DESIGN AND ANALYSIS OF MULTISTABLE COMPLIANT MECHANISMS DESIGN AND ANALYSIS OF MULTISTABLE COMPLIANT MECHANISMS DESIGN AND ANALYSIS OF MULTISTABLE COMPLIANT MECHANISMS DESIGN AND ANALYSIS OF MULTISTABLE COMPLIANT MECHANISMS
國立中興大學精密工程研究所 (National Chung Hsing University, Institute of Precision Engineering) 博士學位論文 (Ph.D Dissertation) 多穩態撓性機構之設計與分析 Design and Analysis of Multistable Compliant Mechanisms 指導教授：王東安 Dung-An Wang 研究生：范輝遵 Huy-Tuan Pham 中華民國一百年七月 Design and Analysis of Multistable Compliant Mechanisms Huy-Tuan Pham Graduate Institute of Precision Engineering Doctor of Philosophy (ABSTRACT) Multistable mechanisms, which provide multi stable equilibrium positions within its operation range, can be adopted to design systems with power efficiency and kinematic versatility, oftentimes two conflicting goals Multistable compliant mechanisms have attracted more and more attention in recent years Two new specified multistable compliant mechanisms are developed in this dissertation: a compliant quadristable mechanism and a constant-force bistable mechanism Finite element analyses are used to characterize the behavior of these multistable mechanisms under static loading A design formulation is proposed to synthesize the shape and size of these specified compliant mechanisms prototypes of them are fabricated and tested Millimeter scale polyoxymethylene The characteristics of these mechanisms predicted by theory are verified by experiments The design examples presented in this investigation demonstrates the effectiveness of the optimization approach for the design of the multistable compliant mechanism The proposed mechanisms have no movable joint and gain their mobility from the deflection of flexible members These compliant mechanisms have the ease of miniaturization and offer a significant advantage in the fabrication of micro actuators, micro sensors and microelectromechanical systems Keywords: bistable, quadristable, constant-force bistable, multistable mechanisms, vibration i ACKNOWLEDGEMENTS First and foremost, I would like to send my deep gratitude to two universities, Ho Chi Minh City Nong Lam University, Vietnam where I have been working and National Chung Hsing University, Taiwan for providing me this valuable scholarship for Ph.D degree Many people deserve thanks for their contributions to this dissertation and my life It is my pleasure to thank my Taiwanese labmates for their help and friendship to overcome my initial culture and language obstacles I must thank Cheng-Hao Ciou, a master student at Micro/Nano Machining Laboratory in NCHU, who helped me with meticulous fabrication by using their CNC milling machine Helpful discussions with Professor Chao-Chieh Lan of National Cheng Kung University, Taiwan, ROC are greatly appreciated Special thanks to Assoc Prof Dung-An Wang, a man I am honored to know as a teacher, an advisor, and a friend He has also spent a considerable portion of his time giving guidance and helping me in countless ways I have learned much more than engineering from him Finally, I am very grateful to my parents, my sister and my girlfriend for their love, for their support and encouragement of my academic pursuits, and for always expressing confidence in my abilities This dissertation was supported by the National Science Council (NSC) ROC, under grant no NSC 96-2221-E-005-095 ii TABLE OF CONTENTS ABSTRACT .i ACKNOWLEDGEMENTS .ii TABLE OF CONTENTS iii LIST OF FIGURES v LIST OF TABLES .viii NOMENCLATURE ix CHAPTER INTRODUCTION 1.1 Motivation 1.2 Contributions .2 1.3 Literature Review 1.3.1 Compliant Mechanism .3 1.3.2 Bistable micromechanism 1.3.3 Multistable mechanism 1.3.4 Contant-force bistable mechanism 1.3.5 Actuation methods of multistable mechanisms .8 1.4 Dissertation Layout .9 CHAPTER 2.1 Design DESIGN OF A BISTABLE MECHANISM 11 .12 2.1.1 Operational principle 12 2.1.2 Modeling 13 2.1.3 Analysis .15 2.2 Fabrication and Testing 19 2.2.1 Fabrication .19 2.2.2 Testing .20 iii 2.3 Results and Discussions 20 2.4 Summary 23 CHAPTER DESIGN OF A QUADRISTABLE COMPLIANT MECHANISM 41 3.1 Design 42 3.1.1 Operational principle 43 3.1.2 Design .46 3.1.3 Optimization 49 3.2 Fabrication and Testing 53 3.3 Results and Discussions 54 3.4 Summary 58 CHAPTER DESIGN OF A CONSTANT-FORCE BISTABLE MECHANISM 75 4.1 Design 75 4.1.1 Operational principle 77 4.1.2 Design .78 4.1.3 Optimization .83 4.2 Fabrication and Testing 85 4.3 Results and Discussions 85 4.4 Summary 88 CHAPTER CONCLUSIONS AND FUTURE WORK 100 5.1 Conclusions 100 5.2 Future work 101 Bibliographies 103 Publications during Ph.D studies .115 iv LIST OF FIGURES Fig 2.1 (a) A schematic of a BM and a permanent magnet served to actuate the mechanism (b) Length l and the angle θ with respect to the y axis 25 Fig 2.2 Two stable equilibrium states of the mechanism .26 Fig 2.3 Four-step operation of the mechanism .27 Fig 2.4 A schematic of a BM 28 Fig 2.5 A typical f-d curve of a BM .29 Fig 2.6 A schematic of a quarter model 30 Fig 2.7 A mesh for the quarter model 31 Fig 2.8 F-d curve and potential energy curve based on the finite element model 32 Fig 2.9 Time responses of the mechanism (a) Switching from FSP to SSP; (b) switching from SSP to FSP 33 Fig 2.10 Fabrication steps 34 Fig 2.11 An array of fabricated devices .35 Fig 2.12 An OM photo of a fabricated device 36 Fig 2.13 A schematic of the experimental setup 37 Fig 2.14 Experimental apparatus placed under a high-speed camera 38 Fig 2.15 Snapshots for forward motion 39 Fig 2.16 Snapshots for backward motion 40 Fig 3.1 A ‘ball-on-the-hill’ analogy for a QM, similar to a figure presented by Chen et al [2009] 61 Fig 3.2 Operational principle 62 Fig 3.3 A typical force versus displacement curve of the QM and the corresponding configurations at displacement a , displacement b , v displacement c , and displacement d , shown in the inlets 63 Fig 3.4 (a) A schematic of a quarter model (b) Dimensions of the guide beam and the shuttle mass .64 Fig 3.5 Flowchart of the optimization procedure 65 Fig 3.6 A mesh for the finite element model 66 Fig 3.7 Distribution of the population of several generations in the optimization process 67 Fig 3.8 (a) f- δ curve and maximum stress versus displacement curve for forward motion; (b) strain energy curve for forward motion; (c) f- δ curve and maximum stress versus displacement curve for backward motion; (d) strain energy curve for backward motion 68 Fig 3.9 Photos of a fabricated QM 69 Fig 3.10 A photo of the experimental setup .70 Fig 3.11 Snapshots for forward motion (a-c) and backward motion (d-f) 71 Fig 3.12 f- δ curves of the fabricated QM for (a) forward, (b) backward motion 72 Fig 3.13 (a) Schematic of the inner bistable structure, BS1 (b) Schematic of the outer bistable structure, BS2 (c) f- δ curves of BS1 and BS2 based on their individual finite element models 73 Fig 3.14 f- δ curve and maximum stress versus displacement curve of the microscale version of the QM for (a) forward motion; (b) backward motion 74 Fig 4.1 Schematic of a CFBM and its operational principle 90 Fig 4.2 (a) A typical force versus displacement curve of the CFBM and the corresponding positions at displacement a (b), displacement c (c), displacement d (d), and displacement g (e) 91 Fig 4.3 (a) A schematic of a quarter model (b) Dimensions of the guide vi beam and the shuttle mass .92 Fig 4.4 Flowchart of the optimization procedure 93 Fig 4.5 A mesh for the finite element model 94 Fig 4.6 (a) A f- δ curve and maximum stress versus displacement curve; (b) strain energy curve based on a finite element model of the optimized solution 95 Fig 4.7 (a) A photo of a fabricated CFBM (b) A close-up view of the flexible hinge 96 Fig 4.8 A photo of the experimental setup .97 Fig 4.9 Snapshots for forward motion (a-c) and backward motion (d-f) 98 Fig 4.10 f- δ curves of the fabricated CFBM for (a) forward, (b) backward motion 99 vii LIST OF TABLES Table 2-1 Values of the coefficients of the nonlinear spring stiffness function 24 Table 2-2 Chemical composition and operation conditions for the low-stress nickel electroplating solution 24 Table 3-1 Lower and upper bounds on the design variables 60 Table 3-2 The values of the design variables of the optimum design 60 Table 3-3 The values of the design variables of the optimum design of the microscale QM 60 Table 4-1 Lower and upper bounds on the design variables 89 Table 4-2 The values of the design variables of the optimum design 89 viii issue but can also expand into energy harvesting perspective While most conventional energy harvesters are based on linear resonators that collect a narrow band of vibrations (Wang and Ko 2010), Ando et al (2010) proves that there is a significant enhancement in device performances when consider the nonlinear behavior of a bistable microelectromechanical system for energy harvesting applications Further study for the nonlinear response of multistable mechanisms with respect to external vibration would be an interesting topic in the future 102 Bibliographies [1] Ando, B., Baglio, S., Trigona, C., Dumas, N., Latorre, L., and Nouet, P., 2010, “Nonlinear Mechanism in MEMS Devices for Energy Harvesting Applications,” Journal of 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727-732 114 Publications during Ph.D studies A Journal [1] Pham, H.T and Wang, D.A., 2011, “A Quadristable Compliant Mechanism with a Bistable Structure Embedded in a Surrounding Beam Structure,” Sensors and Actuators A ! Physical, Vol 167, pp 438-448 (SCI) [2] Pham, H.T and Wang, D.A., 2011, “A Constant-Force Bistable Mechanism for Force Regulation and Overload Protection,” Mechanism and Machine Theory, Vol 46, pp 899-909 (SCI) [3] Wang, D.A., Chuang, W.Y., Hsu, K., and Pham, H.T., 2011, “Design of a Bézier-Profile Horn for High Displacement Amplification”, Ultrasonics, Vol 51, pp 148-156 (SCI) [4] Wang, D.A., Chuang, W.Y., Hsu, K., and Pham, H.T., 2009, “Design and Analysis of a Bezier-Profile Horn,” Journal of Engineering, National Chung Hsing University, Vol 20, pp 161-169 [5] Wang, D.A., Pham, H.T., and Hsieh, Y.H., 2009, “Dynamical Switching of an Electromagnetically Driven Compliant Bistable Mechanism,” Sensors and Actuators A: Physical, Vol 149, pp 143-151 (SCI) 115 B Conferences [1] Wang, D.A., Pham, H.T., Chao, C.W., and Chen, J.M., 2011 “A Piezoelectric Energy Harvester Based on Pressure Fluctuations in Kármán Vortex Street” World Renewable Energy Congress, May 8-11, 2011, Linkoping, Sweden [2] Pham, H.T., Chiu, C.Y., and Wang, D.A., 2011, “An Electromagnetic Energy Harvester Based on Pressure Fluctuation in Kármán Vortex Street,” The 1st International Symposium on Automotive & Convergence Engineering, HCM city University of Technology, Jan 19-21, 2011, Vietnam, pp 33-36 [3] Pham, H.T and Wang, D.A., 2008, “A Microswitch Actuated by Bistable Micromechanism,” Asia-Pacific Conference on Transducers and Micro-Nano Technology, (APCOT 2008), June 22-25, Tainan, Taiwan [4] Wang, D.A and Pham, H.T., 2008, “Vibration – Actuated Bistable Micromechanism for Microassembly,” Technical Proceedings of the 2008 Nanotechnoly Conference and Trade Show, June 1-5, 2008, Vol.3, pp 639-642, Boston, Massachusetts, USA 116 ... Design and Analysis of Multistable Compliant Mechanisms Huy- Tuan Pham Graduate Institute of Precision Engineering Doctor of Philosophy (ABSTRACT) Multistable... al 2005), valves (Wagner et al 1996), feeding systems (Tsay et al 2005), microassembly (Wang and Pham 2008), and energy harvesting (Ando et al 2010; Stanton et al 2010) Low actuation force and