was also e metallurgical characterisation of the material was completed through Vickers microindentation hardness tests, a er polishing the specimens a second time to erase the e ect of etching. Figure 4.16.a shows a detail of pearlite grain in the core material, leading to establish that the reference grain size is of the order of 20 µm. By applying a 100-gf load, burnishing imprints had an average size of around 30 µm, and, therefore, this load was con rmed as adequate. Indeed, as ferrite is considerably ductile and less hard than cementite, and therefore, pearlite formations, the indentation imprints were not localised on single isolated phases and no bias of the overall hardness measurement was detected. Figure 4.16.b con rms that Vickers indentations spanned a mix of both phases in the material core. Table 4.14 shows the average result of 15 hardness measurements along each direction. At sight of these results, the material can be considered isotropic in terms of hardness.

Ti-6Al-4V alloy

e titanium alloy Ti-6Al-4V is a biphase material composed of 𝛼 + 𝛽 structures. e presence of both phases is achieved by the equilibrated combination of 𝛼-stabiliser interstitial Al, and 𝛽-stabiliser element V and Fe, as is shown in Table 4.15. e presence of both allotropic phases makes Ti-6Al-4V a versatile alloy o ering an exceptional balance of strength, ductility, fatigue and fracture properties with application in the aeronautical industry to manufacture pressure vessels, gas turbine disks or compressor blades. e raw material used for the experimental phase was provided as a 105×95×165 mm forged block. e standard properties are included in Table 4.16. Compared to the AISI 1038 alloy, this material presents a higher yield strength, what leads to think that higher forces should be applied to achieve permanent plastic strain via VABB. As the historic of the material is unknown, the structure of the alloy along with its hardness were determine in a preliminary phase. A specimen was extracted from the core material, cut along the longitudinal direction and its perpendicular. Both resulting surfaces were then subjected to encapsulation and polishing treatments explained above. An indentation test was performed to calculate the hardness of the material. Table 4.17 contains the resulting hardness measurements, evidencing the original isotropy of the material. e microstructure was then analysed through SEM observation. Figure 4.17.a con rms the biphase composition of the Ti-6Al-4V, equally distributed in both main directions.

e 𝛼-titanium is depicted as the white regions, whereas the 𝛽-titanium is darkened by the used reagent. Both structures are organised as intergranular 𝛼 embedded in a 𝛽 matrix. As the 𝛽 phase has a BCC structure, a large number of slip planes makes it more ductile and less resistant than the 𝛼 hexagonal crystal structure, hence the relatively low hardness presented by the raw material, with regards to other metallurgical states of the same alloy [START_REF]Titanium: a technical guide[END_REF]. Since the microstructure pa erns of the alloy present an approximate grain size of 15 µm, the Vickers imprints derived from the indentation tests can be considered representative enough to characterise the material hardness. In fact, Figure 4.18 con rms that both phases can be adequately spanned by applying a 100-gf load. x the workpieces to the machine table, they were drilled and screwed to it in order to monitor the forces applied during the burnishing tests ( e workpieces were not removed from that position during the whole machining and burnishing processes. Like that, the perpendicularity of the burnished surface to the VABB tool was guaranteed, and references were kept constant.

e workpiece preparation process started by a rst surfacing operation with a multi-insert front milling tool. On that at surface, the di erent ball-end milling strategies were applied to obtain the desired di erent surfaces, as explained in the next subsection.

Machining of the original surfaces

e in uence of the original surface texture on the burnishing results is of high interest for this thesis, to associate the e ectiveness of the process with a certain nishing degree that can be found in an actual industrial context. To that purpose, three different surfaces were planned to be tested. All of them were obtained by executing a face milling operation using a hemispherical milling tool with a TiN coating. e cu ing speeds selected to perform the machining were 120 m/min and 70 m/min for the AISI 1038 and the Ti-6Al-4V workpieces respectively. Table 4.18 shows the geometrical machining parameters selected for all three surfaces. e generation of the original surfaces by choosing these parameters is fundamental to control and master the peak height and the material distribution on the surface, and, therefore, the expected texture. Furthermore, the chosen parameters can be undoubtedly identi ed with realistic machining conditions applied in an industrial context. De ning these parameters by adopting this approach is not casual, since it is of high importance to take pro t of the derived results for potential industrial applications. To calculate the spindle velocity to be applied during machining through Eq. 4.13, the e ective radius of cut 𝑟 𝑒 , that is, the contact between the hemispherical tool and the material plane, must be determined. is value represents the actual dimension which characterises the contact between the cu ing tool and the objective material, as a function of the selected geometrical cu ing parameters, as shows Figure 4.20. Its determination is important to optimise the tool life, avoid surface integrity defects due to detrimental chip removal mechanism, and preventing the coating to be worn out prematurely.

𝑛 = 1000 𝑣 𝑐 2 𝜋 𝑟 𝑒 (4.13)
where 𝑛 is the spindle speed in min -1 , 𝑣 𝑐 is the cu ing speed in m/min.

All geometrical parameters can be mathematically related through a rectangle triangle. erefore:

𝐷 2 = 𝑟 2 𝑒 + (𝐷 -𝑎 𝑝 ) 2 (4.14)
where 𝐷 is the milling tool diameter and 𝑎 𝑝 is the depth of cut.

As 𝑎 2 𝑐 ≪ 𝐷𝑎 𝑐 , Eq.4.14 can be simpli ed, and the e ective radius can be calculated as:

𝑟 𝑒 = ⌈ 2 𝐷 𝑎 𝑐 (4.15)

Burnishing force measurement

Being able to register the forces while the burnishing operation is being executed allows the control of the force level that is being applied, as well as quantifying the force uctuation during the test. is is the reason why the test pieces are a ached to the Kistler dynamometer. e device delivers a register of the forces applied according to a Cartesian reference system, where 𝐹 𝑧 represents the burnishing force, whereas 𝐹 𝑥 is the tangential force that appears during the execution of the process, opposed to the feed movement of the tool. Although it cannot be formally de ned as a friction force, it shall be referred to as pseudo-frictional due to its dynamic opposition to the feed motion.

As the sampling frequency of the Kistler ampli er is 2 kHz, the registered signals cannot evidence the vibratory component delivered by the piezoelectric. Under this circumstance, the forces acquired during the VABB and the NVABB tests should have in essence the same behaviour, as only the force governed by the spring, 𝐹 𝑝 , is registered. e rst 15 s of each test were acquired to reduce the amount of data to manipulate. is portion of registered forces were exported as .csv les, and processed through a Matlab routine composed of di erent scripts. e observation of the NVABB and VABB forces registered for each testing conditions showed a similar pa ern. Figure 4.21.a shows test #25 performed on Ti-6Al-4V as an example. All forces were equal to zero during an initial timespan during which the VABB tool was plunging onto the target surface. As soon as contact was established between them, the force increased linearly, proportional to the plunging velocity, until the programmed spring compression was achieved. From that point, the registered forces show a repetitive pa ern. 𝐹 𝑧 exhibits an oscillatory behaviour, while 𝐹 𝑥 changes its sign as the di erent burnishing passes are completed in one direction, and the next one starts.

e point in which 𝐹 𝑥 achieves value 0 is used in the script to determine the original point of each burnishing pass, and isolate a single burnishing cycle (two passes in opposite directions), as shows e objective of this strategy is quantifying the singular values that describe the registered forces for all tests and characterise the nature and evolution of that preload to ultimately declare equivalent force level during VABB and the complementary NVABB test. Without this con rmation, the comparability of tests could be questioned. Figure 4.22 shows all mean forces, along with the maximum and minimum values computed for all tests. All means show a consistent correspondence with the objective mean preload established at the experimental design. Furthermore, they present maximum and minimum values of the oscillating cycle which are of similar order of magnitude for all tests. Whereas it is impossible to keep force perfectly constant along all executions according to the desired level, this comparative representation leads to the conclusion that all forces were comprised inside similar levels.

Recapitulation

In this chapter, the issues related to the experimental development of this thesis is presented, including two main types of information which are summarised in this recapitulation section.

1. An L27 Taguchi orthogonal array has been chosen to develop the experimental plan to test the VABB prototype on both AISI 1038 and Ti-6Al-4V workpieces. is arrange allows the analyse of ve di erent factors at three levels, along with three paired interactions among three of them.

2.

e X-ray di raction technique has been selected to perform residual stress measurement, due to the availability of the equipment and the amount of measurements to be carried out.

On the other hand, albeit the descriptive nature of this chapter, some partial results have been presented as auxiliary data to validate and set up the experimental strategy. ey can be presented as follows:

1. A trial-error approach has been applied to decide the size of the patches to acquire of each burnishing test to obtain relevant information about its texture parameters. Finally, it has been decided to acquire patches containing 6 peaks & valleys of each surface. e actual size of the patch changes depending on the target surface, due to the di erent machining strategies from which each of them was obtained.

2. A detailed study considering numerous descriptors of surface topology has lead to the determination of the parameters that adequately can describe the changes in the surfaces. ey shall be included in the result discussion in the next chapter.

3. A metallurgical analysis of the materials was performed, along with an initial hardness measurement assessment through Vickers microindentation tests. A 100 gf load has been set as an adequate level to assess hardness, as it is able to quantify the e ects of all microstructural structures present in both materials.

4. e analysis of forces acquired during all VABB and NVABB specimens revealed that, in mean and absolute terms, both processes do not show a remarkable di erent behaviour. All mean forces representing an approximate value of the preload force show a stable value along all tests. However, if the pseudofrictional force is analysed, the initial surface state shows a conspicuous in uence on its value, reaching the highest relative values for the less nished one, 𝑆 0 3 . On the other hand, an increase in the preload force shows a relative decrease of the pseudo-frictional one. From this point of view, the process shows a more e ective behaviour for higher forces. e next chapter includes the main results arising from the experimental plan that has been designed and explained along the previous pages.

Experimental results and discussion

In this chapter, the results derived from the execution of the Taguchi experimental array on the AISI 1038 and the Ti-6Al-4V alloys are presented and discussed. e chapter is organised by surface integrity parameters, including rst the results regarding the steel alloy, and then those corresponding to the titanium alloy. Figure 5.1 summarises the di erent areas included in the result discussion. Of all aspects of surface integrity that are analysed, some of them are qualitative.

On the other hand, speci c quantitative indicators shall be subjected to an optimisation procedure, since one of the aims of this chapter is de ning the parameter sets that deliver the best surface integrity results. "Optimal" is understood here as the factor levels that can be found in the DOE, that have the most enhancing e ects on the surface. e criteria to de ne the term "best", depends on the optimisation target, and shall be speci ed according to the area of study.

Geometrical parameter: surface texture

is section tackles with the in uence of the VABB process on the topological state of both materials, being later compared with the NVABB e ects. e aim of this section is exploring a new approach for texture assessment a er ball burnishing. With that purpose, the parameters included in Table 5.1 are from a start considered. However, the reader shall notice that, due to the nature of the surfaces derived a er VABB and NVABB, not all parameters are able to systematically represent the way the material is distributed on the surface a er their execution.

To perform the study, and discriminate the best set of parameters to fully describe the topological e ects of ball burnishing, the rst subsection of each material aims to characterise the three machined surfaces, 𝑆 0 . e surface analysis is then performed by considering all S parameters. As the amplitude S parameters shall show to be the best ones to describe the VABB surfaces, they shall be used to nd the optimal parameter set in terms of topology enhancement. e next subsection shall tackle with the V or Abbo -Firestone parameter set, to evaluate whether they deliver additional information to the system of study, or whether, on the contrary, they are redundant in this analysis. is kind of parameters can be considered highly representative of the initial surface texture, due to the planar symmetry that they exhibit as a consequence of the machining strategy performed to obtain them. To calculate the 𝑅 and 𝑃 parameters -roughness and pro le respectively-, a set of 20 evaluation lengths traced along parallel paths perpendicular to direction II were acquired and averaged to obtain a representative value. e roughness parameters were obtained by ltering the whole pro le 𝑃 through a low-pass lter with a 𝜆 𝑐 = 0.8 mm cut-o length was applied to lter the height signals.

All parameters show an increasing trend from 𝑆 0 1 to 𝑆 0 3 . is behaviour was predictable, as surface roughness and topography are expected to be harsher as the o set distance between ball-end milling passes is increased. Furthermore, it is shown that 𝑃 𝑎 and 𝑃 𝑞 , as well as their 𝑅 correspondents, are related by a factor of proportionality 0.87. is relationship between both factors was already observed by King & Spedding (1982) [69] on manufactured surfaces, and proves that both of them can deliver the same information about the surface state. On the other hand, extreme points are also of higher magnitude as the surface becomes more abrupt. If instead of two-dimensional parameters, the three-dimensional parameters that represent surface are considered, results are consistent with the previous observations.

ese parameters have been calculated by establishing a least square mean plane on the acquired height datasets, and without applying lter to retain the texture features. 𝑆 𝑞 in Figure 5.3.a grows until reaching its maximum value for 𝑆 0 3 . Extreme points are also maximum for that surface. Spatial parameters also evidence the larger scale of the 𝑆 0 3 surface, with regards to the other two nishing regions because of their characteristic highest correlation length 𝑆 𝑎𝑙 (Figure 5.3.b). at means that, by calculating of the autocorrelation function, the surface must be folded and displaced along a longer distance on itself to exhibit an actual decay of its value.

𝑆 𝑡𝑟 is for the three cases well below 0.1, and proves that all machining strategies have lead to highly anisotropic surfaces, with a preferential direction. at direction is de ned by the 𝑆 𝑡𝑑 parameter common to all surfaces, not represented in the graph due to its uniform value of -90 ○ regardless of the considered surface. On the other hand, the 𝑆 𝑑𝑞 hybrid parameter shows that the three machined surfaces are next to a nishing state, although the 𝑆 0 1 surface is the smoothest one, and, therefore, this parameter increases as surfaces 𝑆 0 2 and 𝑆 0 3 are considered.

Volumetric parameters also show the higher abruptness of the 𝑆 0 3 surface with regards to the opposite end of the sequence 𝑆 0 1 (Figure 5.4.a). Indeed, all core, peak and valley volumes, are maximum for 𝑆 0 3 , and minimum for 𝑆 0 1 . e descriptors of e visual inspection of the AF curves helps understanding the uneven trend of its descriptors, as not all three surfaces show di erent bearing area distributions, as shown in Figure 5.5. Whereas the bearing capacity of positive heights proves to be higher for 𝑆 0 1 and increases progressively towards 𝑆 0 3 , explaining the behaviour of 𝑆 𝑘 and 𝑆 𝑝𝑘 , the points corresponding to the valleys machined on the material show an overlapping of 𝑆 0 2 and 𝑆 0 3 at high 𝑀 𝑟 values, and a change in concavity di cult to interpret at this point, but that could help explaining the unpredicted behaviour of 𝑆 𝑣𝑘 . e di erent original surfaces were characterised through two-and three-dimensional parameters. Both of them allowed the identi cation of a sequential decrease in the surface scale, and a slightly di erent material distribution, at sight of the Abbo -Firestone curves and the 𝑆 𝑠𝑘 and 𝑆 𝑘𝑢 parameters. However, the uneven evolution of some of the bearing area curve descriptors questions their adequacy to represent systematically the evolution of these surfaces. e next subsections tackle with the results of the 27 VABB tests, and shall reveal whether these original conditions have an impact on the nal results delivered by the process.

Synthesis Original AISI 1038 surfaces

Due to the periodical peak pa ern presented by the original surfaces, obtained through ball-end milling, the basic two-dimensional factors represent well enough the bigger scale of the topologies as the lateral o set between passes is increased, i.e. from 𝑆 0 1 to 𝑆 0 3 . e three dimensional factors also denote that evolution, except for some volumetric descriptors, that shall be taken into account cautiously in the analysis of ball-burnished surfaces.

Two-dimensional Rq parameter

Following the traditional approach to the analysis of ball burnishing results, this rst phase of topological analysis focuses on the two-dimensional roughness. However, a preliminary visual inspection of the burnished patches evidences that the repeatability of two-dimensional 𝑅 parameters cannot be expected to be high. As an example, Figure 5.6 shows the surfaces a er tests #25 and #18, performed on the 𝑆 0 1 surface. Test #25 exhibits a higher heterogeneity of the height distribution, compared to #18, which is clearly still governed by the original machining marks. In fact, the 𝑆 𝑡𝑑 parameter, which indicates the main texture direction, is inverted in the former. erefore, the hypothesis of planar symmetry that was considered in the previous subsection can-not be equally applied to analyse the VABB surfaces. Consequently, the use of this kind of parameters must be taken cautiously. Regardless of having exposed the risks of focusing the analysis exclusively in twodimensional parameters, the traditional approach to burnishing analysis is considered by calculating all 𝑅 parameters, measured 20 times along direction I by applying a 𝜆 𝑐 = 0.8 mm ltering cut-o length. To control the error, and guarantee the representativeness of those values, outliers have been discarded through Chauvenet's criterion. is method assumes normality of the sample, enabling the calculation of an interval based on the error so that every point outside it is discarded. is method of outliers control is controversial, due to the fact that it removes from consideration points that were actually measured on the sample. However, it delivers a fast and uniform sample with a highly representative average value [START_REF]Introduction to error analysis, the study of uncertainties in physical measurements[END_REF].

e mean 𝑅 𝑞 parameters were subjected to an ANOVA. Figure 5.7 shows the graphical results derived from that analysis.

e VABB process proves to decrease roughness, being the preload the most in uential value, followed by the number of passes. On the contrary, the strategy and initial surface state show no in uence in roughness reduction. Nor does the feed considering a 0.05 con dence level, at sight of the associated p-value calculated through the ANOVA test (0.087). e S/N ratio reaches its highest values at those levels that have a higher mean average e ect on the response, con rming that they are also the most robust ones. Finally, no interactions are observed between 𝐹 𝑝 , 𝑛 𝑝 and 𝑣 𝑓 . e only in uence of 𝐹 𝑝 and 𝑛 𝑝 on 𝑅 𝑞 , and the result independence from 𝑆 0 agrees with results obtained previously by other researchers, such as Lee et al. (1993) [START_REF]Ball burnishing of 316L stainless steel[END_REF]. One possible reason for this independence could be due to the fact that, by removing the low frequency features of the surface through the ltering operation to which the sampled 𝑃 pro le must be subjected to extract the 𝑅 pro le, the material that actually interacts with the ball is being obviated. e ltered resulting pro le is less representative of the surface, and does not model the material that interacts with the burnishing ball. e next subsection deepens into texture assessment by analysing a wider set of three-dimensional parameters.

Synthesis

Description of VABB results on AISI 1038 through 2D parameters e direct visual inspection of the height maps caused by VABB has evidenced that VABB operation does not have a homogeneous e ect on the whole target patch.

erefore, the two-dimensional scale factor, 𝑅 𝑞 , lacks quantitative accuracy to describe the VABB e ects. If no other measuring devices are available, two-dimensional parameters could be considered as an alternative by averaging big datasets to make it interpretable.

Sq and S10z amplitude parameters

e rst approach to analyse the three-dimensional amplitude parameters is by performing an ANOVA, taking 𝑆 𝑞 as response variable. Results are depicted in Figure 5.8, proving that the VABB system in uences 𝑆 𝑞 di erently with regards to 𝑅 𝑞 . Indeed, the initial surface texture is the most in uential parameter, followed by the preload and the number of passes. e strategy and feed do not show a signi cant in uence. Again, no interaction between factors can be judged as relevant in this case, and the S/N ratio proves that robustness increases as the factors reach their optimal levels, con rming the low impact of noise variables in the system. e revelation that the initial surface state is more in uential on texture results than 𝐹 𝑝 and 𝑛 𝑝 leads to a recon guration of the strategy for result interpretation, by considering a di erent pa ern for their representation. Accordingly, all topological parameters are rearranged and represented henceforth according to their respective initial surface texture, instead of by their position in the Taguchi experimental array.

is layout recon guration of the experimental array allows the arrangement of the tests by increasing 𝐹 𝑝 , and by reiterative cycles of 1, 3 and 5 𝑛 𝑝 values. is simpli cation obviates the feed and the strategy as in uential factors, and leads to consider the burnishing results as a discrete sequential evolution departing from the original texture, towards surfaces generated by increasing degree of plastic strain, i.e. the 𝐹 𝑝 -𝑛 𝑝 pair.

Following the described pa ern, Figure 5.9 shows the 𝑆 𝑞 and 𝑆 10𝑧 amplitude parameters. Both of them behave similarly, as they generally decrease as the degree of plastic strain increases, that is, by a rise in 𝐹 𝑝 and 𝑛 𝑝 . e only exception to that trend is when shi ing from the 180N-5passes test to 270N-1pass, where 𝑆 𝑞 and 𝑆 10𝑧 increase.

is is due to the fact that rising the preload from 180 N to 270 N is not enough to compensate the decrease of number of passes from 5 to 1. us the lower degree achieved regardless of the higher preload. e lowest 𝑆 𝑞 at the 𝑆 0 1 surface is a ained by applying 180N-5passes (test #18). In fact, further plastic deformation leads to surface harm, revealed by a reproduction of new protuberances on the surface by pile-up due to strain hardening, that could be understood as a recreation of the surface texture along the burnishing direction. 180 N should not be surpassed to treat this kind of surfaces, to prevent a detrimental e ect of the process. is idea shall be further discussed in following subsections. erefore, this surface has a di erent behaviour with regards to the other two. e process seems to be cyclic, at least in terms of scale of the amplitude, as the 270N-5passes test derives in similar texture amplitudes, but, obviously, consuming a larger amount of time. On the contrary, this e ect is not observed in 𝑆 0 2 or 𝑆 0 3 , since these surfaces admit VABB with the highest level of preload and number of passes to achieve the largest amplitude reduction. is fact can be explained due to the higher amount of plastic strain required to compress residually a surface where a higher material volume is present at the peaks of the texture pa ern.

It is also remarkable the high sensitivity of the 𝑆 10𝑧 parameter to outliers, at sight of some anomalous points observed, for instance in tests #7 or #17. Consequently, it 5.1. GEOMETRICAL PARAMETER: SURFACE TEXTURE can be considered as less appropriate than 𝑆 𝑞 to de ne the amplitude e ects of VABB.

VABB optimal parameters according to Sq

e mean e ects calculated through the ANOVA shown at Figure 5.8 allow the best parameters for 𝑆 𝑞 minimisation to be found.

at criterion can be considered the optimisation target in this case. Figure 5.10 shows the procedure that shall be followed in this subsection to perform that optimisation. Results have proved that the optimal set of parameters is di erent for each initial texture. e mean e ects graph con rms that observation, as an optimal 𝐹 𝑝 -𝑛 𝑝 pair can be found for each 𝑆 0 , being the strategy and the feed non-in uential for the results. Furthermore, no interaction can be found in the system, what simpli es the optimisation procedure. Table 5.2 shows the optimal parameters that result from the analysis.

To con rm the condition of these sets as the best combination, they are compared to experimental results, as tests #18, #26 and #27 correspond to the de ned combinations. Indeed, the relative reduction of 𝑆 𝑞 included in the table shows that they correspond to the best obtained conditions, being 𝑆 0 1 where the highest improvement is registered. e topological study continues in the next subsection by considering the skewness and kurtosis of the generated height distributions. e optimal values de ned here shall be also considered in that analysis.

Ssk and Sku amplitude parameters

Skewness and kurtosis parameters are plo ed in Figure 5.11. Both 𝑆 0 2 and 𝑆 0 3 exhibit a uniform increase of 𝑆 𝑘𝑢 as the degree of plastic strain increases, with exception of the singular step from 180N-5passes to 270N-1pass. is trend interruption was already detected in the amplitude parameters. Although 𝑆 𝑘𝑢 increases towards the Gaussian value of 3 in both cases, it is only achieved at 𝑆 0 2 , when the highest levels of preload and number of passes are applied. It seems that higher plastic deformation could modify 𝑆 0 3 towards a Gaussian state. On the other hand, the evolution of 𝑆 𝑠𝑘 proves that the rst burnishing passes shi s the height distribution towards positive values, whereas further plastic strain balances the peak-to-valley proportion of the resulting surface again, as it reaches value zero.

𝑆 0 1 exhibits a di erent behaviour, again consistently with the observations made for 𝑆 𝑞 . 𝑆 𝑘𝑢 reaches a value of 3 for testing conditions 180N-3passes, then falls once again when increasing to 5 passes. Its behaviour is irregular in the following tests, but reaches 3 again at tests 270N-3passes and 270N-5passes, although the former is clearly positively skewed. e evolution of skewness has similarities with the results on the other two initial textures, as it rst decreases, whereas a value next to 0 is achieved when burnishing with 180N-1pass. It then increases and decreases once again to a minimum value at 270N-5passes.

According to the discussed results, both parameters show a certain cyclic evolution in 𝑆 0 1 , clearly linked to the surface regeneration detected in the other amplitude and spatial parameters. As the surface is recon gured along the burnishing direction, with a consequent transient phase where it presents detrimental e ects, the height distribution is unbalanced until achieving another enhanced state, represented by 270N-5passes. On the contrary, 𝑆 0 2 and 𝑆 0 3 reveal an evolution towards a Gaussian state, and the referred cyclic e ect has not been observed. It would seem that it could be achieved by applying higher preload and number of passes.

Furthermore, the e ect of VABB on kurtosis and skewness can hardly lead the surface to states far from Gaussian, probably because of the interaction of the ball with the surface, which creates new peaks but is able to convert them into valleys with subsequent passes.

ese new peaks are originated by the pile-up e ect that materials present when they are plastically deform, due to strain hardening. is analysis can be complemented by checking on the VABB surface height distributions. Figure 5.12 includes the histograms of the original surfaces in the rst column, followed by the ones resulting from the best burnishing conditions that were already included in Table 5.2, along with another singular surface state a er VABB for the purposes of comparison. A Gaussian-bell distribution can be observed at the height histograms obtained a er the best VABB parameters to treat surfaces 𝑆 0 1 and 𝑆 0

2 . e histogram obtained for the optimal test for 𝑆 0 3 , #27, suggests that the surface could still accept a higher force to increase the kurtosis without biasing the skewness, and therefore the Gaussian bell is not totally shaped yet.

Although skewness values are easily identi ed in the histogram shape -positive values are depicted by the concentration of heights at the negative side, and vice versa-, interpreting the kurtosis values is not trivial. Indeed, no purely platykurtic or leptokurtic distributions can be observed at the depicted histograms. e answer lies in the fact that kurtosis is actually a measurement of the relative weight of the tails with regards to the distribution central areas. As Darlington (1970) [19] pointed out, kurtosis can be also associated to distribution bimodality, which is the case of burnishing surfaces far from the ideal nishing state (for instance, test #27 with 𝑆 𝑘𝑢 = 2.266). erefore, the evolution of kurtosis can be understood as a description of the evolution from multimodal height distributions to unimodal ones. e described disappearance of bimodality as the optimal testing conditions are reached, along with a balancing e ect of positive and negative heights can be easily distinguishable by comparing the complete sequence of histograms, which is included in Appendix B for every initial surface.

Synthesis S amplitude parameter optimisation in AISI 1038

e optimal VABB parameters de ned considering 𝑆 𝑞 minimisation as the optimisation target, also result in Gaussian or quasi-Gaussian height distributions -unskewed and kurtosis near to 3. In other words, texture enhancement through VABB implies minimal RMS of heights with respect to the average centre plane min {𝑆 𝑞 } combined with an balanced Gaussian height distribution -𝑆 𝑠𝑘 = 0 & 𝑆 𝑘𝑢 = 3-.

is kind of surfaces combine good lubrication and bearing characteristics, and can be therefore Having explored all amplitude parameters, the next subsection considers whether the VABB process changes the directionality of the surface features, or has any impact on the spatial height distribution.

Sal, Str spatial, Sdq hybrid and Std miscellaneous parameters

e 𝑆 𝑑𝑞 hybrid parameter, as the RMS slope of the surface irregularities, reveals a similar decreasing trend with the increasing level of plastic deformation, which proves that higher deformation leads the surface to a more near-to-nished state (Figure 5.13). On the contrary, both spatial parameters prove to be modi ed to a lower extent by e ect of VABB. On one hand, 𝑆 𝑎𝑙 shows li le variation with the increase of 𝐹 𝑝 and 𝑛 𝑝 . On the other hand, 𝑆 𝑡𝑟 values range between 0.06 and 0.1, con rming that the orthotropic nature of the original surfaces is kept a er VABB.

As for the texture direction parameter, 𝑆 𝑡𝑑 , it is kept at -90 ○ for all tests, except for #21, #23 and #25, whereby the value is zero. ose tests are the ones performed on the 𝑆 0 1 with the highest preload. e only change of 𝑆 𝑡𝑑 in these speci c tests means that VABB reduces e ectively the texture amplitude descriptors in all cases, but it is only able to recon gure the directionality of the main super cial features on the nest surface when a high preload is applied. is observation is an evidence of what was already observed, about the VABB process being detrimental to the surface texture when a too high preload is applied.

e described e ect is not observed in the 𝑆 0 2 and 𝑆 0 3 surfaces, because the maximum preload applied on them is not enough to cause it. Consequently, the initial machining marks are maintained. As an example, Figure 5.14 shows both the initial 𝑆 0 3 surface, and its state a er burnishing with 270N-5passes (test #27). Although the e ects of burnishing are conspicuous, the reader may note that the original nishing grooves caused by the nose of the hemispherical tool, are unaltered a er burnishing. It is the initial peaks the ones that are actually a ected by the plastic deformation, whereas valleys remain untouched. Hence the maintenance of the original preferential direction, clearly driven by these unaltered paths generated during machining. For further graphical evidence of the unchanged texture direction in most of the surfaces except for tests #21, #23 and #25, all sequential colour maps of all VABB surfaces Synthesis S spatial parameter discussion in AISI 1038 e VABB process is only capable of changing the directionality of ball-end milled surfaces if a threshold preload value is surpassed.

e immediate consequence is a detrimental e ect on the surface that is again corrected as more plastic deformation is performed. An ulterior enhanced surface state is observed, but the preferential direction of the surface features results inverted according to the direction of VABB.

at threshold value is lower the more ne the initial surface is. For that reason it has only been found for 𝑆 0

1 . e insu cient plastic deformation applied on 𝑆 0 2 or 𝑆 0

GEOMETRICAL PARAMETER: SURFACE TEXTURE

Abbo -Firestone descriptive curves

So far, the analysis of amplitude parameters has proved that the VABB process reduces the scale of the target surface, and succeeds in redistributing the height histogram towards a Gaussian distribution. e next issue to tackle is nding an answer the following question: do the AF curves reveal further information about the nature of the VABB surfaces? For a rst approach, let us consider those corresponding to the optimal and singular tests in each original surface that were included above in Figure 5.12. Graphically, surface improvement is brought to light by the AF curves as they are sequentially a ened (Figure 5.15).

e highest surface enhancement delivered by VABB was observed in test #13 on surface 𝑆 0 1 . e ulterior harm at the surface by increasing the preload and number of passes, exempli ed by test #21, is depicted by a rebound of the whole AF curve towards the original state. As usual, 𝑆 0 2 and 𝑆 0 3 exhibit a di erent behaviour, as the bearing curves become a er as plastic strain increases, and no harmful e ect is observed in any test. Figure B.5 in the Appendix shows the sequential evolution of all AF curves for a higher comprehension of the e ect. In overall, the highest improvement seems to be a ained at the 𝑆 0 1 surface by applying 180N-3passes, which also derives in the highest bearing capacity. e skewness and kurtosis descriptors of the surfaces also have a representation in the AF curves. is is obvious, as these are an alternative representation of heights, showing the accumulated function from the same dataset. Zero skewness (unbiased height distributions) is associated to curves that cross the 𝑥 axis at the middle point (𝑀 𝑟 = 50%). For instance, test #17, negatively skewed, is represented by a bearing curve which intersect the 𝑥 axis at 55%. Identifying the platykurtic or leptokurtic nature of the surface on these curves is not such a direct task. Platykurtic burnishing patches are characterised by 𝑆 𝑘𝑢 < 3, which also denotes the bimodality of the height distribution. Consequently, they should be re ected in the AF curves as an abrupt gradient change, which could even derive in convexity alternations. At sight of the exemplifying curves shown in Figure 5.15, there are visible convexity changes present at low and high 𝑀 𝑟 values. As the preload and number of passes increase towards the optimal value, the texture evolves towards a Gaussian value of kurtosis, which is re ected by an increase of atness of the curve, while the slope decreases at every point and no convexity change is further present.

To visualise this e ect of VABB on the accumulated height distribution, Figure 5.16 represents the slopes of all tests in surfaces 𝑆 0 1 and 𝑆 0 3 , calculated through numerical derivative of their corresponding AF curves. In 𝑆 0 1 , slope functions are in general more regular as the 𝐹 𝑝 -𝑛 𝑝 pair increases until test #18. From that point, the slopes keep a regular behaviour, meaning that although higher plastic deformation leads to surface harm, it does not redistribute the surface towards the initial distributions, that show an abrupt convexity change at high 𝑀 𝑟 values. Indeed, bimodality is permanently discarded due to VABB execution. In the case of 𝑆 0 3 , slopes stabilise as more plastic strain is applied, until reaching the optimal conditions in test #27, where convexity change in the AF curve is totally erased. e change in convexity is depicted in the slope representation as a local minimum or maximum. Geometrically, it can be related to a higher area between these curves and the 𝑥 axis. Let Σ 𝑠 be the area con ned between the slope numerical function of each test and the 𝑥 axis. It can be calculated by numerical integration of the slope functions. e representation of 𝑆 𝑘𝑢 against Σ 𝑠 in Figure 5.17, evidences a clear linear correlation between them, con rming the hypothesis that allows the identi cation of kurtosis with convexity changes in the AF curves. is nding shall be especially relevant for the analysis to come in the next subsection, where the curves are reduced to quantitative parameters.

Figure 5.17. Linear correlation between 𝑆 𝑘𝑢 and Σ 𝑠 VABB tests.

Abbo -Firestone descriptive parameters

e representation of the AF curves by a set of speci c parameters can help to simplify them in a functional fashion, and can help to systematise the analysis of VABB results through these curves. Volumetric descriptors have been represented in Figure 5.18. e value of both core parameters, 𝑉 𝑚𝑐 and 𝑉 𝑣𝑐 , fall as the degree of plastic deformation increases, with the regular rebound when changing from 180N-5passes to 270N-1pass. is trend is consistent with the decrease in surface texture amplitude detected through the S amplitude parameter analysis. For 𝑆 0 2 and 0 3 , the evolution of 𝑉 𝑣𝑣 is not so regular. Although it seems to decrease in general as the optimal parameters are achieved, its evolution has ups and downs that make it uneven. Similarly, 𝑉 𝑚𝑝 is evidently minimum for the best burnishing conditions, but it exhibits an errant evolution as the degree of plastic strain increases, lacking a de ned pa ern. On the contrary, for 𝑆 0 1 , it seems to account well enough for the creation of new peaks and valleys corresponding to the cyclic phenomenon explained for the nest surfaces. As a consequence, these parameters do not exhibit a speci c relation between process parameters for all surfaces, and their e ect on the resulting extreme volumetric descriptors. Not all V parameters serve to represent the e ects of VABB on a certain surface. e extreme amplitude descriptors of the AF curve are according to the volumetric parameters, as shows Figure 5.19. e core material amplitude, 𝑆 𝑘 , decreases as the preload and number of passes increase, and is minimum for optimal tests #13, #24 and #27. On the contrary, 𝑆 𝑝𝑘 and 𝑆 𝑣𝑘 do not provide reliable information about the evolution of the bearing pro les. For instance, 𝑆 𝑣𝑘 stabilises in a single value from test #13 to #25 in surface 𝑆 0 1 , and does not experience variation from test #3 to #7 tests in 𝑆 0 3 . It then rebounds, achieving a maximum value in test #17. Again, the core parameter agrees with the e ects observed before, but the extreme descriptors are not so clearly related to the process parameters. e bearing potential of the derived surfaces can also be checked through the values of the lowest and highest bearing area percentages, 𝑀 𝑟1 and 𝑀 𝑟2 (Figure 5.20). As expected, they also lead, in some cases, to dubious conclusions about the evolution of the surface a er VABB. 𝑀 𝑟2 evolves in all 𝑆 0 1 tests by growing and stabilising from test #13, consistently with 𝑆 𝑣𝑘 . at e ect is obvious, since 𝑀 𝑟2 denotes the dominion of 𝑆 𝑣𝑘 in the curve. In 𝑆 0 1 and 𝑆 0 2 , 𝑀 𝑟2 increases until the optimal parameters are applied. However, this e ect is not observed in 𝑆 0 3 , where 𝑀 𝑟2 is maximum in tests performed with 90 N, and then decreases. 𝑀 𝑟1 is not more regular. Intuitively, it should increase as the optimal conditions are achieved, since it is associated to an increase in the bearing capacity. However, it does not happen like that. Furthermore, it is also uneven in its pa ern, following di erent trends in all three surfaces, hindering the task of nding a correlation with VABB parameters.

In overall, the V parameters have proved that only the core descriptors seem to represent well enough the scale reduction of the surfaces, whereas the reliability of the change scale reduction of surface texture can be questioned. Neither do the 𝑀 𝑟 values prove descriptive potential of the process results.

is is obvious, as these extreme parameters do not depend on the 40% minimum slope secant method used to calculate the boundaries between the core and the peaks and valleys. ey depend directly of the AF curve, which can have any extreme values. is idea can be related to the observation done about 𝑆 10𝑧 at the beginning of this chapter. For that reason, it is worth questioning at this point whether the V parameter set can help to explain in a systematic fashion the evolution of surface topology a er increasing plastic strain through VABB. e word systematic is here crucial, as the ultimate aim of this analysis is detecting a pa ern in the evolution of the surface heights as the preload and number of passes increase.

Can the source of this lack of de nition be in the method through which the descriptors are obtained? In the previous subsection, the evolution of kurtosis was associated to convexity change reduction in the AF curves. at irregular shape could be the reason of the errant behaviour of most of the V parameters. To prove it, the least 40%-slope method has been reproduced by importing the di erent datasets in a Matlab routine, and calculating the value of the least gradient secant line spanning 40% of bearing area or each of them, denoted 𝑚 𝑚𝑖𝑛 , , as well as the 𝑥 coordinate of the rst secant point, 𝑀 𝑚𝑖𝑛 (Figure 5.21). De ned 𝑚 𝑚𝑖𝑛 , the 𝑆 𝑘 parameter is unambiguously de ned:

𝑆 𝑘 = 40 𝑚 𝑚𝑖𝑛 (5.1)
To check whether the least slope secant method o ers a systematic calculation of the AF curves, a possible correlation between 𝑚 𝑚𝑖𝑛 and 𝑀 𝑚𝑖𝑛 and each curve descriptor is veri ed in Figure 5.22. e parameters which reliably re ected the evolution of VABB surfaces, 𝑉 𝑚𝑐 , 𝑉 𝑣𝑐 , 𝑆 𝑘 , show clear linear correlations with the 𝑚 𝑚𝑖𝑛 descriptor. Speci cally, the perfect t between 𝑆 𝑘 with 𝑚 𝑚𝑖𝑛 , direct consequence of the way it is calculated (Eq. 5.1), serves as a con rmation of the adequacy of the reproduced method, and the doubt about the reliability of extreme values that was already commented above. Secondary inverse correlations can be observed against 𝑀 𝑚𝑖𝑛 , which could evidence a certain relation but in no case a regular pa ern. As 𝑀 𝑚𝑖𝑛 depends on the shape of the curve, this could lead to think. 𝑀 𝑟1 and 𝑀 𝑟2 are directly correlated to 𝑀 𝑚𝑖𝑛 , but only the former shows a linear relationship. On the contrary, the parameters showing an errant behaviour (𝑉 𝑣𝑣 , 𝑉 𝑚𝑝 , 𝑆 𝑣𝑘 , 𝑆 𝑣𝑘 ) are not related to 𝑚 𝑚𝑖𝑛 or 𝑀 𝑚𝑖𝑛 . In overall, this analysis leads to think that not all items inside the V parameter set can be considered as relevant descriptors of the evolution of VABB results as the 𝐹 𝑝 -𝑛 𝑝 pair increase. In the analysed graphs, it is especially remarkable the divergence of the points of tests #3, #5 and #7 in many of them, meaning that these are singular cases that should be taken into consideration, and can help to clear out the way the method should be interpreted. If, in fact, convexity change has to do with a miscalculation of 𝑚 𝑚𝑖𝑛 and 𝑀 𝑚𝑖𝑛 , it can be checked by using the kurtosis parameter, that was presented in the previous subsection as an indicator of that convexity change associated to bimodality. e correlation of 𝑚 𝑚𝑖𝑛 and 𝑀 𝑚𝑖𝑛 with the 𝑆 𝑘𝑢 statistic in Figure 5.24.a, except for tests #3, #5 and #7, could leads to the conclusion that irregular convexity changes in the AF curves can lead to a lack of reproducibility of the method, and, therefore, an incorrect comparative between tests. is result does not imply that this method is not valid to analyse surfaces individually, but must be taken into account to compare di erent topologies, especially if the kurtosis value is not regular enough. e calculation of the minimum slope method parameters can also prove that the reduction of 𝑆 𝑞 is also linked to a a ening e ect of the AF curves, as the absolute value of 𝑚 𝑚𝑖𝑛 increases with an increase of 𝑆 𝑞 , at sight of Figure 5. Synthesis Abbott-Firestone curves of AISI 1038 VABB tests e V parameter analysis has proved that only the core descriptors of the AF curves represent well enough the evolution of surface textures a er VABB. Although they do not add further information with regards to the S amplitude parameters, they can be considered for lubrication or wear applications where the expression of surface texture is more conveniently represented in volumetric terms. Furthermore, the reliability of the extreme parameters to explain the sequential evolution of surface texture has been evidenced, due to a lack of uniformity to apply the 40% minimum slope secant method proposed by the standard to establish the di erentiation between core, peak and valley areas of the surface.

Comparison of VABB to the NVABB process

e direct comparison of VABB results with the NVABB tests included in this subsection allows the relative e ect of each process on the nal texture. Figure 5.25) represents all 𝑆 𝑞 results of both processes, exhibiting that the NVABB can lead to lower values, especially on the 𝑆 0 2 and 𝑆 0 3 surfaces. e results seem to be of the same order for 𝑆 0 1 . At sight of this observation, it can be concluded that the vibration-assisted process leads to detrimental results in higher scale surfaces. Its negative e ect is reduced as the surface has smaller amplitude features, as is the case of 𝑆 0

1 . e causality of this phenomenon cannot be known, but some clues can be inferred from previous results. For instance, the higher infuence of the process on the directionality of the 𝑆 0 1 could lead to think that the engagement of the ball and the material of the surface is higher in this kind of textures, thus increasing the e ect of the vibration-assistance. From a qualitative point of view, both surface states have been observed by SEM inspection. e initial machined surface shows a typical repetitive pa ern caused by the plastic deformation of the remaining material on the surface. Figure 5.26 shows a detail of that pa ern, which appears to be completely deformed a er VABB and NVABB. Although the surface appears to be similarly deformed by both processes, NVABB seems to lead to characteristic scratches on the material along the burnishing sense. ese scratches could be the source of crack nucleation during functioning in service.

eir prevention through the VABB process could be explained by the alternative vertical displacement experienced by the ball during the process, that decreases the detrimental interaction with the surface, and, therefore, prevents the creation of these marks.

At sight of the absence of these marks on the VABB process, the vibration-assisted process can be presented as a more convenient operation to nish an unharmed surface with lower roughness, albeit the slightly higher texture amplitude parameters.

As for the heights distribution, compare the 𝑆 𝑠𝑘 and 𝑆 𝑘𝑢 parameters a er VABB and NVABB are directly compared in Figure 5.27, by representing both parameters in is technique can help to characterize the nature of surfaces a er nishing through a certain process, as explained by Gri ths (1986) [47]. All results prove to be contained inside a tear-shaped enclosed area. erefore, both processes are similar in terms of heights distribution a er the operation, although the concentration of VABB tests at negative skewness positions shows that NVABB is able to generate less skewed surfaces. In the same graphic, two outliers can be observed: tested conditions #13 and #21. e rst set of burnishing parameters executed by the NVABB shows a high kurtosis, whereas the second ones show an especially positiveskewed surfaces.

Synthesis of topological results on AISI 1038

Both the VABB and the NVABB have proved to enhance the di erent surface integrity aspects of AISI 1038 ball-end milled surfaces. e topological state of VABB and NVABB surfaces have been analysed, proving that two-dimensional parameters cannot represent their condition from a functional point of view. Furthermore, not all three-dimensional parameters succeed in accounting for the evolution of textures, which can be explained as follows: • Amplitude S parameters (𝑆 𝑞 , 𝑆 10𝑧 , 𝑆 𝑠𝑘 and 𝑆 𝑘𝑢 ) reveal that VABB and NVABB succeed in reducing the surface scale of di erent AISI 1038 ball-end milled surfaces, and lead to Gaussian or quasi-Gaussian height distributions. • Spatial and miscellaneous S parameters (𝑆 𝑎𝑙 , 𝑆 𝑑𝑞 , and 𝑆 𝑡𝑟 ) are not sensitive enough to describe the evolution of surfaces a er VABB and NVABB, due to the fact that the process only deform the peaks of the surfaces, and cannot erase the mill-nose marks caused during machining • Core Abbo -Firestone parameters (𝑆 𝑘 , 𝑉 𝑣𝑐 , and 𝑉 𝑚𝑐 ) exhibit the surface scale reduction, consistently with the amplitude S parameters. • e rest of the Abbo -Firestone parameters cannot account for the evolution of the surfaces due to VABB or NVABB, either because they are not sensitive enough to detect that change, or because the 40% minimum slope secant line method used to divide the AF curve in core, peak and valley zones cannot be applied on surfaces represented by bimodal height distribution. at bimodality is exhibited in the AF curves by abrupt convexity change.

In summary, the best burnishing conditions found for the NVABB process are the same ones as for VABB. e original texture has proved to be the most in uential parameter, achieving the lowest surface scale on 𝑆 0 1 , and only the 𝐹 𝑝 -𝑛 𝑝 pair exhibited in uence on the results. Considering all these observations, the best burnishing parameters to nish di erent AISI 1038 surfaces can be established as Table 5.3 shows. In absolute terms, the lowest surface texture a er both processes is obtained on 𝑆 0 1 (shadowed in green in the table). e previous table is based on the quantitative results delivered by VABB and NVABB processes, which have lead to similar results. However, from a qualitative point of view, SEM observations lead to conclude that the NVABB process exhibited scratching defects, apparently prevented through VABB. Consequently, for a functional point of view, it is the la er that should be preferred to avoid these surface defects that can harm the in-service performance of workpieces treated through NVABB. e evolution of the amplitude parameters, height distribution histograms and AF curves has evidenced that the process always achieves its best results by simultaneously reducing the texture scale, while generating Gaussian height distributions.

GEOMETRICAL PARAMETER: SURFACE TEXTURE

e evolution towards Gaussian surfaces can be explained due to the selective e ects of the ball burnishing process on the peaks of the surface topology. As they are deformed plastically to reduce their scale, a secondary e ect of piling up due to strain hardening also happens, generating new irregularities in the surface.

is process of peak generation followed by peak compression being generated simultaneously by the burnishing ball accounts for the described cyclic e ect of VABB and NVABB, which can be de ned as characteristic of both processes. In contrast, other other nishing operations based on chip removal, eliminate the material causing the escalation of the surface kurtosis towards high values.

is cyclic e ect is represented by the existence of a critical 𝐹 𝑝 -𝑛 𝑝 pair for each surface, i.e. the optimal pair found for each surface, from which higher plastic deformation leads to immediate surface harm. Further plastic strain degree results in a return to an optimal state. is e ect was evidently observed for the 𝑆 0 1 surface, where a rst optimal level was found at 180N-3passes, and the ulterior return to the same surface texture was achieved with 270N-5passes. On the contrary, that point was not reached in the 𝑆 0 3 texture, leading to think that the maximum plastic strain delivered by 270N-5passes could be still achieved by a higher preload.

Ti-6Al-4V

e analysis of topological results on the AISI 1038 workpiece has lead to identify the key parameters with which it is necessary to tackle to wholly de ne the topological e ects of VABB on di erent surfaces. Consequently, the results shown in this subsection for the Ti-6Al-4V patches take advantage of those observations to synthesise the study and focus on the descriptors that actually deliver information about the process results. First, the three original surfaces are described.

Topologies of the original surfaces

e surfaces machined on the Ti-6Al-4V workpiece present the two-dimensional parameters represented in Figure 5.28. ese values represent the increasing scale of the surface features, being the surface 𝑆 0 1 the smallest. Although the trend is similar as the one presented in the AISI 1038 workpiece, the absolute magnitudes are lower for all surfaces. For instance, 𝑆 0 2 of Ti-6Al-4V can be can be considered in the same way as 𝑆 0 1 in the AISI 1038 workpiece. is issue shall not be momentarily considered, and shall be resumed at the end of the section. Surface parameters depicted in Figure 5.29.a and 5.29.b are also highly descriptive of the increasing trend of all surfaces as they were machined with higher o set between end-ball milling passes. e maximum decay length of the autocorrelation function 𝑆 𝑎𝑙 also grows, showing the larger spacing between the surface features. e second spatial parameter 𝑆 𝑡𝑟 presents values lower than 0.1 in all cases. Although this value is lower for the 𝑆 0 3 , the anisotropy of all three surfaces can be acknowledged. As for the descriptors of the AF curves, the ones referring to the core material are highly consistent with the observations commented above, as shows Figure 5.29.c. Both the core material and the peak material increase from surface 𝑆 0 1 to 𝑆 0 3 . Synthesis Original Ti-6Al-4V surfaces It is con rmed that the surfaces machined on the Ti-6Al-4V workpiece are comparatively of higher scale as the lateral o set between hemispherical tool passes was increased, at sight of the S amplitude parameters and the Abbo -Firestone curves. erefore, it can be stated that all surfaces have been conveniently machined, and are representatively di erent to represent the in uence that they introduce in the application of VABB.

Sq and S10z amplitude parameters

e graphical results of the ANOVA considering 𝑆 𝑞 as response variable are represented in Figure 5.30. e initial topology is again the most important factor on the variation of the amplitude parameters. In fact, its e ect is so remarkable, that the sources of variation due to the rest of the factors are hidden by it. Alternatively, the p-values associated to the statistical tests were consulted, revealing that only the preload is an in uential e ect on the response, if a 5% signi cance level is considered. All texture parameters have been ordered by increasing preload, as were during the AISI analysis, consistently with the resulting ANOVA calculations. Figure 5.31.a shows that the continuous decrease of extreme points, represented by 𝑆 10𝑧 , as well as of the general amplitude parameter 𝑆 𝑞 , can be observed in all surfaces. However, no limit value is achieved in any of the three surfaces, revealing that further improvement could be achieved by a higher degree of plasti cation. An alternative representation of 𝑆 0 1 is presented in Figure 5.31.b to appreciate the decrease of the amplitude values in a proper scale. In essence, the maximum 350N-5passes pair has proved to deliver the best results in terms of topological scale reduction in the three initial textures.

VABB optimal parameters according to Sq

Due to the fact that the in uence of the di erent factors on the surface texture in the Ti-6Al-4V is similar as the one found for the steel alloy, the same optimisation procedure proposed in Figure 5.10 can be followed. e term optimal parameters refer to those factors that generate the lowest scale on the surface. ey are included in Table 5. 4.

eir identi cation with the real experiments #23, #26 and #27 allow the calculation of the relative texture reduction with regards to the initial surface, and prove quantitatively that they are indeed maximum for each initial texture. At sight of the results, the surface 𝑆 0 1 exhibits a higher a ectation a er VABB, with a 60.3% 𝑆 𝑞 reduction. Conjoint to the evolution of the factor observed in the previous subsection, these results suggest that surfaces 𝑆 0 2 and 𝑆 0 3 can still accept further plastic deformation. e origin of the lower a ectation of the Ti-6Al-4V, if compared with the AISI alloy, can lie on the higher yield strength of the rst one, which requires higher preload levels to experience residual plastic strain. e following subsection tackles with the characteristics of the height distributions generated a er VABB, to add more information to this observation. Furthermore, it is necessary to contrast the optimal parameter set found above, based on 𝑆 𝑞 reduction, with the aim of obtaining Gaussian distributions through that set.

Ssk and Sku amplitude parameters

e evolution of skewness and kurtosis amplitude descriptors as more plastic strain is performed on each initial texture are represented in Figure 5.32. In all cases, the application of VABB recti es the skewness of the original surfaces, by reducing to levels near zero. In 𝑆 0 1 , skewness is partially lead to a negative value for test #11, but the absolute value is so small that it can be assimilated to an unskewed state. In the case of 𝑆 0 2 and 𝑆 0 3 , the fact that they depart from a higher positive skewness is more representative of the e ects of VABB, since this parameter is reduced as the preload and number of passes are increased, until it reaches zero with the maximum 𝐹 𝑝 -𝑛 𝑝 pair. e kurtosis factor is not so sensitive to the increase of plastic strain. In fact, the values along the di erent tests are kept practically equal to the original values in the case of 𝑆 0 2 and 𝑆 0 3 . erefore, the VABB process can only account for the scale reduction in this kind of textures, but does not essentially change the height distribution. On the contrary, 𝑆 0 1 presents an increase of the kurtosis parameter as the maximum 𝐹 𝑝 -𝑛 𝑝 pair is reached. Nevertheless, 270N-1pass is the pair that can be associated to the Gaussian state of 𝑆 0 1 a er VABB. Now, let us identify the explained 𝑆 𝑠𝑘 and 𝑆 𝑘𝑢 behaviour with the evolution of height histograms as plastic strain is increased. Figure 5.33 depicts a sequential representation of the histograms of the tests corresponding to the optimal parameter set (shown above in Table 5.4), along with an intermediate test to depict the evolution from their respective raw states. Only is in 𝑆 0 1 the e ect of VABB conspicuous, in terms of bimodality neutralisation and surface scale reduction. Indeed, test #21 presents a Gaussian height distribution with lower extreme points.

Much on the contrary, bimodality cannot be erased from surface 𝑆 0 3 , as it is present along all tests. Consequently, for this kind of surface, the VABB process proves to reduce the scale of its texture, as revealed the analysis of 𝑆 𝑞 factor, but it is not able to change the height distribution.

e behaviour is similar for the 𝑆 0 2 surface. e maintenance of a low kurtosis value on the most abrupt surfaces in Ti-6Al-4V, regardless of the applied preload, could be due to two reasons. First of all, as the Ti-6Al-4V can be described as ductile, the pile-up e ect is more accused, and, therefore, a predominance of extreme height values is always present, no ma er the degree of plastic deformation achieved on the surface. at predominance is represented in the height histogram as peaks at the lowest and highest points. For additional graphical information about this ma er, the complete histogram sequence can be found in the Synthesis S amplitude parameter optimisation for Ti-6Al-4V e optimal parameters have been found for each surface machined on the Ti-6Al-4V workpiece. Results support the idea of surface enhancement is a ained through simultaneous scale reduction while obtaining Gaussian height distribution, but only in the nest surface 𝑆 0 1 . On the contrary, while 𝑆 0 2 and 𝑆 0 3 surfaces register scale reduction, its e ects are not so remarkable, and the nature of height distributions are hardly modi ed as plastic deformation is increased. In general terms, the titanium alloy has proved a lower a ectation by VABB than the steel alloy, although the applied preloads have been higher.

Having analysed the amplitude parameters, the next subsection tackles with spatial and hybrid parameters, to evaluate their representativity of the VABB e ects. Prospects are not very clear, at sight of the antecedent observed for the AISI surfaces, where, although higher amplitude a ectation was con rmed, spatial parameters were insensitive to plastic deformation.

Sal, Str spatial, Sdq hybrid and Std miscellaneous parameters

e visual inspection of spatial parameters do not deliver fundamental information about the variation of the surface directionality, as can be observed in Figure 5.34. 𝑆 𝑎𝑙 reveals stable values at each test, always enclosed inside a range near the value corresponding to the original surface.

erefore, it cannot be considered as a representative descriptor of the surface. 𝑆 𝑡𝑟 is similar in its incapability to describe the surface. Only the miscellaneous parameter 𝑆 𝑑𝑞 seems to fall consistently with the aforementioned amplitude parameters, evidencing a stabilisation of the surface characteristics from a certain plasti cation level in surfaces 𝑆 0 1 and 𝑆 0 2 , and a continuously decreasing trend for 𝑆 0 3 , in which VABB seems to be able to keep still an improving potential by applying a higher preload. In this case, the value of the main texture direction given by 𝑆 𝑡𝑟 is kept at -90 ○ , with no direction inversion as was observed in the AISI alloy. It con rms the lower a ectation of the Ti-6Al-4V alloy by the VABB process. To exemplify this statement, Figure 5.35 represents the raw 𝑆 0 1 surface along with tests #18, performed with a succession of perpendicular passes due to the bn90/0 strategy, and #25, executed through the nb0 strategy. e raw Ti-6Al-4V surface shows clearly the marks of the end-ball milling tool nose, which are not erased a er VABB processing, neither through constant passes along one direction, nor with a change of directionality. e colour map representation of the height distributions also depicts this lack of in uence on the directionality of the surface. In order to exemplify it, Figure 5.36 represents how the initial pa ern that de nes 𝑆 0 3 is practically maintained, even with the test performed with the highest 𝐹 𝑝 -𝑛 𝑝 pair, although the e ects of deformation on the peaks is clearly observed through the evolution of the height scale. Furthermore, even being the texture most a ected by the process, 𝑆

Synthesis S spatial parameter discussion in Ti-6Al-4V

e Ti-6Al-4V surfaces keep in practice the same spatial and hybrid parameter levels a er VABB, with regards to their original surfaces.

is conclusion can be easily identi ed with the AISI results, since both of them show that the trails caused by the hemispherical tool on the surfaces are not erased by VABB. at pa ern determines the preferential direction of the surface, regardless of the applied burnishing strategy.

Abbo -Firestone descriptive curves and parameters

e complete analysis performed through on the AISI 1038 material revealed that the AF curves do not reveal extra information about the resulting surface. However, they constitute an alternative approach to quantify the distribution of material according to a peak-core-valley di erentiation that can be useful for functional calculations.

e 40% least gradient method applied to calculate the volumetric parameters also proved to be highly biased for surfaces showing a specially low kurtosis values, which could be translated into undesired convexity changes in the curve that invalidated the method to systematise the topological analysis of the surface through the majority of the AF parameters. e described remarks are taken in this subsection as the basis to facilitate tackling with the titanium alloy results. First, the correlation between the 𝑆 𝑘𝑢 parameter and the slope change of the AF curves is con rmed. Albeit the low values of kurtosis, the parameter representing the area con ned between the slope curves and the 𝑥 axis, Σ 𝑠 , proves to be correlated with the core parameters derived from the processing of the AF curves, as shows Figure 5.37. Again, only the core parameters derived from the minimum slope method should be considered as reliable descriptors of the evolution of the surface by e ect of the VABB process. Indeed, only 𝑉 𝑚𝑐 and 𝑉 𝑣𝑐 (Figure 5.38), along with 𝑆 𝑘 (Figure 5.39), show a decreasing trend as more plastic deformation is a ained. is observation evidences the scale reduction that was already evidenced through the amplitude S parameters. A very di erent case is evidenced by the rest of the extreme volumetric parameters, that show the errant behaviour typical of surfaces represented by AF curves with abrupt slope change, as the one that we are dealing with. e case of the material ratios are hardly exploitable, as 𝑀 𝑟2 is practically constant for all tests, and 𝑀 𝑟1 Tests corresponding to surface 𝑆 0 1 present a regular slope, except for the tests performed with the lowest preload. On the contrary, all the resulting surfaces on 𝑆 0 3 show constant convexity change, revealing that, indeed, the minimum slope method is due to lead to biased results. e analysis of the adequacy of the V parameter set, based on the method developed in the analogous section of the AISI 1038 analysis, leads to conclude that thy cannot be considered stable enough to deliver reliable information about the evolution of material distribution in the surface as more plastic deformation is achieved. For further reference, AF curves can be observed in the Appendix Figure C.5.

Synthesis Abbott-Firestone curves discussion in Ti-6Al-4V

e core parameters inside the V parameter set have proved to be representative of the evolution of Ti-6Al-4V surfaces a er VAB. eir evolution support the idea of surface enhancement by scale reduction and, in the case of 𝑆 0 1 , nal Gaussian height distributions. Considering the volumetric parameters does not add new information about the nal surfaces, but o ers an alternative approach to the subject for functional applications of surface metrology.

Comparison of VABB to the NVABB process

e direct comparison of the 𝑆 𝑞 parameter in of all VABB and NVABB tests performed on the Ti-6Al-4V workpiece leads to interesting results. Whereas 𝑆 0 2 and 𝑆 0 3 evidence similar results, the process is capable of producing lower surface scale in 𝑆 0 1 (Figure 5.42). is result suggests that the introduction of vibrations as a mean of reducing the surface scale is only e ective on surfaces that are characterised by 𝑆 𝑞 around 1 µm. Furthermore, the potential bene cial e ects of the process increases as the amplitude of the surface decreases.

is statement was also true for the AISI surfaces. is statement reinforces the incidence that the initial texture has on the ball burnishing results, as well as the e ectiveness of the vibration-assistance.

Synthesis of topological results on Ti-6Al-4V

e topological results obtained on the Ti-6Al-4V surfaces have been analysed based on the strategy that was outlined a er the AISI results. Indeed, the 𝑆 amplitude parameters and the 𝑉 core parameters have been proved to describe correctly the sought amplitude reduction and redistribution of the titanium surfaces to quantify texture improvement. Again, the most in uential parameter on the results was the initial surface, followed by the 𝐹 𝑝 -𝑛 𝑝 pair. Table 5.5 shows the best parameter combination from a topological point of view. It can be observed that the maximum preload is required in all cases to achieve the best improvement. e in uence of the initial surface on the Ti-6Al-4V material has exhibited interesting results in terms of process assistance. First of all, the introduction of vibrations has proved to be positive to increase texture reduction only if the initial surface has a reduced scale similar to the one shown by 𝑆 0 1 . Secondly, no boundary 𝐹 𝑝 -𝑛 𝑝 value was observed in these surfaces, what leads to think that the Ti-6Al-4V could still accept higher preload to achieve higher plastic deformation.

Comparison of topological results of AISI 1038 and Ti-6Al-4V

e results that were analysed for both materials individually have lead to conclude that they are di erently a ected through the VABB and NVABB processes. On one hand, AISI 1038 surfaces were not a ected by the introduction of the vibration-assistance, while Ti-6Al-4V exhibited enhanced results by VABB only in the initial surface that showed smallest features. In overall, the 𝑆 0 1 surface were the ones delivering the best results in both materials, by applying a di erent set of burnishing parameters. e descriptors of the di erent initial surface topographies were compared, as is shown in Table 5.6.

is direct contrast reveals that applying the same ball-end milling parameters on both of them did not generate the same surfaces. In fact, the steel 𝑆 0 1 surface cannot be directly compared with its titanium homonymous. On the contrary, it seems more alike 𝑆 0 2 surface (aquamarine values inside the table ). at means that the titanium 𝑆 0 1 has no direct equivalent in the AISI 1038 workpiece. Since it has been the topology that has proved to deliver be er results by the introduction of vibrations in the process, it can be questioned whether the lack of in uence of vibration assistance in the AISI material has been caused by an insu cient surface reduced scale, being the AISI 𝑆 0 1 surface excessively abrupt to perceive the in uence of vibration-assistance. For this reason, a second experimental phase was executed to tackle with this issue, as is described in the next subsection A second test piece was machined by reducing the o set length between passes during the milling operation, se ing it to 𝑎 𝑒 = 0.3 mm. is surface has been called 𝑆 0 0 to follow the sequential denomination of textures. Its main descriptors are included in Table 5.6, con rming that it can be assimilated to the Ti-6Al-4V 𝑆 0 1 surface. is newly machined surface was subjected to VABB and NVABB by xing the feed at 600 mm/min and strategy at nb0. e preload was varied at the same three levels -90, 180 and 270 N-and 𝑛 𝑝 was tested at 3 and 5 passes. A total of 12 new burnishing patches resulted from this full factorial plan. Figure 5.43 shows the main amplitude parameters of all tests performed on 𝑆 0 0 . All results are congruent with the observations that were discussed above. First, the in ection point from where surface is damaged due to an excessive degree of plastic deformation is found at 90N-5passes, lower than 180N-3passes found for 𝑆 0 1 , proving that lower scale surfaces require lower 𝐹 𝑝 -𝑛 𝑝 pairs to achieve positive results. If a threshold level is surpassed the already described cyclic process of surface recreation and re-correction happens, by increasing the processing time unnecessarily from the texture point of view. Furthermore, this pair is associated to 𝑆 𝑘𝑢 near 3 and an unskewed surface, con rming that surface texture improvement is also achieved in terms of a aining a Gaussian height distribution by the application of these parameters. e second main result obtained from this analysis is that, indeed, the vibrationassisted process leads to similar height distributions, but delivers be er results in terms of scale. At sight of this result, it could be concluded that the lack of e ect of vibrations on the AISI surfaces, while present on the least rough Ti-6Al-4V texture, was not caused by an insensitivity of the material towards acoustoplasticity, but because of the need to so en the texture features to guarantee the good contact between the burnishing ball and the material. In fact, the introduction of vibrations prove to be detrimental in tests applied with 270 N, suggesting that an excessive preload can lead to further surface degradation if the VABB process is applied, probably due to excessive plasti cation arising from the vibration-assistance. Indeed, Figure 5.44 shows that the VABB process consistently generates deeper grooves due to the explained e ect. Consequently, 𝐹 𝑝 should be limited to avoid detrimental e ects of the acoustoplasticity during the VABB process. e AF curves represented in Figure 5.45 con rm that 90N-5passes correspond to the best VABB parameters that could be applied on 𝑆 0 0 , and lead to similar results as 350N-5passes on the 𝑆 0 1 surface of Ti-6Al-4V. Both original surfaces are slightly di erent in terms of bearing area ratio, as proves this gure, but were highly comparable at sight of their main 𝑆 descriptors. e rebound of the AF curves present at surfaces burnished through 180 N is the graphical manifestation of the detrimental e ects that were detected on 𝑆 0 0 at sight of the parameters represented above.

Kurtosis and skewness comparison

e comparison of the VABB and NVABB e ects on the AISI 1038 and the Ti-6Al-4V workpieces must not just be read in terms of scale reduction, but also as a means of material redistribution at the surface of the workpiece. e conjoint representation of the 𝑆 𝑠𝑘 -𝑆 𝑘𝑢 pair shows of all VABB and NVABB surfaces obtained on both materials are di erently distributed in the plane (Figure 5.46). Whereas most surfaces are platykurtic, di erent values of skewness are taken by the di erent results. e kurtosis parameter shows a higher variation in the AISI tests, whereas it is practically unvaried in Ti-6Al-4V surfaces. is can be understood as the highest a ectation of the steel alloy by the process. Nevertheless, all VABB and NVABB results are contained inside a certain area of the space which is near to Gaussian surfaces. Now, the question is whether this variation is signi cant enough to state that both processes are di erent among them, or that both materials react di erently to them? To establish a referential point, all the obtained 𝑆 𝑠𝑘 -𝑆 𝑘𝑢 points have been represented along with other results corresponding to other machining and nishing processes, taking the results compiled by Gri ths et al. (1986) [47] (Figure 5.47). NVABB and VABB show the unique capability of generating both positively and negatively skewed surfaces, as well as unskewed ones, whereas other processes lead to clearly negatively skewed (e.g. honing) or positively skewed surfaces (e.g. turning). Furthermore, ball burnished surfaces can be characterized by low kurtosis values. Although the Gaussian value 3 can be a ained with the correct application of parameters in AISI surfaces and Ti-6Al-4V 𝑆 0 1 surface, it is hardly modi ed in harsher textures of the last material. e clearly controlled area in which ball burnishing results are enclosed with regards to other nishing processes is a direct consequence of the mechanism on which each one is based. For instance, chip-removal operations, such as honing, remove the peaks of the material texture, generating a certain a ening e ect that leads to high kurtosis values and a predominant weight of positive heights (negative skewness). On the contrary, ball burnishing actually redistributes the target material that composes the surface texture, as the excerpted compression mechanism causes its ow towards the burnished track, thus creating new irregularities on the surface, only of a lower scale. As was shown in the previous subsection, too high plastic strain can lead the surface to over-strain, generating new irregularities that can be detrimental to its surface texture, by regenerating the initial peaks and valleys of the milled areas.

erefore, the e ect of ball burnishing can be then described as a self-reproducing or cyclic process, that redistributes material causing similar lower-scaled surfaces. By e initial topology has proved to determine to what extent it can be modi ed after ball burnishing, as well as the e ectiveness of the vibration assistance, which has proved to be negligible for surfaces conformed of relatively more abrupt height distributions. In other words, the introduction of vibrations has proved to be more e ective as the surface texture has a smaller scale. e rst hypothesis concerning this observation is that the interaction of the ball with the surface material changes substantially with the scale and distribution of the surface features.

It would be desirable to observe and measure this contact by optical means, enabling its quanti cation. Unfortunately, this task is technically complex and costly, due to the scale of the contacts and the reduced accessibility to the manufacturing environment. At sight of this limitation, and seeking evidence to con rm this hypothesis, the idea of developing a Finite Element Model (FEM) to have comparative data to compare the interface between the ball and the surfaces was embraced. e development of this model is however not at all the aim of this dissertation. Its complete and comprehensive development would be the object of an entire thesis. erefore, the results presented here have a preliminary condition, and constitute a rst approach to the issue to bring light from a theoretical point of view to the e ects that are being experimentally observed through the topological analysis.

Many ball burnishing FEM can be found in the bibliography.

ey are mostly based on lathe ball burnishing, being the objective of all of them identifying the results in terms of residual stress distribution with experimental results. Another critical issue in modelling the ball burnishing process is the method used to pilot the preload. Authors have usually controlled the preload by geometrical means, imposing a depth of penetration of the ball inside the material [10,[START_REF] S ¨ | Finite element modeling of burnishing of aisi 1042 steel[END_REF]. is solution is o en adopted because of its easiness of implementation. However, an improved model should discard this option, as the real depth of penetration of the ball in the material changes as it moves, due to the surface irregularities. Furthermore, as the material is deformed, the hardening e ect can have an impact on the initially programmed depth. In the model proposed here, the preload is directly imparted on the burnishing ball, and is kept constant along the whole process.

e bibliographical review reveals that there is still work to do about ball burnishing FE models, by making them more adapted to real burnishing conditions. e model that has been developed here to support the result analysis of this dissertation, constitutes the rst step of a more sophisticated model that shall be developed in the future, and that includes the following main di erential features:

• It incorporates a 3D ball-end periodical texture pa ern, based on real machined surfaces used in the experimental phase of this thesis. • It allows preload control by direct application of the force on the burnishing ball, preventing the results of being in uenced by self-hardening e ects or variations due to the topology height variations of the material.

e ball burnishing model shall be executed for surfaces 𝑆 0 1 and 𝑆 0 3 textures, on which 270 N and 1 pass shall be executed. Only the NVABB process shall be mod-5.1. GEOMETRICAL PARAMETER: SURFACE TEXTURE elled, as the 40-kHz vibration-assisted operation includes dynamical interactions that should be object of a more thorough study, far from the scope of this dissertation. e ANSYS so ware was used to perform the model.

Model geometry and material properties

A 5.5 × 1.7 × 2 mm AISI 1038 block was generated and meshed as the target material of NVABB. e 𝑆 0 1 and 𝑆 0 3 textures were overlapped on top of the volume by reproducing a simpli cation of their original pro les along the width coordinate, thus generating two respective blocks that exhibited planar symmetry and periodical texture features. e base curves were generated by juxtaposing spline curves characterised by their opening width and their depth, extracted from the real 𝑃 pro le traced on the real surface, as shows Figure 5.49. e mechanical properties of the steel alloy were taken from Table 4.13, whereas its plastic behaviour was modelled through the von Mises yield criterion (Eq. 5.2). e meshing was generated through solid186 elements, that allow us to model three-dimensional solids with quadratic displacement behaviour.

𝜏 𝑚𝑎𝑥 = 𝜎 𝑦 ⌋ 3 (5.2)
where 𝜏 𝑚𝑎𝑥 is the maximum shear stress due to friction force, and 𝜎 𝑦 is the yield strength of the material.

e ∅ 10-mm ball was modelled as an rigid solid characterised by the mechanical properties of a standard hardened chromium steel taken from a standard material database (Table 5.7). e contact between the two solids was modelled through conta174-and tar-get170-type elements, to adequately represent the sliding mechanism between the ball and the surface, governed by the Coulomb-Mohr classical friction law. e friction is deliberately introduced in the model, as although it does not have e ect on the force variation, it is an important drive for material pile-up a er deformation, which is fundamental for the nal texture a er the process. e execution of the model was programmed through the implicit ANSYS so ware, due to the lack of e ect of inertial forces, so that a succession of three main steps were considered as follows:

1. Loading phase: preload is actuated on the burnishing ball to plunge it into the material.

2. Burnishing phase: displacement of the burnishing ball through frictional sliding continuously along a longitudinal path formed by 3 peaks of the surface, with a 600-mm/min feed, and a 0.3-mm lateral o set displacement. Repeat the process ve times to obtain 5 parallel burnishing paths. e shown displacement values correspond to the relative change of position of each node a er the NVABB process, and should be added or subtracted to each correspondent coordinate before the operation. However, this is not the aim of the analysis, and, therefore, shall not be tackled here. On the contrary, it shall focus on the quantication of the contact area of the ball and the nodes that compose the surface is sought. To do that, instantaneous states of the whole simulation were considered during the lateral displacements along the o set length between adjacent passes, coded according to the numbers represented at Figure 5.50. For that instant, the nodes that were simultaneously in contact with the ball and the surface solids were retained. Being known the instantaneous size of the elements, the addition of all single areas allows the calculation of the contact surface between the ball and the surface material. Figure 5.52 shows one set of retained elements to calculate the area as an example, as well as a graphical representation of the areas retained for each analysed simulation step. Considering that all treating conditions are the same ones, the areas calculated for the two calculated cases are comparable among them. In overall, the contact are of the ball with the material surface is not constant, and evolves as the lateral pass width is progressively taken. However, the interaction area between the ball and the 𝑆 0 1 surface is in all cases lower with regards to 𝑆 0 3 . is area di erence can explain the di erent e ects of the process depending on the kind of surface on which it is actuating. Being the contact surface smaller in 𝑆 0 1 can account for the higher e ectiveness of the process in a ecting this kind of texture, as the total actuated stress is higher. It can also give clues about the higher e ectiveness of the VABB process, although this should have to be investigated by developing a model which is able to incorporate the vibration movement.

MECHANICAL PARAMETER: RESIDUAL STRESS

e nite element model has evidenced a di erent a ectation of the surfaces, just by the fact that the interface contact area between both solids changes with the different scale of the texture features. It was only calculated on an AISI 1038 workpiece to serve as a starting point for future works, and to observe the e ects of the process on the material that exhibited the highest contrast between results depending on the initial surface. e next subsection starts the study of mechanical e ects of the VABB and NVABB, by studying the results on the super cial residual stress.

Mechanical parameter: residual stress

e residual stress (RS) results calculated by applying the sin 2 𝜓 method through Xray di raction were provided by the lab as a two-dimensional tensor represented as in Eq.5.3. It contains the normal stress along the two main reference directions (I and II), and the shear stress associated to the measured patch. e error associated to each stress value was automatically quanti ed by the calculation so ware as a result of noise estimation and uncertainty in the identi cation of the Bragg's di raction peak registered through the equipment. All errors are lower than 5%, meaning that the measurements are highly reliable to represent the RS of every machined and burnished surface.

𝜎 RS = 𝜎 𝐼 𝜏 12 𝜏 21 𝜎 𝐼𝐼 ± 𝑒 𝐼 𝑒 12 𝑒 21 𝑒 𝐼𝐼 (5.3)
where 𝜎 𝑖 is the normal component of the tensor along direction 𝑖, 𝜏 𝑖𝑗 is the shear stress components of the tensor, 𝑒 𝑖 is the error associated to 𝜎 𝑖 , and 𝑒 𝑖𝑗 is the error associated to 𝜏 𝑖𝑗 .

AISI 1038 5.2.1.1 Residual stress state of the original surfaces

All three machined surfaces result in compressive RS, as is shown in Figure 5.53. is condition is not rare in this kind of machined materials, which are obtained by perpendicular ball-end milling, due to the near-zero cu ing velocity at the tool nose, which is detrimental for clean chip removal. Instead, the tool presses on the surface as it traverses the material along the programmed trajectory [49]. 𝑆 0 1 shows higher compressive RS than for 𝑆 0 2 and 𝑆 0 3 . As this surface is obtained by parallel passes with the lowest o set between them, the aforementioned detrimental cut dynamics are actually substituted by a compressive action that deforms the surface near to the tool nose. e low o set length makes more passes necessary to cover a certain amount of surface, increasing the described compressive action. e material presents a remarkable anisotropy, as 𝜎 𝐼𝐼 > 𝜎 𝐼 , meaning that the higher residual compression on the surface is accounted along the feed direction followed by the hemispherical tool. e shear components of the tensor, 𝜏 12 and 𝜏 21 , are almost negligible if compared to the normal ones, and considering the incertitude associated to them. erefore, the machined surfaces can be described through a biaxial stress state, being directions I and II its principal directions. Figure 5.53 also represents the von Mises stress, which has been calculated for the three surfaces through Eq. 5.4, provided their biaxial stress state. e von Mises stress can be considered as a comprehensive descriptor of the RS state of the material [51].

𝜎 𝑣𝑚 = ⌉ 𝜎 2 𝐼 + 𝜎 2 𝐼𝐼 -𝜎 𝐼 𝜎 𝐼𝐼 + 3 𝜏 12 𝜏 21 (5.4)
e incertitude associated to the von Mises stress can be calculated by error propagation:

𝑒 𝑣𝑚 = ⟨ ⧸ ⧸ ⟩ 𝑛 1 𝜕𝜎 𝑣𝑚 𝜕𝑥 𝑖 𝑒 2 𝑟,𝑖 (5.5)
Applying Eq. 5.4 to 5.5, the von Mises stress incertitude, 𝑒 𝑣𝑚 , can be calculated as Comparing the von Mises stress calculated on all three initial surfaces, a general decrease in the stress state is detected as a higher o set distance is taken between adjacent passes, while the incertitude is of a similar same order of magnitude.

Overview of residual stress results a er ball burnishing

A rst approach to the VABB and NVABB RS results analysis is performed by colourcoding and representing the normal components of the stress tensors of each test (Figure 5.54). Whereas RS are still compressive, the absolute values of some of them are lower than their as-machined correspondents, meaning that certain some burnishing conditions can lead to stress relaxation. Now, would this e ect be the same one in surfaces that are not in such a compressive state? at would mean a net positive e ect of ball burnishing, that should be checked on another set of workpieces in future works. e anisotropy that was observed in the initial surfaces is however maintained a er the VABB and NVABB processes. e higher values of 𝜎 𝐼𝐼 with regards to 𝜎 𝐼 are in general con rmed for all burnishing states, except for speci c conditions where this trend is reverted: tests #7, #18, #22 and #26.

ese testing conditions have in common that they are all executed with 3 or 5 passes combined with the bn90/0 strategy. Consequently, whereas the strategy proved not to be in uential in topological results, it can actually a ect the directionality of RS. Indeed, applying a burnishing strategy based on more than 3 criss-crossed passes, turns out to have the e ect of reverting the anisotropy that was detected a er machining. e von Mises stress calculated for all patches, and represented against 𝜎 𝐼𝐼 , reveals that the la er dominates the overall RS state of every VABB and NVABB surfaces, except for the singular group of tests that were detected as signi cantly in uential (Figure 5.55). is fact reinforces the idea of the strategy as a modi er of the preferential direction of RS. On the other hand, the highest von Mises stress are a ained at the tests performed on the 𝑆 0 1 and 𝑆 0 2 surfaces.

is rst visual analysis has delivered valuable information, but cannot describe preload, number of passes, strategy, initial surface texture and feed velocity on the normal stress components and the von Mises stress. is analysis shall lead to parameter optimisation in order to maximise compressive residual stress on the surfaces.

Parameter optimisation for RS maximisation based on ANOVA mean e ects

e analysis performed in the previous section evidenced that the anisotropy of the machined surfaces was maintained a er the execution of both NVABB and VABB processes. A direct deduction of this observation is that the optimisation target is not unique in this case. Indeed, many variables could ful l that role, namely 𝜎 𝐼 , 𝜎 𝐼𝐼 , or 𝜎 𝑣𝑚 as a general descriptor of the RS state. Although the ideal objective would be maximising 𝜎 𝐼 and 𝜎 𝐼𝐼 simultaneously, the reader shall realise that this is not possible at sight of the results that are to be presented throughout the next subsections. e optimisation procedure that shall be followed is represented graphically in Figure 5.56. First, the set of optimal values shall be decided based on the mean e ects and interactions graphs delivered by the ANOVA calculations considering as response variables the absolute RS components, and their relative improvement with regards to the reference values related to the machined surfaces. e "higher is best" criterion is considered to calculate the S/N ratios. To complete the analysis, the parameter set found through this deduction shall be compared to experimental values.

ANOVA mean e ects on absolute residual stress e mean e ects of each parameter on the di erent RS components calculated through ANOVA are represented in Figure 5.57.

e rst observation that can be made agrees with the general remarks performed in the previous subsection, by identifying the strategy as a modi er of the preferential direction. While bn90/0 reinforces 𝜎 𝐼 , 𝜎 𝐼𝐼 is enhanced by nb0. Being true for both VABB and NVABB, this consideration is a fundamental nding in terms of productivity, as it implies that by planning correctly the trajectory of the burnishing tool, for instance concentrating all ball passes along one direction, the surface orthotropy can be modi ed conveniently, sparing productive time.

Secondly, the VABB process generates higher compressive RS in average, especially along direction I. erefore, VABB can be considered as thee preferential process over the NVABB one. Focusing then on te VABB factors, the 𝐹 𝑝 can be xed in 270 N, whereas 5 passes should be recommended for 𝜎 𝐼 and 3 passes for 𝜎 𝐼𝐼 . Ironically, the low in uence of the initial texture is also an interesting result in this case, due to the fact that the surfaces departed from very di erent stress states. Indeed, as the original RS values of 𝑆 0 3 are lower than those of 𝑆 0 1 and 𝑆 0 2 , its enhancement can be described as more remarkable a er VABB. Consequently, 𝑆 0 3 can be declared as the surface that has been more positively in uenced by the VABB process. Taking into consideration the results delivered by the absolute RS states leaves many questions open. erefore, an additional approach to the subject is undertaken in the next subsection by considering the factors that deliver the highest pro t from the introduction of vibration-assistance.

ANOVA mean e ects on the residual stress relative improvement

To consider the in uence of the introduction of vibration-assistance in the R results, the ANOVA has been performed taking the nal-to-initial ratio of each RS component as response variables:

𝛥𝜎 𝑖 = 𝜎 𝑖 𝜎 𝑖0 (5.7)
where 𝛥𝜎 𝑖 is the nal-to-initial RS ratio, being 𝑖 = {𝐼, 𝐼𝐼, 𝑣𝑚} e mean e ect graphs are represented in Figure 5.58. e red line delimits the boundary between the area where RS is improved a er burnishing that is, 𝛥𝜎 > 1. Again, the VABB process shows superior e ects on the RS, as it is able to deliver a higher improvement to the surface with regards to its non-assisted complementary. Results also show that this superiority must be read di erently according to the initial surface texture, that, again proves to be a remarkable focus of response variation. e 𝑆 0 3 surface shows that it experiences the highest RS improvement by the introduction of vibrations. On the other hand, results on surfaces 𝑆 0 1 and 𝑆 0 2 show that the NVABB process causes stress relaxation. However, by introducing the vibration-assistance, the VABB maintains in average the initial RS level of 𝑆 0 2 tests, and reduces stress relaxation in 𝑆 0 1 . is statement reinforces the idea of discarding the NVABB process, and considering the VABB process as the most adequate to deliver positive RS results on AISI 1038 surfaces. In this case, it seems that a 900 mm/min feed should be discarded, as the only values that improve RS are 300-600 mm/min. e rest of the results are consistent with the observations made in the previous absolute RS analysis: 270N-3passes is recommended to increase 𝜎 𝐼 , while 270N-5passes should be the selected pair to achieve the highest enhancement of 𝜎 𝐼 . e strategy evidences again its e ects in the same sense as when the absolute RS values were considered: bn90/0 reinforces 𝜎 𝐼𝐼 , while nb0 a ects positively to 𝜎 𝐼 .

Interaction analysis through ANOVA results on the residual stress relative improvement e ANOVA calculations evidence that, in this case, the 𝐹 𝑝 *𝑣 𝑓 and 𝑛 𝑝 *𝑣 𝑓 interactions cannot be neglected from the analysis (5.59). Starting by 𝜎 𝐼 , for which 270N-5passes were established as best, the interactions seem to favour 600 mm/min. For 𝜎 𝐼𝐼 , the observed 270N-3passes combination is more adequate to be applied with 300 mm/min. Finally, the overall RS represented by 𝜎 𝐼𝐼 , should be executed by 270N-5passes, and the feed interval 300-600 mm/min is adequate. e feed values de ned by this deductive process might seem di erent, but can be actually read from a single scope: they discard 900 mm/min as a possible value, and accept in general, al feeds lower than 600 mm/min. is means that the e ciency of the process is delivered by a su ciently low ball displacement on the surface.

All S/N ratios gures can be observed in Appendix D. e higher values of the S/N ratios for every level that has been found optimal prove their higher robustness in terms of results. e optimal values that must be taken to maximise compressive residual stress a er VABB, at sight of the mean e ects of the factors calculated through an ANOVA, can be found in Table 5.8. Of all the values, the initial texture must be taken very carefully. e 𝑆 0 3 has proven to be extraordinarily enhanced by VABB, reaching also the highest 𝜎 𝐼 . However, the 𝑆 0 1 and 𝑆 0 2 have proved to deliver the maximum 𝜎 𝐼𝐼 and 𝜎 𝑣𝑚 , although RS have been relaxed.

is is due to the fact that they depart from a higher compressive state, so that their superior RS results are actually not caused by the VABB process, but because it is able to keep the same level as the machined surfaces. e fact that all factors have been declared in uential in the RS results makes it di cult to nd the exact experimental realisation in the Taguchi array. Only the test #25 can be found to represent the optimal parameter set to maximise 𝜎 𝑣𝑚 , which is, indeed, the test for which that parameter achieves its highest improvement. Albeit the positive result, this test is performed on 𝑆 0 1 , where RS should be relaxed at sight of the mean e ect analysis. is observation does not invalidate the previous results, as they proceed from real experimental data. However, it leads to think that there might be tests that, although do not t the found optimal factor combination, could also derived in positive results. ese tests are discussed in the following subsection.

Optimal parameter set for RS maximisation based on individual Taguchi experimental results

Figure 5.60 shows the RS components of the experimental tests were they resulted to be maximum. e respective parameter sets that characterise those tests are included in table 5.9. It is evident that these combinations are not exactly coincident with the optimal sets obtained from the ANOVA mean e ect deductive process. e feed is the factor showing a highest disagreement, as it presented be er mean results for low values, but some of the real best tests are performed with 900 mm/min. A possible source of variation could be identi ed with the fact that there are still 6 second-order interactions that are not being studied through the L27 experimental design, and that could indeed be relevant for the case study. At this point, it seems that a reasonable strategy to obtain conclusions about ball burnishing for compressive RS maximisation, is nding the facts that are common between both theoretical and experimental approach. ese • e VABB process has proved to deliver superior results both in mean terms, and also in the speci c experimental tests. • e strategy is a fundamental factor to de ne the preferential RS stress direction. On one hand, bn90/0 reinforces direction I, while nb0 reinforces direction II. However, it must not be forgo en that the reinforcement of one direction proves to be detrimental to the perpendicular one, at sight of the experimental results.

• 270 N is the preload level that derives in the best results. Although the best VABB conditions for 𝑆 0 1 is obtained with 180 N, it is still a high preload level. erefore, in general terms, it can be stated that a high preload are desired to achieve higher compressive RS in the workpieces. • e number of passes is not exactly the same one in all tests. However, in all cases, 3 o 5 passes are considered, agreeing that 1 pass is not suitable. A general conclusion to this ma er is that the best 𝑛 𝑝 is between 3 and 5.

e RS analysis on the AISI material has proved to be more complicated than the result discussion performed for the texture issue. Indeed, the relevance of all parameters on the responses, as well as the interactions, has complicated this task. In the next subsection, the titanium alloy results in terms of RS are analysed, by following a similar proceeding.

Ti-6Al-4V

5.2.2.1 Residual stress state of the original surfaces e assessment of the residual stress of the initial surfaces machined on the Ti-6Al-4V workpiece was performed by performing the X-ray di raction method on three di erent points for each surface. e resulting 9 measurements show that the residual stress condition of each one is stable at all assessed coordinates, since although 𝜎 𝐼 and 𝜎 𝐼𝐼 can slightly vary from one point to another, the equivalent von Mises stress is equivalent for all of them (Figure 5.61). at means that the in uence of the machining operation on RS can be considered uniform, but that a variation of the relative weight of the two normal stress components in the overall RS state might occur depending on the speci c measuring point. All in all, anisotropy is detected in all measurements, being 𝜎 𝐼 > 𝜎 𝐼𝐼 . is observation is contrary to the one found in the AISI 1038 workpiece, where the direction showing the higher RS was 𝜎 𝐼𝐼 . is di erence can be easily explained by considering the di erent background of both raw materials, which were processed through lamination and forge respectively, and the consequent variation in residual stress state. In any case, this di erence should be considered when comparing and discussing the results found for both materials.

In absolute terms, it is 𝑆 0 1 the surface with highest RS components, which descend sequentially as the o set distance between passes is reduced to generate 𝑆 0 2 and 𝑆 0 3 . is e ect was also observed on the AISI 1038 surfaces, and can be a ributed to the pressing force performed by the tool nose in this kind of orthogonal ball-end milling operation, increased as the passes are less separated among them.

Overview of residual stress results a er ball burnishing

e resulting normal components of the RS tensor associated to every burnishing patch are represented in Figure 5.62. As warm colours are associated to higher compressive residual stress level, it is evident that the resulting 𝜎 𝐼 values are maintained higher a er the VABB and NVABB process, in most of the cases. Consequently, it can be stated that neither of the two processes succeed in reverting the preferential direction presented by the original residual stress state. is e ect was also observed on the AISI 1038 burnishing patches, where the main direction was kept in all cases along II, except for those tests performed by combining the bn90/0 strategy with 3 and 5 passes -#7, #18, #22 and #26-, which reverted the preferential direction. For the Ti-6Al-4V patches, where the initially favoured direction is I, the e ect of VABB and NVABB tests is the reinforcement of this initially preferential direction. Indeed, tests #7, #18, #22 and #26 show the highest 𝜎 𝐼 inside their initial texture groups.

e 𝜎 𝐼𝐼 results also show a more clear progressive increase as the degree of plastic deformation grows, represented by a degradation from cool to warm colours. e e ect of the preload can be expected to be more remarkable in this case, as show the ANOVA results included in the next subsection. On the other hand, the singular tests #7, #18, #22 and #26 do not seem to modify the level of stress, and no inversion can be detected in this case. Instead, the preferential RS directions presented by the raw material were reinforced by the application of these tests. Although this result seems opposed to the one obtained on the AISI workpiece, they are both very consistent.

e favoured directions of both materials a er machining were inverted. Since the preferential burnishing direction was maintained along I, the e ect of applying each 5.2. MECHANICAL PARAMETER: RESIDUAL STRESS strategy must be consequently changed. What was inverted in the AISI surfaces is reinforced in the Ti-6Al-4V workpiece.

Parameter optimisation for RS maximisation based on ANOVA mean e ects

e overview of all RS results has reinforced the idea of VABB and NVABB as processes able to reinforce the orthotropy presented by a machined surface. e following step is nding out whether an optimal parameter set can be found in order to take advantage as much as possible of VABB and NVABB to increase the compressive residual stress on the material surface.

e sequential proceeding that is followed below is based on the same approach that was taken for the AISI results, shown in Figure 5.56. First, the optimisation shall be tackled by considering the mean e ects of the factors and interactions included in the model, all of them calculated through ANOVA. ese ideal parameter sets shall be then compared to experimental results. Finally, the best experimental results shall be identi ed, to compare them to the ideal set and extracting conclusions about this ma er.

ANOVA mean e ects on absolute residual stress e mean e ect of each factor included in the Taguchi design is assessed by performing the ANOVA taking the di erent RS components as response variables. e mean e ect graphs are represented in Figure 5.63. e rst immediate remark to do about the result is that both VABB and NVABB seem to deliver comparable mean effects. Secondly 𝜎 𝑣𝑚 is only in uenced by the 𝐹 𝑝 -𝑛 𝑝 pair, meaning that the overall RS modi cation is basically dependent on the degree of plastic deformation. Speci cally, 350N-5passes are the best conditions to be applied in both VABB and NVABB.

As for 𝜎 𝐼 and 𝜎 𝐼𝐼 , the strategy proves again to be an e ective driver through which reinforcing a desired surface direction, being bn90/0 the strategy favouring the former, and nb0 the la er. is result is identical to the case observed in the AISI workpiece.

e mean e ects of the initial surface on the results is also inverted from 𝜎 𝐼 and 𝜎 𝐼𝐼 . e interpretation must be related to the initial surface state. A er burnishing, the relationship 𝜎 𝐼 > 𝜎 𝐼𝐼 is maintained in average as in the machined surfaces. However, 𝑆 0 1 being more residually compressed than 𝑆 0 3 is only maintained in 𝜎 𝐼𝐼 a er VABB and NVABB whereas it is inverted in 𝜎 𝐼 . e only reason why this happens is because 𝑆 0 3 is more positively a ected by VABB and NVABB, and its 𝜎 𝐼 (main burnishing direction) is increased to a higher extent.

Finally, the combination 350N-5passes is the best in meand terms to maximise 𝜎 𝐼𝐼 . On the contrary, 𝜎 𝐼 re ects be er results by the application of 90 or 180 N with 5 passes. is observation could imply that a certain stress relaxation can be associated to both processes as the preload is increased. is e ect contradicts the results obtained in the AISI 1038 results, were relaxation was only detected for the NVABB process.

e RS assessment a er the mean e ects calculated through the ANOVA has shown that the in uence of all factors is relevant for the case study. However, there are still some issues to tackle with, such as the di erent in uence of the process depending on the initial surface texture. erefore, the relative improvement caused by the processes is analysed in the next subsection.

ANOVA mean e ects on the residual stress relative improvement e initial-to-nal residual stress component ratio calculated through Eq. 5.7, has been subjected to an ANOVA calculation. Figure 5.64 shows that both processes are able to in uence positively all surfaces, being the red line the boundary from where surface stress relaxation is caused a er the process. It is remarkable that, in general terms, 𝜎 𝑣𝑚 is kept constant before and a er ball burnishing, while it increases the most in 𝑆 0 3 , through 350N-5passes, and independently from the strategy. Other direct results arise from this analysis. First, no substantial di erence between VABB and NVABB can be observed. Secondly, the strategy in uence follows exactly the same pa ern than in the absolute results. ird, no in uence of the feed is observed. Last of all, the same 𝐹 𝑝 -𝑛 𝑝 that were identi ed as ideal to maximise the nal RS, also delivers the highest advantage of the process. e only di erence, is that 270 N proves to be more e ective in the VABB than in the NVABB process. at means that a high preload is required to take advantage of the vibration assistance.

ese ANOVA results are highly interesting to understand the e ect of the initial surface on the process e ectiveness. 𝑆 0 3 is the most positively a ected by VABB and NVABB. However, 𝑆 0 1 experiences RS relaxation along direction I, con rming what was observed in the analysis of the absolute results: this relaxation justi es the lower 𝜎 𝐼 in 𝑆 0 1 than in 𝑆 0 3 , being the only relative trend that is inverted a er ball burnishing. e direct consequence of this observation is that applying the bn90/0 process on the 𝑆 0 1 surface, which de nes 𝜎 𝐼 should be avoided.

e last step to con rm the de nition of the best parameters must be completed by checking the interactions between factors, that proved to be relevant in the case of the AISI alloy. is study is presented below.

Interaction analysis through ANOVA results on the residual stress relative improvement e interaction analysis shown in Figure 5.65 proves that these are not so relevant in this case as they were for the AISI 1038 material.

e 𝐹 𝑝 *𝑣 𝑓 interaction for 𝜎 𝐼 , makes recommendable to chose a 900 mm/min feed for the 150 N preload that was selected. e lack of remarkable interactions for the other two RS components allows the con rmation that all feeds could be eligible to apply the process, at sight of the lack of in uence on the result e search for optimal parameter set according to the mean e ects of each factor on the di erent RS components has resulted in the respective parameter sets included in Table 5.10. Both processes can be recommended to improve the RS state of the material, due to their similar mean e ects, and the strategy is again the main facilitator for the reinforcement of a speci c surface direction. As this solution is based on mean e ects, it is necessary to compare them to actual experimental results. Only the sets determined for the 𝜎 𝐼𝐼 and 𝜎 𝑣𝑚 can be found in the Taguchi array, con rming that they are able to increase the compressive residual stress over 40%. Now, to complete this validation, the direct consideration of the experimental results is undertaken in the next subsection. e direct inspection of all RS results has delivered the identi cation of the highest compressive residual stress results on the tested surfaces.

ese singular tests are represented in Figure 5.66. e processing parameters corresponding to these tests can be found in Table 5.11. ese selected tests con rm that, indeed, both VABB and NVABB can improve the RS state of all surfaces. Also, it is indi erent to apply the NVABB or the VABB processes due to their similar results, although 𝑆 0 3 exhibits a tendency to register be er results with the NVABB process.

• Both the VABB and NVABB are able to cause similar e ects in terms of residual stress on the Ti-6Al-4V surfaces. • e highest preload 350 N is recommended to improve any of the di erent RS components, except for 𝜎 𝐼 in the 𝑆 0 1 texture, for which 250 N is recommended. Although the main e ect results xed that recommended preload at 150 N, both cases indicate that a lower preload should be applied on 𝑆 0 1 , so that it does not have a detrimental e ect on the RS along direction I. • 5 passes should be performed in all cases to achieve the highest RS improvement. • e bn90/0 surface favours direction I, and bn0 favours direction II, although this fact had an inverse e ect on the Ti-6Al-4V workpiece due to the fact that the relative weight of each RS component was reverted a er machining in both materials.

• No speci c feed seems to be more adequate to perform the NVABB or the VABB processes.

Optimal parameter sets according to texture and RS criteria: synthesis

Having reached this point in the result discussion chapter, it is necessary to make a synthesis of all the results derived from the topological and RS analysis, with the aim of deciding whether they can be uni ed to establish one or various priority parameter set to apply the VABB process; and, in those cases where NVABB is recommended over it, propose an alternative.

e derived ball burnishing parameter sets have been organised by material, in two di erent Tables: 5.12 and 5.13. ese charts are organised by initial surface texture, which should actually be considered as a contextual requisite for burnishing application, and no longer as a factor of study. Indeed, it was concluded that the application of the VABB process requires not only calibration and testing on a speci c target material, but the process parameters should also be decided according to the initial surface presented by the speci c workpiece. e aforementioned tables include all optimal parameter set, obtained a er diverse criteria, including statistical and experimental evidence. In the case of texture enhancement, the optimal burnishing parameter combination arising from the observation of individual experimental texture results are in agreement with those derived from the ANOVA analysis. erefore, no di erentiation is made in this regard. On the contrary, those two criteria lead to di erent solutions in the case of RS component maximisation, thus having been speci ed in the Table as "Taguchi" -direct observation in the experimental results-, and "ANOVA" -concluded a er the mean e ects calculation. e inspection of both tables leads to conclude that, although not all parameter sets lead to the same target, some factors are recommended in the same or similar values regardless of the objective. It is the case of the preload and the number of passes, which are in most of cases recommended at their highest levels. For that reason, the last column of the tables propose a uni ed parameter and process descriptors that could be applied in a general case to enhance texture and residual stress at the same time. However, it should not be forgo en that one direction of the space is prone to be less a ected. A special mention should be done regarding the case of the AISI 1038 𝑆 0 1 surface improvement. e uni ed parameter set has been set in 270N-5passes, what seems to be incoherent with the 180N-3passes recommended in terms of texture. ee explanation is simple: in the already known cyclic e ect of VABB, 270N-5passes was found to deliver also good surface texture, although being a longer process, and it allows in addition the RS enhancement. e reader shall notice that the strategy is not included in the cell that gathers a uni ed parameter set. Since one of the main conclusions derived from this result discussion was that they were indifferent for texture scale reduction, they should be chosen according to the preferential direction that must be reinforced.

Metallurgical parameter: hardness and metallography

e previous section has shown that, although not all aspects of surface integrity can be simultaneously improved, a certain optimal set can be established to nd a balanced solution for all of them. In this section, a third aspect of surface integrity is tackled to complete the assessment of the impact of VABB. Although it is not expected to observe specially remarkable results from the metallurgical point of view, SEM metallographic observations have also been performed.

Due to the highly time-consuming sequence of specimen preparation and hardness measurement execution, this section focuses on a speci c parameter set derived from the previous analysis. Since the strategy has proved to modify the directionality of the material, this parameter has been included in two di erent levels, to assess its e ects of VABB on both materials. NVABB tests are also performed to establish a comparison point.

AISI 1038

A new AISI 1038 workpiece was machined to generate an 𝑆 0 1 -type surface. is texture was chosen due to the fact that is the one that evidenced higher a ectation by the VABB process.

e in uence of strategy in the directionality of the RS results lead into consider both bn90/0 and nb0 strategies, to evaluate whether there can also be a reinforcement e ect in the case of the hardness. In total, four new patches were burnished on the machined surface, as shows Table 5.14.

To study the in-depth a ectation of the material due to VABB and NVABB processes, every burnishing patch was cut in the middle in both directions I and II, thus generating the respective surfaces parallel to both of them (Figure 5.67.a). A er pol- .68 shows the resulting hardness pro les along with their respective error bars. e comparison of the as-machined subsurface hardness measurements con rm the original anisotropy: along direction II, the core hardness is achieved at around 250 µm, whereas this value is reached at 500 µm along direction I. e lack of further data does not allow us to state a de nitive explanation to this fact. However, a certain link between RS and hardness could be proposed as possible, as RS can be understood as elastically deformed grains con ned inside plasti ed boundary grains. Under this perspective, hardness measured on the plane parallel to direction I could be dominated by the compressive 𝜎 𝐼𝐼 residual stress (Figure 5.67.a.). 𝜎 𝐼 presents lower values, and so do the hardness datasets measured on that plane. Although there seems to be a link between both magnitudes, the main drawback to this approach is that, as the X-ray di raction method applied to calculate RS has only a few µm of penetration, it is not sure that they keep that level to a 50-µm depth, which is the rst available hardness measurement. Neither VABB nor NVABB modify substantially the hardness level at the nearsurface depth, considering the error bars.

is observation was already con rmed by evidence presented previously by other researchers, included in the state of the e material hardness is, however, a ected at deeper layers, spanning from 250 to 500 µm along direction II and 150 to 250 µm along I. Direction II must be considered as the one a ected to a highest extent in terms of hardness. is deep e ect of ball burnishing can be explained by the elastic-plastic Hertzian contact mechanics, that characterise stress propagation inside solids by e ect of a super cial load [37]. e strategy has a clear e ect on the hardening e ects a er both processes, being nb0 the one resulting in higher hardness, especially along direction II. Only the bn90/0 strategy seems to have a slight more positive e ect along direction I, from 100 to 150 µm. e nb0 strategy clearly favours the same direction as it did in RS terms, and so does bn90/0 at the near subsurface layers, although its e ect is more modest. Now, considering the di erence between vibration-assistance and conventional ball burnishing, results change.

e VABB process executed according to the nb0 strategy exhibits in overall a more remarkable positive e ect, from 250 to 500 µm depths. To visually detect the di erent result delivered by vibration-assistance, if present, an alternative representation is proposed through the VABB-to-NVABB ratio, 𝛥𝐻𝑉 , calculated as follows:

𝛥𝐻𝑉 = 𝐻𝑉 𝑉 𝐻𝑉 𝑁 (5.8)
where 𝐻𝑉 𝑉 is the average Vickers hardness obtained through the VABB process, and 𝐻𝑉 𝑁 is the average Vickers hardness obtained through the NVABB process.

e incertitude bars have been calculated by error propagation on 𝛥𝐻𝑉 , as was indicated in Eq. 5.5. e resulting expression can be formulated as follows:

𝑒 𝑟 = 𝛥𝐻𝑉 } 𝑒 𝐻𝑉 𝑉 𝐻𝑉 𝑉 2 + 𝑒 𝐻𝑉 𝑁 𝐻𝑉 𝑁 2
(5.9)

where 𝑒 𝐻𝑉 𝑉 is the error associated to 𝐻𝑉 𝑉 , and 𝑒 𝐻𝑉 𝑁 is the error associated to 𝐻𝑉 𝑁 .

Figure5.69 represents the values of the 𝛥𝐻𝑉 ratio for all the explored depths. It is the bn0 strategy the one that delivers be er results through VABB, from 250 µm depth, whereas bn90/0 hardly takes advantage of vibration-assistance. erefore, it can be stated that, in terms of deep a ectation, it is the nb0 strategy the one that registers more advantage from vibration-assistance. As repeated passes along the same path, clearly help take pro t of the vibrations incorporated to the process, whereas this e ect is dissolved for the bn90/0 by the change of direction of the passes. e specimens that were subjected to the previously described hardness tests were chemically etched to perform SEM observations. Figure 5.70 exhibits a surface layer of deformed material, being the grains of ferrite and cementite reduced due to the plastic residual strain. Some shear marks can be observed in the ferrite phase a er VABB, which leads to conclude that the depth of a ectation due to this process is slightly higher. However, this is not necessarily positive for the surface, as this e ect cannot be momentarily assessed in functional terms.

e only metallography that exhibits a substantial di erent result is the one corresponding to direction I of the nb0 strategy performed through VABB. e cementite at the surface seems to be smashed and mixed with the ferrite matrix. e reason could be, again, the repetitive passes caused by this kind of strategy along the same direction while the ultrasonic signal is transmi ed inside the material. e consequence of this change should be further assessed in future works.

Ti-6Al-4V

To complete the characterisation of the e ects of VABB on the Ti-6Al-4V surfaces, a metallurgical analysis was performed on a new specimen. e 𝑆 0 1 surface was taken as basis, and the parameters that were de ned as most appropriate were selected to perform the operations (Table 5.15). Specimens were prepared as speci ed for the steel alloy, to subject them to hardness measurement through a matrix as the one represented at Figure 5.67. .71 shows the resulting deep hardness pro les of the explored surfaces. In this case, the machining process has a hardening e ect on the workpiece that spans to a 100-µm depth. However, the hardness pro les are substantially more similar among them than in the case of the AISI alloy.Both the NVABB and VABB processes cause a residual hardening along direction I, but that e ect is inconspicuous along direction II, except for one processing condition: nb0 and VABB. e combination of both is in overall positive along both directions, although the depths where it can be observed, is di erent: the e ect along direction II seems more super cial. It must be considered the error introduced my the manual measurement with the Vickers microindenter, which is not automatised, and might deliver undesired bias in the depth control.

erefore, it should be highlighted the positive impact of nb0 and VABB, regardless of the exact depth represented in the Figure. 5.4.2.2 SEM observation of the Ti-6Al-4V surface and sub-surface layers e specimens that were used for the hardness measurements were chemically etched to distinguish the di erent phases of the Ti-6Al-4V material, and assess a possible change in microstructure caused by VABB and NVABB. Figure 5.72 represents the subsurface layers of the nb0 patches, exhibiting the typical white layer formed by this kind of alloys [155], mixed with some oxygen uorides coming from the chemical etching with Kroll's reagent. e main e ect of ball burnishing is represented by the 𝛼 phase oriented along the surface, by e ect of the plastic deformation. However, the depth of a ectation is lower than in the case of the AISI material, and, in all cases, di cult to distinguish.

Synthesis of metallurgical results

e performed metallurgical analysis allowed the assessment of the e ects of VABB and NVABB in deep layers of the AISI 1038 and Ti-6Al-4V tested alloys. It proved that both processes a ect positively the hardness of the subsurface layers of the target material.

e only relevant result is the remarkably more e ective combination of nb0 strategy with the VABB process, that achieves higher hardness. It even has a metallurgical e ect, as it is able to break the cementite phase. e implications of the metallurgical analysis, which has not been so extensive due to the time-consuming activities required with that aim, reveals that the e ect of both VABB and NVABB is present down to around 500 µm. Deeper material layers can be considered to have the properties of the bulk material, and cannot be described through the surface integrity approach.

6

Conclusions and perspectives e present dissertation tackled with the issue of executing the vibration-assisted ball burnishing process through a designed tool, and has explored its application on two di erent industrial alloys: AISI 1038 and Ti-6Al-4V.

Being 40 kHz the frequency of the signal transmi ed by the prototype designed to execute the process, the most complex technological challenge was being able to acquire, sample and postprocess this kind of high frequency signal. Acoustic emission tests allowed the measurement of the signal transmi ed inside an AISI 1038 block. It evidenced to be characterised by a 39.1-kHz frequency, independent of the preload excerpted by the tool. A second characterisation phase was undertaken by direct dynamometric measurement, to quantify the vibratory force overlapped on the spring preload.

is force resulted to experience relatively low variations with regards to the preload value, inside a ± 4-5.5 N interval. Since the Blaha e ect is not based on stress addition but on signal transmission through the material while it is deformed, this range of forces is considered as valid.

ese characterisation activities proved that the prototype was able to function inside stable levels, with no dependence on process parameters. e test of VABB on AISI 1038 and Ti-6Al-4V surfaces proved to have a highly positive impact in the surface integrity of the treated surfaces. However, the industrial implementation of the process requires a preliminary study to determine the adequate parameters that must be applied, considering the target material and the topology of the target surface. Additionally, both the topological and residual stress results showed that the search for the best process parameters cannot be detached from the original surface texture on which they shall be applied.

is statement is based on several evidence, explained along the following paragraphs.

From a topological point of view, VABB has a triple e ect on the surfaces where it is applied, as follows:

• General scale reduction.

• Surface height redistribution according to Gaussian or quasi-Gaussian surfaces.

• Change of the main directionality of the surface texture features, if enough preload is applied.

e results showed that plastic deformation performed through VABB delivers a net reduced scale surface. Furthermore, as the process is not based on chip removal, the resulting topologies are always represented by Gaussian or quasi-Gaussian height distributions, which are known for their balanced characteristics of lubricant retention and low wear. at result can be explained due to the fact that the ball has a simultaneous e ect on the texture: it reduces its original peaks while generating new low-scale valleys. e AISI 1038 material registered texture scale reductions higher than 80% in the nest tested original surface, whereas the improvement was of around 60.3% for the Ti-6Al-4V alloy.

On the other hand, given a speci c texture machined on a material, a single preload and number of passes pair of values, 𝐹 𝑝 -𝑛 𝑝 , can be found to achieve the best texture scale reduction. From that point, higher combinations delivering more plastic deformation lead to detrimental e ects on the surface. Nevertheless, a cyclic e ect of VABB can be observed as further plastic deformation always leads to a reconguration of the surface. In this sense, a second threshold that delivers again good texture results can be found.

at recon guration includes texture scale reduction with Gaussian height distributions, accompanied with a change in the directionality of the surface topology features, which are reoriented according to the main VABB direction. e singular 𝐹 𝑝 -𝑛 𝑝 values must be selected regarding the target material and the texture machined on it. e topological characteristics of the original surfaces also have an impact in the e ectiveness of vibration-assistance to generate lower scale textures. is observation was con rmed in both materials. If the initial surface presented an 𝑆 𝑞 parameter of 1 µm or less, the VABB presented superior results, compared to NVABB. is observation reinforces the idea of the initial surface being a fundamental variable to consider when selecting VABB process parameters. e results also showed that, as the scale of the texture increases, both the VABB and the NVABB lead to similar results. A second threshold is found for the singular value of around 10-µm 𝑆 𝑞 , from which NVABB starts to deliver be er results. Vibration assistance can only be taken advantage of on ne enough surfaces, whereas it is detrimental in too high scale ballend milled textures. e second response evaluation parameters that were considered is the change of the compressive residual stress tensor components a er VABB. e e ects of VABB were not always positive in this regard, as the original surfaces were originally residually compressed as a consequence of the machining process. e nest surface presented the highest residual stress from the beginning. e VABB process proved to avoid stress relaxation in that surface, which was on the contrary observed a er the non-assisted process. e other original surfaces, less compressed originally, registered remarkable higher RS a er VABB, proving its positive e ects with regards to the non-assisted operation (e.g. in some cases, compressive RS increased by 36%). Results are slightly di erent in the Ti-6Al-4V workpiece, where both NVABB and VABB resulted in similar results, also more modest compared to those on the AISI 1038 alloy. ese results lead to think that the materials react completely di erent to the vibration-assistance, besides their original texture. For the explored values, the Ti-6Al-4V was less sensitive to vibration-assistance.

Regarding the residual stress results, it must be highlighted the relevance of the burnishing strategy to de ne the direction of the surface that should be reinforced. All original surfaces exhibited a high anisotropy a er machining that could be corrected or balanced by choosing the direction along which VABB should be applied. is result is fundamental to simplify the implementation of the VABB process, according to the state of the machined surface on which it shall be executed.

Last of all, the deep hardness analysis exhibited that the VABB process delivered deeper a ectation of the material, especially if the process was always performed along the same direction (nb0 strategy). erefore, the transmission of the ultrasonic signal during the VABB process seems to result in a higher penetration of the e ects of the process. However, the direct consequence of this result should be addressed in future research lines, as is highlighted in the next subsection. e presented evidence, found a er the di erent experimental outcomes, lead to the conclusion that the industrial application of the process can only successfully be performed if the processing parameters are linked to the outcomes of the previous machining procedure. A previous assessment to characterise the original surface integrity shall always be necessary, including two main variables: the target material and initial surface (Figure 6.1). As a result of that combination, the 𝐹 𝑝 -𝑛 𝑝 pair should be xed to achieve the best topological and RS results. e strategy must be then selected according to the preferential direction that is expected to be subjected to higher load and stress during its functioning in service.

Future works

e experimental database and the holistic approach taken in this dissertation to the VABB process must be used in future works to succeed in developing new insights into the process. Many questions remain open about the phenomenology of associated to the process, and the direct consequences of the vibration assistance on the material.

e ultimate result of that assessment should be its industrial implementation. Under this perspective, the following activities are proposed as next steps:

PUBLICATIONS DERIVED FROM THIS DISSERTATION

• Performing similar analysis on a greater variety of topologies, particularly those being originally neutral in terms of residual stress. Furthermore, to study in detail the described cyclic e ect of VABB on the surface texture, higher preloads could be applied on the already assessed surfaces, to establish that threshold value in more abrupt topologies.

• Development of a new version of the prototype, to overcome the mechanical drawbacks provided by the one presented in this dissertation. For instance, to reduce the relative movement between its components.

• An improved FEM that allows to understand in depth the interaction of the burnishing ball with the surface features. is study must derive in a phenomenological explanation of the e ects of NVABB based on the way that the ball performs the pressure to cause the residual plastic strain.

• An optimisation procedure should be performed, to nd real optimal values for the operation. e results presented in this thesis are based on di erent optimisation methods. But the term "optimal" refers to the best parameters inside the explored boundaries included in the design of experiments.

  Inkscape. Dissertation presented by Ramón Jerez Mesa in partial ful llment of the requirements for the degrees of Doctor per la Universitat Politècnica de Catalunya and Doctorat de l'Université de Toulouse Für Harald

2. 1 23 3. 1 80 xiii 4 . 3 A. 1 L27(3 13 )

 12318043113 Ball burnishing references on steel, aluminium and cuprous alloys. Light grey: milling-machine tools. White: lathe tools. . . . . . . . . . . . 21 2.2 Ball burnishing references on stainless steel, titanium and nickel alloys. Light grey: milling-machine tools. White: lathe tools. . . . . . . . . Spring calibration parameters calculated at di erent compression velocities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2 Dynamic speci cations imposed for the VABB prototype. . . . . . . . . 48 3.3 Properties of hard PZT8 material used for the piezoelectric actuators in the VABB tool. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.4 Measuring conditions tested during the acoustic emission acquisitions. 55 3.5 Fundamental frequency found for each measured signal and its amplitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.6 Conditions measured during the dynamometric tests. . . . . . . . . . . . 59 3.7 Average goodness of t of 𝐹 𝑣 sine ts through the Pearson 𝑅 2 parameter. 63 3.8 Average descriptors of sine ts of 𝐹 𝑣 and maximum and minimum values registered. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.9 Average frequency of all sine ts that model the 𝐹 𝑣 , and standard deviation (𝑆𝐷). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.10 Mesh size for the image processing of the tool. . . . . . . . . . . . . . . . 68 3.11 Absolute and relative pivoting angles of each part of the prototype for both preload levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.1 NC codes for every absolute strategy pa ern resulting from the combination of the 𝑛 𝑝 and St. factors. In brackets the Taguchi run in which they are to be executed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2 Experimental design derived from a 𝐿27(3 13 ) Taguchi orthogonal array.Factors and levels at the Taguchi array for AISI 1038 and Ti-6Al-4V specimens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Descriptors and factors kept constant in the tests. . . . . . . . . . . . . . 4.5 Calculation of the signal-to-noise ratio in function of the goal of the experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 12 S parameter set for surface topography assessment, as de ned in the ISO 25178. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Central moments of a surface height distribution. A er King & Davis (1982) [69] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 e 13 V parameter set, as de ned in the ISO 25178. . . . . . . . . . . . . 4.9 Errors calculated from the repeatability of S parameters on the machined surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10 Retained topological parameters from the S set. . . . . . . . . . . . . . . 4.11 Experimental characteristics of X-ray di raction measurements. . . . . 4.12 AISI 1038 weight composition. . . . . . . . . . . . . . . . . . . . . . . . . . 4.13 AISI 1038 properties, as characterised by Travieso-Rodríguez (2010) [148]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.14 Hardness measurements performed on the AISI 1038 specimens. . . . . 4.15 Ti-6Al-4V weight composition according to AFNOR L14-601. . . . . . . 4.16 Grade 23 Ti-6Al-4V properties. . . . . . . . . . . . . . . . . . . . . . . . . . 4.17 Hardness measurements performed on the Ti-6Al-4V specimens. . . . . 4.18 Machining parameters applied to obtain the three original surface topologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Summary of retained two-and three-dimensional topological parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Parameters to apply VABB on AISI 1038 end-milled surfaces, based on ANOVA mean results. Optimisation target: minimum texture amplitude. 5.3 Recommended parameters to ball-burnish AISI 1038 end-milled surfaces. Optimisation target: Gaussian surface with minimum texture amplitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Parameters to apply VABB on Ti-6Al-4V end-milled surfaces, based on ANOVA mean results. Optimisation target: minimum texture amplitude. 5.5 Recommended parameters to ball-burnish Ti-6Al-4V ball-end milled surfaces. Optimisation target: Gaussian surfaces with minimum texture amplitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv LIST OF TABLES 5.6 Main topology descriptors of machined surfaces, including 𝑆 0 0 (AISI 1038). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.7 60Cr3 chromium steel mechanical properties. . . . . . . . . . . . . . . . . 163 5.8 Optimal parameters to apply VABB on AISI 1038 surfaces according to di erent RS targets, based on ANOVA mean e ects. . . . . . . . . . . 176 5.9 Optimal parameters to ball burnish AISI 1038 surfaces based on real experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 5.10 Optimal parameters to ball burnish Ti-6Al-4V surfaces according to di erent RS targets, based on ANOVA mean e ects. . . . . . . . . . . . . 185 5.11 Optimal parameters to ball burnish Ti-6Al-4V surfaces based on real experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 5.12 Summary of optimal parameters to ball burnish AISI 1038 surfaces based on texture and RS criteria. . . . . . . . . . . . . . . . . . . . . . . . . 188 5.13 Summary of optimal parameters to ball burnish Ti-6Al-4V surfaces based on texture and RS criteria. . . . . . . . . . . . . . . . . . . . . . . . . 189 5.14 Tested conditions for hardness tests on AISI 1038 𝑆 0 1 . . . . . . . . . . . . 191 5.15 Tested conditions for hardness tests on Ti-6Al-4V 𝑆 0 1 . . . . . . . . . . . . 195 Taguchi orthogonal array. A er Taguchi et al., 2005 [142] . . 206 A.2 Taguchi array followed for the experimental testing of AISI 1038. . . . 207 A.3 Taguchi array followed for the experimental testing of Ti-6Al-4V. . . . 208 A.4 Actions included in the model and their degrees of freedom. . . . . . . 209 A.5 Sisson-Vigier incidence matrix of orthogonality of the experimental design. ∪: coupled actions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 xv LIST OF TABLES xvi List of Symbols

Figure 1 . 1 .

 11 Figure 1.1. Hemispherical milling of engineering surfaces. A er Fontaine et al., 2006 [38]. a. Overview of a ball-end milled surface. b. Ball-end milling kinematic parameters and scheme of the process.

Figure 2 . 1 .

 21 Figure 2.1. Schematic representation of the ball burnishing process.

CHAPTER 2 .Figure 2 . 2 .

 222 Figure 2.2. Items and descriptors comprising the burnishing manufacturing system.

Figure 2 . 3 .

 23 Figure 2.3. Classical burnishing tool con gurations on lathe and milling machines. A er Murthy, 1981 [103]

Figure 2 . 4 .

 24 Figure 2.4. Special burnishing tool con gurations. a. Milling & burnishing tool [127] b.Center rest multi-ball tool[28] c. Multi-roller tool[START_REF]Using specially designed high-sti ness burnishing tool to achieve high-quality surface nish[END_REF] d. Multi-ball tool[START_REF]Adjustable roller tool[END_REF] e. Adjustable roller tool [107] f. Multi-ball tool[START_REF]Using a high-sti ness burnishing tool for increased dimensional and geometrical accuracies of openings[END_REF]

Figure 2 . 5 .

 25 Figure 2.5. Force regulation systems in classical burnishing tools. a. Depth-of-penetration tool [80]. b. Hydrostatic tool [119]. c. Spring-regulated tool [52]

2. 1 .

 1 GENERAL ASPECTS OF THE BURNISHING OPERATION which traverses the tool (Figure 2.5.b).

Figure 2 . 6 .

 26 Figure 2.6. Experimental measure of force unevenness during a burnishing process. A er Lye & Leong, 1990 [91].

22

 22

2. 2 .

 2 EXPERIMENTAL RESULTS ON SURFACE INTEGRITY AFTER BALL BURNISHING

  (2009) [70] studied the dependence of 𝑅 𝑎 as a function of the preload and the ball diameter, on Inconel 718 specimens (Figures 2.7

  .a and 2.7.b). In that case, increasing the burnishing pressure from 150 bar to 250 bar2.2. EXPERIMENTAL RESULTS ON SURFACE INTEGRITY AFTER BALL BURNISHING

Figure 2 .

 2 Figure 2.7. 𝑅 𝑎 results of burnished INCONEL 718 surfaces. a. In uence of burnishing pressure [70]. b. In uence of ball diameter [70]. c. In uence of burnishing pressure [128]. d.In uence of ball diameter[START_REF]Surface integrity of Inconel 718 by ball burnishing[END_REF]

Figure 2 . 8 .

 28 Figure 2.8. SEM images of the surface microstructure of burnished specimens at di erent pressure levels, and surface Vickers hardness. A er López de la Calle et al., 2007 [87]. a. Inconel 718. b. AISI P20 pre-heated steel

Figure 2 .

 2 Figure 2.9. SEM images of 20Cr4 steel specimens. a. 200-N normal force. b. 400-N normal force. c. Subsurface shear instability caused by excessive plastic deformation. A er Kuznetsov et al., 2015 [75]

Figure 2 .

 2 Figure 2.10. Microstructure and hardness of turned (𝑣 𝑐 = 150 m/min, 𝑓 = 0.18 mm/rev, 𝑎 𝑝 = 0.6 mm) and turned+burnished (250 N, 𝑛 𝑏 = 1 pass, 6-mm diameter ball) 15-5PH specimens. A er Chomienne et al., 2016 [18].

2. 2 .

 2 EXPERIMENTAL RESULTS ON SURFACE INTEGRITY AFTER BALL BURNISHING (a) (b)

Figure 2 .

 2 Figure 2.11. a. Di erent residual stress scales 𝑙 0,𝐼 , 𝑙 0,𝐼𝐼 and 𝑙 0,𝐼𝐼𝐼 . b. Examples of sources of macro and micro residual stress states. A er Withers & Bhadeshia, 2001 [157]

Figure 2 .

 2 Figure 2.12. Mechanical surface integrity results of ball burnished AISI 1045 specimens. A er Avilés et al., 2015 [4]. a. Depth dependence of residual stress. b. S-N fatigue diagram of burnished specimens.

Figure 2 . 13 .

 213 Figure 2.13. Deep residual stress measured on Inconel 718. a. In uence of pressure. b. In uence of ball diameter. A er Klocke et al., 2009 [70]

Figure 2 .

 2 Figure 2.14. Comparison of residual stress measurement of ball burnished surfaces through X-ray di raction and incremental hole drilling. a. Results by Klocke et al. (2009) on Inconel 718 [70]. b. Results by García-Granada et al. (2017) [40].

Figure 2 .

 2 Figure 2.15. E ect of superimposed 800 kHz ultrasound on zinc crystal specimens deformation. without, and ----with vibrations. A er Blaha & Langenecker, 1955, [7]

Figure 2 .

 2 Figure 2.16. Stress reduction during compressive tests due to acoustoplasticity with di erent amplitudes. a. Mild steel. b. Copper. c. Al-Al 2 O 3 alloy. A er Izumi et al., 1966 [62]

Figure 2 .

 2 Figure 2.17. Linear correlation between the vibration sensitivity, 𝑘, and work-hardening coe cient, acoustic impedance and Young's module. A er Izumi et al. 1966[START_REF]E ects of superimposed ultrasonic vibration on compressive deformation of metals[END_REF]

Figure 2 .

 2 Figure 2.18. Interaction of the burnishing force and the vibrations amplitude in a. ultrasonic burnishing (a er Marakov, 1973 [94]) and b. vibratory burnishing (a er Pande & Patel, 1984 [109]) on mild steel specimens.

Figure 2 .

 2 Figure 2.19. In uence of burnishing force and frequency on a. surface roughness and b. surface hardness, a er Pande & Patel, 1984 [109]).

Figure 2 .

 2 Figure 2.20. Deep residual stress pro le comparison a er conventional (CDCR) and ultrasonic burnishing (UDCR). A er Bozdana, 2008 [12].

CHAPTER 3 . 3 . 1

 331 DESIGN AND CHARACTERISATION OF THE VABB TOOL excited. Mechanical construction e tool presented herea er is based on a design patented in Spain, and published on 2017 June 2 in the Spanish O cial Bulletin of the Industrial Property with number 2615002 [66]. Obtaining the PCT extension is a work-in-progress due to be se led by mid 2018.

Figure 3 . 1 .

 31 Figure 3.1. Structure of the ultrasonic vibration-assisted ball burnishing tool.

Figure 3 . 2 .

 32 Figure 3.2. Diagram of the FTU. a. Exploded view. b. Assembled parts and spring compression.

3. 1 .

 1 MECHANICAL CONSTRUCTION length of the spring.

  .3.a).

Figure 3 . 3 .

 33 Figure 3.3. Calibration of the VABB prototype. a. Overview of experimental setup. b. Curve obtained by compression at 100-mm/min velocity.

  tool) 10 µm e principle on which the generation of 𝐹 𝑣 is based, is the change of the thickness of a polarized piezoelectric material when it is subjected to a di erence of potential.

Figure 3 . 4 .

 34 Figure 3.4. Stacked piezoelectric plates inside the VTU of the VABB prototype.

Figure 3 . 5 .

 35 Figure 3.5. Frequency sweep and register of electrical impedance of the circuit which excites the tool.

Figure 3 . 6 .

 36 Figure 3.6. Schematic representation of the force transmission unit. a. Detail of bearing balls on hemispherical track machined on the sonotrode tip. b. Assembled section of FTU components.

Figure 3 . 7 .

 37 Figure 3.7. Experimental setup for the measurements through acoustic emission.

Figure 3 . 8 .

 38 Figure 3.8. Time history and frequency spectrum of signals registered the burnishing line tests 270 N, 𝐴 = 50%

Figure 3 .

 3 Figure 3.9 shows the whole experimental setup next to the milling machine where it was conducted.e press force sensor was mounted on the vise on the milling machine, with the help of a copper shell to protect it. e tool would be directly compressed on the sensor surface to a ain the di erent preload levels. With that aim, the following equipment was implemented:

Figure 3 . 9 .

 39 Figure 3.9. Experimental setup for the dynamometric measurements.

Figure 3 .

 3 Figure 3.10. Comparison of calibration lines measured through continuous force acquisition and Kitsler dynamometric measurements.

Figure 3 . 11 .

 311 Figure 3.11. Sinus t calculated for the recorded signal at 𝐹 𝑝 = 600 N and 𝐴 = 100%.

Figure 3 .

 3 Figure 3.12. Half-cycle vibratory force variation, and extreme values, for di erent preload levels. a. 𝐴 = 50%. b. 𝐴 = 100%.

Figure 3 . 13 .

 313 Figure 3.13. Half-cycle vibratory force variation, and extreme values, for di erent preload levels. a. 𝐹 𝑝 = 300 N. b. 𝐹 𝑝 = 600 N.

3. 4 .

 4 Figure 3.14. Preliminary burnishing imprints performed on a milled AISI 1038 surface.

Figure 3 .

 3 Figure 3.15. Meshes I-IV de ned on the tool for the image treatment routine.

Figure 3 .

 3 Figure 3.16. Points composing the mesh of part I.

Figure 3 .

 3 Figure 3.17. Raw and smoothed curves representing the slope presented by the mesh of part I with a 90-N preload.

Figure 3 .

 3 Figure 3.18. Angle and slope nomenclature related to the calculation of the relative angle between tool sections.

Figure 4 . 1 .

 41 Figure 4.1. Burnishing strategies included in the DOE and nomenclature of the directions referenced in the text.

  1,#12,#20) B (#5,#13,#24) C (#9,#17,#25) bn90/0 A (#2,#10,#21) D (#6,#14,#22) E (#7,#18,#26) bn0 A (#3,#11,#19) F (#4,#15,#23) G (#8,#16,#27)

Figure 4 . 2 .

 42 Figure 4.2. Linear graph associated to the L27 Taguchi array. Balls: factors. Lines: interactions.

  .

  2.

Figure 4 . 3 .

 43 Figure 4.3. Schematic representation of the VABB (non-contoured yellow patches) and NVABB (contoured blue patches) tests performed on a general workpiece and reference directions considered in this work.

Figure 4 . 4 .

 44 Figure 4.4. Planned experimental tests represented on the three di erent machined 𝑆 0 . Striped patches: VABB tests. a. AISI 1038. b. Ti-6Al-4V.

Figure 4 . 5 .

 45 Figure 4.5. Measurement of burnished track width on Ti-6Al-4V applying 150 N.

Table 4 . 5 .

 45 Calculation of the signal-to-noise ratio in function of the goal of the experiment.

Figure 4 .

 4 Figure 4.6. Sampled 3D surface transformed into a height function. A er Dong et al., 1992 [23]

Figure 4 . 7 .

 47 Figure 4.7. Surface pro les and height distributions showing the e ects of skewness and kurtosis. Top to bo om: positively skewed, negatively skewed, leptokurtic and platykurtic distributions. A er omas, 1981[START_REF]Characterization of surface roughness[END_REF]

4. 2 .

 2 MEASUREMENT OF THE SURFACE INTEGRITY PARAMETERS by a certain sampling line. ey are calculated according to an areal autocorrelation function of the sampled surface, AACF , which describes the dependence of the height data at one position on the values at another position of the same dataset [26]. ) ⌉ ⌉ ⌉ ⌉ ⌉ ⌉ ⌉ ⌋ ⌉ ⌉ ⌉ ⌉ ⌉ ⌉ ⌉ ] 𝐴𝐴𝐶𝐹 (𝑡 𝑖 , 𝑡 𝑗 ) = 1 (𝑀 -𝑖)(𝑁 -𝑗) ∑ 𝑁 -𝑗 𝑙=1 ∑ 𝑀 -𝑖 𝑘=1 𝜂(𝑥 𝑘 , 𝑦 𝑙 )𝜂(𝑥 𝑘+𝑖 , 𝑦 𝑙+𝑗 ) 𝑖 = 0, 1, ..., 𝑚 < 𝑀 ; 𝑗 = 0, 1, ..., 𝑛 < 𝑁 𝑡 𝑖 = 𝑖𝛥𝑥; 𝑡 𝑗 = 𝑗𝛥𝑦 (4.3)

  Figure 4.8 [68].

Figure 4 . 8 .

 48 Figure 4.8. Main V parameters related to the bearing area curve, represented in 2D. Extrapolation to 3D can be easily visualised.

Figure 4 . 9 .

 49 Figure 4.9. Evolution of some S parameters with respect to the sampling size. a. 𝑆 𝑠𝑘 and 𝑆 𝑘𝑢 . b. 𝑆 𝑞 and 𝑆 𝑧10 .

Figure 4 .

 4 Figure 4.10. Overview of specimen positioned on the encapsulating machine plate.

Figure 4 . 11 .

 411 Figure 4.11. Vickers microindentation hardness test scheme.

Figure 4 .

 4 Figure 4.12. X-ray di raction in a non-deformed crystal (le ) and a deformed crystal (right).

Figure 4 .

 4 Figure 4.13. X-ray di raction spectrum showing a di raction peak at 2𝜃 𝜓 position, with regards to the spectrum registered for the reference material, 2𝜃 0 .

Figure 4 .

 4 Figure 4.14. Linear representation of the sin 2 𝜓 method. A er Guillemot (2010) [49].

Figure 4 .

 4 15.a shows the core material along direction I, as a matrix of pearlite and ferrite, usual in this kind of carbon steels. On the other hand, Figure4.15.b shows that grains are aligned along direction II, as a clear e ect of the lamination operation through which the raw material was obtained.

Figure 4 .

 4 Figure 4.15. Metallographic observations of the AISI 1038 specimen at 50x. a. Direction I. b. Direction II (lamination).

Figure 4 .

 4 Figure 4.16. . a. SEM image of pearlite nucleation. b. Imprints a er Vickers indentation spanning ferrite and pearlite structures.

  104

4. 3 .

 3 MATERIAL CHARACTERISATION Table 4.15. Ti-6Al-4V weight composition according to AFNOR L14-601. 88.1-91 5.5-6.75 3.5-4.5 ≤0.25 ≤0.2 ≤0.08 ≤0.05 ≤0.01

Figure 4 .

 4 Figure 4.17. Metallographic observations of the Ti-6Al-4V specimen along direction I (a) and direction II (b).

Figure 4 .

 4 Figure 4.18. Detail of Vickers indentation performed on the Ti-6Al-4V.

Figure 4 .

 4 19.a). e data measured through the Kistler 5019A ampli er was registered through the DynoWare so ware. e experimental setup was completed by the external power circuit to which the VABB tool is connected and excited (Figure 4.19.b).

Figure 4 .

 4 Figure 4.19. Experimental setup. a. Detail of workpiece a ached to a Kistler dynamometer. b. HURON KX10 milling machine where experiments were developed.

Table 4 .

 4 18. Machining parameters applied to obtain the three original surface topologies.Machining parametersOriginal surface 𝑎 𝑒 (mm) 𝑎 𝑝 (mm) tool diameter (mm)

Figure 4 .

 4 Figure 4.20. Hemispherical front milling geometric system.

Figure 4 .

 4 21.a.

Figure 4 . 21 .

 421 Figure 4.21. 𝐹 𝑥 and 𝐹 𝑧 measurement during the VABB and NVABB tests #25 in Ti-6Al-4V workpiece. a. Identi cation of burnishing cycles through ed signal (red). b. Extracted forces at two burnishing cycles.

Figure 4 . 22 .

 422 Figure 4.22. Mean 𝐹 𝑧 registered for all burnishing cycles, and maximum and minimum forces registered. a. AISI 1038. b. Ti-6Al-4V.

Figure 5 . 1 .

 51 Figure 5.1. Summary of items included in the result analysis.

1

 1 Topologies of the original surfaces e rst approach to topology characterisation of all three original surface nishing textures is undertaken by considering a simple set of two-dimensional parameters, represented in Figure5.2.

Figure 5 . 2 .

 52 Figure 5.2. Two-dimensional descriptors of original surfaces (AISI 1038).

Figure 5 . 3 .

 53 Figure 5.3. 𝑆 parameters describing the initial surfaces of AISI 1038. a. Amplitude parameters. b. Spatial and hybrid parameters.

Figure 5 . 4 .

 54 Figure 5.4. 𝑉 parameters describing the initial surfaces of AISI 1038. a. Volumetric parameters. b. AF parameters.

Figure 5 . 5 .

 55 Figure 5.5. AF curves for the three original surfaces on AISI 1038.

Figure 5 . 6 .

 56 Figure 5.6. Topological images of VABB tests #25 and #18 performed on AISI 1038.

Figure 5 .

 5 Figure 5.7. VABB mean e ects, S/N ratios and interaction plots. ANOVA response variable: 𝑅 𝑞 of AISI 1038.

Figure 5 .

 5 Figure 5.8. VABB mean e ects, S/N ratios and interaction plots. ANOVA response variable: 𝑆 𝑞 of AISI 1038.

Figure 5 .

 5 Figure 5.9. 𝑆 𝑞 and 𝑆 10𝑧 amplitude parameters of AISI 1038 VABB patches.

Figure 5 .

 5 Figure 5.10. Procedure to nd the best VABB parameters based on 𝑆 𝑞 reduction.

5. 1 .

 1 Figure 5.11. 𝑆 𝑠𝑘 and 𝑆 𝑘𝑢 amplitude parameters of AISI 1038 VABB patches.

Figure 5 . 3 (

 53 Figure 5.12. AISI 1038 height histograms of VABB tests on 𝑆 0 1 (top), 𝑆 0 2 (middle), and 𝑆 0 3

5. 1 .

 1 GEOMETRICAL PARAMETER: SURFACE TEXTURE considered appropriate optimisation targets.

Figure 5 .

 5 Figure 5.13. 𝑆 𝑎𝑙 and 𝑆 𝑡𝑟 spatial parameters and 𝑆 𝑑𝑞 hybrid parameter of AISI 1038 VABB patches.

Figure 5 .

 5 Figure 5.14. Optical images of 𝑆 0 3 and #27VABB surfaces.

Figure 5 .

 5 Figure 5.15. Singular AF curves with convexity change linked to platykurtic surfaces, and detail showing 𝑆 𝑠𝑘 related to 𝑥 intersection point.

Figure 5 .

 5 Figure 5.16. AF curve slopes of all 𝑆 0 1 and 𝑆 0 3 tests.

Figure 5 .

 5 Figure 5.18. Volumetric parameters of AISI 1038 burnishing patches.

Figure 5 .

 5 Figure 5.19. AF amplitude parameters of AISI 1038 burnishing patches.

Figure 5 .

 5 Figure 5.20. AF bearing percentages parameters of AISI 1038 burnishing patches.

Figure 5 . 21 .

 521 Figure 5.21. Nomenclature of parameters describing the AF curve and the least slope method applied to obtain the core area.

Figure 5 . 22 .

 522 Figure 5.22. Correlation between AF parameters and the least slope curve traced to calculate them. Surfaces: 𝑆 0 1 : ○ 𝑆 0 2 : × 𝑆 0 3 : △. Descriptors: Blue: 𝑚 𝑚𝑖𝑛 . Green: 𝑀 𝑚𝑖𝑛 .

Figure 5 .

 5 [START_REF]Comprehensive study of parameters for characterizing three-dimensional surface topography I: Some inherent properties of parameter variation[END_REF] represents graphically the least slope secant method through the calculated lines on each of the aforementioned AF curves. Apparently, an abrupt change in convexity of the curves at low 𝑀 𝑟 values displaces the position of the least slope secant line to the other extreme of the curve. Inversely, the AF curve resulting from test #17, that presents that convexity change at its tail, has caused an inverse e ect. e AF curves for the optimal tests #13 and #27, essentially at, derive in secant lines positioned in intermediate sections of the AF curve.

Figure 5 . 23 .

 523 Figure 5.23. Secant according to ISO 10350 to calculate the AF descriptive parameters.

  24.b.

Figure 5 . 24 .

 524 Figure 5.24. Correlation between AF parameters with a. 𝑆 𝑘𝑢 , and b. 𝑆 𝑞 .

Figure 5 . 25 .

 525 Figure 5.25. Direct comparison of the 𝑆 𝑞 parameter of VABB and NVABB tests on AISI 1038.

Figure 5 . 26 .

 526 Figure 5.26. SEM images of the 𝑆 0 1 surface burnished by 5 passes and the nb strategy. NVABB surfaces show scratches along the feed direction.

Figure 5 . 27 .

 527 Figure 5.27. Skewness and kurtosis amplitude parameters represented for all VABB and NVABB tests.

Figure 5 . 28 .

 528 Figure 5.28. Bidimensional descriptors of original surfaces (Ti-6Al-4V).

Figure 5 .

 5 Figure 5.29. S parameters describing the initial surfaces of Ti-6Al-4V. a. Amplitude parameters. b. Spatial and hybrid parameters. c. AF parameters. d. Volumetric parameters.

Figure 5 . 30 .

 530 Figure 5.30. VABB mean e ects, S/N ratios and interaction plots. ANOVA response variable: 𝑆 𝑞 of Ti-6Al-4V.

Figure 5 .

 5 Figure 5.31. a. 𝑆 𝑞 and 𝑆 10𝑧 amplitude parameters of Ti-6Al-4V burnishing patches. b. Detail of 𝑆 0 1 results.

Figure 5 .

 5 Figure 5.32. 𝑆 𝑠𝑘 and 𝑆 𝑘𝑢 amplitude parameters of Ti-6Al-4V burnishing patches.

Figure 5 . 3 (

 53 Figure 5.33. Ti-6Al-4V height histograms of VABB tests on 𝑆 0 1 (top), 𝑆 0 2 (middle), and 𝑆 0 3

Figure 5 .

 5 Figure 5.34. 𝑆 𝑎𝑙 and 𝑆 𝑡𝑟 spatial parameters and 𝑆 𝑑𝑞 hybrid parameter of Ti-6Al-4V burnishing patches.

Figure 5 .

 5 Figure 5.35. Optical images of 𝑆 0 1 surface, and VABB tests #18 and #25.

  0 1 is hardly redistributed by e ect of VABB with 350N-5passes. For further reference, Figures C.1 to C.3 in the appendix show the complete whole colour map collection.

Figure 5 .

 5 Figure 5.36. Colour map of heights composing the VABB surfaces of singular tests.

Figure 5 .

 5 Figure 5.37. Correlation between Σ 𝑠 and 𝑆 𝑘 , 𝑉 𝑚𝑐 and 𝑉 𝑣𝑐 of VABB tests on Ti-6Al-4V.

Figure 5 . 38 .

 538 Figure 5.38. Volumetric parameters of Ti-6Al-4V burnishing patches.

Figure 5 .

 5 Figure 5.39. Abbot-Firestone amplitude parameters of Ti-6Al-4V burnishing patches.

5. 1 .

 1 Figure 5.40. AF bearing percentages parameters of Ti-6Al-4V burnishing patches.

Figure 5 . 41 .

 541 Figure 5.41. Slopes of AF curves resulting from VABB on the Ti-6Al-4V material, on 𝑆 0 1 (le ) and 𝑆 0 3 (right).

Figure 5 .

 5 Figure 5.42. a. Direct comparison of the 𝑆 𝑞 parameter of VABB and NVABB tests on Ti-6Al-4V. b. Detail of 𝑆 0 1 results.

Figure 5 .

 5 Figure 5.43. Amplitude parameters de ning the surfaces.

Figure 5 .

 5 Figure 5.44. Colour maps of NVABB and VABB tests performed on 𝑆 0 0 , applying 270N-5passes

Figure 5 .

 5 Figure 5.45. AF curves of 𝑆 0 0 tests on the AISI 1038 material. Discontinuous lines: VABB process.

Figure 5 .

 5 Figure 5.46. 𝑆 𝑠𝑘 -𝑆 𝑘𝑢 plot of VABB and NVABB results obtained on AISI 1038 and Ti-6Al-4V tests.

Figure 5 .

 5 Figure 5.47. Position of the VABB and NVABB process with respect to other nishing process. A er data found at Gri ths (1986) [47].

5. 1 .

 1 GEOMETRICAL PARAMETER: SURFACE TEXTURE this e ect, kurtosis and skewness values are always kept inside a speci c enclosed area of the Cartesian plane, whereas the scale may vary from test to test.

5. 1 . 4

 14 Approach to the surface-ball interface through a finite element model

  Rodríguez et al. (2012) found a model that could predict deep residual stress of ball burnished AISI 1042 cylinders, but no initial surface texture was considered. Yen et al.(2004) [160] developed two 2D and 3D FE model to predict the nal roughness a er ball burnishing. Other authors, such as Balland et al. (2013)[5], considered saw-shaped periodic roughness, but the unrealistic condition of the surface makes results non-comparable with real results. As an alternative, the model developed for this dissertation, and presented below, implements the real surface texture obtained a er machining in 3D, based on a similar 2D approach developed by Sartkulvanich et al. (2007)[START_REF]Finite element modeling of hard roller burnishing: an analysis on the e ects of process parameters upon surface nish and residual stresses[END_REF], repre-sented in Figure5.48.

Figure 5 .

 5 Figure 5.48. 2D periodical texture pro le used by Sartkulvanich et al. (2007) [124].

Figure 5 .

 5 Figure 5.49. 3D periodical textures modelling 𝑆 0 1 and 𝑆 0 3 . Red line: spline curves modelling the initial texture peaks.

5. 1 . 4 . 2

 142 Boundary conditions and model development e boundary conditions of the model comprise no displacement at the bo om and the three sides of the block, as shows Figure 5.50.

5. 1 .

 1 GEOMETRICAL PARAMETER: SURFACE TEXTURE 3. Unloading phase: the ball is raised, ending its contact with the surface.

Figure 5 .Figure 5 .

 55 Figure 5.50. Steps comprising the FEM and boundary conditions imposed on the material.

Figure 5 .

 5 Figure 5.51. Texture a er burnishing modelled by vertical displacement of the FEM nodes due to plastic deformation on 𝑆 0 1 (top) and 𝑆 0 3 (bo om). Scale in m.

Figure 5 .

 5 Figure 5.52. Contact areas between ball and 𝑆 0 1 and 𝑆 0 3 surfaces in di erent stages during lateral displacements.

Figure 5 . 53 .

 553 Figure 5.53. Residual stress descriptors at 𝑆 0 1 , 𝑆 0 2 and 𝑆 0 3 AISI 1038 surfaces.

Figure 5 . 55 .

 555 Figure 5.55. Correlation between 𝜎 𝐼𝐼 and 𝜎 𝑣𝑚 .

Figure 5 . 56 .

 556 Figure 5.56. Procedure to nd the best ball burnishing parameters to maximise residual stress.

Figure 5 . 57 .

 557 Figure 5.57. VABB and NVABB mean e ects. ANOVA response variable: RS stress components of AISI 1038.

Figure 5 . 58 .

 558 Figure 5.58. VABB and NVABB mean e ects, S/N ratios and interaction plots. ANOVA response variable: nal-to-initial stress components ratio of AISI 1038.

Figure 5 . 59 .

 559 Figure 5.59. VABB interaction charts. ANOVA response variables: RS components of AISI 1038.

5. 2 .

 2 Figure 5.60. AISI 1038 experimental tests with highest compressive residual stress.

Figure 5 . 61 .

 561 Figure 5.61. Residual stress descriptors at 𝑆 0 1 , 𝑆 0 2 and 𝑆 0 3 Ti-6Al-4V surfaces.

Figure 5 . 62 .

 562 Figure 5.62. Normal components of the residual stress tensor measured for all VABB and NVABB patches of the Ti-6Al-4V workpiece.

Figure 5 .

 5 Figure 5.63. VABB and NVABB mean e ects. ANOVA response variable: RS stress components of Ti-6Al-4V.

Figure 5 .

 5 Figure 5.64. VABB and NVABB mean e ects, S/N ratios and interaction plots. ANOVA response variable: nal-to-initial stress components ratio of Ti-6Al-4V.

Figure 5 .

 5 Figure 5.65. VABB and NVABB interaction charts. ANOVA response variables: RS components of Ti-6Al-4V.

Figure 5 .

 5 Figure 5.66. Ti-6Al-4V experimental tests with highest compressive residual stress.

= 5 ;

 5 𝑣 𝑓 = 600 mm/min NVABB bn90/0 ishing, a Vickers imprint indentation matrix was performed, at di erent deep layers every 50 µm, until 300 µm, from where three more 100 µm steps were measured (Figure 5.67.b). At every depth level, a minimum of 10 indentations were performed. Outliers were discarded through the Chauvenet's criterion, and the resulting samples were averaged to obtain the representative value. e error was calculated as explained in subsection 4.2.2.1.

Figure 5 .

 5 Figure 5.67. Hardness pro les of VABB and NVABB 𝑆 0 1 AISI 1038 surfaces. a. Along direction I. b. SEM view of the Vickers microindentation matrix performed on the subsurface layers of the non-burnished AISI 1038 specimen.

Figure 5

 5 Figure 5.68 shows the resulting hardness pro les along with their respective error bars. e comparison of the as-machined subsurface hardness measurements con rm the original anisotropy: along direction II, the core hardness is achieved at around 250 µm, whereas this value is reached at 500 µm along direction I. e lack of further data does not allow us to state a de nitive explanation to this fact. However, a certain link

Figure 5 .

 5 Figure 5.68. Hardness pro les of VABB and NVABB 𝑆 0 1 AISI 1038 surfaces. a. Along direction I. b. Along direction II.

5. 4 .

 4 METALLURGICAL PARAMETER: HARDNESS AND METALLOGRAPHY art chapter.

  Figure5.69 represents the values of the 𝛥𝐻𝑉 ratio for all the explored depths. It is the bn0 strategy the one that delivers be er results through VABB, from 250 µm depth, whereas bn90/0 hardly takes advantage of vibration-assistance. erefore, it can be stated that, in terms of deep a ectation, it is the nb0 strategy the one that registers more advantage from vibration-assistance. As repeated passes along the same path, clearly help take pro t of the vibrations incorporated to the process, whereas this e ect is dissolved for the bn90/0 by the change of direction of the passes. e described higher residual hardening a er VABB can be associated to the transmission

Figure 5 .

 5 Figure 5.69. HV ratio between VABB and NVABB tests of 𝑆 0 1 AISI 1038 surfaces. a. Along direction I. b. Along direction II.

5. 4 .Figure 5 .

 45 Figure 5.70. x2000 SEM observations of ball-burnished AISI 1038.

Figure 5

 5 Figure 5.71 shows the resulting deep hardness pro les of the explored surfaces. In this case, the machining process has a hardening e ect on the workpiece that spans to a 100-µm depth. However, the hardness pro les are substantially more similar among them than in the case of the AISI alloy.Both the NVABB and VABB processes

Figure 5 .

 5 Figure 5.71. Hardness pro les of VABB and NVABB 𝑆 0 1 Ti-6Al-4V surfaces. a. Along direction I. b. Along direction II.

Figure 5 .

 5 Figure 5.72. x2000 SEM observations of ball-burnished Ti-6Al-4V.

Figure 6 . 1 .

 61 Figure 6.1. Summary of the conclusions regarding VABB.

  Electric displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 𝑑 𝑖𝑗 Piezoelectric strain constant along 𝑗 due to electric eld along 𝑖 . . . . . . 50 𝐼 Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 𝑞 Number of piezoelectric disks in a stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 S E Piezoelectric compliance coe cient matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 50 𝜎 Piezoelectric stress vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 𝑡 Piezoelectric thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

	General parameters
	𝐴	Piezoelectric amplitude
	𝐴

0 Fundamental frequency amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 𝛥𝐹 𝑣 Half-cycle amplitude of the vibratory component . . . . . . . . . . . . . . . . . . . . 61 𝛥𝑧 Spring compression length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 𝐸 Young's module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 𝑓 0 Fundamental frequency transmi ed by VABB prototype . . . . . . . . . . . . . 58 𝐹 0 Spring precompression force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 𝐹 𝑏 Burnishing force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 𝐹 𝑝 Burnishing preload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 𝐹 𝑣 Vibratory component of burnishing force . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 𝜑 0 Sine phase of ed ultrasonic signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 ℎ 𝑝 Depth of penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 𝜂 Low-frequency burnishing force variation . . . . . . . . . . . . . . . . . . . . . . . . . . 45 𝑘 Spring elastic constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 𝜔 Sine angular frequency of ed ultrasonic signal . . . . . . . . . . . . . . . . . . . . 61 𝜌 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Piezoelectricity D 𝑉 Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 xvii 1 Introduction 1.1 Motivations and antecedents

Table 2

 2

	.1 summarises the most relevant

Table 2 . 1 .

 21 Ball burnishing references on steel, aluminium and cuprous alloys. Light grey: milling-machine tools. White: lathe tools.

	Reference	Material	Force
	Loh et al., 1989,1990 [80, 82]	AISI 1045	d.o.p.
	Loh et al., 1989,1990,1991 [81, 83, 84] AISI 1045	d.o.p.
	Morimoto et al., 1991 [102]	JIS-S38C	d.o.p.
	Loh et al., 1993 [85, 86]	ASSAB XW-5	d.o.p.
	Hassan et al., 1996 [54, 55]	pure Al & brass	spring
	Lee & Loh, 1996 [77]	AISI P20	d.o.p.
	Hassan, 1997 [53]	pure Al & AS 1573 brass spring
	Hassan, 1998 [52]	unde ned brass	spring
	Hassan, 1999 [56]	unde ned brass	spring
	Hassan et al., 2000 [57]	brass & Al-Cu alloy	spring
	Hassan et al., 2000 [58]	pure Al & AS 1573 brass spring
	Némat & Lyons, 2000 [104]	ASTM A113 & AA6463-E spring
	Shiou & Chen, 2003 [132]	PDS5 mould steel	spring
	Prevéy et al., 2001 [112]	AA7075-T6	H
	Bouzid et al., 2004 [11]	AISI 1042	spring
	El-Axir et al., 2005 [28]	unde ned steel	d.o.p.
	Luca et al., 2005 [89]	unde ned steel	H
	Basak et al., 2007 [6]	AA7075-T6 & H62 brass	H
	Hamadache et al., 2006 [50]	Rb40 steel	spring
	Rao et al., 2008 [115]	unde ned steel	d.o.p.
	Seemikieri et al., 2008 [126]	AISI 1045	H
	Shiou & Cheng, 2008 [131]	NAK80 mould steel	d.o.p.
	Gharbi et al., 2008 [41]	AISI 1010	spring
	El-Axir et al., 2008 [29]	AW 2014	d.o.p.
	El-Axir et al., 2008 [30]	AW 2014	d.o.p.
	Sagbas, 2008 [121]	AA 7178	spring
	Majzoobi et al., 2009 [92]	AA 7075-T6	spring
	El-Taweel et al., 2009	brass	spring
	Shiou & Chuang, 2010 [133]	PDS5 mould steel	spring
	Ugur, 2010 [154]	AA 7075	mill
	L. de la Calle et al., 2011 [88]	AISI 1045 & DIN 1.2379	H
	Travieso-Rodriguez et al., 2011 [149] A92017 & G10380	H
	Grzesik & Zak, 2012 [48]	EN 41Cr4	spring
	Rodriguez et al., 2012 [48]	41Cr4 steel	spring
	Aviles et al., 2015 [4]	AISI 1045	H
	Kuznetsov et al., 2015 [75]	EN 20Cr4 & EN X20Cr13 H
	Tadic et al., 2016 [140]	AW6082	d.o.p.
	Amdouni et al., 2017 [3]	AW2017-T4	d.o.p.

d.o.p.: depth of penetration; H: hydrostatic tool

Table 2 . 2 .

 22 Ball burnishing references on stainless steel, titanium and nickel alloys. Light grey: milling-machine tools. White: lathe tools.

	Reference	Material	Force
	Stainless steel
	Lee et al., 1993 [78]	316L	d.o.p.
	Prevéy et al., 2003 [114]	17-4PH	H
	Jayaraman et al., 2003 [65]	17-4PH	H
	Zhang et al., 2014 [161]	17-4PH	H
	Chomienne et al., 2016 [18]	15-5PH	H
	Titanium alloys
	Schuh et al., 2007 [125]	Ti-6Al-7Nb H
	Tsuji et al., 2008 [152]	Ti-6Al-4V	H
	Revankar et al., 2014 [117, 118]	Ti-6Al-4V	H
	Nickel-based alloys
	López de la Calle et al., 2007 [87] Inconel 718 H
	Klocke et al., 2009 [70]	Inconel 718 H
	Sequera et al., 2014 [128]	Inconel 718 H
	Fu et al., 2014 [39]	Nitinol	H

d.o.p.: depth of penetration; H: hydrostatic tool have proved the impact of microgeometric deviations on the mechanical behaviour of parts [69]. is includes fatigue life [106] or tribological mechanisms

Table 3 . 1 .

 31 Spring calibration parameters calculated at di erent compression velocities.

	𝑣 𝑐𝑜𝑚𝑝 (mm/min)	Calibration parameters Pearson's 𝑅 2 𝐹 0 (N) 𝑘 (N/mm)
	1	30.33	83.12	0.9991
	10	29.26	83.65	0.9999
	100	28.31	84.34	0.9992

Table 3 . 2 .

 32 Dynamic speci cations imposed for the VABB prototype.

Table 3 .

 3 3. Properties of hard PZT8 material used for the piezoelectric actuators in the VABB tool.

	Property	value	units
	𝜌	7700	kg/m 3
	𝐸	63	MPa
	𝑑 13 𝑑 33	120 ⋅ 10 -12 m/V 275 ⋅ 10 -12 m/V
	𝑑 15

Table 3 . 4 .

 34 Measuring conditions tested during the acoustic emission acquisitions.

	Test	𝐹 𝑝 (N) 𝐴 (%)
		90	0
		90	25
	burnishing point	90 270	50 0
		270	25
		270	50
		90	0
		90	25
	burnishing line	90 270	50 0
		270	25
		270	50

Table 3 . 5 .

 35 Fundamental frequency found for each measured signal and its amplitude.

		90	25	39.1	70.1
	burnishing point	90 270	50 25	39.1 39.1	63.5 55.9
		270	50	39.1	54.6
		90	25	39.1	69.0
	burnishing line	90 270	50 25	39.1 39.1	61.4 52.1
		270	50	39.1	69.1

Test

𝐹 𝑝 (N) 𝐴 (%) 𝑓 0 (kHz) 𝐴 0 (mV)

Table 3 .

 3 6. Conditions measured during the dynamometric tests.

Table 3 .

 3 7. Average goodness of t of 𝐹 𝑣 sine ts through the Pearson 𝑅 2 parameter.

				𝐹 𝑝 (𝑁 )
	𝐴	100	200	300	400	500	600
	10% 85.3% 97.3% 95.5% 95.5% 94.8% 94.0%
	20%	-	-	-	-	-	94.4%
	30%	-	-	-	-	-	94.0%
	40%	-	-	-	-	-	93.4%
	50% 85.5% 97.4% 95.1% 95.4% 94.1% 94.0%
	60%	-	-	-	-	-	94.3%
	70%	-	-	-	-	-	94.3%
	80%	-	-	-	-	-	94.3%
	90%	-	-	-	-	-	94.3%
	100% 85.1% 97.4% 95.8% 95.5% 94.6% 94.0%

Table 3 .

 3 8. Average descriptors of sine ts of 𝐹 𝑣 and maximum and minimum values registered.

	100	50% 100%	1.70 1.67	0.079 0.033	-3.38 -3.06	0.285 0.388	3.11 3.03	0.202 0.247
	200	50% 100%	4.53 4.80	0.055 0.040	-5.77 -5.89	0.298 0.196	5.47 5.99	0.248 0.268
	300	50% 100%	3.23 3.23	0.051 0.030	-4.53 -4.41	0.347 0.250	4.30 4.39	0.297 0.279
	400	50% 100%	3.13 3.17	0.049 0.042	-4.41 -4.22	0.250 0.261	4.33 4.39	0.279 0.243
	500	50% 100%	2.87 2.89	0.040 0.018	-4.16 -4.07	0.320 0.324	4.03 4.12	0.247 0.244
		10%	2.77	0.025	-3.75	0.178	4.11	0.203
		20%	2.78	0.031	-3.85	0.236	4.03	0.217
		30%	2.78	0.039	-3.64	0.331	4.39	0.264
		40%	2.76	0.028	-3.78	0.162	3.97	0.304
	600	50% 60%	2.75 2.76	0.030 0.026	-3.76 -3.64	0.178 0.343	4.11 4.02	0.329 0.221
		70%	2.77	0.043	-3.64	0.321	4.02	0.221
		80%	2.76	0.054	-3.64	0.351	3.93	0.234
		90%	2.76	0.045	-3.65	0.187	3.86	0.202
		100%	2.84	0.048	-3.86	0.285	3.95	0.

𝐹 𝑝 (𝑁 ) 𝐴 𝛥𝐹 𝑣 (N) SD (N) 𝐹 𝑣,𝑚𝑖𝑛 (N) SD (N) 𝐹 𝑣,𝑚𝑎𝑥 (N) SD (N)

Table 3 .

 3 9. Average frequency of all sine ts that model the 𝐹 𝑣 , and standard deviation (𝑆𝐷).

							𝐹 𝑝 (N)
		100		200		300		400		500		600
	𝐴	𝜈	SD 𝜈 (Hz) SD	𝜈	SD	𝜈	SD	𝜈	SD	𝜈	SD
	10%	39.2 25	39.2	12 39.2 8 39.2 12 39.2 11 39.2 11
	20%	-	-	-	-	-	-	-	-	-	-	39.2 25
	30%	-	-	-	-	-	-	-	-	-	-	39.2 24
	40%	-	-	-	-	-	-	-	-	-	-	39.2 26
	50%	39.2 17	39.2	13 39.2 13 39.2 11 39.2 11 39.2 15
	60%	-	-	-	-	-	-	-	-	-	-	39.2 16
	70%	-	-	-	-	-	-	-	-	-	-	39.2 15
	80%	-	-	-	-	-	-	-	-	-	-	39.2 13
	90%	-	-	-	-	-	-	-	-	-	-	39.2 18
	100% 39.2 25	39.2	8 39.2 17 39.2 16 39.2 9 39.2 23

Units: 𝜈 (kHz); SD (Hz)

Table 3 .

 3 10. Mesh size for the image processing of the tool.

	Mesh nodes node distribution
	I	15	3 × 5
	II	36	6 × 6
	III	176	16 × 11
	IV	10	2 × 5

Table 4 .

 4 1. NC codes for every absolute strategy pa ern resulting from the combination of the 𝑛 𝑝 and St. factors. In brackets the Taguchi run in which they are to be executed.

Table 4 . 2 .

 42 Experimental design derived from a 𝐿27(313 ) Taguchi orthogonal array. 𝐹 𝑝 𝑛 𝑝 𝑣 𝑓 𝑆 0 St.

	Col. 1	2	5 10 12
	No. 1	1	1	1 1	1
	2	1	1	2 2	2
	3	1	1	3 3	3
	4	1	2	1 2	3
	5	1	2	2 3	1
	6	1	2	3 1	2
	7	1	3	1 3	2
	8	1	3	2 1	3
	9	1	3	3 2	1
	10	2	1	1 3	2
	11	2	1	2 1	3
	12	2	1	3 2	1
	13	2	2	1 1	1
	14	2	2	2 2	2
	15	2	2	3 3	3
	16	2	3	1 2	3
	17	2	3	2 3	1
	18	2	3	3 1	2
	19	3	1	1 2	3
	20	3	1	2 3	1
	21	3	1	3 1	2
	22	3	2	1 3	2
	23	3	2	2 1	3
	24	3	2	3 2	1
	25	3	3	1 1	1
	26	3	3	2 2	2
	27	3	3	3 3	3

Table 4 .

 4 3. Factors and levels at the Taguchi array for AISI 1038 and Ti-6Al-4V specimens.

	Levels

Table 4 .

 4 4. Descriptors and factors kept constant in the tests.

	Factor	Value
	lateral pass width	0.3 mm
	burnishing ball diameter	∅10 mm
	ball material	60Cr3 hardened chromium steel
	lubrication	none

Table 4 .

 4 7. Central moments of a surface height distribution. A er King & Davis (1982) [69]

	Function	Order Statistical descriptor

Table 4 .

 4 8. e 13 V parameter set, as de ned in the ISO 25178. 𝑆 𝑝𝑘 Average height of protruding peaks above the core Reduced valley height 𝑆 𝑣𝑘 Average height of protruding valleys below the core Peak material ratio 𝑀 𝑟1 Ratio of the area which separates the peak and the core Valley material ratio 𝑀 𝑟2 Ratio of the area which separates the core and the valley

	Name and symbol		De nition
			Areal parameters
	Core distance	𝑆 𝑘	Distance between highest and lowest level of core
	Reduced peak height
	Plateau root mean	𝑆 𝑝𝑞	Slope of linear regression on the plateau region
	square deviation
	Dale root mean square	𝑆 𝑣𝑞	Slope of linear regression on the valley region
	deviation
	Relative material ratio 𝑆 𝑚𝑞 Peak-to-valley material ratio
			Void volumes
	Valley void volume	𝑉 𝑣𝑣	Void volume in the valleys
	Core void volume	𝑉 𝑣𝑐	Void volume in the core material
			Material volumes
	Peak material volume	𝑉 𝑚𝑝 Material volume in the peaks
	Core material volume	𝑉

𝑚𝑐 Material volume in the core material Other Peak extreme height 𝑆 𝑥𝑝 Di erence of heights at the average plane and peaks on the surface a er especially high peaks on the surface are removed 4.2.1.6 Surface registration and influence of the acquired surface size

Table 4 .

 4 9. Errors calculated from the repeatability of S parameters on the machined surfaces. 𝑆 𝑞 (µm) 𝑆 10𝑧 (µm) 𝑆 𝑠𝑘 𝑆 𝑘𝑢 𝑆 𝑝 (µm) 𝑆 𝑣 (µm) 𝑆 𝑑𝑞 𝑆 𝑑𝑟 (%)

		Av.	5.163	22.985	0.155	1.681 14.834	9.210	0.141 0.983
	𝑆 0 1	St.Dev. 0.143	2.642	0.009	0.050 2.001	0.453	0.006 0.077
		Error	2.78%	11.49%	5.47%	2.94% 13.49%	4.92%	4.37% 7.80%
		Av.	8.165	39.175	-0.058 1.814 38.0764 14.912	0.155 1.158
	𝑆 0 2	St.Dev. 0.055	3.298	0.006	0.026 9.830	0.433	0.005 0.049
		Error	0.68%	8.42%	10.48% 1.45% 25.82%	2.90%	3.15% 4.19%
		Av.	11.052	46.625	0.266	1.771 33.687	18.979	0.128 0.767
	𝑆 0 3	St.Dev. 0.106	4.433	0.018	0.035 4.813	1.378	0.004 0.039
		Error	0.96%	9.51%	6.58%	1.95% 14.29%	7.26%	2.73% 5.09%

Table 4 .

 4 10. Retained topological parameters from the S set.

	Surface feature	Retained parameter Rejected parameters
	Amplitude -scale	𝑆 𝑞	𝑆 𝑎
	Amplitude -extreme points 𝑆 10𝑧	𝑆 𝑝 , 𝑆 𝑣
	Spatial	𝑆 𝑎𝑙 , 𝑆 𝑡𝑟	-
	Hybrid	𝑆 𝑑𝑞	𝑆 𝑑𝑟

Table 4 .

 4 [START_REF]Di erent residual stress scales 𝑙 0,𝐼 , 𝑙 0,𝐼𝐼 and 𝑙 0,𝐼𝐼𝐼 . b. Examples of sources of macro and micro residual stress states. A er Withers & Bhadeshia[END_REF]. Experimental characteristics of X-ray di raction measurements.

	Item	AISI 1038	Ti-6Al-4V
	Anode type	CrK𝛼	V𝛼
	Exposition time	40 s	360 s
	# measures	13	13
	2𝜃 0	156 ○	143.5 ○
	{ℎ𝑘𝑙}	Fe(𝛼) {211}	Ti(𝛼) {213}
	estimated depth	15 µm	10 µm
	post-processing method FWHM and peak height curve ing
	4.3 Material characterisation
	4.3.1 AISI 1038 alloy

Table 4 .

 4 12. AISI 1038 weight composition.

Table 4 .

 4 [START_REF]X-ray di raction spectrum showing a di raction peak at 2𝜃 𝜓 position, with regards to the spectrum registered for the reference material[END_REF]. AISI 1038 properties, as characterised by Travieso-Rodríguez (2010)[START_REF] T R | Estudio para la mejora del acabado super cial de super cies complejas aplicando un proceso de deformación plástica (Bru ñido con Bola)[END_REF]. Both of them were prepared as explained at the precedent subsection, and etched by chemical action of a Nital solution.

	Property	Value
	Density	7.84 g/cm 3
	Young's Modulus	211 GPa
	Poisson's Modulus	0.29
	Yield strength	416 MPa
	Self-hardening coe cient 0.19
	extracted.

Table 4 .

 4 14. Hardness measurements performed on the AISI 1038 specimens.

	Direction	HV100 Error Average 𝑑 (µm) max 𝑑 (µm) min 𝑑 (µm)
	Direction I 175	10.6	32.08	30.12	32.86
	Direction II 180	10.5	31.86	29.99	32.74

Table 4 .

 4 16. Grade 23 Ti-6Al-4V properties.

	Property	Value
	Density	4.4 g/cm 3
	Young's Modulus	110 GPa
	Poisson's Modulus	0.32
	Yield strength	870 MPa
	Self-hardening coe cient 0.3

Table 4 .

 4 17. Hardness measurements performed on the Ti-6Al-4V specimens.

	HV100 Error Average 𝑑 (µm) max 𝑑 (µm) min 𝑑 (µm)
	Direction I 311	9.1	24.5	16.19	23.16
	Direction II 308	7.4	24.7	15.64	22.98
	A er the Vickers microindentation tests, chemical etching through Kroll's reagent
	was performed.

Table 5 . 1 .

 51 Summary of retained two-and three-dimensional topological parameters.

	Two-dimensional parameters
	Roughness parameters	𝑅 𝑎 : average; 𝑅 𝑞 : RMS
	Pro le parameters	𝑃 𝑎 : average, 𝑃 𝑞 : RMS
	S parameters
	Amplitude
	Root mean square height	𝑆 𝑞
	Skewness	𝑆 𝑠𝑘
	Kurtosis	𝑆 𝑘𝑢
	Ten-point height	𝑆 10𝑧
	Spatial
	Fastest decay autocorrelation length	𝑆 𝑎𝑙
	Texture aspect ratio	𝑆 𝑡𝑟
	Hybrid
	Root mean square gradient	𝑆 𝑑𝑞
	Miscellaneous
	Texture direction angle	𝑆 𝑡𝑑
	V parameters
	Areal parameters
	Core distance	𝑆 𝑘
	Reduced peak height	𝑆 𝑝𝑘
	Reduced valley height	𝑆 𝑣𝑘
	Peak material ratio	𝑀 𝑟1
	Valley material ratio	𝑀 𝑟2
	Volumetric parameters
	Valley void volume	𝑉 𝑣𝑣
	Core void volume	𝑉 𝑣𝑐
	Peak material volume	𝑉 𝑚𝑝
	Core material volume	𝑉 𝑚𝑐

Table 5 . 2 .

 52 Parameters to apply VABB on AISI 1038 end-milled surfaces, based on ANOVA mean results. Optimisation target: minimum texture amplitude.

	Initial surface	𝐹 𝑝 (N) 𝑛 𝑝	𝑣𝑓 (mm/min)	Strategy	test	scale reduction: 𝛥𝑆 𝑞
	𝑆 0 1	180	3	300-900	nb0, bn90/0 or bn0	#18	81.3%
	𝑆 0 2	270	3	300-900	nb0, bn90/0 or bn0	#26	73.4%
	𝑆 0 3	270	5	300-900	nb0, bn90/0 or bn0	#27	61.5%

Table 5 .

 5 3. Recommended parameters to ball-burnish AISI 1038 end-milled surfaces. Optimisation target: Gaussian surface with minimum texture amplitude.

	Initial surface	Process	𝐹 𝑝 (N) 𝑛 𝑝	𝑣𝑓 (mm/min)	Strategy	test	scale reduction: 𝛥𝑆 𝑞
	𝑆 0 1	VABB or NVABB	180	3	300-900	nb0, bn90/0 or bn0	#18	81.3%
	𝑆 0 2	NVABB	270	3	300-900	nb0, bn90/0 or bn0	#26	73.4%
	𝑆 0 3	NVABB	270	5	300-900	nb0, bn90/0 or bn0	#27	61.5%

Table 5 .

 5 4. Parameters to apply VABB on Ti-6Al-4V end-milled surfaces, based on ANOVA mean results. Optimisation target: minimum texture amplitude.

	Initial surface	𝐹 𝑝 (N) 𝑛 𝑝	𝑣𝑓 (mm/min)	Strategy	test	scale reduction: 𝛥𝑆 𝑞
	𝑆 0 1	350	3	300-900	nb0, bn90/0 or bn0	#23	60.3%
	𝑆 0 2	350	5	300-900	nb0, bn90/0 or bn0	#26	28.9%
	𝑆 0 3	350	5	300-900	nb0, bn90/0 or bn0	#27	25.7%

Table 5 . 5 .

 55 Recommended parameters to ball-burnish Ti-6Al-4V ball-end milled surfaces. Optimisation target: Gaussian surfaces with minimum texture amplitude.

	Initial surface	Process	𝐹 𝑝 (N) 𝑛 𝑝	𝑣𝑓 (mm/min)	Strategy	test	scale reduction: 𝛥𝑆 𝑞
	𝑆 0 1	VABB	350	3	300-600	nb0, bn90/0 or bn0	#23	60.3%
	𝑆 0 2	VABB or NVABB	350	5	300-900	nb0, bn90/0 or bn0	#26	28.9%
	𝑆 0 3	VABB or NVABB	350	5	300-900	nb0, bn90/0 or bn0	#27	25.7%

Table 5 .

 5 6. Main topology descriptors of machined surfaces, including 𝑆 0 0 (AISI 1038).

		𝑆 𝑞 (µm)	𝑆 10𝑧 (µm)	𝑆 𝑠𝑘	𝑆 𝑘𝑢
		AISI TA6V	AISI	TA6V	AISI TA6V	AISI TA6V
	𝑆 0 0 𝑆 0 1 𝑆 0 2 𝑆 0 3	1.662 5.058 1.243 20.839 9.503 -7.9547 -8.154 5.956 39.448 28.071 -0.038 0.602 0.653 -0.144 0.415 11.205 8.836 43.446 35.631 0.330 0.341	2.3040 1.642 2.686 -1.839 2.017 1.881 2.139

Table 5 .

 5 7. 60Cr3 chromium steel mechanical properties.

	Property	Value
	Young's Modulus	200 GPa
	Poisson's Modulus 0.3

  𝐼 (2𝜎 𝐼 -𝜎 𝐼𝐼 )⌋ 2 + (𝑒 𝐼𝐼 (2𝜎 𝐼𝐼 -𝜎 𝐼 )⌋ 2 + 9 (𝜏 12 𝑒 21 + 𝜏 21 𝑒 12 )

			5.2. MECHANICAL PARAMETER: RESIDUAL STRESS
	follows:
	𝑒 𝑣𝑚 =	1 2 𝜎 𝑣𝑚	⌉ (𝑒 2	(5.6)

Table 5 .

 5 8. Optimal parameters to apply VABB on AISI 1038 surfaces according to di erent RS targets, based on ANOVA mean e ects.

	Opt. target	Process 𝐹 𝑝 (N) 𝑛 𝑝	𝑣𝑓 (mm/min)	𝑆 0	Strategy	test	RS increase: 𝛥𝜎 𝑖
	𝜎 𝐼 𝜎 𝐼𝐼 𝜎 𝑣𝑚 VABB VABB VABB	270 270 270	5 3 5	600 300 300-600 𝑆 0 𝑆 0 3 𝑆 0 1 or 𝑆 0 2 1 or 𝑆 0 2	bn90/0 nb0 nb0	--#25	--21.1%

Table 5 .

 5

	Strategy test	VABB 𝛥𝜎 𝑖	NVABB 𝛥𝜎 𝑖

9. Optimal parameters to ball burnish AISI 1038 surfaces based on real experimental results Initial surface Opt. target Process 𝐹 𝑝 (N) 𝑛 𝑝 𝑣𝑓 (mm/min)

Table 5 .

 5 10. Optimal parameters to ball burnish Ti-6Al-4V surfaces according to di erent RS targets, based on ANOVA mean e ects.

	Opt. target	Process	𝐹 𝑝 (N) 𝑛 𝑝	𝑣𝑓 (mm/min)	𝑆 0	Strategy	test	RS increase: 𝛥𝜎 𝑖
	𝜎 𝐼	NVABB 150	5	900	𝑆 0 3	bn90/0	-	-
	𝜎 𝐼𝐼	VABB or NVABB	350	5	300-600	𝑆 0 1	nb0	#25	21.0%
	𝜎 𝑣𝑚	VABB or NVABB	350	5	300-600	𝑆 0 1 or 𝑆 0 2	nb0, bn0 or bn90/0	#26	39.1%
	5.2.2.4 Optimal parameter set for RS maximisation based on individual Taguchi
		experimental results

Table 5 .

 5 5.3. OPTIMAL PARAMETER SETS ACCORDING TO TEXTURE AND RS CRITERIA:SYNTHESIS 11. Optimal parameters to ball burnish Ti-6Al-4V surfaces based on real experimental results

	Initial surface	Opt. target	Process	𝐹 𝑝 (N) 𝑛 𝑝	𝑣𝑓 (mm/min)	Strategy test	VABB 𝛥𝜎 𝑖	NVABB 𝛥𝜎 𝑖
		𝜎 𝐼	NVABB 250	5	900	bn90/0	#18	49.8%	66.6%
	𝑆 0 1	𝜎 𝐼𝐼	VABB or NVABB	350	5	300	nb0	#25	21.0%	16.9%
		𝜎 𝑣𝑚	VABB or NVABB	350	5	300	nb0	#25	19.7%	15.9%
	𝑆 0 2	𝜎 𝐼 𝜎 𝐼𝐼	VABB or NVABB VABB or NVABB	350 350	5 5	900 600	bn90/0 bn90/0	#26 #26	76.8% 18.4%	74.6% 10.2%
		𝜎 𝑣𝑚	VABB or NVABB	350	5	600	bn90/0	#26	39.1%	34.4%
		𝜎 𝐼	NVABB 350	5	900	bn0	#27	81.0%	100.3%
	𝑆 0 3	𝜎 𝐼𝐼	NVABB 350	5	900	bn0	#27	66.3%	71.9%
		𝜎 𝑣𝑚	NVABB 350	5	900	bn0	#27	68.8%	85.7%

Table 5 .

 5 12. Summary of optimal parameters to ball burnish AISI 1038 surfaces based on texture and RS criteria.

	Initial surface	Opt. target	Process	𝐹 𝑝 (N) 𝑛 𝑝	𝑣𝑓 (mm/min)	Strategy	Overall optimal set
		Texture	VABB or NVABB	180	3	300-900	nb, bn0 or bn90/0	VABB
	𝑆 0 1	𝜎 𝐼 Taguchi	VABB	180	5	900	bn90/0	270 N
		𝜎 𝐼𝐼 Taguchi	VABB	270	5	300	nb0	5 passes
		𝜎 𝐼𝐼 ANOVA	VABB	270	3	300	nb0	300-900 mm/min
		𝜎 𝑣𝑚 Taguchi	VABB	270	5	300	nb0	Strategy according to target
		𝜎 𝑣𝑚 ANOVA	VABB	270	5	300-900	nb0
		Texture	VABB or NVABB	270	3	300-900	nb, bn0 or bn90/0	VABB
	𝑆 0 2	𝜎 𝐼 ANOVA	VABB	270	5	600	bn90/0	270 N
		𝜎 𝐼𝐼 Taguchi	VABB	270	3	900	nb0	5 passes
		𝜎 𝐼𝐼 ANOVA	VABB	270	3	300	nb0	300-900 mm/min
		𝜎 𝑣𝑚 Taguchi	VABB	270	3	900	nb0	Strategy according to target
		𝜎 𝑣𝑚 ANOVA	VABB	270	5	300-600	nb0
		Texture	NVABB	270	5	300-900	nb, bn0 or bn90/0	VABB
	𝑆 0 3	𝜎 𝐼 Taguchi	VABB	270	5	900	bn90/0	270 N
		𝜎 𝐼 ANOVA	VABB	270	5	600	bn90/0	5 passes
		𝜎 𝐼𝐼 Taguchi	VABB	270	3	600	nb0	300-900 mm/min
		𝜎 𝑣𝑚 Taguchi	VABB	270	3	600	nb0	Strategy according to target

Table 5 .

 5 [START_REF]X-ray di raction spectrum showing a di raction peak at 2𝜃 𝜓 position, with regards to the spectrum registered for the reference material[END_REF]. Summary of optimal parameters to ball burnish Ti-6Al-4V surfaces based on texture and RS criteria.

	Initial surface	Opt. target	Process	𝐹 𝑝 (N) 𝑛 𝑝	𝑣𝑓 (mm/min)	Strategy	Overall optimal set
		Texture	VABB	350	3	300-600	nb, bn0 or bn90/0	VABB
	𝑆 0 1	𝜎 𝐼 Taguchi	NVABB	250	5	900	bn90/0	350 N
		𝜎 𝐼𝐼 Taguchi	VABB or NVABB	350	5	300	nb0	5 passes
		𝜎 𝐼𝐼 ANOVA	VABB or NVABB	350	5	300-600	nb0	300-900 mm/min
		𝜎 𝑣𝑚 Taguchi	VABB or NVABB	350	5	300	nb, bn0 or bn90/0	Strategy according to target
		𝜎 𝑣𝑚 ANOVA	VABB or NVABB	350	5	300-600	nb0
		Texture	VABB or NVABB	350	5	300-900	nb, bn0 or bn90/0	VABB or NVABB
	𝑆 0 2	𝜎 𝐼 Taguchi	VABB or NVABB	350	5	900	bn90/0	270 N
		𝜎 𝐼𝐼 Taguchi	VABB or NVABB	350	5	900	nb0	5 passes
		𝜎 𝑣𝑚 Taguchi	VABB or NVABB	350	5	600	nb0	300-900 mm/min
		𝜎 𝑣𝑚 ANOVA	VABB or NVABB	350	5	300-600	nb, bn0 or bn90/0	Strategy according to target
		Texture	NVABB	350	5	300-900	nb, bn0 or bn90/0	NVABB
	𝑆 0 3	𝜎 𝐼 Taguchi	NVABB	350	5	900	bn0	270 N
		𝜎 𝐼 ANOVA	NVABB	150	5	900	bn90/0	5 passes
		𝜎 𝐼𝐼 Taguchi	NVABB	350	5	900	bn0	600-900 mm/min
		𝜎 𝑣𝑚 Taguchi	NVABB	350	5	900	bn0	Strategy according to target

Table 5 .

 5 14. Tested conditions for hardness tests on AISI 1038 𝑆 0 1 .

	Process Strategy Fixed parameters
	VABB	nb0	𝐹 𝑝 = 270 N ; 𝑛 𝑝

Table 5 .

 5 15. Tested conditions for hardness tests on Ti-6Al-4V 𝑆 0 1 . 𝑛 𝑝 = 5 ; 𝑣 𝑓 = 600 mm/min NVABB bn90/0 5.4.2.1 Ti-6Al-4V deep a ectation: Vickers hardness profiles

	Process Strategy Fixed parameters
	VABB	nb0	𝐹 𝑝 = 350 N ;

Table A .

 A 2. Taguchi array followed for the experimental testing of AISI 1038.# 𝐹 𝑝 (N) 𝑛 𝑝 𝑣 𝑓 (mm/min) 𝑆 0 St. Table A.3. Taguchi array followed for the experimental testing of Ti-6Al-4V. # 𝐹 𝑝 (N) 𝑛 𝑝 𝑣 𝑓 (mm/min) 𝑆 0 St.

	1 90 1 150	1	1 300	300	1	1 nb0	nb0
	2 90 2 150	1	1 600	600	2	2 bn90/0 bn90/0
	3 90 3 150	1	1 900	900	3	3 bn0	bn0
	4 90 4 150	3	3 300	300	2	2 bn0	bn0
	5 90 5 150	3	3 600	600	3	3 nb0	nb0
	6 90 6 150	3	3 900	900	1	1 bn90/0 bn90/0
	7 90 7 150	5	5 300	300	3	3 bn90/0 bn90/0
	8 90 8 150	5	5 600	600	1	1 bn0	bn0
	9 90 9 150	5	5 900	900	2	2 nb0	nb0
	10 180 10 250 1	1 300	300	3	3 bn90/0 bn90/0
	11 180 11 250 1	1 600	600	1	1 bn0	bn0
	12 180 12 250 1	1 900	900	2	2 nb0	nb0
	13 180 13 250 3	3 300	300	1	1 nb0	nb0
	14 180 14 250 3	3 600	600	2	2 bn90/0 bn90/0
	15 180 15 250 3	3 900	900	3	3 bn0	bn0
	16 180 16 250 5	5 300	300	2	2 bn0	bn0
	17 180 17 250 5	5 600	600	3	3 nb0	nb0
	18 180 18 250 5	5 900	900	1	1 bn90/0 bn90/0
	19 270 19 350 1	1 300	300	2	2 bn0	bn0
	20 270 20 350 1	1 600	600	3	3 nb0	nb0
	21 270 21 350 1	1 900	900	1	1 bn90/0 bn90/0
	22 270 22 350 3	3 300	300	3	3 bn90/0 bn90/0
	23 270 23 350 3	3 600	600	1	1 bn0	bn0
	24 270 24 350 3	3 900	900	2	2 nb0	nb0
	25 270 25 350 5	5 300	300	1	1 nb0	nb0
	26 270 26 350 5	5 600	600	2	2 bn90/0 bn90/0
	27 270 27 350 5	5 900	900	3	3 bn0	bn0

1.3. THIS DISSERTATION IN BRIEF

2.2. EXPERIMENTAL RESULTS ON SURFACE INTEGRITY AFTER BALL BURNISHING

2.2. EXPERIMENTAL RESULTS ON SURFACE INTEGRITY AFTER BALL BURNISHING(a) (b) (c)

e intensity of frequency peaks in the spectrum should actually not be considered, as they depend on the distance between the sensor and the measuring point, which has not been calibrated. Indeed, the objective of these measurements is the frequency characterisation of the signal emi ed by the VABB prototype. erefore, a slight saturation of signals does not bias the results expected from these measurements.On the other hand, all recorded signals are represented by similar frequency spectrum, showing an harmonic response from the same fundamental frequency regardless of the preload level, or the presence of a feed movement during the process. is

"#" shall denote henceforth the number of test in the Taguchi experimental array

is exempli ed by the machining marks being still visible a er VABB.

Acknowledgements

Fist of all, I would like to sincerely thank all professors that honour me by participating of the evaluation of this dissertation: Irene Buj, Medi Chérif, Philippe Darnis, Giovanni Gomez and Guillermo Reyes.

Por supuesto, me gustaría dar las gracias a mis directores espa ñoles, José Antonio Travieso y Jordi Llumà, tanto por vuestra implicación para con esta tesis, como por la amistad compartida, forjada en el día a día. Juntos, siempre llegamos.

Iberoamericano de Ingeniería Mecánica, Lisboa (Portugal), 23-26 October 2017.

Patent

Jerez-Mesa, R., Travieso-Rodríguez, J.A., Gómez-Gras, G., Llumà-Fuentes, J. Herramienta de bru ñido con bola asistida por vibraciones ultrasónicas. Published en el Boletín Espa ñol de la Propiedad Intelectual, 2 de junio de 2017. Número de publicación: 2 615 002.

A L27 Taguchi arrays for experimental design

Table A.1. L27(3 13 ) Taguchi orthogonal array. A er Taguchi et al., 2005 [START_REF]Taguchi's quality engineering handbook[END_REF] No. 1 2 3 4 5 6 7 8 9 10 11 12 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 2 2 2 2 2 2 2 3 1 1 1 1 3 3 3 3 3 3 3 A. 4. Consequently, the designed experimental plan requires ∑ 𝑑𝑜𝑓 𝑖 = 22 degrees of freedom. erefore, a 27-run plan based on the L27 array as proposed complies satisfactorily with this condition.

A.2 Compliance of the orthogonality condition

A common methodology to prove that all actions in the model are orthogonal among them, and consequently prove the orthogonality of the experimental array, is to represent the Sisson-Vigier incidence matrix (Table A .5). It depicts the necessary minimum runs to analyse the e ect of every uncoupled actions, which is the product of their levels inside the proposed array. For instance, the combination of 𝐹 𝑝 and 𝑛 𝑝 , at three levels each, requires the execution of 3 2 tests to have enough information about their e ects. e orthogonality between the 𝑛 𝑝 & 𝑣 𝑓 interaction and the 𝑆 0 factor is satis ed if 3 ⋅ 3 3 runs are executed.

e experimental plan to analyse the desired model must be a multiple of the least common multiple of all of them, that is 𝑙𝑐𝑚 (9, 27) = 27, which con rms the orthogonality condition for the designed experimental setup based on the L27 array.

216

C

VABB Ti-6Al-4V texture figures [98] M , W. E ect of dislocations on ultrasonic wave a enuation in metals. Bell System Technical Journal 34, 5 (1955), 903-942.

[99] M , J., P , P. Characterization of the shape of the roughness pro le ordinate distribution of honed cylinder surfaces. Wear 161, 1-2 (1993), 135-143.

[100] M , B., M , V., B , V. Ultrasonic drawing of tungsten wire for incandescent lamps production. Ultrasonics 42, 1 (2004), 109-111.

[101] M , B. N., P , G. I. Ultrasonic impact peening for the surface properties' management. Journal of Sound and Vibration 308, 3 (2007), 855-866.

[102] M , T., T , K. E ect of tool-material on burnishing process. Bulletin of the Japan Society of Precision Engineering 24, 3 (1990), 219-220.

[103] M , R., K , B. Burnishing of metallic surfaces-a review. Precision Engineering 3, 3 (1981), 172-179.

[104] N´ , M., L , A. An investigation of the surface topography of ball burnished mild steel and aluminium.

e International Journal of Advanced Manufacturing Technology 16, 7 (2000), 469-473.

[105] N , H. S. New approaches to surface roughness evaluation of special surfaces. Precision Engineering 10, 4 (1988), 209-213.

[106] N , D., D , R., A , D., V , W., B , P. e e ect of machined topography and integrity on fatigue life. International Journal of Machine Tools and Manufacture 44, 2 (2004), [START_REF]Deep rolling of titanium rods for application in modular total hip arthroplasty[END_REF] [156] V ´ , J. P., T , A., B , B., C , P., F , J. J. Sub-surface and surface analysis of high speed machined Ti-6Al-4V alloy. Materials Science and Engineering: A 527, 10 (2010), 2572-2578. [159] X , H., W , Q., L , K., P , F., D , X., W , J. Investigation of in uence of direct-current pulses on springback during V-bending of AZ31B magnesium alloy sheet. Journal of Materials Processing Technology 219 (2015), 321-327. [161] Z , T., B , N., M , I. D. Burnishing of aerospace alloy: A theoretical-experimental approach. Journal of Manufacturing Systems (2014).

[162] Z , R. B. e e ect on surface texture of material addition and removal processes. Surface and Interface Analysis 11, 6-7 (1988), 291-301.