Harmonic Poly-Actuator: Design and Control of a New Piezoelectric Mechanism by James Torres B.S., Mechanical Engineering, Massachusetts Institute of Technology, 2010 M.S., Mechanical Engineering, Massachusetts Institute of Technology, 2012 Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of ARCHIVES Doctor of Philosophy in Mechanical Engineering MASSACHUSETTS INSTITUTE OF TECHNOLOGY at the OCT 01 2015 MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2015 LIBRARIES @ Massachusetts Institute of Technology 2015. All rights reserved. Signature redacted Author.. Department of Mechanical Engineering September 1, 2015 Signature redacted Certified by ......................... y H. Harry Asada Ford Professor of Mechanical Engineering Thesis Supervisor Signature redacted A ccepted by ........................... David E. Hardt Chairman, Department Committee on Graduate Students Department of Mechanical Engineering 2 Harmonic Poly-Actuator: Design and Control of a New Piezoelectric Mechanism by James Torres Submitted to the Department of Mechanical Engineering on September 1, 2015, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Abstract Piezoelectric devices, e.g. piezoelectric stack actuators, have several salient features inherent to their structure. They are efficient, have a high bandwidth, and their capacitive loading allows for static loads to be maintained with virtually no power consumption. The major preventative drawback that limits more widespread use is the small strain, on the order of 0.1%. For marco-scale applications, the displace- ment must be amplified, typically through mechanical or frequency leveraging. Both have inherent limitations: mechanical devices can increase the stroke but is naturally limited; and frequency devices relies on friction and is limited to nanopositioning. In this thesis, we investigate combining a unique mechanical amplification with a frequency amplification device that does not rely on friction to produce an arbitrarily large stroke linear actuator. The first stage of amplification aims to achieve the great- est displacement amplification without sacrificing force capabilities. The second stage relies on the coordinated actuation of multiple copies of the mechanically amplified device to produce a long stroke, smooth force poly-actuator. The theoretical design concepts for each stage of amplification are explicitly derived. The mechanical ampli- fication device uses rolling contact joints to maintain stiff connections to transmit the force without losses due to friction; and the frequency amplification uses a sinusoidal Transmission interface to exploit a passive balancing of undesirable non-linearities, proven by harmonic analysis. A unique control algorithm is developed to produce a wide variety of capabilities. The theoretical findings are supported by experimen- tal prototypes. The mechanical amplification device produces a comparable energy density while amplifying the displacement by an additional factor 10. The proof- of-concept poly-actuator prototype can continually produce 100 Newtons of force over a stroke of 200 mm. We conclude with simulations, which are verified through physical experiments, used to estimate several performance metrics for comparison. Thesis Supervisor: H. Harry Asada Title: Ford Professor of Mechanical Engineering 3 4 Acknowledgments First and foremost, I would like to thank Professor Asada. Over the past two years he has acted as my mentor and has helped develop my creativity, an attribute I never considered a strength prior to working with him. I greatly appreciate the patience he afforded me, while constantly pushing to me strive forward. Furthermore, I would also like to thank the Sumitomo Heavy Industries, for their generous financial support that allowed me to pursue this captivating research and continue to grow as a student, an engineer, and a person. I am grateful to my colleagues at the d'Arbeloff Laboratory. They were always available to provide another mind to brainstorm with, or a laugh when needed. Specif- ically, I thank Shinichiro Tsukahara who unquestionably helped me develop as an engineer, who taught me practices and tips not available in the classroom and how' to attack a problem from all directions, and who I am blessed to call a friend. Finally, and most importantly, I must thank my parents for their unwavering love and who serve as constant pillars of support. I am proud to say that I would not be the person I am today without the teaching, motivation, and care they have always provided me. 5 6 Contents 1 Introduction 21 1.1 Piezoelectric Actuator Technology . . . 21 1.2 Previous Work . . . . . . . . . . . . . . 22 1.2.1 Amplification Mechanisms . . . . 22 1.2.2 Additional Actuator Types . . . . 24 1.3 Thesis Scope . . . . . . . . . . . . . . . . 24 2 Amplification Mechanism 27 2.1 Analysis of the Output Work Cycle . . . . . . . . . . . . . . . 27 2.2 Buckling Amplification Concept . . . . . . . . . . . . . . . . . 30 2.2.1 Kinem atics . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2.2 Functional Requirements of the Rotational Joint . . . . . . . 34 2.3 Rolling Contact Flexure-Free Rotational Joint . . . . . . . . . 34 2.3.1 Kinematics of Rolling Contact Joint . . . . . . . . . . . 36 2.3.2 Maximizing Transmissibility . . . . . . . . . . . . . . . 39 3 Harmonic Poly-Actuator 49 3.1 Harmonic Poly-Actuator Concept . . . . . . . . . . . . . . . . . . . . 49 3.2 Theoretical Analysis . ... . . . . . . . . . . . . . . . . . . . . . . . . 51 3.2.1 Formulation of Unit Properties and Output Force . . . . . . . 51 3.2.2 Elimination of the Effect of Non-Linear Stiffness . . . . . . . . 53 3.2.3 Transmission of Dynamics . . . . . . . . . . . . . . . . . . . . 56 3.2.4 Single Frequency Sinusoidal Inputs . . . . . . . . . . . . . . . 58 7 3.2.5 Input Null Space . . . . . . . . . . . . 62 3.3 Force Ripple due to Unit Imbalance . . . . . . 64 3.3.1 Unit Properties . . . . . . . . . . . . . 64 3.4 Generalization of the Transmission Function . 67 3.5 Control Synthesis . . . . . . . . . . . . . . . . 69 3.5.1 On-Off Control Timing . . . . . . . . . . . . . . . . . . . . 70 3.5.2 Continuous Control . . . . . . . . . . . . . . . . . . . . . . 73 4 Implementation 77 4.1 Buckling Amplification Unit . . . . . . . . . . 77 4.1.1 Proof-of-Concept Unit . . . . . . . . . 77 4.1.2 Poly-Actuator Buckling Unit . . . . . . 81 4.1.3 Design Optimization . . . . . . . . . . 85 4.2 Poly-Actuator . . . . . . . . . . . . . . . . . . 87 4.2.1 Additional Considerations . . . . . . . 90 4.3 Experimental Implementation . . . . . . . . . 91 4.3.1 Implementation of Electronics . . . . . 91 4.3.2 Force Ripple Compensation Based on E rror Model 91 4.3.3 Unit Force Control . . . . . . . . . . . 93 4.3.4 Position Control . . . . . . . . . . . . . 94 4.3.5 Simulation . . . . . . . . . . . . . . . . 95 5 Experimental and Simulation Results 97 5.1 Unit Results . . . . . . . . . . . . . . . . . . . 97 5.1.1 Proof-of-Concept Unit . . . . . . . . . 97 5.1.2 Poly-Actuator Unit . . . . . . . . . . . 99 5.1.3 Discussion . . . . . . . . . . . . . . . . 100 5.2 Poly-Actuator Results . . . . . . . . . . . . . 101 5.2.1 Experimental Results . . . . . . . . . . 101 5.2.2 Simulation Results . . . . . . . . . . . 110 5.2.3 Discussion . . . . . . . . . . . . . . . . 117 8 6 Conclusion and Future Work 119 6.1 Project Goals ....... ............................... 119 6.2 Contributions ....... ............................... 120 6.3 Future Wo rk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 A Derivation of the Mechanism Transmissibility 125 9 10