Modeling and Simulation of Non-Linear and Hysteresis Behavior of Magneto-Rheological Dampers in the Example of Quarter-Car Model
International Journal of Theoretical and Applied Mathematics
Volume 2, Issue 2, December 2016, Pages: 170-189
Received: Nov. 13, 2016; Accepted: Dec. 2, 2016; Published: Jan. 23, 2017
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Sulaymon L. Eshkabilov, Dynamics & Control Lab, Tashkent Institute of Automotive Road Design, Construction and Maintenance, Tashkent, Uzbekistan
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This paper presents reviews of mathematical formulations and numerical simulation models of non-linear and dynamic hysteresis behaviors of magneto-rheological liquid dampers, viz. Bingham, Dahl, LuGre and Bouc-Wen models, developed in MATLAB®/Simulink® in the example of quarter-car model with the Golden Car parameters. It demonstrates numerical simulations of the magneto-rheological liquid damper models with different sets of parameters and discusses simulation results and performances of these four models for different road profile excitation signals, such as Heaviside step function, sine wave, random noise and white Gaussian noise.
Suspension, Bingham, Dahl, LuGre, Bouc-Wen, MATLAB/Simulink
To cite this article
Sulaymon L. Eshkabilov, Modeling and Simulation of Non-Linear and Hysteresis Behavior of Magneto-Rheological Dampers in the Example of Quarter-Car Model, International Journal of Theoretical and Applied Mathematics. Vol. 2, No. 2, 2016, pp. 170-189. doi: 10.11648/j.ijtam.20160202.32
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Mitu A. M., Popescu I., Sireteanu T. (2012), “Mathematical modeling of semi-active control with application to building seismic protection,” BSG Proceedings, Vol. 19, 2012, pp. 88-99.
Sarkar Chiranjit and Hirani Harish (2015), “Synthesis and Characterization of Nao Silver Particle-based Magnetorheological Fluids for Brakes,” Defence Science journal, Vol. 65, No. 3, May 2015, pp. 252-258.
Sapinski B. (2009) “Magneto-rheological dampers in vibrational control of mechanical structures,” Mechanics Vol. 28, No 1. 18-25 pp.
Braz Cesar M., R. Carneiro de Barros R. (2012), “Properties and Numerical Modeling of MR dampers,” 15th international conference on experimental mechanics, Porto, Portugal.
Zhang H., et al. (2004), “Study on the design, test and simulation of a MR damper with two-stage electromagnetic coil,” – viewed on March 13, 2016.
Eshkabilov S., Grimheden M. E. (2015), “Car seat damper controller design with magneto-rheological fluids,” Int. Conf., Nov., 2015, Navoi, Uzbekistan.
Lee T. Y., Kawashima K., Chen P. C. (2008), "Experimental and Analytical Study on a Nonlinear Isolated Bridge under Semi-active Control", 14th World Conference on Earthquake Engineering, October 12-17, 2008, Beijing, China.
Jolly M. R., Al-Bender B. F., and Carlsson J. D. (1999), “Properties and applications of commercial magneto-rheological fluids.” Journal of Intelligent Materials Systems and Structures, 10 (1): 5-13.
Stanway R., Sproston J. L., and Stevens N. G. (1987), Non-linear modelling of an electro-rheological vibration damper. Journal on Electrostatics, 20: 167-184.
Dahl P. R. (1968), A solid friction model. Technical Report, TOR-158(3107-18) (El-Segundo, CA: The Aerospace Corporation).
Canudas de Wit C, Olsson H. J., Astrom K. J., Lischinsky P (1993), Dynamics friction models and control design. American Control Conference, San Francisco, USA, pp. 1920-1926.
Canudas de Wit C., Olsson H., Astrom K. J., and Lischinsky P. (1995), “A new model for control of systems with friction,” IEEE Trans. Autom. Contr., vol. 40, no. 3, pp. 419–425.
Bouc R. (1967), Forced vibrations of mechanical systems with hysteresis, Proceeding of the 4th Conference on Nonlinear Oscillations, Prague, Czechoslovakia 315-321.
Wen Y. K. (1976), Method for random vibration of hysteretic systems, Journal of the Engineering Mechanics Division, 102 (2) (1976) 249-263.
Spencer B. F. Jr., Dyke S. J., Sain M. K. and Carlson D. (1997), Phenomenological model of a magnetorheological damper, Journal of Engineering Mechanics ASCE, 123 (3) (1997) 230-238.
Mat Hussain Ab Talib, Intan Z. Mat Darus (2013), "Self-tuning PID Controller with MR damper And Hydraulic Actuator For Suspension System", Fifth International Conference on Computational Intelligence, Modelling and Simulation, IEEE-Computer Society, DOI 10.1109/CIMSim.2013.27, pp. 119-124.
Lampaert V., Al-Bender F. (2003), “A generalized Maxwell slip friction model appropriate for control purposes,” IEEE – Physics Conference, St. Petersburg, Russia, pp. 1170-1177.
Nguyen B. D., Aldo A. F., Olivier A. B. (2007), “Efficient Simulation of a Dynamic System with LuGre Friction,” Journal of Computational and Nonlinear Dynamics, Vol. 2, pp. 281-289.
Armstrong-H´elouvry B. (1991), “Control of Machines with Friction.” Boston, MA: Kluwer, 1991.
Ikhouane F., Rodellar J. (1987), “Systems with hysteresis: analysis, identification and control using the Bouc-Wen model.” Wiley, Chichester (UK), 1987.
Gillespie, T. D., Sayers, M. W., and Segel, L. (1980), “Calibration of Response-Type Road Roughness Measuring Systems.” Journal: National Cooperative Highway Research Program Report. No. 228, December 1980.
Loizos, A., Plati C. (2008), Evolutional Process of Pavement Roughness Evaluation Benefiting from Sensor Technology, International Journal on Smart Sensing and Intelligent Systems, Vol. 1, No 2, June 2008, pp. 370-387.
Ahlin K., Granlund J. (2001), International Roughness Index, IRI, and ISO 2631 Vibration Evaluation, Transportation Research Board: Committee on Surface Properties - Vehicle Interaction, Washington DC, January 2001.
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