The servo mechatronic system design process usually covers two different engineering domains: structure design and system control. The relationship between these two domains is much closed. In order to reduce the disturbance caused by parameters in either one, the domain knowledge from those two different fields needs to be integrated. Thus, in order to reduce the disturbance caused by parameters in either one, the mechanical and controller design domains need to be integrated. Therefore, the integrated design method Design For Control (DFC), will be employed in this thesis. In this connect, it is not only applied to achieve minimal power consumption but also enhance structural performance and system response at same time. To investigate for the integrated design method, there are two common servo mechatronic systems: feed drive system and legged servo mechatronic system are used as the design platform. 1. Mechatronic Feed Drive System To investigate the method for integrated optimization, a mechatronic feed drive system of the machine tools is used as a design platform. The 3D software, Pro/Engineer is first used to build the 3D model to analyze and design structure parameters such as elastic deformation, nature frequency and component size, based on their effects and sensitivities to the structure. Additionally, in order to achieve system robust, Quantitative Feedback Theory (QFT), will be applied to determine proper control parameters for the controller. Therefore, overall physical properties of the machine tool will be obtained in the initial stage. Following this Design Then Control process, the iterative design process is following to enhance some of system performance. Finally, the technology design for control will be carried out to modify the structural and control parameters to achieve overall system performance. Hence, the corresponding productivity is expected to be greatly improved. 2. Legged Servo Mechatronic System The goal of this study is to develop a one-degree-of-freedom (DOF) legged servo mechatronic system with DFC. For this system, the kinematics and control dynamic analysis of legged servo mechatronic system have been solved by using four bar linkage with symmetrical coupler point, pantograph, and common position and velocity controller. In addition, in order to improvement system dynamic performance and reduce the control cost, the counterweight, that base on mass redistribution is employed to integrate structure and control into one design step for reduce shaking moment. Additionally, in order to improvement the system performance, the complete force balance is not only to take advantage of control cost, but also easy to control.

Le chapitre 1 porte sur une équation des ondes monodimensionnelle soumise à une condition aux limites unilatérale. Sous des hypothèses de régularité appropriées sur les données initiales, une nouvelle preuve d’existence et d’unicité est proposée. La méthode de redistribution de masse qui repose sur une redistribution de la masse d’un corps de telle sorte qu’il n’y ait pas d’inertie au niveau du nœud de contact est introduite et sa convergence est prouvée. Une approximation de ce problème d’évolution combinant la méthode des éléments finis ainsi que la méthode de redistribution de masse est analysée dans le chapitre 2. Puis deux problèmes ainsi que leurs solutions analytiques respectives (l’une étant nouvelle) sont présentés et des discrétisations possibles en utilisant différentes méthodes d’intégration en temps sont décrites. Enfin, des simulations numériques de ces problèmes sont reportées. Dans le chapitre 3, la masse des nœuds de contact est redistribuée sur les autres nœuds et sa convergence ainsi qu’une estimation de l’erreur en temps sont établies. Ensuite, une solution analytique déjà introduite dans le chapitre 3 est comparée aux approximations obtenues pour plusieurs redistributions de masse possibles mettant ainsi en évidence que plus une redistribution de masse d’un corps se fait à proximité des nœuds de contact meilleures sont les solutions approchées obtenues. Les problèmes de contact élastodynamique en dimension d’espace deux et trois sont étudiés dans le chapitre 4. Comme pour les problèmes de contact monodimensionnels, une solution approchée combinant les éléments finis et la redistribution de masse est exposée. Quelques simulations numériques utilisant des méthodes d’intégration en temps mettent en évidence les propriétés de convergence de la méthode de redistribution de masse. / The chapter 1 focuses on a one–dimensional wave equation being subjected to a unilateral boundary condition. Under appropriate regularity assumptions on the initial data, a new proof of existence and uniqueness results is proposed. The mass redistribution method based on a redistribution of the body mass such that there is no inertia at the contact node is introduced and its convergence is proved. An approximation of this evolutionary problem combining the finite element method as well as the mass redistribution method is analyzed in chapter 2. Then two benchmark problems (one being new) with their analytical solutions are presented and some possible discretizations using different time–integration schemes are described. Finally, numerical experiments for these benchmark problems are reported. In chapter 3, the mass of the contact nodes is redistributed on the other nodes and its convergence as well as an error estimate in time are established. Then an analytical solution already introduced in chapter 3 is compared to approximate ones obtained for different choices of mass redistribution highlighting that more a mass redistribution of the body is done near the contact nodes better the approximate solutions are obtained. The two and three–dimensional elastodynamic contact problems are studied in chapter 4. As for the one–dimensional contact problems, an approximated solution combining the finite element and mass redistribution methods is exhibited. Some numerical experiments using time–integration methods highlighted the convergence properties of the mass redistribution method.

Title: Approximation, numerical realization and qualitative analysis of contact problems with friction Author: Tomáš Ligurský Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Jaroslav Haslinger, DrSc., Department of Numerical Mathe- matics Abstract: This thesis deals with theoretical analysis and numerical realization of dis- cretized contact problems with Coulomb friction. First, discretized 3D static contact prob- lems with isotropic and orthotropic Coulomb friction and solution-dependent coefficients of friction are analyzed by means of the fixed-point approach. Existence of at least one solution is established for coefficients of friction represented by positive, bounded and con- tinuous functions. If these functions are in addition Lipschitz continuous and upper bounds of their values together with their Lipschitz moduli are sufficiently small, uniqueness of the solution is guaranteed. Second, properties of solutions parametrized by the coefficient of friction or the load vector are studied in the case of discrete 2D static contact problems with isotropic Coulomb friction and coefficient independent of the solution. Conditions under which there exists a local Lipschitz continuous branch of solutions around a given reference point are established due to two variants of the...