Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Gradient Index Based Robust Optimal Design Method for MEMS Structures

구배 지수에 근거한 MEMS 구조물의 강건 최적 설계 기법

  • 한정삼 (한국과학기술원 기계기술연구소) ;
  • 곽병만 (한국과학기술원 기계공학과)
  • Published : 2003.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we present a simple and efficient robust optimal design formulation for MEMS structures and its application to a resonant-type micro probe. The basic idea is to use the gradient index (GI) to improve robustness of the objective and constraint functions. In the robust optimal design procedure, a deterministic optimization for performance of MEMS structures is followed by design sensitivity analysis with respect to uncertainties such as fabrication errors and change of operating conditions. During the process of deterministic optimization and sensitivity analysis, dominant performance and uncertain variables are identified to define GI. The GI is incorporated as a term of objective and constraint functions in the robust optimal design formulation to make both performance and robustness improved. While most previous approaches for robust optimal design require statistical information on design variations, the proposed GI based method needs no such information and therefore is cost-effective and easily applicable to early design stages. For the micro probe example, robust optimums are obtained to satisfy the targets for the measurement sensitivity and they are compared in terms of robustness and production yield with the deterministic optimums through the Monte Carlo simulation. This method, although shown for MEMS structures, may as well be easily applied to conventional mechanical structures where information on uncertainties is lacking but robustness is highly important.

Keywords

References

  1. Shoemaker, A.C., Tsui, K.L. and Wu, C.F.J., 1991, 'Economical Experimentation Methods for Robust Parameter Design,' Technometrics, Vol. 33, pp. 415-427 https://doi.org/10.2307/1269414
  2. Chen, W., Allen, J.K., Tsui, K.L. and Mistree, F., 1996, 'A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors,' J. Mech. Des., Vol. 118, pp. 478-485 https://doi.org/10.1115/1.2826915
  3. Gao, X., Low, T.S., Chen, S. and Liu, Z., 2001, 'Structural Robust Design for Torque Optimization of BLDC Spindle Motor Using Response Surface Methodology,' IEEE Transactions on Magnetics, Vol. 37, No. 4, pp. 2814-2817 https://doi.org/10.1109/20.951315
  4. Parkinson, A., Sorensen, C. and Pourhassan, N., 1993, 'A General Approach for Robust Optimal Design,' J. Mech. Des., Vol. 115, pp. 74-80 https://doi.org/10.1115/1.2919328
  5. Wu, Y.T, Millwater, H.R. and Cruse, T.A., 1990, 'Advanced Probabilistic Structural Analysis Method for Implicit Performance Functions,' AIAA Journal, Vol. 28, No. 9, pp. 1663-1669 https://doi.org/10.2514/3.25266
  6. Hasofer, A.M. and Lind, N.C., 1974, 'Exact and Invariant Second-Moment Code Format,' ASCE Journal of the Engineering Mechanics, Vol. 100, pp. 111-121
  7. Ayyub, B.M. and Haldar, A., 1984, 'Practical Structural Reliability Techniques,' Journal of Structural Engineering, Vol. 110, No. 8, pp. 1707-1724 https://doi.org/10.1061/(ASCE)0733-9445(1984)110:8(1707)
  8. Nikolaidis, E. and Burdisso, R., 1988, 'Reliability based Optimization: a Safety Index Approach,' Computers & Structures, Vol. 28, No. 6, pp. 781-788 https://doi.org/10.1016/0045-7949(88)90418-X
  9. Kwak, B.M. and Lee, T.W., 1987, 'Sensitivity Analysis for Reliability-based Optimization Using an AFOSM Method,' Computers & Structures, Vol. 27, No.3, pp. 399-406 https://doi.org/10.1016/0045-7949(87)90064-2
  10. Jung, D. H. and Lee, B.C., 2000, 'Development of an Efficient Optimization Technique for Robust Design by Approximating Probability Constraints,' Transactions of the KSME, A, Vol. 24, No. 12, pp. 3053-3060
  11. Seo, H.S. and Kwak, B.M., 2002, 'Efficient Statistical Tolerance Analysis for General Distributions Using Three-Point Information,' Int. J Prod. Res., Vol. 40, No. 4, pp. 931-944 https://doi.org/10.1080/00207540110095709
  12. Ko, J.S., Cho, Y.H., Kwak, B.M. and Park, K.H., 1996, 'Design, Fabrication and Testing of a Piezoresistive Cantilever-Beam Microaccelerometer for Automotive Airbag Applications,' Transactions of the KSME, A, Vol. 20, No. 2, pp. 408-413
  13. Ko, J.S., Lee, M.L., Lee, D.S., Choi, C.A. and Kim, YT, 2002, 'Development and Application of a Laterally Driven Electromagnetic Microactuator,' Appl. Phys. Lett., Vol. 81, pp. 547-549 https://doi.org/10.1063/1.1494462
  14. Chiao, M. and Lin, L., 2000, 'Self-Buckling of Micromachined Beams under Resistive Heating,' J. Microelectromech. Syst., Vol. 9, No. 1, pp. 146-151 https://doi.org/10.1109/84.825789
  15. Han, J.S. and Kwak, B.M., 2001, 'Robust Optimal Design of a Vibratory Micro Gyroscope Considering Fabrication Errors,' J. Micromech. Microeng., Vol. 11, pp. 662-671 https://doi.org/10.1088/0960-1317/11/6/307
  16. Han, J.S. and Kwak, B.M., 2002, 'Robust Design in Terms of Minimization of Sensitivity to Uncertainty and Its Application to Design of Micro Gyroscopes,' Transactions of the KSME, A, Vol. 26, No. 9, pp. 1931-1942 https://doi.org/10.3795/KSME-A.2002.26.9.1931
  17. Hwang, K.H., Lee, K.H., Park, G.J., Lee, B.L., Cho, Y.C. and Lee, S.H., 2002, 'Robust Design of the Vibratory Gyroscope with Unbalanced Inner Torsion Gimbal Using Axiomatic Design,' Transactions of the KSME, A, Vol. 26, No. 5, pp. 914-923 https://doi.org/10.3795/KSME-A.2002.26.5.914
  18. Delauche, F., Affour, B. and Dufaza, C., 2002, 'Parametric Yield Optimization of MEMS,' DTIP of MEMS/MOEMS, Proc. SPIE, Vol. 4755, pp. 126-135 https://doi.org/10.1117/12.462802
  19. Muchow, J., Kretschmann, A., Henn, R., Skrobanek, K., Finkbeiner, S. and Krauss, H.R., 2002, 'Influence of Process Variation on the Functionality of a High Pressure Sensor,' DTIP of MEMS/MOEMS, Proc. SPIE, Vol. 4755, pp. 143-148 https://doi.org/10.1117/12.462804
  20. Germer, C., Hansen, U., Franke, H.J. and Buttgenbach, S., 2002, 'Tolerance Analysis and Synthesis in Micro Systems,' DTIP of MEMS/MOEMS, Proc. SPIE, Vol. 4755, pp. 355-364 https://doi.org/10.1117/12.462832
  21. Vanderplaats, G.N., 1984, 'Numerical Optimization Techniques for Engineering Design with Applications,' McGraw-Hill, New York
  22. DOT Users Manual version 4.20, 1995, VR&D
  23. Lebrasseur, E., Bourouina, T, Pourciel, J., Ozaki, M., Masuzawa, T and Fujita, H., 2000, 'Resonant-Type Micro-Probe for Vertical Profiler,' 2000 International Conference on Modeling and Simulation of Microsystems, pp. 285-288