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Modeling and sensitivity analysis of a pneumatic vibration isolation system with two air chambers. (English) Zbl 1377.74008

Summary: This paper aims at accurate modeling and sensitivity analysis for a pneumatic vibration isolation system (PVIS) as a foundation for practical design. Even though the PVIS is widely used for its effective performance in vibration isolation, its design has depended largely on trial-and-error methods. In previous studies, nonlinear characteristics of the diaphragm and the air flow restrictor, which significantly affect the performance of a PVIS, have been investigated. However, several hurdles, such as the absence of a mathematical model for the diaphragm, still remain with regard to the model-based prediction of performance. Therefore, a fractional derivative model for the diaphragm and a quadratic damping model for the air flow restrictor are newly developed based on the careful examination of previous studies. Then, sensitivities of vibration isolation performance indices with regard to major design variables are analyzed and new approximation formulas are created based on the dynamic characteristics of the PVIS. Our models with a transmissibility-computing algorithm are verified by comparison with experimental data. The sensitivity analyses and approximation formulas are expected to be useful for practical PVIS design owing to their simplicity and accuracy.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S99 Numerical and other methods in solid mechanics
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[1] Ungar, E. E.; Sturz, D. H.; Amick, H.: Vibration control design of high technology facilities, Sound and vibration July, 20-27 (1990)
[2] Gordon, C. G.: Generic criteria for vibration-sensitive equipment, Proceedings of SPIE 1619, 71-85 (Nov 1991)
[3] Amick, H.; Gendreau, M.; Busch, T.; Gordon, C.: Evolving criteria for research facilities: I – vibration, , 1-13 (2005)
[4] Heiland, K. P.: Recent advancements in passive and active vibration control systems, Vibration control in microelectronics, optics, and metrology 1619, 22-33 (Feb 1992)
[5] Newport corporation homepage, http://www.newport.com (Accessed 29 July 2008).
[6] Technical manufacturing corporation homepage, http://www.techmfg.com (Accessed 29 July 2008).
[7] Lee, C. -M.; Goverdovskiy, V. N.; Temnikovb, A. I.: Design of springs with negative stiffness to improve vehicle driver vibration isolation, Journal of sound and vibration 302, 865-874 (2007)
[8] Ahn, K. G.; Pahk, H. J.; Jung, M. Y.; Cho, D. W.: A hybrid-type active vibration isolation system using neural networks, Journal of sound and vibration 192, No. 4, 793-805 (1996)
[9] Han, D. K.; Chang, P. H.: A robust two-time-scale control design for a pneumatic vibration isolator, , 1666-1672 (Dec 2007)
[10] Kato, T.; Kawashima, K.; Sawamoto, K.; Kagawa, T.: Active control of a pneumatic isolation table using model following control and a pressure differentiator, Precision engineering 31, 269-275 (2007)
[11] Porumamilla, H.; Kelkar, A. G.; Vogel, J. M.: Modeling and verification of an innovative active pneumatic vibration isolation system, Transactions of the ASME: journal of dynamic systems, measurement, and control 130, No. 3, 1-12 (2008)
[12] Erin, C.; Wilson, B.; Zapfe, J.: An improved model of a pneumatic vibration isolator: theory and experiment, Journal of sound and vibration 218, No. 1, 81-101 (1998)
[13] Lee, J. H.; Kim, K. J.: Modeling of nonlinear complex stiffness of dual-chamber pneumatic spring for precision vibration isolations, Journal of sound and vibration 301, No. 3-5, 909-926 (2007)
[14] Debra, D. B.: Design of laminar flow restrictor for damping pneumatic vibration isolators, CIRP annals 33, No. 1, 351-356 (1984)
[15] Popov, G.; Sankar, S.: Modelling and analysis of non-linear orifice type damping in vibration isolators, Journal of sound and vibration 183, No. 5, 751-764 (1995) · Zbl 1055.74533
[16] Heertjes, M.; Wouw, N.: Nonlinear dynamics and control of a pneumatic vibration isolator, Transactions of the ASME: journal of vibration and acoustics 128, 439-448 (2006)
[17] Nieto, A. J.; Morales, A. L.; Gonzalez, A.; Chicharro, J. M.; Pintado, P.: An analytical model of pneumatic suspensions based on an experimental characterization, Journal of sound and vibration 313, 290-307 (2008)
[18] Harris, C. M.; Crede, C. E.: Shock and vibration handbook, (1961)
[19] Hino, M.; Sawamoto, M.; Takasu, S.: Experiments on the transition to turbulence in an oscillating flow, Journal of fluid mechanics 75, 193-207 (1976)
[20] Washio, S.; Konishi, T.; Nishii, K.; Tanaka, A.: Research on wave phenomena in hydralic lines (9th report, experimental investigation of oscillatory orifice flows), Bulletin of the JSME 25, No. 210, 1906-1913 (1982)
[21] Fujita, T.; Okumura, H.; Yamada, T.; Inoue, N.; Endoh, S.; Kagawa, T.: Affection of connecting conduit to characteristics of air spring with subtank, Journal of JSME (part C) 63, No. 610, 1920-1926 (1997)
[22] Lee, J. H.; Kim, K. J.: A method of transmissibility design for dual-chamber pneumatic vibration isolator, Journal of sound and vibration 323, 67-92 (2009)
[23] Ibrahim, R. A.: Recent advances in nonlinear passive vibration isolators, Journal of sound and vibration 314, 371-452 (2008)
[24] Caputo, M.: Linear models of dissipation whose Q is almost frequency independent – II, Geophysical journal of the royal astronomical society 13, 529-539 (1967)
[25] Pritz, T.: Analysis of four-parameter fractional derivative model of real solid materials, Journal of sound and vibration 195, 103-115 (1996) · Zbl 1235.34026
[26] Jones, D. I. G.: Handbook of viscoelastic vibration damping, (2001)
[27] Nashif, A. D.; Jones, D. I. G.; Henderson, J. P.: Vibration damping, (1985)
[28] Xing, J. T.; Xiong, Y. P.; Price, W. G.: Passive-active isolation systems to produce or infinite dynamic modulus: theoretical and conceptual design strategies, Journal of sound and vibration 286, 615-636 (2005)
[29] Tse, F. S.; Morse, I. E.; Hinkle, R. T.: Mechanical vibrations: theory and applications, (1978)
[30] J.H. Moon, Analysis and optimal design of a pneumatic vibration isolation system, PhD Thesis, Seoul National University, 2002.
[31] White, F.: Fluid mechanics, (1994)
[32] Zhao, T. S.; Cheng, P.: Experimental studies on the onset of turbulence and frictional losses in an oscillatory turbulent pipe flow, International journal of heat and fluid flow 17, No. 4, 356-362 (1996)
[33] Saltelli, A.; Chan, K.; Scott, E. M.: Sensitivity analysis, (2000) · Zbl 0961.62091
[34] Arora, J. S.: Introduction to optimum design, (2004)
[35] Luenberger, D. G.: Linear and nonlinear programming, (1984) · Zbl 0571.90051
[36] Firestone Airstroke Actuator/Airmount Isolator Catalog, Firestone company, USA, 1996.
[37] Snowdon, J. C.: Vibration and shock in damped mechanical systems, (1968)
[38] Burden, R. L.; Faires, J. D.: Numerical analysis, (1997) · Zbl 0671.65001
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