Gianmauro Fontana
email: gianmauro.fontana@itia.cnr.it

Serena Ruggeri
email: serena.ruggeri@itia.cnr.it

Giovanni Legnani
email: giovanni.legnani@ing.unibs.it

Irene Fassi
email: irene.fassi@itia.cnr.it

Precision Handling of electronic components for PCB rework

Keywords:

Introduction

In the last decades, a number of mechatronic devices have been developed for different purposes and have been broadening more and more in various fields. They result from a suitable integration of mechanical, information technology and electronic features that allow both to enhance the capabilities and the performance of standard products and to enable the conception and development of new generation systems facing the high-demanding requirements of an increasing market.

Products of daily usage such as cars, mobile phones and computers for example rely on electronics and contain Printed Circuit Boards (PCBs). They can mount few or hundreds components such as ball grid array (BGA) packages for integrated circuits, resistances or capacitors, often of tiny size. Indeed, a heavy trend to miniaturization has recently appeared, reflecting the need of getting smaller final products with integrated functionalities.

Despite the manufacturing technologies for electronic components and PCBs appear consolidated, few attention has been paid in the years to the development of suitable techniques to repair, reuse or recycle this kind of products when a malfunctioning or a breakdown occur. Most of times, due to economic reasons, the PCB is substituted with a new one and disposed, wasting many parts that could still have value and be recovered.

However, it has been estimated that, from an environmental point of view, remanufacturing is 80% more energy efficient than traditional manufacturing and, from an economic point of view, 60% more cost efficient [START_REF] Errington | A business process model of inspection in remanufacturing[END_REF].

If a repair plan is expected, the rework of PCBs is often performed manually, or in few cases with highly dedicated machines, and can result in a very expensive and complex operation; in the same way, the recovering of components in case of irreparable PCBs is not efficient.

According to the emerging "De-manufacturing" paradigm, innovative approaches and methodologies should be implemented to improve the management of electronic products at their end of life [START_REF] Brusaferri | Integrated Demanufacturing systems as new approach to End-of-Life management of mechatronic devices[END_REF].

Consider for example the recovery of a working BGA from a defective PCB. In this case, the BGA is de-soldered from the PCB, by heating and consequently melting the soldering balls (with diameter <1mm). Then, a procedure called "re-balling" is needed to prepare the chip for the re-use, consisting in attaching new solder balls on the bottom surface of the BGA support. Nowadays, this operation is performed mainly manually with the help of fixtures and stencils or using preforms [START_REF] Solderquik | [END_REF]. Specific stencils or preforms have to be used for each particular BGA support type, then limiting the flexibility of the process, and the operator ability influences the accuracy of the result. Recently, automatic rework stations have been developed [START_REF] Solderquik | [END_REF], but still there is a need for more flexible and cost efficient automated equipment.

In this context, the present paper focuses on the study of methods and tools for handling miniaturized components to move towards a flexible and efficient rework of PCBs. The study is devoted to two main related aspects: the re-balling of BGA packages and the replacement of different surface-mount components (SMCs) on the PCBs. To overcome the limits of the current procedures, the work addressed the development of simple and low-cost gripping devices and strategies for both a complete or selective re-balling, then able to pick and place a whole grid of small solder balls or a single ball precisely and reliably. In the same way, the tools should be able to accomplish the replacement of SMCs of different size and mounted on the PCB with a generic orientation.

In particular, an innovative device and method to manipulate by vacuum a component has been conceived and prototyped. A patent application has been filed in March 2013 [START_REF] Ruggeri | Dispositivo di manipolazione e metodo per manipolare a vuoto un componente[END_REF]. This device has been compared with a conventional vacuum microgripper in the execution of pick and place tests of both solder balls of various diameter and resistances.

The investigation of their performance considered both the gripping and the release phases. Indeed, at the microscale, due to the predominance of adhesion forces (e.g. capillary, electrostatic and Van der Waals forces) over the gravitational force, the release of microcomponents is often prevented or uncertain. In literature many solutions have been proposed to cope with this issue [START_REF] Chen | A hybrid-type electrostatically driven microgripper with an integrated vacuum tool[END_REF], but the search of effective and efficient methods is still an undergoing study. For this reason, a special releasing system has been designed and integrated in the innovative gripping device to release the components precisely, reliably and safely, avoiding an excessive increase in weight of the device itself or complexity of its structure.

The two types of handling devices are presented in Section 2. Section 3 describes the experimental tests and the performance indices considered for the comparison and discuss the preliminary results, highlighting the benefit of the proposed solution.

2

The handling devices

A convenient solution for the manipulation of electronic components is represented by the use of vacuum grippers, commonly used for macrocomponents and here adapted to the tiny size of the microcomponents. They are based on the pressure difference between the gripper and the atmosphere and have a generally simple structure, since they are mainly based on a small suction hose; they are not expensive and can be used to manipulate a wide range of components, even fragile.

In this work, two types of vacuum microgrippers were considered. The former is a standard microgripper: it is a commercially available needle for dispensing, basically consisting of a cannula connected to a vacuum generation system. The cannula has an internal diameter of 260 µm, which is attached to the hollow needle body that can be connected to the end-effector of a robot through a proper mechanical interface.

However, in [START_REF] Ruggeri | Handling and manipulation of Microcomponents: Work-Cell Design and Preliminary Experiments[END_REF], it has been shown that the release is greatly affected by the presence of the adhesion forces and that the simple switch off of the vacuum is often not sufficient. Therefore, suitable expedients need to be found. For example, the adhesion due to the electrostatic force can be reduced coating the glass pipette for the suction with a conductive layer connected to the ground. Moreover, the microcomponent could be guided to hit a sharp edge or rolled on the release plane. The inertial force of the component, generated by moving the gripper brusquely upwards for a short stroke, can also be exploit to ease the release, although results can be inaccurate [START_REF] Ruggeri | Handling and manipulation of Microcomponents: Work-Cell Design and Preliminary Experiments[END_REF]. Finally, the application of positive pressure, that is of a soft blow for some milliseconds, allows the achievement of a high release percentage and does not affect negatively the final precision of positioning. However, the tuning of the parameters related to the blow (e.g. its intensity) could sometimes be difficult and a trade-off between percentage and precision of release of the specific component has to be found.

On the basis of the results obtained in past experiments and the study of the detected behaviours, a new vacuum micro-gripping tool (No. 1 in Fig. 1) has been conceived and developed, able to cope with the micropart release issues. Similarly to a standard vacuum microgripper, this device is based on the pressure difference between the gripper and the atmosphere and basically consists of a cannula or suction hose connected to a vacuum generation system for picking a component by suction on the gripping end. It integrates an innovative mechanical system to assist the release phase of micro components precisely, reliably and safely, avoiding a considerable increase in weight of the device itself or an excessive complication of the system. In details, the mechanical system is inserted at least partially in the manipulation device and movable from a release position where a release portion projects externally from the gripping end, and a gripping position where the release portion returns into the manipulation device. The mechanical system includes a transversal extension, that in the current case is a holed disc, and a needle attached to the disc and having a diameter smaller than the internal diameter of the cannula. The needle is inserted at least partially inside the cannula and includes the release portion.

The mechanical release system is designed to be moved from the release position to the gripping position through activation of the vacuum generating system, which sucks in the mechanical release system in opposition to a return force pulling it toward the release position, for example the force of gravity acting on the mechanical release system. It is also designed to be moved from the gripping position to the release position by the said return force following a reduction or elimination of the pressure difference between the inside and outside of the manipulation device operated by the vacuum generating system.

A main feature consists in using the actuation principle for the part picking to move the release system, without the need of additional actuators, that would make the system more complex, heavier, bigger and more expensive.

Preliminary experiments and results

In this section, the results obtained through a set of preliminary experiments are presented. The tests evaluated the performance of the two types of grippers both in gripping and releasing different components. In particular, the handling of solder balls with diameter of 500 microns and mass of 0.00055 g, and SMD resistances with size 1.5 x 0.8 x 0.45 mm and mass of 0.002 g was evaluated. Each test consisted in the execution of a set of 30 standard pick and place cycles, representative of the real trajectory that the gripper with the component should perform for assembly or PCB rework.

The tests were carried out exploiting the setup available in our micro-manipulation work-cell [START_REF] Fontana | Flexible vision based control for microfactories[END_REF]: a Mitsubishi Electric RP-1AH robot (Fig. 1) was used as motion system, while the measurements of the position and orientation of the microparts was obtained by a suitable vision system consisting of a camera combined with a macro lens, providing a bottom view of working (gripping and releasing) area with a spatial resolution of about 8.1 µm. The gripping performance was evaluated comparing the measured position of the barycenter and the orientation of the component in two images acquired before and just after the gripping respectively. Similarly, the release was evaluated by detecting and measuring its pose before and after the release.

With the same approach adopted in [START_REF] Ruggeri | Handling and manipulation of Microcomponents: Work-Cell Design and Preliminary Experiments[END_REF], the performance indices we calculated for each test cycle were the repeatability and accuracy, according to the definition given by the international standard ISO 9283. Moreover, the gripping and release percentages, representing the success of the correspondent operations, were calculated.

As introduced above, in previous studies we demonstrated that the use of the positive pressure, in practice a soft blow, represented an acceptable method to assist the microcomponent release.

For this reason, the first class of experiments we executed considered the use a standard vacuum gripper, grasping the component by simple activation of the vacuum generation system, but releasing it by providing a blow for few milliseconds. A set of pick and place cycles was performed. While the gripping of the ball was always successful (gripping percentage of 100%), the release phase highlighted a strong dependence of the release performance on the blow pressure. Therefore two sets of experiments were carried out varying the blow pressure, the former trying to obtain an accurate and repeatable release independently from the release percentage, the latter trying to maximize the release percentage. The results for repeatability and accuracy for the first condition are graphically reported in Fig. 2, those related to the second condition are reported in Fig. 3. The origin of the reference system in the graphs represented the target position, while the small crosses indicated the barycenter of the ball for each cycle. release of the microcomponents, often prevented or uncertain with traditional handling devices due to the presence of adhesive forces, has been investigated. The results demonstrated that the innovative microgripper is able to manipulate submillimetric components better than the conventional vacuum microgripper and that the special releasing system allowed a reliable and safe release. However, the values of orientation accuracy and are still high for ultra-precise manipulation, therefore additional expedients should be considered. Moreover, it can be noticed that, for both microgrippers, the repeatability values in the gripping and release phases are much higher than the accuracy values. For this reason, further efforts will be required to better comprehend this phenomenon and try to improve the grippers' performance.

Concluding, the innovative device represents an interesting solution for handling electronic components for PCBs rework and, more in general, for micromanipulation and assembly of different microproducts.

In the next future, the handling of other microcomponents with this gripper will be also tested and it will investigated more deeply in order to highlight advantages and limitations.

Fig. 1 .

 1 Fig. 1. The micromanipulation workcell and the innovative gripper with release needle

Fig. 2 .

 2 Fig. 2. Results for standard vacuum gripper manipulating the ball: gripping percentage of 100% and release percentage of 82.14%

Fig. 4 .Fig. 5 .

 45 Fig. 4. Results for the standard vacuum gripper manipulating the resistance: gripping and release percentage of 100% Gripping Test

Table 1 .

 1 Orientation accuracy and repeatability for the standard microgripper manipulating the resistance.

	Resistance: values for orientation	Gripping	Release (by positive pressure)
	Accuracy [°]	-0.550	-8.331
	Repeatability [°]	17.293	43.322
	Gripping Test		Release Test
	AC = 0.154 mm		AC = 0.030 mm
	RP = 0.479 mm		RP = 0.581 mm

Aknowledgements

This research has been partially funded by Regione Lombardia, in the framework of the Accordo Quadro RL-CNR, project 'FIDEAS: Fabbrica Intelligente per la Deproduzione Avanzata e Sostenibile'.

The experiments were repeated with the resistance and the results are shown in Fig. 4. Opposite to the ball, the resistance could have various orientations, therefore the accuracy and the repeatability values of the gripping and the release operations have been calculated to evaluate the orientation error and reported in Table 1.

As shown in Fig. 23, the percentage of release is not 100% while the accuracy and repeatability values are sometimes too high for ultra-precise manipulation. This is evident in Table 1, showing high values for both the orientation accuracy and repeatability.

The results in Fig. 4 also shows values of the gripping accuracy and repeatability for the resistance higher than those for the solder ball, most likely due to a sort of auto-centering property of the ball on the gripper tip. Moreover, the tuning of the pressure parameters can be onerous and the performance indices very sensitive to small changes of their values.

The innovative microgripper has been designed to combine the advantages of the vacuum gripping method and overcome all the difficulties related to the use of positive pressure, since no external actuation is needed to assist this phase. To investigate this gripper and the manipulation method, we repeated the experiments on the solder ball.

The gripping and release accuracy and repeatability are reported in Fig. 5. In this case, the performance indices for the release are much better than those obtained with the standard gripper and the positive pressure assisting the release. Note also that, in both cases, the percentage of success of the gripping and release operations was 100%, validating the expected effectiveness of this method.

release percentage of 100%

The experiments were then repeated with the resistance and the results are shown in Fig. 6. Note that the performance of the two microgrippers in terms of both precision and reliability are comparable. As for the case of the standard microgripper, the accuracy and the repeatability values of the gripping and the release operations have been calculated to evaluate also the orientation error (Table 2).

Conclusions

Considering the current need for more flexible and cost efficient automatic PCBs rework stations to move towards the actual implementation of the de-manufacturing paradigm, the present work devoted to the study of handling devices for the re-balling of BGA packages and PCBs and the replacement of different surface-mount components (SMCs) on the PCBs.

An innovative device and method to manipulate by vacuum a microcomponent has been presented and compared with a conventional vacuum microgripper in the execution of grasping and releasing tests of electronic components. In particular, the


Zoran Cenev

Timo Prusi

Reijo Tuokko

Image Stitching Based Measurements of Medical Screws


Raphael Adamietz
email: adamietz@ipa.fraunhofer.de

Tobias Iseringhausen

Alexander Verl

Process Module Construction Kit for Modular Micro Assembly Systems

Keywords:

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The production environment in Europe is characterized by a number of different challenges. Production volumes are hardly predictable due to the turbulent market [START_REF] Nyhuis | Wandlungsfähige Produktionssysteme: Ergebnisse der BMBF-Vorstudie "Wandlungsfähige Produktionssysteme[END_REF]. Product life cycles become increasingly shorter [START_REF] Wu | Updating a modular product: How to set time to market and component quality[END_REF]. Customers demand more individual and customized products, which leads to increasingly diversified product pallets [START_REF] Westkämper | Modulare Produkte -Modulare Montage[END_REF]. The occurrence of changes on product and process, even for running productions, increases continuously [START_REF] Westkämper | Wandlungsfähige Produktionsunternehmen: Das Stuttgarter Unternehmensmodell[END_REF]. At the same time the field of tension between assurance of quality, reduction of lead times and reduction of cost remains present [START_REF] Westkämper | Produktion im turbulenten Umfeld[END_REF].

The trend of miniaturization with the concurrent trend of integration of functions is a central topic in the product development in different fields of application [START_REF] Hesselbach | Mikromontage[END_REF], like optics, electronics, medical technology, bio technology, information technology and aeronautical technology. With ongoing miniaturization many companies face challenges of precision and ultra-precision assembly technology. Therewith increases the cost and complexity of the required process equipment and the demands to skilled personnel [START_REF] Popa | Micro and mesoscale robotic assembly[END_REF].

The development of the markets in micro system technology shows that many new and innovative developments in the field of hybrid microsystems cannot achieve a satisfactory success [START_REF] Schilp | Adaptive Montagesysteme für hybride Mikrosysteme unter Einsatz von Telepräsenz[END_REF]. This can be attributed to the high complexity of microtechnical products and processes, a lack of interdisciplinary knowledge in process development, limited flexibility of the applied manufacturing and assembly systems and the high investment risk due to uncertain forecasts of growth [START_REF] Hesselbach | Untersuchung zum internationalen Stand der Mikroproduktionstechnik[END_REF]. From the economic point of view, often only mass production is reasonable [START_REF] Hesselbach | Untersuchung zum internationalen Stand der Mikroproduktionstechnik[END_REF]. Modular micro assembly systems are often regarded as suitable link between the requirements of the market environment and the current state of development in micro production technology [START_REF] Onori | Final Report -EUPASS (Evolvable Ultra-Precision Assembly Systems)[END_REF][START_REF] Muir | Minifactory: A precision assembly system adaptable to the product life cycle[END_REF][START_REF] Gaugel | Advanced modular production concept for miniaturized products[END_REF]. Approaches such as the Agile Assembly Architecture [START_REF] Muir | Minifactory: A precision assembly system adaptable to the product life cycle[END_REF], Evolvable Assembly Systems [START_REF] Onori | Final Report -EUPASS (Evolvable Ultra-Precision Assembly Systems)[END_REF] or the Reconfigurable Micro Assembly System [START_REF] Gaugel | Advanced modular production concept for miniaturized products[END_REF] are parts of ongoing research and have been partly transferred to commercial products.

Modular production systems are characterized by standardized components and defined interfaces [START_REF] Nyhuis | Wandlungsfähige Produktionssysteme: Theoretischer Hintergrund zur Wandlungsfähigkeit von Produktionssystemen[END_REF]. Single modules can be exchanged rapidly and re-installed in other systems. This provides many advantages over the whole product life cycle. In the field of micro production these effects are increased, due to the increased investment cost and higher complexity of the production equipment.

However, the market share of modular machines does not match the predictions [START_REF] Kluge | Methodik zur fähigkeitsbasierten Planung modularer Montagesysteme[END_REF]. This can be mainly attributed to the fact that the initial investment into a modular machine is significantly higher than into a special purpose machine. Repetition effects by re-use of equipment in form of process modules are necessary to make modular machines more attractive.

The authors of this paper suggest an open interface which allows the integration of process equipment of different providers into machinery of different providers. This would significantly improve the possibility to continuously adapt assembly machines. Particularly companies with broad product ranges could potentially benefit strongly.

Based on this open interface a common platform for the exchange of process modules is suggested [START_REF] Adamietz | A First Step towards Cross-Platform Integration in Modular Micro-assembly Systems-Concept for a Process Module Construction Kit[END_REF]. By a certification step, the compatibility of the offered process modules and platforms is ensured. Providers and users of modular production equipment can then offer and exchange their equipment. This way the application of one process module is not bound to one platform, but can be transferred across different platforms of different providers. This would have a strong effect on the availability of process equipment.

To support the development and set-up of process modules, a construction kit is proposed. Within this paper, the basic concept of a construction kit for process modules is described. Furthermore examples of configurations of process modules based on the construction kit are presented.

Qualitative and Quantitative Analysis

The approach of modular micro assembly machines has been compared to state-ofthe-art micro assembly machinery in previous work. For qualitative analysis a SWOT1 analysis was presented and for quantitative analysis a net present value analysis was performed. [START_REF] Adamietz | A First Step towards Cross-Platform Integration in Modular Micro-assembly Systems-Concept for a Process Module Construction Kit[END_REF] The quantitative analysis showed potential for risk management by the application of a modular system. If for example the production volumes deviate from the predictions, the modular approach allows adapting to these changes.

The qualitative analysis revealed many opportunities such as simultaneous engineering, standardized modules which can be used already during process development and reuse of production equipment. However, the analysis also revealed several threats, like decrease of process stability and product quality which might be caused by the changes of the assembly system. The largest threat, however, was that process modules might not be available as required. As an approach to improve this situation, the concept of a process module construction kit is presented here.

3

Concept of a Process Module Construction Kit

Complex interface

Also proposed within previous work, was the 'Complex Interface' [START_REF] Adamietz | A First Step towards Cross-Platform Integration in Modular Micro-assembly Systems-Concept for a Process Module Construction Kit[END_REF]. It consists of three concepts: The 'mechanical interface', the 'supply interface' and the 'control interface'.

The 'mechanical interface' comprises the definition of a generic, blank module. Spaces for process, feeding and control equipment as well as working spaces are defined. Within the 'supply interface' a supply connector is defined which includes supply of compressed air and electricity as well as connection to Ethernet and field bus. The 'control interface' defines the interface and function blocks for control integration. The overall complex interface definition is a prerequisite for cross-platform integration. It allows machine constructors to provide a compliant interface to a common process module specification. Furthermore, it allows third parties to develop and to build process modules for different machines providing the complex interface.

Process Module Construction Kit

The effort required to develop and to set up process modules could be potentially reduced by a construction kit. A concept for such a construction kit has been designed and is presented here. The design process is depicted in Fig. 1 and Fig. 2.

It is assumed the requirements and boundary conditions have been determined and the process equipment has been chosen as the pre-condition for application of the construction kit (1). Process equipment is here referred to as e.g. a dispenser or a gripper.

Within the next step it is checked if the chosen process equipment can be integrated to a process module according to the specifications (2). This comprises the mechanical specifications and interfaces, the supply of the process module and an integration of the control system. Many process module systems work with different pitches, making the choice of an applicable process module necessary (3).

If the result of the check against the specification is positive, the process module can be designed. It is the aim to provide as many pre-defined elements as possible with known properties to ease the design process. These 'reference solutions' (4) comprise components required to build up the process module, such as axis systems with different kinematics (xy-tables, xyz-systems, 6-axis-kinematics, …), pre-defined portal elements, sensors and calibration equipment (TCP-measuring units, vision systems, …), feeding equipment (waffle pack feeder, vibrational feeder) and supportive equipment (cleaning devices, trays). With this equipment a process module, based on reference solutions can be designed [START_REF] Westkämper | Produktion im turbulenten Umfeld[END_REF].

Fig. 1. Process module construction kit based on reference solution

To support the design and the set-up process a mechatronic tool interface is provided [START_REF] Hesselbach | Mikromontage[END_REF]. It allows instant integration of process equipment, like e.g. a gripper, a dispenser or a camera system. While the complex interface provides interfacing between process module and machine, the mechatronic tool interface provides a standard interface between equipment on the process module itself. The interface is also comprehensive and provides a mechanical, supply and control interface. However, the specifications necessary for a tool interface differ from those of a module interface. The applied interface could be based for example on an ISO 29262 tool exchange interface [START_REF]DIN ISO 29262 -Fertigungsmittel für Mikrosysteme -Schnittstelle zwischen Endeffektor und Handhabungsgerät[END_REF]. An adaption to feed through field bus, Ethernet and media is additionally required.

Fig. 2. Process modules based on reference solution

Once the process module with adapted tool is designed [START_REF] Popa | Micro and mesoscale robotic assembly[END_REF], control and auxiliary equipment are required. Reference solutions for control and auxiliary equipment are also provided [START_REF] Schilp | Adaptive Montagesysteme für hybride Mikrosysteme unter Einsatz von Telepräsenz[END_REF]. This comprises reference control programs, reference electrical and pneumatic circuitry, axis controllers, power supplies and safety technology. The next step is the completion of the process module [START_REF] Hesselbach | Untersuchung zum internationalen Stand der Mikroproduktionstechnik[END_REF]. This includes the design, manufacturing and set-up of the parts which are not covered in the construction kit. Furthermore testing is necessary before commissioning. Although the elements of the kit are depicted in a linear way in

Sample configurations of process modules

Different sample configurations process modules have been realized as CAD models. One of these configurations is shown in Fig. 3. Based on the third module variant, a xyz-positioning system was applied. Additionally control, pneumatic and electric circuitry solutions are provided from the construction kit.

Conclusions and Outlook

A concept for a construction kit for process modules is presented in this paper. The principle and the basic elements were described. Aim is to reduce the effort for design and set-up of process modules. The approach is to provide as many pre-defined elements as possible and to provide standard interfaces. However, it turned out that room for individual adaptions needs to be foreseen, as different applications have different requirements and that a one-fits-all solution is hardly achievable. Therefore the construction kit provides a pool of elements, which the developer can choose from and still provides room for individual design towards the specific requirements of the application.

To test the construction kit, a number of reference solutions were modeled. Based on these elements a number of different process modules were realized in CAD. The effort during modeling was significantly reduced by access to the pre-defined elements. However, the effect was not compared to commercially available solutions yet.

A prototype of a process module based on the construction kit will now be realized to evaluate the concept. The results will be used to re-iterate and optimize the concept and the included elements. An extension towards adaption of already existing solu- tions to new requirements will be included. The framework will furthermore be extended by supportive software tools for the construction kit and the specification micro assembly tasks.

Fig 1 and

 1 Fig 2, re-iterations during the design phase are possible and part of the concept.

Fig. 3 .

 3 Fig. 3. Sample configuration of a process module

Fig. 4 .

 4 Fig. 4. Sample configurations of process modules based on the process module construction kit

SWOT -Strength, Weaknesses, Opportunities, Threats

ACKNOWLEDGEMENTS

This paper has emerged from the project «PRONTO/VOLPROD», which has been sponsored by the German Federal Ministry of Education and Research (BMBF) in the funding program "SpitzenCluster MicroTec SüdWest" and is administered by the project sponsor VDIVDE-IT in Berlin.


Imane Ballouki
email: imane.ballouki@gmail.com

Latifa Ouzizi
email: louzizi@yahoo.fr

Mohammed Douimi
email: mdouimi@yahoo.fr

A multi-agent approach to support simultaneous design of a product and its supply chain

Keywords: simultaneous design, product design, supply chain design, multi-agent system, I

in recent decades, the simultaneous design of a product and its supply chain has become a trend in the manufacturing industry. This approach, requiring massive data sharing, allows different designers to collaborate in order to choose the best product design along with its corresponding supply chain, taking into account cost, quality, and time.

To get a successful collaboration between designers, we need to model communication flow between product and supply chain designers during all product lifecycle. This model must be simple and easy to adopt by any company structure.

In this paper, we present a multi-agent approach that aims to support communication between product and supply chain designers in a simultaneous design.

Unified modeling language (UML) is used to model this approach.

INTRODUCTION

Several research focuses on the product and supply chain design. Indeed, most previous works have treated supply chain design only after the product design is finalized. Recently, research studies showed that 85% of logistics costs are driven by design choices [START_REF] Laurentie | Processus et méthodes logistiques[END_REF] and over 70% of product cost is determined by decisions during this phase of development [START_REF] H'mida | L'estimation des coûts en phase de conception: un cadre d'aide à la décion[END_REF]. Also, most benefits of collaboration among supply chain partners lie in the design phase of the product lifecycle since the cost of design changes increases as the design phase of the product lifecycle ends and the manufacturing phase starts [START_REF] Mehmet | development of a simultaneous design for supply chain process for the optimization of the produc design and supply chain[END_REF]. Therefore, it is important to integrate product architecture decisions and supply chain decisions during the early stages of the product development. [START_REF] Nepal | Matching product architecture with supply chain design[END_REF].

Thus, a lot of value is given to cooperation and coordination between supply chain partners and product designers. Following these findings, many studies, approaches, tools and methods were conducted.

The majority of works dealing with the simultaneous design are based on analytical modeling approaches (analytical deterministic models, stochastic analytical models …) [START_REF] Yang | Joint Optimization for Coordinated ConÞguration of Product Families and Supply Chains by a Leader-Follower Stackelberg Game[END_REF]. However, these studies have several limitations: they do not model the interactions between the different actors. Models proposed do not explicit the behavior of actors, particularly their reactive, independent and proactive nature [START_REF] Anane | Les approches agents pour la coordination d'activités dans les chaines graphiques[END_REF]. Indeed, simultaneous design needs multidisciplinary workgroups to communicate and cooperate [START_REF] Yeh-Chun Juan | A process-oriented multi-agent system development approach to support the cooperationactivities of concurrent new product development[END_REF] in order to choose the best product design and supply chain configuration in terms of cost, quality and time. This leads to the emergence of a new kind of need: the creation of systems involving all actors of the designing activity (product designers and supply chain partners) and facilitating communication among product lifecycle.

Multi agent-systems (MAS) have been considered as very promising enablers for providing a computer supported cooperative environment in areas that require coordination, negotiation, and communication among various organization units [START_REF] Nwana | Software agents: An overview[END_REF]. That is why the agent approach is an interesting technology to model the complexity of productsupply chain design.

Actually, in all works dealing with concurrent design of product and its supply chain, we could not distinguish a study that adopts the multi-agent approach. In addition to that, the agent approach was either used in the product design only [START_REF] Yeh-Chun Juan | A process-oriented multi-agent system development approach to support the cooperationactivities of concurrent new product development[END_REF] or in the management of the supply chain [START_REF] Habib Nfaoui | AN APPROACH OF AGENT-BASED DISTRIBUTED SIMULATION FOR SUPPLY CHAINS: NEGOTIATION PROTOCOLS BETWEEN[END_REF] [START_REF] Gamoura | Modélisation et Simulation des Processus Collaboratifs dans les Chaînes Logistiques : Une Approche Multi Agents[END_REF]. From this came the idea of modeling a system based on autonomous and intelligent agents that aim to understand and study the behavior of designing actors promoting collaboration.

In this work, we study the case of product re-design. The modified product needs a reconfiguration of the old supply chain (for example: new supplier, new production site or technologies, contract termination with a former supplier...). We propose a framework of product-supply chain design processes and a multi agent system for communication and negotiation between partners.

This paper is organized as follow: the next section presents a literature review of works that of simultaneous design and multi-agent systems. In the section III, we propose a framework of simultaneous design of product and its supply chain. Then, the agent approach adopted to support the collaboration between designers of a product and its supply chain is discussed in a detailed way. Finally, a meta-model is presented with UML explaining the MAS approach that was adopted in our research.

II. LITERATURE REVIEW

Researches that are considering the simultaneous design of the product and its supply chain are very recent. Before that, the priority was given to the product design. [START_REF] Appelqvist | Modelling in product and supply chain design: literature survey and case study[END_REF] [START_REF] Appelqvist | Modelling in product and supply chain design: literature survey and case study[END_REF] justify this by the fact that the cost of products is usually much higher than the cost of production and logistics. However, logistics costs have undergone significant changes in recent years. Many researches dealt with simultaneous design of product and its supply chain, use analytic models. [START_REF] Salvador | Supply chain configurations for mass customization[END_REF] [START_REF] Salvador | Supply chain configurations for mass customization[END_REF] qualitatively analyze how the supply chain including manufacturing and distribution networks should be configured when different degrees of customization, i.e. high-level or moderate level, are adopted. [START_REF] Huang | Towards integrated optimal configuration of platform products, manufacturing processes, and supply chains[END_REF] [START_REF] Huang | Towards integrated optimal configuration of platform products, manufacturing processes, and supply chains[END_REF] explore the integrated optimization of platform products, manufacturing processes and supply chains using Generic Bill of-Material (GBOM) for representing product families and the genetic algorithm for solving the optimization problem, respectively. Also, in recent works [START_REF] Huang | Integrated configuration of platform products and supply chains for mass customization: A game theoretic approach[END_REF] Huang et al. apply Nash game theory to optimize platform product family and supplier selection decisions. For El Maraghy and Mahmoudi (2009) [START_REF] Elmaraghy | Concurrent design of product modules structure and global supply chain configurations[END_REF], they proposed a multi-period model that optimizes simultaneously BOM and supply chain choices. The model proposed for every product several BOM alternatives and one of them is selected in the optimal solution. In addition to that , Baud-Lavigne et al. (2012) [START_REF] Baud-Lavigne | Conception conjointe de nomenclatures et de la chaine logistique pour une famille de produits : outils d'optimisation et analyse[END_REF] proposed an analytical approach using mixed linear programming to optimize the supply chain with product standardization. In this work, Baud Lavigne et al. showed the impact of product standardization on supply chain configuration. [START_REF] Kumar | A heuristic-based approach to integrate the product line selection decision to the supply chain configuration[END_REF] [START_REF] Kumar | A heuristic-based approach to integrate the product line selection decision to the supply chain configuration[END_REF] also developed a mixed integer linear programming (MILP) models to simultaneously optimize product line decisions and supply chain configuration. Finally, Dong Yang,et al (2015) [START_REF] Yang | Joint Optimization for Coordinated ConÞguration of Product Families and Supply Chains by a Leader-Follower Stackelberg Game[END_REF] formulates joint configuration of a product family and its supply chain as a leader-follower Stackelberg game that is enacted through a bi-level hierarchical optimization mechanism to model the coordination between two selfinterested decision makers for product family configuration and supply chain configuration, .Dong Yang, et.al formulates A nonlinear, mixed integer programming model for the bi-level joint decision in the leader-follower game.

In the other side, recent years have known an important scientific production focusing on the principles of collaboration via multi-agent systems. These works generally deal with the product design or the supply chain management. For example, Nfaoui (2007) [START_REF] Habib Nfaoui | AN APPROACH OF AGENT-BASED DISTRIBUTED SIMULATION FOR SUPPLY CHAINS: NEGOTIATION PROTOCOLS BETWEEN[END_REF] present a generic model allowing a flexible modelling of the supply chain by multi-agent properties. He tested a set of negotiation protocols that were modeled with the AUML (Agent unified modeling language). The used tests show that it is possible, by connecting the agents to the information systems of supply chain actors (APS or ERP, etc.), to bring an important help to the collaborative decision-making. Gamoura and Chehbi (2013) [START_REF] Gamoura | Modélisation et Simulation des Processus Collaboratifs dans les Chaînes Logistiques : Une Approche Multi Agents[END_REF] propose an approach based on agents for modeling and simulating a collaborative supply chain, Gamoura proposes a framework of modeling and simulating called "MACSC" that is based on BDI (Belief-desire-intention) agents operating in an AGR organization . Concerning product design using MAS, Yeh-Chun Juan (2009) [START_REF] Yeh-Chun Juan | A process-oriented multi-agent system development approach to support the cooperationactivities of concurrent new product development[END_REF] propose a process-oriented multi-agent system development approach to support the cooperation-activities of concurrent new product development among workgroups that are working on product design. These researches have proven the effectiveness of MAS in a collaborative environment.

In the next section, we will present a framework modeling simultaneous design of product and its supply chain. This model will be a basis of our studies.

III. A FRAMEWORK TO MODEL SIMULTANEOUS DESIGN OF PRODUCT AND ITS SUPPLY CHAIN:

The proposed framework for simultaneous design of product and its optimized supply chain is shown in figure 1. This framework uses two conceptual viewpoints: product design and supply chain configuration.

Several design scenarios or alternatives of bill-ofmaterial are generated in the re-design step of product. In fact, the new product design (redesign) can affect either product components or the configuration of the supply chain or both at once. That means we can have problems of allocation or/and location of different partners. We assume that marketing studies about the future demand of product are done (it's not the object of this paper).

Fig. 1 describes the structural links between product design and supply chain configuration. These links presents the information flow. The supply chain is designed as a set of levels [START_REF] Latifa | Planification de la production par CO-décisione et négociation de l'entreprise virtuelle[END_REF] following the levels of bill of materials of the product, starting from supplier level. The supply chain design consists on choosing each level in relationship with a predecessor level (customer) and a successor level (supplier).

Figure 2 shows an illustrative example of the initial product P and the two redesign alternatives suggested. We suppose that the initial product is composed of components C1, C2, and C3 and raw materials Rm1, Rm2 and Rm3. Components C4, C5, and C6 are new ones. To each product design alternative corresponds a supply chain that ensures the achievement of all operations related to the life cycle of a product. We evaluate the cost of each supply chain alternative (fig. 3) so as the best product alternative is chosen according to supply chain costs. To facilitate the communication between product designers and supply chain partners following this framework, we suggested an agent approach based on levels. The architecture of the proposed model will be detailed in the next section. As each design project, we need a collaborative system for information exchanging and negotiating to make the best decision.

Based on the framework presented in the previous section, the multi-agent system proposed is divided into two levels: product design level and supply chain configuration level.

A. Conceptual model : a multi-agent system for simultaneous design of product and its supply chain : According to Ouzizi [START_REF] Latifa | Planification de la production par CO-décisione et négociation de l'entreprise virtuelle[END_REF], an architecture based on levels enables the control of consistency at each level. It ensures horizontal coordination (between agents of the same level) and vertical coordination (between agents of different levels). The system contains two different multi agent systems that communicate and negotiate design choices (fig. 4). -Communication in a horizontal structure: between agents that are at the same level. There is no supervisor, or client server. This is the case of collaborative work in which each agent performs a task to complete one job.

-Communication in a vertical structure: the agents are structured by levels, and locally, a horizontal communication can be found at the same level. In the proposed framework, communication is done by two main agents: "Communication agent" and "Negotiation agent". In addition to communication agents, the framework contains Design agents with decision making tools that are supporting designers in design activities. In the next section, we will present and model multi-agent systems according to each level (product design and supply chain configuration)

B. Modeling the multi-agent system for product design:

Many alternatives of the initial product P are proposed P (i). The product design agent is a software agent that assist human designers in product design activities. It integrates CAD (Computer Aided Design) systems .This agent is used by the designer to perform key design tasks through cooperation with other software agents. The product agent design ensures Constraints satisfaction. These constraints are: -Product design constraints: among product elements (i.e. features, parts, or sub-assemblies) in different forms, such as equation, rule...etc., corresponding to the design requirements.

-Supply chain constraints: in fact, in a simultaneous design both product design and supply chain constraints must be involved, so supply chain constraints must be respected by product designers. All these constraints are defined before starting product design.

The role of this agent is presented using UML class diagram. It illustrates the links between different parts of design activity and the product design agent. C. Modeling the multi agent system of supply chain configuration: Supply chain configuration contains several levels, these levels are hierarchically configured according to the bill of materials of product alternatives. When receiving a product alternative, the supply chain configuration starts from suppliers' selection, then comes the production process design, distribution configuration, and finally recycling process and centers are selected.

To each supply chain level, we associate an agent that is fitted out of a decision support tool according to each design activity, selected designs must have the lowest cost and respond to product constraint.

The different agents that constitutes the multi agent system of supply chain configuration are: -Supplying agent: this agent is responsible of supplier's selection. The supplier network may contain a set of existing suppliers S (1,1,1) or a set of new suppliers S (1,1,2). Actually, after receiving the product alternative P(i) from product design, supplying agent select from the set S(1,1,1) the appropriate suppliers that can provide the raw materials necessary for P(i) assembly and that are respecting both product design constraints and supply chain design constraints. In case there is a lack of raw materials (no existing suppliers or suppliers cannot provide the required quantity), supplying agent sends a tender to new suppliers S(1,1,2). New suppliers propose different offers, and then the supplying agent select the best offer that respond to design constraints. -Production agent: After suppliers' selection, production configuration must be done according to product bill-ofmaterial and assembly modules. At this stage, different choices must be made, different constraints are imposed: product demand, delay constraints, existing centers' capacities, type of existing technologies, technologies' capacity, labors' capacities...etc. According to this constraints, production agent select existing production centers or existing technologies that has the capacity to deal with product demand or delay constraints. In case product demand is high and/or delay is short, production agent can select the implementation of new technologies, and/or new centers or asking for subcontractors. -Distribution agent: After selecting production elements, many constraints are added to design constraints. The distribution agent is responsible of selecting warehouses and transport according to product characteristics like product package model. Actually, constraints changes and design tasks that are made by the previous agents can affect the distribution network or transport. On the one hand, if capacity of existing warehouse is low, new warehouses must be implemented, and more transport must be added. On the other hand, product package constraints can affect transports' choice. Fig. 8 is a class diagram that present different links that distribution agent is making: In the end of supply chain configuration, alternative and supply chain cost are send to the product designer who decide to validate the proposed configuration or making another product alternative. In the next part, we present how this two levels can communicate and manage their negotiations.

D. Modeling communication between product and supply chain designers:

To make a link between product and supply chain designers, we need to model agents that facilitate communication, and data transfer. These agent can make horizontal communication (between agents of the same level) or vertical communication (between product designers and supply chain designers). These agents are: communication agent and negotiation agent.

 Communication agent:

This agent is responsible of communicating information, documents, costs and alternatives related to the design. It works primarily with a communication protocol (fig. 10). This protocol can achieve two mainly main-method: -SendProposal(): to send proposals of designers.

-AcceptProposel(): to confirm acceptance of the proposal. The negotiation is the mechanism by which the agents can establish a common agreement. In case of intelligent agents and MAS (multi-agent system), the negotiation is considered as a basic component of interaction because the agents are autonomous [START_REF] Jennings | Automated negociation : Prospects,methods and challenges[END_REF]. Negotiation agent is defined as follow:

In designing steps, many constraints are generated from different design agents. If a constraint is not respected by a design agent, negotiation agent intermediate and then the design agent responsible of constraint violation has two choices: -Modify his design as to respect constraints imposed by other designers -Negotiate with design agent that imposed the violated constraint to change it. In fact, when there is a constraint violation associated to the parts designed by different designers, the constraint violation message should be delivered to the designers who might be affected by the proposed changes. This agent can achieve these main methods:

-SendProposal() : design agent send the proposed design to the design agent that imposed the violated constraint.

-Accept_proposal(): permits to end the conversation between the two members if they agree on changes. If a member is still not satisfied with the changes he can:

-RefuseProposal(): we choose a maximum number of iterations n (number of modifications). If the number of iterations is exceeded, the Product design agent will be involved as a mediator and decide about changes that must be done (Fig 11). In this paper, we present a model of multi agent system that ensure the simultaneous design of product and its supply chain. This model present a general view of proposed system and interactions between different designers.

The presented model will be a basis for our next works that will deal with decision making tools in order to give to the design agents the capacity to make decisions and choose the best product alternative according to its supply chain costs.

Figure 1 :

 1 Figure 1: simultaneous design (product-supply chain) framework

Figure 2 :

 2 Figure 2: Illustrative example of redesign alternatives bill-of-material

Figure 3 :

 3 Figure 3: Examples of Supply chain configuration corresponding to different bill-of-material

Figure 4 :

 4 Figure 4: Multi agent system for simultaneous design Communication between levels is done as follows:-Communication in a horizontal structure: between agents that are at the same level. There is no supervisor, or client server. This is the case of collaborative work in which each agent performs a task to complete one job.-Communication in a vertical structure: the agents are structured by levels, and locally, a horizontal communication can be found at the same level. In the proposed framework, communication is done by two main agents: "Communication agent" and "Negotiation agent". In addition to communication agents, the framework contains Design agents with decision making tools that are supporting designers in design activities. In the next section, we will present and model multi-agent systems according to each level (product design and supply chain configuration)

Figure 5 :

 5 Figure 5: class diagram of product design process

Fig. 6

 6 present a class diagram model of supplying agent activities and its relation with other design elements.

Figure 6 :

 6 Figure 6: class diagram of supplier's selection process

Figure. 7

 7 is a class diagram modeling production agent activities.

Figure 7 :

 7 Figure 7: class diagram of production choices

Figure 8 :

 8 Figure 8: class diagram of distribution choices -Recycling agent: Constraints added by the other agents can affect the recycling means, or centers' network. In fact, the type of raw materials and assembly means are important constraints that should be taken by recycling agent. Fig.9 present class diagram that model different tasks made by recycling agent.

Figure 9 :

 9 Figure 9: class diagram of recycling choices

Figure 10 :

 10 Figure 10:Communication protocol  Negotiation agent:The negotiation is the mechanism by which the agents can establish a common agreement. In case of intelligent agents and MAS (multi-agent system), the negotiation is considered as a basic component of interaction because the agents are autonomous[START_REF] Jennings | Automated negociation : Prospects,methods and challenges[END_REF]. Negotiation agent is defined as follow:In designing steps, many constraints are generated from different design agents. If a constraint is not respected by a design agent, negotiation agent intermediate and then the design agent responsible of constraint violation has two choices: -Modify his design as to respect constraints imposed by other designers -Negotiate with design agent that imposed the violated constraint to change it. In fact, when there is a constraint violation associated to the parts designed by different designers, the constraint violation message should be delivered to the designers who might be affected by the proposed changes. This agent can achieve these main methods:-SendProposal() : design agent send the proposed design to the design agent that imposed the violated constraint.-Accept_proposal(): permits to end the conversation between the two members if they agree on changes. If a member is still not satisfied with the changes he can:-RefuseProposal(): we choose a maximum number of iterations n (number of modifications). If the number of iterations is exceeded, the Product design agent will be involved as a mediator and decide about changes that must be done(Fig 11).

Figure 11 :

 11 Figure 11: Negociation protocol E. Class diagram of the general multi-agent system model: In the following class diagram we regroup all agents presented in previous parts, this model show the links between all agents. In this model, Product designers and supply chain designers makes different design alternatives using "Design agents", and generate supply chain "costs". At the end of every design step, "constraints" are added by "designers" and must be respected by design agents. Design agents can communicate with each other and send different proposals via communication agent. If a constraint conflict is triggered, negotiation agent intermediate to make negotiation between the design agent and other agents concerned by constraint violation. (fig.12)

Xème Conférence Internationale : Conception et Production Intégrées, CPI 2015, 2-4 Décembre 2015, Tanger -Maroc. Xth International Conference on Integrated Design and Production, CPI 2015, December 2-4, 2015, Tangier -Morocco. Identify applicable sponsor/s here. If no sponsors, delete this text box (sponsors).


Fatima Ezzahra Saber
email: fatimaezzahra.saber@usmba.ac.ma

Mohamed Ouahi
email: mohamed.ouahi@usmba.ac.ma

Abdelmjid Saka
email: abdelmjid.saka@gmail.com

Vehicle Dynamics and Steering Angle Estimation Using a Virtual Sensor

Keywords: Virtual Sensor, State Space, Modeling, Vehicle Dynamics, Yaw-rate, Steering Angle

Vehicle stability control systems called ESP, vehicle dynamics control (VDC), yaw stability control (YSC), and so forth are important active safety systems used for maintaining lateral stability of the vehicles under such adverse conditions. This paper investigates the notion of virtual sensing which is a promising concept for yaw stability control and is an attractive option for vehicle manufactures as it reduces sensor cost, maintenance, and machine downtime.

A frequent situation in automotive control applications is when an unknown input needs to be estimated from available state measurements. The virtual sensor proposed use measurements of lateral acceleration, steering angle as unknown input signals and provide the yaw rate angle estimate as output. Stability conditions of this virtual sensor are given in terms of Linear Matrix Inequalities (LMI). To illustrate the proposed methodology, a linear bicycle model is considered. The observer(virtual sensor) is confronted to data issued from the Callas vehicle simulator.

I. INTRODUCTION

Road vehicle yaw stability control systems like electronic stability program (ESP) are very important for the safety of the driver and passengers during extreme lateral maneuvers or during lateral maneuvers under adverse environmental conditions like driving on snow or ice, sudden tire pressure loss, or sudden side wind.These mechatronics systems used for maintaining lateral stability of the vehicle, based their calculations on measurements from sensors (accelerometers, gyrometers, steering wheel angle, wheels position sensors . . .). Nevertheless, some variables are actually unreachable to measure (longitudinal acceleration, side slip angle,yaw rate, tire/road forces. . .) Vehicle yaw rate is the key parameter that needs to be known by a yaw stability control system. In this paper, yaw rate is estimated using a virtual sensor Some observers can be done to estimate these variables [START_REF] Stéphant | Contribution à l'étude et à la validation expérimentale d'observateurs appliqués à la dynamique du véhicule[END_REF], [START_REF] Baffet | Estimation of vehicle sideslip, tire force and wheel cornering stiffness[END_REF]. Researches are conducted to develop low cost sensors to acquire tire/road forces [START_REF] Gobbi | A smart wheel for improving the active safety of road vehicles[END_REF], [START_REF] Frayer | Measurement of bearings loads using ductile wire inserts[END_REF]. Such instrumentation has been considered especially by builders automotive [START_REF] Takahashi | Development of tire and moment measurement system mounted on a wheel hub unit[END_REF], of Roulementier [START_REF] Mol | Method and sensor arrangement for load measurement on rolling element bearing based on model deformation[END_REF] by SNR-NTN company [START_REF] Duret | Method for estimating the components of the force torsor that are applied to a bearing[END_REF], [START_REF]Method for estimating the components of the force torsor that are applied to a bearing[END_REF], with partners [START_REF] Kwapisz | Instrumented bearing for force and moment measurements[END_REF], [START_REF] Kwapisz | Reconstruction du torseur des efforts transmis par le roulement de roue à partir de mesures de déformation[END_REF] or SKF company [START_REF] Holweg | Vehicle dynamics and safety[END_REF] of have show the feasibility of the integration of forces measurements in a future generation of affordable wheel bearing.

Since the experience of most drivers is limited to driving within the linear range of vehicle handling behavior, It is generally considered desirable to reduce the difference between the normal vehicle behavior and that at the limit. This improves the chances of a typical driver to maintain control of the vehicle in emergency situations. This goal can be accomplished by active chassis control systems such as brake control systems or active rear wheel steer. The purpose of control is to bring the vehicle yaw rate response and/or the vehicle slip angle into conformance with the desired yaw rate and/or slip angle.

With this objective, this article presents a virtual sensor to estimate simultaneously vehicle side slip angle, yaw rate and the steering angle considered as an unknown input. The yaw rate is considered as the only available measure.

The estimated state and unknown input can then be used as input of actual ADAS (Advanced driver assistance systems). Several studies were conducted to estimate the unknown inputs the linear dynamical systems [START_REF] Guan | A novel approach to the design of unknown inputs observers[END_REF], [START_REF] Maquin | Estimation of unknown inputs in linear systems[END_REF], [START_REF] Stotsky | Simple unknown input estimation techniques for automotive applications[END_REF], [START_REF] Daafouz | Une approche intrinsèque des observateurs linéaires à entrées inconnues[END_REF] and [START_REF] Darouach | Complements to full order observer design for linear systems with unknown inputs[END_REF]. Edwards and Spurgeon have proposed two methods based on sliding mode observers for detect and estimate the sensor fault [START_REF] Edwards | Sliding mode observers for fault detection and isolation[END_REF].

The article of [START_REF] Solmaz | real-time multiplemodel estimation of center of gravity position in automotive vehicles[END_REF] uses a bicycle model to estimate the center of gravity of a motor vehicle. [START_REF] Marino | asymptotic sideslip angle and yaw rate decoupling control in four-wheel steering vehicles[END_REF] present this model, a four wheel steering, for control side slip angle and yaw rate.

In this first study, a vehicle bicycle model [START_REF] Segel | Theorical prediction and experimental substantiation of the response of the automobile to steering control[END_REF] is used to design the observers. The longitudinal speed of the vehicle is supposed to be constant, lateral tires forces linear with respect to side slip angle and sprung mass movements are neglected. This kind of model is valid for low lateral dynamics (|ÿ| < 0, 4g ). Observer is designed using the "unknown input with unknown input is independent of the output" framework [START_REF] Boutayeb | Generalized state-space observers for chaotic synchronization and secure communication[END_REF], [START_REF] Liu | Synthèse d'observateurs à entrées inconnues pour les systèmes non linéaires[END_REF] and [START_REF] Darouach | Full-order observers for linear systems with unknown inputs[END_REF]. The gain of the observer is computed by solving linear matrix inequalities [START_REF] Boyd | Linear matrix inequalities in system and control theory[END_REF] and [START_REF] Hassibi | A path-following method for solving bmi problems in control[END_REF]. The organization of the rest of the paper is as follows. In Section 2 and its subsections presents the vehicle modeling and dynamic virtual sensor design is explained. Simulation results obtained using the virtual sensor are given, observer is tested and confronted to data issued from the vehicle simulator Callas distributed by Oktal company In Section 3, and the paper ends with conclusions. Notations are explained in section VI.

II. VEHICLE DYNAMICS MODEL

Fig. 1. bicycle Model [START_REF] Ouahi | Redefining automotive supervision using new sensor technology[END_REF] Lateral vehicle dynamics has been studied since the 1950s. In 1956, Segel [START_REF] Segel | Theorical prediction and experimental substantiation of the response of the automobile to steering control[END_REF] presented a vehicle model with three degrees of freedom in order to describe lateral movements including roll and yaw. If roll movement is neglected, a simple model known as the bicycle model is obtained. This model is currently used for studies of lateral vehicle dynamics (yaw and sideslip).

The bicycle model (1) used in this paper is obtained by application of the fundamental principal of dynamics. Variables are presented on Fig. 1. Inputs of model are lateral tire/road forces projected onto the vehicle frame,The equations of this model are described as follows:.

β = (F yf + F yr )/(V G M V ) - ψ ψ = (L f F yf -L r F yr )/I zz (1)
Using the assumptions of low lateral dynamics, small steering and side slip angle, lateral forces are proportional to the tires side slip angles. They can be written as:

F yf = D f β f F yr = D r β r (2)
Tires side slip angles (front and rear) can be approximated using kinematic relations. The side slip angle of front tires β r is between P 1 and V f . The side slip angle of rear tires β r is between P 2 and V r .

β f = δ -β - L f ψ V G β r = -β + Lr ψ V G (3)
Linear tire forces are:

F yf = D f (δ -β -L f ψ V G ) F yr = D r (-β + Lr ψ V G ) (4)

III. LINEAR UNKNOWN INPUT OBSERVER WITH UNKNOWN INPUT IS INDEPENDENT OF THE OUTPUT

The aims of the observer presented in this paper are to calculate the vehicle lateral state variables and the steering angle that is not measured. Assuming that the only available measure is the yaw rate and we want to estimate center of gravity side slip angle, yaw rate (states) and the steering angle (unknown input). The proposed observer will be an linear Unknown Input Observer with Unknown Input is Independent of The Output UIO.

A. State-space model

By substituting F yf and F yr (4) in equation ( 1), the dynamics of the bicycle model can be written as a linear system with unknown input:

Σ ẋ = Ax + Rδ y = Cx (5)
In this expression,

x = β ψ is the state vector, δ is the unknown input and y = ψ is the output vector. A is the state matrix, R is the input matrix associated with the unknown input, C is the observation matrix.

A = -D f -Dr M V V G LrDr-L f D f M V V 2 G -1 LrDr-L f D f Izz -L 2 r Dr-L 2 f D f IzzV G R = D f M V V G L f D f Izz C = 0 1

B. Observer design

It often happens that all state variables of a system are not accessible to measurement or input not measurable because of very expensive sensors or absence of technology. The idea is to rebuild the state and the input not measurable from information available that is to say the output and known inputs.

An unknown input observer (UIO) estimates simultaneously the state x and the unknown input δ by using the available measurements that constitute the output y (Fig. 2).

Fig. 2. Unknown inputs observer principle

For the linear time invariant (LTI) systems, a lot of observation techniques can be applied (Kalman filter, Luenberger observer, sliding mode observer, ...). To be able to characterize the robustness performances, the gains of observer UIO are obtained by solving a Linear Matrices Inequalities problem.

The full order observer ( [START_REF] Boutayeb | Generalized state-space observers for chaotic synchronization and secure communication[END_REF] and [START_REF] Liu | Synthèse d'observateurs à entrées inconnues pour les systèmes non linéaires[END_REF]) for system (5) can be expressed as:

The system (5) respects the following assumptions :

• The unknown inputs are not involved in the measure.

• The number of unknown inputs is less or equal to the number of measures. • The measure is one of the state variables..

• The matrix R is full column rank Rank(R) = 1.
An unknown input observer exists if and only if the system (1) is detectable (observable) and the number of unknown inputs less than or equal to the number of measures [START_REF] Darouach | Full-order observers for linear systems with unknown inputs[END_REF].

The observability matrix of this new system is written as:

O = C CA The observability matrix (O) is full rank (rank(O) = 2), so the system (5) is observable. It is noted that (L r D r = L f D f ) is always available.
The numerical value of the determinant of this matrix in the case of the studied vehicle is -32.3171.

C. Observer design UIO with Unknown Input is Independent of The Output

The full order observer ( [START_REF] Darouach | Full-order observers for linear systems with unknown inputs[END_REF], [START_REF] Yang | Observers for linear systems with unknown inputs[END_REF], [START_REF] Guan | A novel approach to the design of unknown inputs observers[END_REF] and [START_REF] Liu | Synthèse d'observateurs à entrées inconnues pour les systèmes non linéaires[END_REF]) for system (1)can be expressed as:

obs ż = N z + Ly x = z -Ey (6)
Where z is the dynamic of the observer. x = β ψ T is the observed state. N , L and E are unknown matrices which must be determined such that x will asymptotically converge to x.

Define the observer reconstruction error by:

e = x -x = z -x -Ey
Then, the dynamic of this observer error is:

ė = (I + EC)(Ax + Rδ) -(N x + (LC + N EC)x) Let P = I + EC (7)
Then, the observation error dynamic is

ė = N e + P Rδ + (P A -N P -LC)x (8)
The estimation error converges asymptotically to 0 if and only if the matrices N , L and E are choose to satisfy the following conditions:

   N is a stable matrix (Hurwitz matrix) P R = (I + EC)R = 0 LC = P A -N P (9)
Equation ( 8) reduces to the homogeneous equation

ė = N e (10)
The following paragraphs present the determination of matrices N , E and L satisfying the constraints [START_REF] Kwapisz | Instrumented bearing for force and moment measurements[END_REF].

1) Matrix E:

This matrix E is calculated using the second equation of system [START_REF] Kwapisz | Instrumented bearing for force and moment measurements[END_REF], the numerical solution of this equation is based on the calculation of the pseudo inverse of matrix CR, a possible solution is:

E = -R(CR) T [(CR)(CR) T ] -1 (11)
From equations ( 7) and ( 11), the matrix P can then be expressed as:

P = I -R(CR) T [(CR)(CR) T ] -1 C (12)
2) Matrix L: The matrix L is determined from the third equation [START_REF] Kwapisz | Instrumented bearing for force and moment measurements[END_REF].

LC -P A + N P = 0 ⇒ N (I + EC) + LC -P A = 0 Then N = P A -KC (13)
With

K = (P A -KC)E + L (14)
Therefore, the matrix L is given by:

L = K(I + CE) -P AE (15)
3) Matrix N : Determining the matrix L requires the determination of the matrix N (matrix K).

The Matrix L is chosen so that the observation error ( 10) is asymptotically stable.

Using the Lyapunov theorem, the convergence of the observer is guaranteed if there exists a symmetric positive matrix X that the Lyapunov function V (e) = e T Xe presents the following properties:

∀e = 0 V (e) > 0 V (e) < 0
This can be reformulated using equation [START_REF] Kwapisz | Reconstruction du torseur des efforts transmis par le roulement de roue à partir de mesures de déformation[END_REF]:

X > 0 N T X + XN < 0
Applying the Schur complement [START_REF] Boyd | Linear matrix inequalities in system and control theory[END_REF], [START_REF] Hassibi | A path-following method for solving bmi problems in control[END_REF] -X 0 0 N T X + N X < 0

Since N = P A -KC (equation ( 13)), which allows:

-X 0 0 (P A -KC) T X + X(P A -KC) < 0 (16)
Noticing that the inequality ( 16) is bilinear compared to the variables K and X. A resolution method is to conduct a change of variable:

W = XK
The linear matrix inequalities system ( 16) can be written as:

-X 0 0 (P A) T X + X(P A) -(C T W T -W C) < 0
The gain matrix is obtained by first solving the LMI with respect to X and W . In a second time, K is determined by:

K = X -1 W (17)
Then, the matrices L and N is written:

N = P A -X -1 W C L = X -1 W (I + EC) -P AE (18)
4) Estimation of unknown input: The unknown input δ can be expressed from the output of system (5):

δ = R + ( ẋ -Ax) (19)
If state x is known, we can estimate δ (steering angle) from equations [START_REF] Marino | asymptotic sideslip angle and yaw rate decoupling control in four-wheel steering vehicles[END_REF]. What gives, when we replace x (6) by its expression:

δ = R + ( ż -E ẏ -Ax)
In practice the derivative can be approximated by the formula:

sY (s) s 1 + τ s Y (s)
Where s the Laplace operator and τ is a real number chosen to have ẏ sy , so τ must be small compared to the time constraint of the system to determine.

5) In summary:

To summaries, the observer linear Unknown Input Observer with Unknown Input is Independent of The Output UIO allows calculating simultaneously vehicle side slip angle, yaw rate and steering angle (unknown input) by using front lateral tire forces. It's written

U IO                ż = N z + L ψ βψ = z -E ψ δ = R + ż -E s 1 + τ s ψ -A βψ (20)

IV. NUMERICAL RESULTS

A. Vehicle simulator

Callas is a realistic vehicle simulator software distributed by Oktal company (http://www.oktal.fr). According to [START_REF] Lechner | Méthodologie de validation du logiciel de dynamique automobile callas[END_REF], it has been validated by car manufacturers and French research institutions including INRETS ("Institut national de recherche sur les transports et leur sécurité"). Callas is a physical based model that takes into account numerous aspects among which vertical dynamics (suspension, tires, road profile), kinematics, elasto-kinematics, tire adhesion, aerodynamics, . . .

B. Simulation environment

Data used to evaluate observer performance are issued from the Callas simulator and the simulation environment is Matlab-Simulink.

Parameterization of open-loop model ( 5) used in the construction of observers is verified using a linear stationary bicycle model, whose input is the steering angle measured and considered as known δ m . This model ( 5) is called OLM in the paper.

The results of observer UIO ( 20) is compared with the outputs of the simulator CALLAS.

The observer has been tested in the case of an ISO double lane change at 40km/h and 90km/h. Initial conditions of the model and observers states are zero.The route to the lateral strain of the vehicle is given in Fig. 3. yaw rate of the vehicle (bicycle model) is given in Fig. 4 for the test at 40km/h and in Fig. 5 for the test at 90km/h.

These figures illustrate the validity domain of the linear bicycle model. At 40km/h, the lateral acceleration is low and the model is representative. On the other hand, at 90km/h, tires are positioned in their transient zone, model is less representative. For this test, the maximum lateral acceleration is 5m.s -2 .

E. ISO Double lane change 40km/h

Fig. 6. Observer : side slip angle and steering angle estimations for ISO double lane change 40km/h. Callas simulation compared with unknown input observers UIO [START_REF] Segel | Theorical prediction and experimental substantiation of the response of the automobile to steering control[END_REF]. Recall that the steering angle is not measured.

Estimations of vehicle side slip angle, yaw rate (state variables) computed by observer UIO are compared to the values issued from the Callas simulator used here as reference. The estimation of the steering angle (the unknown input) is compared to the reference computed by the virtual driver of the simulator. The side slip angle, yaw rate and unknown steering is treated on Fig. 6. This indicates that not measured states and the unknown input are correctly calculated by observer based on yaw rate measures. However, it is noteworthy that observer (and the underlying open-loop model) under estimated the side slip angle. It is important to remind here that the steering angle is supposed not measured but is well computed. [START_REF] Segel | Theorical prediction and experimental substantiation of the response of the automobile to steering control[END_REF]. Recall that the steering angle is not measured.

F. ISO Double lane change 90km/h

For the ISO double lane change test at 90km/h, vehicle side slip angle is presented and unknown steering angle on Fig. 7 This shows the good performances for observer for all estimations. The used tire model (linear and constant cornering stiffness) reached its representative limits. This over estimation is amplified by observer. Performances on yaw rate estimation of their part are enhanced. Computation of the unknown steering is quite good.

G. Errors of estimates

The error of the observer UIO for estimate side slip angle, yaw rate and steering angle of an ISO double lane change at 40 and 90km/h data by Fig. 8 and Fig. 9.

V. CONCLUSION

In this paper we have presented a steering angle estimator based on a recently proposed direct approach for the design of virtual sensors. Current virtual sensors for steering angle estimation based on yaw stability control are used in the electronic stability control (ESC) system for diagnostic International Journal of Vehicular Technology. The obtained steering virtual sensor has been tested on number of different manoeuvres, including double lane change using a linear bicycle model at constant speed and a linear tire model have been used to characterize the vehicle lateral dynamics. This model is valid only if the lateral dynamics are low. But, the LTI framework makes easier the design of unknown input observers.This kind of observers allows not only compute variables usually measured (yaw rate and steering wheel angle) but also the side slip angle. The obtained results showed that the proposed linear estimator is able to provide a good steering angle estimation in a large range of operation and the proposed yaw stability controller is expected to improve yaw stability within linear tire regions. Gain of the observer has been computed by solving linear matrix inequalities.This methodology provides a robust design (in a future work). Finally, the designed virtual sensor was tested using data issued from the Callas vehicle simulator and the results were found to be quite satisfactory.

C. Vehicle parameters •

 parameters Front tire cornering stiffness: D f = 96000 [N.rad -1 ]. • Rear tire cornering stiffness: D r = 69500 * 2 [N.rad -1 ]. • Half-wheelbase front: L f = 1.1824 [m]. • Half-wheelbase rear: L r = 1.5176 [m]. • Total vehicle mass: M V = 1683 [kg]. • Yaw inertia: I zz = 3015 [kg.m 2 ].

Fig. 3 .

 3 Fig. 3. Chicane ISO: positioning corridors.

Fig. 5 .

 5 Fig. 5. YawRate for ISO double lane change 90km/h. Callas simulation compared with open-loop model (5).

Fig. 7 .

 7 Fig. 7. Observer : side slip angle and steering angle estimations for ISO double lane change 90[km/h]. Callas simulation compared with unknown input observers UIO[START_REF] Segel | Theorical prediction and experimental substantiation of the response of the automobile to steering control[END_REF]. Recall that the steering angle is not measured.

Fig. 8 .

 8 Fig. 8. Errors of Observer : Errors estimates of side slip angle and steering angle for ISO double lane change 40[km/h]. Recall that the steering angle is not measured.

Fig. 9 .

 9 Fig. 9. Errors of Observer: Errors estimates of side slip angle and steering angle for ISO double lane change 90[km/h]. Recall that the steering angle is not measured.

  VI. NOTATIONSD f : Front tire cornering stiffness [N.rad -1 ] D r : Rear tire cornering stiffness [N.rad -1 ] L f : Half-wheelbase front [m] L r : Half-wheelbase rear [m] I zz : Yaw inertia [kg.m 2 ] M V : Total vehicle mass [kg] V G : Norm of speed of center of gravity [m.s -1 ] ψ : Yaw rate [rad.s -1 ] F yf : Front lateral tire force [N ]

F

  yr : Rear lateral tire force [N ] β : Center of gravity side slip angle [rad] β f : Front wheel side slip angle [rad] β r : Rear wheel side slip angle [rad] δ: Front wheel steering angle [rad] σ f : Front relaxation length [m] σ r : Rear relaxation length [m] x: Estimation of x

Xème Conference Internationale : Conception et Production Intégrées, CPI 2015, 2-4 Décembre 2015, Tanger -Maroc. Xth International Conference on Integrated Design and Production, CPI 2015, December 2-4, 2015, Tangier -Morocco.


EL Lahjouji Imane
email: imanelahjouji14im@gmail.com

Gadari Mhammed

Radouani Mohammed
email: m.radouani@ensam-umi.ac.ma

Effect of the shaft roughness on the performance of rotary lip seals: Hydrodynamic Model

Keywords: Hydrodynamic lubrication, roughness, Reynolds equation, finite differences, leakage rate, friction torque I

Most of the numerical studies of rotary lip seal are performed by considering lip or shaft as smooth surfaces. Although this assumption is far from practice, it is, the best approach to avoid the transient term of Reynolds equation.

In the present work, Reynolds equation was resolved by taking into account: the roughness of the both surfaces and also the cavitation effect. In order to investigate the shaft roughness effect, an implicit with "finite differences" was used. A comparison was made between results of the current numerical results and the finite volume method published in the international literature.

Numerical simulations show that the shaft roughness affects significantly the friction torque, the leakage and the load support of the lip seal.

INTRODUCTION

The lip seals are the dynamic sealing device the most used in the industry. Since the seventies, it has been shown that under steady state conditions, a lubricating film separates the lip and the shaft surfaces.

Numerically and experimentally, it has been proved that the asperities of the shaft and lip produce a hydrodynamic force that carries the lip surface. Indeed, when the liquid is moved over each asperity, the film thickness varies and produces a pressure elevation on the upstream side, and cavitation occurs on the downstream side.

The resultant of the hydrodynamic pressure in the vicinity of the asperities generates the lift force which keeps the lip separated from the shaft. To understand the film behavior, several lubrication models were studied namely HD (Hydrodynamic) EHD (Elastohydrodynamic), TEHD (Thermo-Elastohydrodynamic), and VEHD (Visco-Elastohydrodynamic).

In the transient condition, theoretically, it is tedious to couple the thermal phenomenon to the mechanical behavior of the lip (viscoelastomeric or elastomeric law). Indeed, if assuming shaft as smooth surface predicts easily the lip performance, with rough finish, several numerical limitations are to challenge; a lot of loops are used to stabilize solutions of energy equation, thereby the lip elasticity, the lubricant viscosity and also the active and non active zones.

In this work we will investigate the effect of the shaft roughness on the rotary lip seal performance, through the HD modeling. This study resolves Reynolds equation [START_REF] Gadari | Étude expérimentale et numérique du comportement des joints à lèvre[END_REF] in the active and non-active zone by taking into the consideration the lip and shaft roughness.

A numerical analysis of the isothermal hydrodynamic lubrication was performed by using the implicit temporal scheme and the finite difference spatial method. The purpose of this paper is to identify the parameters related to shaft roughness that affects the lip seal life expectancy: hydrodynamic force, friction torque, leakage rate and to compare the results with those of Shen [START_REF] Shen | Deterministic modeling of a rotary lip seal with microasperities on the shaft surface[END_REF].

II. MODEL USED

The lip seal and the sealing zone are shown in Figure 1. The rotating shaft is considered rough, and the lip seal is aligned [START_REF] Maoui | Effect of 3D lip deformations on elastohydrodynamic lip seals behaviour[END_REF]. In the practice, the ratio of width contact between lip and shaft by the perimeter is about 10 -6 . Such weak domain induces numerical difficulty to mesh and resolve Reynolds equation. In order to avoid this limitation a cyclic cell is considered. Indeed, the lip roughness is periodically distributed along the «x-axis » direction with a circumferential wavelength equal to «L» .Therefore; we just consider a single cell having a length «L» and an axial contact width « b » and multiply the local results by cell numbers to deduce the global performances.

The film thickness

The film thickness between the lip seal and the shaft is computed by subtracting the lip roughness h 1 , the shaft roughness h 2 . Because the full film lubrication is considered, it is important to note that the average film thickness h 0 is considered so as to represent the gap separating the surfaces and also to neglect the contact between the asperities. Then, the expression of the film thickness [START_REF] Gadari | Étude expérimentale et numérique du comportement des joints à lèvre[END_REF] is given by (1):

h = h 1 (x, y)-h 2 (x, y, t) + h 0 (1)

Fluid mechanics

The pressure field is described by Reynolds equation. The cavitation zones are assumed to be filled with a homogeneous lubricant-air mixture. The film thickness is smaller than the radius of the shaft therefore the shaft curvature can be neglected. The Reynolds equation (2):

∂ ∂x (h 3 F ∂ D ∂x ) + ∂ ∂y (h 3 F ∂ D ∂y ) = 6μU ∂ h ∂x + 12μ ∂ h ∂t + 6μ(1-F) (U ∂ D ∂x + 2 ∂ D ∂t ) (2)
In the active zone (3):

{ D = p, D ≥ 0 F = 1 (3)
In the cavitation zone (not active) (4):

{ D = r-h, D < 0 F = 0 (4)
And r = ρh ρ 0

(5)

Where "r" is the replenishment ratio, "ρ" is the lubricant density and "ρ 0 " is the air density.

III. LIP AND SHAFT ROUGHNESS

The surface roughness is considered as double sinusoidal function and the average film thickness is equal to 1μm. Thus, the lip roughness is modeled by (6):

ℎ 1 (𝑥, 𝑦) = 𝐴 1 cos ( 2𝜋 𝑙 11 (𝑥 -𝑐 𝑔 )) cos ( 2𝜋 𝑙 12 𝑦) (6)
where c g is shearing deformation of the lip, with:

{ c g = l 11 ( 2y y b - y 2 y b 2 ) if y < y b c g = l 11 ( 1-2y b + 2y b y-y 2 ) if y ≥ y b (7)
and y b represents the location of the maximum dry contact pressure (results of structural analysis with the commercial simulation software « Abaqus ») as shown in Figure 2.

We assume that shaft roughness is given by:

The Reynolds equation is resolved by the finite differences method [START_REF] Kouatchou | Finite Differences and Collocation Methods for the solution of two dimensional[END_REF] using the algorithm shown in Figure 3.

As soon as the Reynolds equation is solved, the lifting load is calculated by (9), the leakage rate by (10) and the friction torque by (11).

Finite Differences model

In this part the Reynolds equation is discretized using the finite difference approach. This method employs approximations to the partial derivatives then the area of study should be mesh.

As previously cited the domain is a rectangle with "b" as length and "L" as width shown in Figure 3, thereby, we discretize cyclic cell to « (Nx-1)•(Ny-1) » regular elements. Where "Nx•Ny" nodes representing the hydrodynamic pressure. The time step is given by « Nt » partition throughout the time period. Therefore, we discretize the terms of the partial derivative using the Taylor-Young formulation: « i » is the index of knot and « n » is the index of time.

The boundary conditions is given by: at y=0: p=pa; at y=b: p=ps.

Replacing the partial in Eq. 2 by their finite difference analogs given in Eq. 12, it yields:

-A • D n (i) + B • D n (i + 1) + C • D n (i-1) + E • D n (i + Nx) + F • D n (i-Nx) = G + H • D n-1 (i) (14)
Where: In order to find the vector [D n ] the second part of the (Eq15) is multiplied by the reverse of the pentadiagonal matrix [A (i, n)]. Then we conclude the pressure values: if « D n (i) » is positive the pressure « P n (i) » takes the value of « D n (i) » if not the pressure is nil since it's the cavitation pressure. At this time we start computing the load support, the reverse pumping rate and the friction torque by the expressions above (Eq.9, 10 and 11).

𝐴 = (2ℎ 𝑛 3 (𝑖) + ℎ 𝑛 3 (𝑖 + 1) + ℎ 𝑛 3 (𝑖 -1)) 𝐹 𝑛 (𝑖) 2𝛥𝑥 2 + (2ℎ 𝑛 3 (𝑖) + ℎ 𝑛 3 (𝑖 + 𝑁𝑥) + ℎ 𝑛 3 (𝑖 -𝑁𝑥)) 𝐹 𝑛 (𝑖) 2𝛥𝑦 2 + 12𝜇(1 -𝐹 𝑛 (𝑖)) 𝛥𝑡 𝐵 = (ℎ 𝑛 3 (𝑖 + 1) + ℎ 𝑛 3 (𝑖)) 𝐹 𝑛 (𝑖 + 1) 2𝛥𝑥 2 -6𝜇𝑈 (1 -𝐹 𝑛 (𝑖 + 1)) 2𝛥𝑥 𝐶 = (ℎ 𝑛 3 (𝑖) + ℎ 𝑛 3 (𝑖 -1)) 𝐹 𝑛 (𝑖 + 1)

IV. VALIDATION CODE

The problem parameters are b=0.5.10 -4 m, L=0.5.10 -4 m, μ= 2.5.10 -2 Pa•s, ps=1.02.10 5 Pa, pa= ps=1.02.10 5 Pa, A 1 =0.5.10 -6 m, l11=b, l12=L, l22=b/2, l21=L/2, yb =3b/4. A parametric study was made; in order to determinate the nodes number according to x-axis and y-axis. Indeed, by choosing Nx=30 and Ny=30 the numerical results are stabilized.

The results are computed with program set on the calculation software Matlab. To validate our numerical study, the formulation in finite volumes supplied by Shen [START_REF] Shen | Deterministic modeling of a rotary lip seal with microasperities on the shaft surface[END_REF], was compared to the current model. Figure .6 shows the variation of the reverse pumping rate according to the variation of roughness .When Ra(shaft) is 5% of Ra(lip) the reverse pumping rate is increased by 13.5% above Q 0 (the reverse pumping rate for a smooth shaft surface), and even if we increase the shaft roughness Ra(shaft) the reverse pumping rate stills significant in comparison with the one of the smooth shaft.

We can also say that the roughness of the shaft has an effect on the time-averaged reverse pumping rate. The numerical results predict well the rotary lip performance comparing to finite volumes method given by Shen [START_REF] Shen | Deterministic modeling of a rotary lip seal with microasperities on the shaft surface[END_REF]. The differences are about 0.36% for the load support and 1.56% for the reverse pumping rate curve, as shown in figure.4 and figure.5. Thus, the current model is validated.

In order to study the effect of shaft roughness on rotary lip seal performance, we consider two influencing parameters: the roughness shape and the wavelength according to x-axis and yaxis.

V. EFFECT OF THE SHAFT ROUGHNESS

Effect of the shaft surface wavelength l 21 and l 22

This part is about taking different cases of the shaft surface wavelengths, and presenting the variation of the load support and the reverse pumping rate in function of time. However, while changing the values of the shaft surface wavelength according to the "y" direction « l 22 » », it is observed that the amplitude of load and reverse pumping are significantly increased and the averaged results are similar.

Thus, the effect of the shaft surface wavelength according to the x direction « l 21 » reduces the averaged reverse pumping rate and the load support though « l 22 » fluctuates more the amplitude of reverse pumping and lifting load, however the averaged values are quite the same.

Effect of the shaft roughness form

In order to investigate the effect of shaft roughness shape, we consider three cases as shown in figure . For the second case we find that it raises both the load support and the reverse pumping rate contrary to the third case wish reduces the two parameters to 0.

Effect of the shaft roughness on the friction torque

The curves plotted in Figure 14, show the variation of the friction torque for the different cases mentioned below. It is remarkable that the shaft surface form or wavelengths fluctuations have the same effects, found for the load support or the reverse pumping rate, on the friction torque « C ». While changing the shaft surface wavelengths it is noticed that the pressure varies feebly. However, if the shaft surface form varies: for SH#2 the pressure rises significantly and the cavitation zone is smaller than the other cases, besides for SH#3 the cavitation zone is enormous which allow as to conclude that in this case the shaft and the lip are no more separated so this case should be avoided for a better use of the lip seal. This work has twofold objectives, in one hand to compare numerical results between the finite differences and the volume differences approaches, in order to resolve Reynolds equation. This study confirms an accordance of the current model and the results published in the international literature.

In the other hand, this work underlines the effect of shaft roughness on rotary lip seal performance. The simulations show that the wavelength according to "x-axis" decreases the reverse pumping rate, the load support and the friction torque. Nevertheless, the wavelength according to "y-axis" rises these parameters.

In the same time, the shaft surface form has a great effect on lip seal behavior. Effectively, while taking only the positive bumps the reverse pumping rate, the load support and the friction torque rise significantly, yet if we consider only the negative bumps the parameters reduce and even approaches zero. Similarly, for the pressure distribution, while changing the shaft shape, the pressure decreases for the negative bumps however it raises significantly for the positive bumps.

Fig. 1 .

 1 Fig. 1. Lip seal structure and location of the tightness area

ℎ 2 (

 2 𝑥, 𝑦, 𝑡) = 𝐴 2 cos (

Fig. 2 .Fig. 3 .

 23 Fig.2. The maximum circumferential strain location[START_REF] Gadari | Étude expérimentale et numérique du comportement des joints à lèvre[END_REF]

Fig. 4 .

 4 Fig. 4. Schematic representation Finite differences mesh

  𝐹 𝑛-1 (𝑖)) 𝛥𝑡The linear system is transformed to matrix formulation: [M].D + R={0}, where [M] is stiffness matrix given by A, B, C, E and F and [R] is second right member.

Figure. 5

 5 Figure.5 represents the variation of time averaged load support divided by W 0 (the time averaged load support for a smooth shaft surface during a period) according to the variation of roughness of the shaft surface. We notice that when Ra(shaft) is 5% of Ra(lip), the load support rises significantly by 25% and even if we increase the shaft roughness Ra(shaft) the load support stills considerable in comparison with the one of the smooth shaft.

Fig. 5 .

 5 Fig. 5. Effect of Shaft Surface on Load Support

Figure. 7

 7 Figure.7 shows that by increasing « l 21 » the averaged lifting load and reverse pumping fall.

Fig. 7 .

 7 Fig. 7. Effect of Shaft Surface wave length in x direction on load support

2 

 2 Fig.11. Shaft surface roughness profile

 2  2  3  2  2 

 22322 SH#1: l 21 =l 11 /2 and l 22 =l 12 /SH#2: h 22 = (|h 21 (x,y,t)|+ h 21 (x,y,t)))/SH#3: h 23 = (-|h 21 (x,y,t)|+ h 21 (x,y,t)))SH#4: l 21 =l 11 and l 22 =l1 2 /SH#5: l 21 =2.l 11 and l 22 =l 12 /SH#6: l 21 =l 11 /2 and l 22 =l 12  SH#7: l 21 =l 11 /2 and l 22 =2.l 12 4. Numerical simulation The curves figured in figure.15 show the Hydrodynamic pressure plotted in function of the x and y coordinates, for different cases studied previously with an average film thickness h 0 =3 μm. The curves are elaborated on the golden software surfer 9.

Fig. 14 .

 14 Fig. 14. Effect of Shaft Surface form on the pumping rate

TABLE I .

 I NOMENCLATURE

Nomenclature A 1 half amplitude of lip surface fluctuation [m]