Systematic Design of Displacement-Amplifying Mechanisms for Piezoelectric Stacked Actuators Using Topology Optimization

Abstract

Displacement-amplifying mechanisms can be systematically designed using topology optimization. Due to the special need for large displacement amplification of piezoelectric stacked actuators, suitable objective functions should be formulated. Among various possible formulations, this work considers maximum output stroke, magnification factor and mechanical efficiency as objective functions. As the formulation of maximum magnification factor performs better numerically than the rest, it is recommended as a suitable design goal for displacement amplifiers undergoing undamped harmonic response. The design problem is solved as a 2D material distribution problem using Method of Moving Asymptotes (MMA). Plane stress solid is assumed for the design domain. Stiffness of the actuator and the workpiece is included in the analysis. To show the viability of this design methodology, two examples of magnification mechanisms for printer heads driven at different excitation frequencies were presented.

Get full access to this article

View all access options for this article.

References

Ananthasuresh, G. K. 1994. “A new paradigm for Micro-Electro-Mechanical systems and investigations on compliant mechanisms synthesis,” Ph.D. Thesis (Ann Arbor: University of Michigan).

ANSYS 1998. Structural Analysis Guide, Release 5.5. ANSYS Inc: Canonsburg, PA.

Ballandras, S. , Basrour, S. , Robert, L. , Megtert, S. , Blind, P. , Rouillay, M. , Bernede, P. and Daniau, W. 1997. “Microgrippers fabricated by the LIGA technique,” Sensors and Actuators A, 58: 265-272.

Bendsøe, M. P. 1989. “Optimal shape design as a material distribution problem,” Structural Optimization, 1: 193-202.

Bendsøe, M. P. and Kikuchi, N. 1988

“Generating optimal topologies in structural design using a homogenization method,”

Comput. Meth. Appl. Mech. Engrg., 71: 197-224.

Chonan, S. , Jiang, Z. W. and Shimizu, H. 1995. “Modeling of miniature finger driven by piezoceramic stacked actuator,” Advanced Computational and Design Techniques in Applied Electromagnetic Systems, Elsevier, New York, pp. 277-280.

Frecker, M. I. and Canfield, S. 1999. “Methodology for design of compliant mechanisms with integrated smart materials,” Proceedings 1999 NSF Design and Manufacturing Division Grantees Conference, Long Beach, California.

Garcia-Bonito, J. , Brennan, M. J. , Elliott, S. J. , David, A. and Pinnington, R. J. 1998. “A novel high-displacement piezoelectric actuator for active vibration control,” Smart Mater. Struc., 7: 31-42.

Haertling, G. H. 1994. “Rainbow ceramics—a new type of ultra-high-displacement actuator,” American Ceramic Society Bulletin, 73: (1) 93-96.

10.

Haftka, R. T. and Gurdal, Z. 1991. Elements of Structural Optimization. Dordrecht: Kluwer.

11.

King, T. 1998. “Piezo actuators—can they give enough displacement for ‘real world’ applications?” IEE Colloquium on Limited Motion Electrical Actuation Systems (Digest No. 1998/494) pp. 2/1-2/6.

12.

Lau, G. K. , Du, H. and Lim, M. K. 1999. “Use of functional specifications as objective functions in topological optimization of compliant mechanism,” Submitted for publication.

13.

Nishiwaki, S. , Frecker, M. I. , Min, S. and Kikuchi, N. 1998. “Topology optimization of compliant mechanisms using the homogenization method,” Int. J. Numer. Meth. Engng., 42: 535-559.

14.

Physika Instrumente, Theory and applications of piezo actuators and PZT nano positioning systems, http://www.physikinstrumente.com/tutorial/index.html.

15.

Robbins, W. P. , Polla, D. L. and Glumac, D. E. , 1991. “High-displacement piezoelectric actuator utilizing a meander-line geometry—part I: experimental characterization,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 38: (5) 454-460.

16.

Rossow, M. P. and Taylor, J. E. 1973. “A finite element method for the optimal design of variable thickness sheets,” AIAA Journal, 11: (11) 1566-1569.

17.

Samak, D. K. and Chopra, I. 1996. “Design of high force, high displacement actuators for helicopter rotors,” Smart Mater. Struct., 5: 58-67.

18.

Sigmund, O. 1997. “On the design of compliant mechanisms using topology optimization,” Mech. Struct. & Mach., 25: (4) 493-524.

19.

Sugawara, Y. , Onitsuka, K. , Yoshikawa, S. , Xu, Q. C. , Newnham, R. E. and Uchino, K. 1992. “Metal-ceramic composite Actuators,” J. Am. Ceram. Soc., 75: (4) 996-998.

20.

Suzuki, K. and Kikuchi, N. 1992. “A homogenization method for shape and topology optimization,” Comput. Meth. Appl. Mech. Engrg., 93: 291-318.

21.

Svanberg, K. 1987. “The method of moving asymptotes—a new method for structural optimization,” Int. J. Numer. Meth. Engng., 24: 359-373.

22.

Uchino, K. 1986. “Electrostrictive actuators: materials and applications,” American Ceramic Society Bulletin, 65: 647-652.

23.

Xu, W. and King, T. G. 1995. “Mechanical amplifier design for piezo-actuator applications,” IEE Colloquium on Innovative Actuators for Mechatronic Systems, pp. 1/1-1/5.

24.

Zienkiewicz, O. C. and Taylor, R. L. 1991. The Finite Element Method Volume 2, McGraw-Hill, UK, pp. 336-342.