Open Access Open Access  Restricted Access Subscription or Fee Access

Stiffness of a Nonlinear Adiabatic Polytropic Air Spring Model: Quantitative and Conductive Investigation


(*) Corresponding author


Authors' affiliations


DOI: https://doi.org/10.15866/iremos.v13i3.18761

Abstract


The conservation of mass and energy formulas along with the Newton’s second law of motion are used to derive a simple nonlinear adiabatic air spring model. The purpose of this paper is to evaluate air spring stiffness and identify the characteristic behavior of this model. The model consists of six coupled nonlinear differential equations. The assessment of this model is based on solving these governing equations numerically using the Runge Kutta routine Matlab based platform. It has been found out that the air spring stiffness increases exponentially with the increase in the air spring piston diameter. Due to its sensitivity and its nonlinearity, the model shows signs of chaos, which have been observed in the vertical motion or in the control volume, pressure for the chosen range of parameters.
Copyright © 2020 Praise Worthy Prize - All rights reserved.

Keywords


Air spring; Newton’s Second Law; Conservation of Energy; Isentropic Relations; Runge Kutta Method; Compressible Bernoulli’s Equation; Orifice Flow; Chaos; Poincaré Map

Full Text:

PDF


References


Bachrach, B. I., Rivin, E., Analysis of a Damped Pneumatic Spring, Journal of Sound and Vibrations, 86(2), pp. 191-197, 1983.
https://doi.org/10.1016/0022-460x(83)90748-4

Rivin E., Passive Vibration Isolation, John Wiley & Sons, 2003.

Karnopp D., Active and Semi-Active Vibration Isolation, Journal of Vibrations and Acoustics, vol. 117, No. 3B, pp. 177-185, 1995.
https://doi.org/10.1115/1.2838660

Erin C., Wilson B., Zapfe J., An Improved Model of a Pneumatic Vibration Isolator: Theory and Experiment, Journal of Sound and Vibration, 218(1), pp. 81-101, 1998.
https://doi.org/10.1006/jsvi.1998.1777

Quaglia, G., Sorli, M., Air suspension dimensionless analysis and design procedure, Vehicle System Dynamics, 35 (6), pp. 443-475, 2001.
https://doi.org/10.1076/vesd.35.6.443.2040

Qing, O., Yin, S., The non-linear mechanical properties of an airspring, Mechanical Systems and Signal Processing, 17 (3), pp. 705-711, 2003.
https://doi.org/10.1006/mssp.2001.1434

Lee J. H., Kim K. J., 2007, Modeling of Nonlinear Complex Stiffness of Dual-Chamber Pneumatic Spring for Precision Vibration Isolations, Journal of Sound and Vibrations, 301, pp. 909-926, 2007.
https://doi.org/10.1016/j.jsv.2006.10.029

Cor-Jacques Kat and Pieter Schalk Els, Interconnected air spring model, Mathematical and Computer Modelling of Dynamical Systems, vol. 15, No. 4, pp. 353-370, 2009.
https://doi.org/10.1080/13873950902955783

Alonso, A., Gimenez, J.G., Nieto, J., Vinolas, J., Air suspension characterization and effectiveness of a variable area orifice, Vehicle System Dynamics, 48 (Suppl. 1), pp. 271-286, 2010.
https://doi.org/10.1080/00423111003731258

Holtz, M.W., van Niekerk, J.L., Modelling and design of a novel air-spring for a suspension seat, Journal of Sound and Vibration, 329 (21), pp. 4354-4366, 2010.
https://doi.org/10.1016/j.jsv.2010.04.017

Alonso, A., Gil-Negrete, N., Nieto, J., Gimenez, J.G., Development of a rubber component model suitable for being implemented in railway dynamic simulation programs, J. Sound Vib., 332 (12), pp. 3032–3048, 2013.
https://doi.org/10.1016/j.jsv.2013.01.002

Mazzola, L., Berg, M., Secondary suspension of railway Vehicles-Air spring modeling: performances and critical issues, Proc. Inst. Mech. Eng., Part F: J. Rail Rapid Transit, 228 (3), pp. 225–241, 2014.
https://doi.org/10.1177/0954409712470641

Renno, F., Strano, S., Terzo, M., Air spring and magnetorheological damper: An integrated solution for vibration control, Lecture Notes in Engineering and Computer Science, 2218, pp. 945-950, 2015.

Renno, F., Strano, S., Terzo, M., Development and validation of an air spring multiphysical model, Engineering Letters, 25 (2), pp. 176-182, 2017.

Zhu, H., Yang, J., Zhang, Y., Feng, X., A novel air spring dynamic model with pneumatic thermodynamics, effective friction and viscoelastic damping, Journal of Sound and Vibration, 408, pp. 87-104, 2017.
https://doi.org/10.1016/j.jsv.2017.07.015

Pintado, P., Ramiro, C., Morales, A.L., Nieto, A.J., Chicharro, J.M., The dynamic behavior of pneumatic vibration isolators, Journal of Vibration and Control, 24 (19), pp. 4563-4574, 2018.
https://doi.org/10.1177/1077546317730243

Razdan, S., Bhave, S., Pathak, C., Awasare, P., Active Air Suspension for a Vehicle Based on Control of Air Mass Flow Rate, (2018) International Review of Mechanical Engineering (IREME), 12 (6), pp. 501-515.
https://doi.org/10.15866/ireme.v12i6.14313

Bu, W., Shi, L., He, L., Xu, W., Multi-objective coordinated attitude control method for dual layer air spring vibration isolation mounting, (2019) Guofang Keji Daxue Xuebao/Journal of National University of Defense Technology, 41 (6), pp. 70-74.

Yu, Q., Xu, D., Zhu, Y., Guan, G., Li, Q., Dynamics analysis on the horizontal isolation effect of an air spring vibration isolator in series with an inverted pendulum, (2019) Zhendong yu Chongji/Journal of Vibration and Shock, 38 (14), pp. 176-180.

Guan, Z.-H., Wei, Z., Shangguan, W.-B., Study on the Influence of Nonlinearity of Bushing and Air Spring Stiffness in Truck Suspension System on Joint Forces and Moments Calculation, (2020) SAE Technical Papers.
https://doi.org/10.4271/2020-01-1395

Munson, Bruce Roy, Fundamentals of Fluid Mechanics, John Wiley & Sons, Inc., 2013.

White, F. M., 1991, Viscous Fluid Flow, McGraw-Hill, Inc., 2nd edition, New York, 1991.

Moran, M. J. and Shapiro H. N., Fundamentals of Engineering Thermodynamics, 6th edition, Wiley, New Jersey, 2015.

Wark, K., Advanced Thermodynamics for Engineers, McGraw-Hill Inc., New York, 1995.

Shampine, L. F., Gladwell, I. and S. Thompson, Solving ODEs with MATLAB, Cambridge University Press, Cambridge UK, 2003.
https://doi.org/10.1017/cbo9780511615542

Shampine, L. F. and Reichelt, M. W., The MATLAB ODE Suite, SIAM Journal on Scientific Computing, vol. 18, pp. 1–22, 1997.
https://doi.org/10.1137/s1064827594276424

Moon, F. C., 1992, Chaotic and Fractal Dynamics, John Wiley & Sons, Inc., New York, 1992.


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize