Investigation on effect of surface roughness pattern to dynamic performance of mems resonators in various types of gases and gas rarefaction

Lam Minh Thinh, Phan Minh Truong, Trinh Xuan Thang, Ngo Vo Ke Thanh, Le Quoc Cuong, Nguyen Chi Cuong
Author affiliations

Authors

  • Lam Minh Thinh Research Laboratories of Saigon High-Tech-Park, Lot I3, N2 street, Saigon Hi-Tech-Park, district 9, Ho Chi Minh city, Viet Nam
  • Phan Minh Truong Institute for Computational Science and Technology, Room 311(A&B), SBI building, Quang Trung Software City, Tan Chanh Hiep ward, district 12, Ho Chi Minh city, Viet Nam
  • Trinh Xuan Thang Research Laboratories of Saigon High-Tech-Park, Lot I3, N2 street, Saigon Hi-Tech-Park, district 9, Ho Chi Minh city, Viet Nam
  • Ngo Vo Ke Thanh Research Laboratories of Saigon High-Tech-Park, Lot I3, N2 street, Saigon Hi-Tech-Park, district 9, Ho Chi Minh city, Viet Nam
  • Le Quoc Cuong Department of Information and Communications, Ho Chi Minh City, Viet Nam, 59 Ly Tu Trong street, Ben Nghe ward, district 1, Ho Chi Minh city, Viet Nam
  • Nguyen Chi Cuong Research Laboratories of Saigon High-Tech-Park, Lot I3, N2 street, Saigon Hi-Tech-Park, district 9, Ho Chi Minh city, Viet Nam

DOI:

https://doi.org/10.15625/2525-2518/59/5/15478

Keywords:

Quality factor of micro-beam resonator, squeeze film damping (SFD), surface roughness, gas rarefaction, types of gases.

Abstract

The average modified molecular gas lubrication (MMGL) equation, which is modified with pressure flow factors and effective viscosity, is utilized to analyze the squeeze film damping (SFD) on micro-beam resonators considering effect of surface roughness pattern in various types of gases and gas rarefaction. Then, effect of surface roughness pattern (film thickness ratio and Peklenik number) is discussed on the quality factor (Q-factor) of micro-beam resonators in various types of gases and gas rarefaction. Thus, effect of surface roughness pattern is significantly reduced as effective viscosity of gas decreases in higher mode of resonator and higher gas rarefaction.

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References

Zhang W. M., Hu K. M., Peng Z. K. and Meng G. – Tunable Micro- and Nanomechanical Resonators, Sensors. 15 (10) (2015) 26478-26566. DOI: https://doi.org/10.3390/s151026478

Veijola T., Kuisma H., Lahdenperä J. and Ryhänen T. – Equivalentcircuit model of the squeezed gas film in a silicon accelerometer, Sensor. Actuat. A-Phys. 48 (3) (1995) 239–248. DOI: https://doi.org/10.1016/0924-4247(95)00995-7

Li W. L., Weng C. l. and Hwang C. C. – Effects of roughness orientations on thin film lubrication of a magnetic recording system, J. Phys D: Appl. Phys. 28 (1995) 1011-1021. DOI: https://doi.org/10.1088/0022-3727/28/6/001

Hamrock B. J. – Fundamentals of Fluid Film Lubrication, McGraw-Hill, New York, 1994.

Fukui S. and Kaneko R. – Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized Boltzmann Equation: First Report—Derivation of a Generalized Lubrication Equation Including Thermal Creep Flow, J. Tribol-T. ASME. 110 (2) (1988) 253-261. DOI: https://doi.org/10.1115/1.3261594

Mitsuya Y. – A Simulation Method for Hydrodynamic Lubrication of Surfaces with Two-Dimensional Isotropic or Anisotropic Roughness Using Mixed Average Film Thickness, Bulletin of JSME. 27 (231) (1984) 2036-2044. DOI: https://doi.org/10.1299/jsme1958.27.2036

Li W. L. and Weng C. I. – Modified average Reynolds equation for ultra-thin film gas lubrication considering roughness orientations at arbitrary Knudsen numbers, Wear. 209 (1-2) (1997) 292-300. DOI: https://doi.org/10.1016/S0043-1648(97)00019-7

Li W. L. – Analytical modelling of ultra-thin gas squeeze film, Nanotechnology. 10 (4) (1999) 440–446. DOI: https://doi.org/10.1088/0957-4484/10/4/314

Li W. L. – Modeling of Head/Disk Interface—An Average Flow Model, Tribol. Lett. 17 (3) (2004) 669-676. DOI: https://doi.org/10.1023/B:TRIL.0000044518.79255.03

Li W. L. – Squeeze film effects on dynamic performance of MEMS μ-mirrors-consideration of gas rarefaction and surface roughness, Microsyst. Technol. 14 (3) (2008) 315-324. DOI: https://doi.org/10.1007/s00542-007-0479-x

Zhang W. M., Meng G., Peng Z. K. and Chen D. – Coupled Nonlinear Effects of Random Surface Roughness and Rarefaction on Slip Flow in Ultra-Thin Film Gas Bearing Lubrication, J. Tribol-T. ASME. 134 (2012a) 024502. DOI: https://doi.org/10.1115/1.4006443

Patir N. and Cheng H. S. – An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication, J. Tribol-T. ASME. 100 (1) (1978) 12-17. DOI: https://doi.org/10.1115/1.3453103

Bhushan B. and To̸nder K. – Roughness-Induced Shear- and Squeeze-Film Effects in Magnetic Recording—Part I: Analysis, J. Tribol-T. ASME. 111 (1989a) 220-227. DOI: https://doi.org/10.1115/1.3261892

Bhushan B. and To̸nder K. – Roughness-Induced Shear- and Squeeze-Film Effects in Magnetic Recording—Part II: Applications, J. Tribol-T. ASME. 111 (1989b) 228-237. DOI: https://doi.org/10.1115/1.3261893

Chang K. M., Lee S. C. and Li S. H. – Squeeze film damping effect on a MEMS torsion mirror, J. Micromech. Microeng. 12 (2002) 556-561. DOI: https://doi.org/10.1088/0960-1317/12/5/307

Pandey A. K. and Pratap R. – Coupled nonlinear effects of surface roughness and rarefaction on squeeze film damping in MEMS structures, J. Micromech. Microeng. 14 () (2004) 1430–1437. DOI: https://doi.org/10.1088/0960-1317/14/10/020

Li W. L. – A Database for Interpolation of Poiseuille Flow Rate for Arbitrary Knudsen Number Lubrication Problems, J. Chin. Inst. Eng. 26 (4) (2003) 455-466. DOI: https://doi.org/10.1080/02533839.2003.9670799

Nguyen C. C. and Li W. L. – Effect of gas rarefaction on the quality factors of micro-beam resonators, Microsyst. Technol. 23 (2016a) 3185–3199. DOI: https://doi.org/10.1007/s00542-016-3068-z

Nguyen C. C. and Li W. L. – Effects of surface roughness and gas rarefaction on the quality factor of micro-beam resonators, Microsyst. Technol. 23 (2016b) 3489–3504. DOI: https://doi.org/10.1007/s00542-016-3140-8

Nguyen C. C. and Li W. L. – Influences of temperature on the quality factors of micro-beam resonators in gas rarefaction, Sens. Actuators. A. Phys. 261 (2017) 151–165. DOI: https://doi.org/10.1016/j.sna.2017.04.050

Nguyen C. C., Ngo V. K. T., Le H. Q. and Li W. L. – Influences of relative humidity on the quality factors of MEMS beam resonators in gas rarefaction, Microsyst. Technol. 25 (2018) 2767–2782. DOI: https://doi.org/10.1007/s00542-018-4239-x

Sutherland W. – The viscosity of gases and molecular force, Philos. Mag. Series. 5 (36) (1893) 507-531. DOI: https://doi.org/10.1080/14786449308620508

Chapman S. and Cowling T. G. – The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases, Cambridge University Press, Cambridge, England, 1970, pp. 86-96.

Kennard E. H. – Kinetic Theory of Gases with an Introduction to Statistical Mechanics, McGraw-Hill, New York and London, 1938, pp. 149.

Leissa A. W. – Vibration of Plates, NASA, Washington DC, 1969, pp. 1–6.

Reddy J. N. – An introduction to the finite element method, McGraw-Hill, New York, 1993.

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Published

26-10-2021

How to Cite

[1]
L. M. Thinh, P. M. Truong, T. X. Thang, N. V. K. Thanh, L. Q. Cuong, and N. C. Cuong, “Investigation on effect of surface roughness pattern to dynamic performance of mems resonators in various types of gases and gas rarefaction ”, Vietnam J. Sci. Technol., vol. 59, no. 5, pp. 643–661, Oct. 2021.

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Section

Mechanical Engineering - Mechatronics

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