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Mathematical Modeling in Vehicle Ride Dynamics
ISSN: 0148-7191, e-ISSN: 2688-3627
Published April 16, 2012 by SAE International in United States
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Ride is considered to be one of the criteria for evaluating the performance of a vehicle. However, the evaluation of ride quality of a car varies from person to person. There are many mathematical models which are used to study vehicle ride dynamics. The development of electronics, sensors and actuators has enabled the use of control systems to enhance the ride quality of a vehicle.
This work deals with some of the commonly used ride models viz. Quarter Car model, 2 Degree of Freedom (DoF) Half Car Model and 4 DoF Half Car Model. A complete analysis of these models from a designer's perspective, e.g., variation of suspension stiffness, damping coefficient etc. is being presented. The response of these models to random excitation is being studied. The above mentioned models are based on the rigid body assumption. They do not incorporate a tire model which takes into account the stiffness and damping properties of the tire. The Flexible Ring Tire model is being incorporated into the 4 DoF Half Car model and effect of tire flexibility on vehicle ride is being analyzed. A flexible 2 DoF model, which models the chassis as an Euler beam on springs is also analyzed and a comparison with the rigid 2 DoF model is being done. Semi-active suspensions enable the variation of suspension properties to improve vehicle ride quality. These kinds of systems are becoming popular with high end cars. A simulation of MR dampers (semi-active suspension) using Bouc-Wen Model has been incorporated into the quarter car model using PID controller.
CitationTalukdar, S., Mazumdar, A., Mullasseril, M., Kalita, K. et al., "Mathematical Modeling in Vehicle Ride Dynamics," SAE Technical Paper 2012-01-0056, 2012, https://doi.org/10.4271/2012-01-0056.
- Howard, G. Bastow, D. Whitehead, J.P. “Car Suspension and Handling,” SAE International Warrendale, PA 978-0-7680-0872-2 2004 10.4271/R-318
- Wong, J.Y. “Theory of Ground Vehicles” John Wiley & Sons 978-0-470-17038-0
- Sun, T. Zhang, Y. Barak, P. “4-DOF Vehicle Ride Model,” SAE Technical Paper 2002-01-1580 2002 2002-01-1580
- Verros, G. Natsiavas, S. “Ride Dynamics of Nonlinear Vehicle Models Using Component Mode Synthesis” Journal of Vibration and Acoustics 124 3 427 434 July 2002 10.1115/1.1473828
- Gong, S. “A Study of In-Plane Dynamics of Tires” Ph. D. Thesis Faculty of Mechanical Engineering and Marine Technology, Delft University of Technology Netherlands
- Newland, D.E. “An Introduction to Random Vibration, Spectral & Wavelet Analysis” Dover Publications 0-486-44274-8 2005
- Savarsi, S. Vassal, C.P. Spelta, C. Sename, O. Dugard, L. “Semi-Active Suspension Control Design for Vehicles” Butterworth Heinemann 978-0-08-096678-6
- Butz, T. Von Stryk, O. “Modeling and Simulation of Electro and Magnetorheological fluid Dampers” ZAMM 82 1 3 20 2002
- Dyke, S.J. Spencer, B.F Sain, M.K. Carlson, J.D. “Modeling and Control of Magnetorheological dampers for seismic response reduction” Smart Materials and Structures 5 565 575 1996
- He, J. Fu, Z. “Modal Analysis” Butterworth-Heinemann 0-7506-5079-6
- Rajamani, R. “Vehicle Dynamics and Control” Springer 0-387-26396-9
- Miege, A. “Tyre model for truck ride simulations” CPGS Dissertation University of Cambridge June 2004
- ISO 8608 1995 “Mechanical vibration - road surface profiles - Reporting of measured data” International Organization for Standardization (ISO)
- de Silva, C.W. “Vibration and Shock Handbook” Taylor & Francis Group, CRC Press 0-8493-1580-8
- Mazumdar, A. et al “Comparative Analysis of an Elastic 2 Degree of Freedom Vehicle Ride Model with a Rigid 2 Degree of Freedom Model” SAE Technical Paper 2012-01-0057 SAE World Congress & Exhibition 2012 Detroit, USA 24 26 April 2011
- Goldstein, H. Poole, C.P. Safko, J. “Classical Mechanics” Pearson 978-81-317-5891-5
- Timoshenko, S.P. Goodier, J.N. “Theory of Elasticity” Tata McGraw-Hill 978-0-07-070122-9
- Ogata, K. “Modern Control Engineering” Pearson Education 81-7808-579-8
- Soliman, A. “Effect of Road Roughness on the Vehicle Ride Comfort using Semi-Active Suspension System,” SAE Technical Paper 2010-01-0384 2010 10.4271/2010-01-0430
- Soliman, A. “Adaptive LQR Control Strategy for Active Suspension System,” SAE Technical Paper 2011-01-0430 2011 10.4271/2011-01-0430
- Soliman, A. Moustafa, S. Shogae, A. “Parameters Affecting Vehicle Ride Comfort Using Half Vehicle Model,” SAE Technical Paper 2008-01-1146 10.4271/2008-01-1146