Par Pengfei HUYAN Electromagnetic digital actuators array : characterization of a planar conveyance application and optimized design Thèse présentée pour l’obtention du grade de Docteur de l’UTC Soutenue le 27 mars 2015 Spécialité : Advanced Mechanics D2178 Thèse Présentée pour obtenir le grade de DOCTEUR De UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE Spécialité Mécanique Avancée Par Pengfei HUYAN Réseau d’actionneurs électromagnétiques numériques : caractérisation d’une application de type convoyage et conception optimisée Y. Haddab (FEMTO-ST – ENSMM, Besançon) Rapporteur F. Formosa (SYMME - Polytech Annecy Chambéry, Annecy ) Rapporteur B. Lemaire-Semail (L2EP – Polytech'Lille, Lille) Membre du jury A. Hubert (LEC – UTC, Compiègne) Membre du jury C. Prelle (Laboratoire Roberval – UTC, Compiègne) Directeur de thèse L. Petit (Laboratoire Roberval – UTC, Compiègne) Directeur de thèse Laboratoire Roberval, UMR 7337, UTC / CNRS 2 Table of contents Table of contents CHAPTER I: STATE OF ART I.1. DEFINITION............................................................................................................................... 12 I.1.1. DIGITAL ACTUATOR ................................................................................................................. 12 I.1.2. DIGITAL ACTUATOR CLASSIFICATION ............................................................................................ 13 I.2. TECHNOLOGICAL SOLUTIONS ............................................................................................ 16 I.2.1. SWITCHING METHODS ............................................................................................................. 16 I.2.1.1. ELECTROMAGNETIC PRINCIPLE ................................................................................................ 16 I.2.1.2. THERMAL PRINCIPLE ............................................................................................................ 21 I.2.1.3. ELECTROSTATIC PRINCIPLE ..................................................................................................... 24 I.2.1.4. PIEZOELECTRIC PRINCIPLE ...................................................................................................... 26 I.2.2. HOLDING METHODS ............................................................................................................... 27 I.2.2.1. MAGNETIC HOLDING PRINCIPLE ............................................................................................... 28 I.2.2.2. BUCKLED STRUCTURE HOLDING PRINCIPLE.................................................................................. 29 I.2.2.3. HOLDING FUNCTION REALIZED VIA COMPLEX MECHANISM/EXTERNAL ACTUATORS ............................... 31 I.2.2.4. HOLDING FUNCTION REALIZED VIA CONTINUOUS SWITCHING FUNCTION ............................................ 33 I.3. APPLICATIONS ......................................................................................................................... 35 I.3.1. SINGLE ACTUATION ................................................................................................................ 35 I.3.1.1. DISCRETE DISPLACEMENT OUTPUT ........................................................................................... 35 I.3.1.2. MECHANICAL SWITCH .......................................................................................................... 37 I.3.1.2.1. Fludic Switch ........................................................................................................................... 37 I.3.1.2.2. Optical Switch ......................................................................................................................... 38 I.3.1.2.3. Electrical Switch...................................................................................................................... 39 I.3.2. MULTIPLE ACTUATION BASED APPLICATIONS ................................................................................. 40 I.3.2.1. MULTIPLE APPLICATION WITHOUT COLLABORATION ..................................................................... 41 I.3.2.1.1. Tactile display ......................................................................................................................... 41 I.3.2.1.2. Optical Switch array ............................................................................................................... 42 I.3.2.1.3. Mechanical memories ............................................................................................................ 43 I.3.2.2. MULTIPLE APPLICATION WITH COLLABORATION .......................................................................... 44 I.3.2.2.1. Digital robots .......................................................................................................................... 44 I.3.2.2.2. Digital to analog converters ................................................................................................... 45 I.3.2.2.3. Displacement table ................................................................................................................. 46 I.4. CONCLUSION ............................................................................................................................. 47 5 Table of contents CHAPTER II: PRINCIPLE AND MODELLING OF DIGITAL ELECTROMAGNETIC ACTUATORS ARRAY II.1. ACTUATORS ARRAY ARCHITECTURE ............................................................................. 51 II.1.1. ELEMENTARY ACTUATOR PRINCIPLE ........................................................................................... 51 II.1.2. ACTUATORS ARRAY PRINCIPLE .................................................................................................. 54 II.1.3. APPLICATION OF THE ARRAY ..................................................................................................... 56 II.2. MODELLING OF THE ARRAY .............................................................................................. 58 II.2.1. CHOICE OF MODELING TOOLS ................................................................................................... 58 II.2.2. SEMI-ANALYTICAL MODELING WITH RADIA ................................................................................. 60 II.2.2.1. MAGNETIC HOLDING FORCE .................................................................................................. 60 II.2.2.2. MAGNETIC INTERACTION FORCE ............................................................................................. 61 II.2.2.3. MAGNETIC BALANCE FORCE .................................................................................................. 63 II.2.2.4. TOTAL MAGNETIC FORCE ...................................................................................................... 64 II.2.3. ANALYTICAL MODELING WITH MATLAB ..................................................................................... 65 II.2.3.1. MODELLING OF THE ELEMENTARY ACTUATOR ............................................................................ 66 II.2.3.1.1. Magnetic flux density ............................................................................................................ 66 II.2.3.1.2. Magnetic holding force ......................................................................................................... 67 II.2.3.1.3. Electromagnetic force modelling .......................................................................................... 70 II.2.3.1.4. Self-returning zone calculation ............................................................................................. 71 II.2.4. COMPARISON OF THE TWO MODELS ........................................................................................... 76 II.3. CONCLUSION ........................................................................................................................... 77 CHAPTER III: EXPERIMENTAL REALIZATION AND CHARACTERIZATION OF THE ACTUATORS ARRAY III.1. PRESENTATION OF THE PROTOTYPE ................................................................................. 80 III.2. GEOMETRICAL STUDY OF THE PROTOTYPE ARRAY .......................................... 81 III.2.1. MEASUREMENT TOOLS ....................................................................................................... 82 III.2.2. MEASUREMENT OF THE DIMENSION AND POSITION ERRORS ......................................................... 82 III.2.3. INFLUENCE OF THE ERRORS ON MAGNETIC HOLDING FORCE .......................................................... 85 III.3. EXPERIMENTAL CHARACTERIZATION .................................................................. 87 III.3.1. EQUIPMENT SETUP ............................................................................................................ 88 III.3.2. NON CONTACT MEASUREMENT TECHNIQUE .............................................................................. 89 III.3.3. EXPERIMENTAL RESULTS ...................................................................................................... 91 III.3.4. CONCLUSION .......................................................................................................... 103 6 Table of contents CHAPTER IV: OPTIMIZATION DESIGN OF THE PROTOTYPE ARRAY IV.1. OPTIMIZATION TECHNIQUES ........................................................................................ 105 IV.1.1. CONTEXT OF THE OPTIMIZATION STUDY .................................................................................... 105 IV.1.2. MULTI-OBJECTIVES OPTIMIZATION TECHNIQUES.......................................................................... 106 IV.1.2.1. WEIGHTING OBJECTIVE METHOD ......................................................................................... 108 IV.1.2.2. MULTI-LEVEL OPTIMIZATION METHOD .................................................................................. 109 IV.1.2.3. TRADE-OFF METHOD ........................................................................................................ 109 IV.1.2.4. GENETIC ALGORITHM ........................................................................................................ 110 IV.1.3. COMPARISON OF THE MO METHODS ....................................................................................... 112 IV.2. GENETIC OPTIMIZATION REALIZED IN MATLAB .................................................... 113 IV.2.1. PERFORMANCE INDICATORS ................................................................................................... 113 IV.2.2. DESIGN PARAMETERS ........................................................................................................... 115 IV.2.3. SINGLE-OBJECTIVE OPTIMIZATION ........................................................................................... 116 IV.2.3.1. OPTIMIZATION SETUP ........................................................................................................ 116 IV.2.3.2. SINGLE-OBJECTIVE OPTIMIZATION RESULTS ............................................................................. 117 IV.2.4. MULTI-OBJECTIVE OPTIMIZATION ............................................................................................ 119 IV.2.4.1. OPTIMIZATION SETUP ........................................................................................................ 120 IV.2.4.2. MULTI-OBJECTIVE OPTIMIZATION RESULTS ............................................................................. 120 IV.2.5. COMPARISON OF THE TWO METHODS ...................................................................................... 124 IV.3. CONCLUSION ........................................................................................................................ 127 CHAPTER V: CONCLUSION AND PERSPECTIVES V.1. CONCLUSION ......................................................................................................................... 129 V.2. PERSPECTIVES ...................................................................................................................... 130 V.2.1. PERSPECTIVES OF THE EXISTING ACTUATORS ARRAY ...................................................................... 131 V.2.1.1. DYNAMIC MODELLING OF THE PLANAR CONVEYANCE DEVICE ........................................................ 131 V.2.1.2. OPTIMIZATION OF THE FRICTION CONDITIONS BETWEEN THE PLATE AND MPMS ............................... 131 V.2.2. NEW DEVELOPMENTS .................................................................................................... 132 V.2.2.1. DIGITAL ACTUATOR WITH THREE DISPLACEMENT DIRECTIONS ....................................................... 132 V.2.2.2. ACTUATORS ARRAY WITH DIFFERENT STROKES .......................................................................... 133 V.2.2.3. MICRO-FABRICATED DIGITAL ACTUATORS ARRAY ....................................................................... 134 7 Abbreviations Abbreviations PM Permanent Magnet MPM Mobile Permanent Magnet FPM Fixed Permanent Magnet AFPM Additional Fixed Permanent Magnet PCB Printed Circuit Board UW Upper Wire LW Lower Wire SRZ Self-Returning Zone IZ Intermediate Zone MO Multi-Objectives SO Single-Objective IF Interference Force VF Variation Force GOT Global Optimization Toolbox 8 Introduction ntroduction I In mechanical or mechatronical systems, actuators are the components used to convert input energy, generally electrical energy, into mechanical tasks such as motion, force or a combination of both. The most frequently encountered actuators in such systems are based on an analogical principle because their mobile part can reach any position within their operating stroke. Analogical actuators present several advantages. Besides their ability to perform continuous actions within their working limits, analogical actuators can achieve high performances with high reliability levels. For these purposes, closed-loop controls are generally implemented with the need of feedback sensors. However depending on the actuator design, the physical phenomenon used to generate the motion or the actuator environment, their control can become very complex to ensure high performances levels or complex tasks. The integration of feedback sensors can also be a problem and is not always possible especially for compact or highly integrated mechanical or mechatronical systems. Moreover to keep the mobile part in a given position within rejecting disturbances, continuous energy supply is needed that can generate heating or deterioration of these systems. In order to try to overcome these drawbacks, an alternative type of actuators based on a digital principle has been developed in literature. The mobile part of these digital actuators can switch between a finite number of well defined and repeatable discrete positions. All the positions located between two discrete positions are only transient states and cannot be held in normal functioning. The discrete positions are theoretically well defined during the manufacturing step of these actuators. Feedback sensors are then not required and their control is realized in open-loop. Due to their digital principle, these actuators have several advantages as low energy consumption because energy is only needed for the switching of the mobile part between the discrete positions and there is no energy consumption to hold a position. The control of digital actuators is also very simple because only energy pulses are needed. Very simple open-loop controls based on digital outputs of data acquisition boards can then be used. However compared to analogical actuators, digital actuators present two main drawbacks. The manufacturing errors of these actuators have to be precisely controlled because, unlike to analogical actuators, a manufacturing error cannot be compensated using the control law. Another drawback is their inability to realize continuous tasks because of their discrete stroke. An assembly of several digital actuators can nevertheless realize multi- 8 Introduction discrete tasks. In a former thesis realized at the Roberval laboratory of the Université de Technologie de Compiègne [PETI 2009], a digital electromagnetic actuator has been studied and developed. The originality of this work is based on the selected architecture that enables to realize displacements along two independent and orthogonal axes. In this thesis, a single digital actuator has been firstly designed, modeled and manufactured. The performances of this experimental actuator have been characterized (switching time along the two displacement axes, energy consumption, positioning repeatability error, displaceable mass) and a comparison between simulated and experimental results has shown a good agreement. An array composed of 25 elementary actuators arranged in a 5 × 5 matrix configuration has then been designed by considering the magnetic and electromagnetic interaction between the elementary actuators of the array. A prototype of the array has finally been manufactured and assembled. The present thesis has been realized in the continuity of the work realized in the thesis described in the previous paragraph. The first main objective of the present thesis is focused on the characterization of the existing actuators array and also a planar conveyance application based on the actuators array. For that purpose, a modeling of the actuators array and experimental tests have been carried out in order to determine the influence of some parameters on the actuators array behavior. The second objective is to design a new version of the actuators array based on the experience of the first prototype. An optimization of the design has then been realized using genetic algorithm techniques while considering several criteria. The work realized in the thesis is described in this manuscript which is divided into five chapters. Chapter 1 provides a state of art of the digital actuation. The definition and the properties of digital actuators are firstly given. Then the different physical principles and technical solutions used in literature for digital actuators are described. A classification of digital actuators based on the number of stable position is also proposed. Finally, the applications of digital actuators described in literature are detailed. Chapter 2 presents the principles of the elementary electromagnetic digital actuator and of the actuators array. The properties of the existing actuators array prototype are given and the planar conveyance application and the dedicated control strategy are detailed. At the end of 9 Introduction this chapter, an analytic static model developed to characterize the digital actuators array is presented in detail. Chapter 3 is focusing on the experimental characterization of the digital actuators array prototype especially the planar conveyance application. The manufacturing errors of the prototype have been firstly measured and their influences on the performances of the digital actuators array have been determined using the developed model. The experimental setup of the prototype and the non-contact measurement technique used for characterization are then presented. Experimental tests of the digital actuators array as a planar conveyance device are presented and displacements along the two axes are shown. In this chapter, the influences of several controlling parameters as the controlling current values, the shape of the current pulses or the displaced mass are shown. Based on the experience of the first prototype, an optimization of the actuators array design is presented in chapter 4. The objective of this study is to improve the performances of the array while considering three performance indicators which characterize the behavior homogeneity, the independent functioning and the digital behavior respectively. An overview of the existing multi-objective optimization techniques is firstly presented and then the genetic algorithm technique has been selected for this optimization study. The implementation of the genetic algorithm on MATLAB is then presented. Single-objective and multi-objective optimizations have both been realized and finally an optimized design of the actuators array is proposed. Chapter 5 gives a conclusion of the work realized in the thesis. Short-term and long-term perspectives of this work are finally proposed. 10 Chapter 1: State of art Chapter 1: State of art The work presented in this thesis focuses on a digital actuators array. In order to define the digital actuation and to identify the existing needs and solutions related to this kind of actuation, the first chapter provides a state of art on this subject. The objective is to detail the different architectures of digital actuators and digital actuators array, the physical principles used for the different functions and also the applications of the digital actuators. This chapter begins with a general definition of the different types of digital actuators. A classification of digital actuators is then given. The physical principles encountered in literature to realize the elementary functions of digital actuators are presented with examples. The advantages and disadvantages of these physical principles are also presented. At the end, applications based on digital actuators are described. These applications are classified into two types. The first one regroups applications based on a single digital actuator and called “single actuation”. The second one regroups applications based on an assembly of several digital actuators and called “multi actuation”. Examples of these two types are given to explain different applications. 11