Abstract
As more and more researchers begin to analyse the dynamics characteristics of high-degree-of-freedom and nonlinear vehicle models, it is very important and valuable to propose a new analysis method for this type of model. Moreover, it is a promising research direction to propose quantitative indicators for analysing global vehicle dynamics. Therefore, on the basis of classic works, this paper proposes and verifies a quantitative analysis method — dissipation of energy method for 5-DOF nonlinear vehicle plane motion model for the first time. The quantitative indicators for vehicle nonlinear dynamics is expanded. The transfer relationship between the energy components is revealed, which shows that the dissipation of energy method can reflect the dynamics characteristics and stable region characteristics of the nonlinear 5-DOF vehicle system. The effects of tire force lateral-longitudinal coupling and driving modes on global dynamics are analysed. Finally, the prospect of this method is discussed.
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References
Abe, M. (2015). Vehicle Handling Dynamics: Theory and Application. 2nd edn. Butterworth-Heinemann. Oxford, UK.
Brandt, A., Jacobson, B. and Sebben, S. (2021). High speed driving stability of road vehicles under crosswinds: An aerodynamic and vehicle dynamic parametric sensitivity analysis. Vehicle System Dynamics, 1–24.
Chen, G., Hill, D. J. and Yu, X. (Eds.). (2003). Bifurcation control: Theory and applications (Vol. 293). Springer Science & Business Media. Heldelberg, Germany.
Escalona, J. L. and Chamorro, R. (2008). Stability analysis of vehicles on circular motions using multibody dynamics. Nonlinear Dynamics 53, 3, 237–250.
Genesio, R., Tartaglia, M. and Vicino, A. (1985). On the estimation of asymptotic stability regions: State of the art and new proposals. IEEE Trans. Automatic Control 30, 8, 747–755.
Horiuchi, S. (2012). Evaluation of chassis control method through optimisation-based controllability region computation. Vehicle System Dynamics 50, supl, 19–31.
Horiuchi, S., Okada, K. and Nohtomi, S. (2008). Analysis of accelerating and braking stability using constrained bifurcation and continuation methods. Vehicle System Dynamics 46, S1, 585–597.
Hu, H., & Wu, Z. (2000). Stability and Hopf bifurcation of four-wheel-steering vehicles involving driver’s delay. Nonlinear Dynamics 22, 4, 361–374.
Inagaki, S., Kushiro, I. and Yamamoto, M. (1995). Analysis on vehicle stability in critical cornering using phase-plane method. JSAE Review 2, 16, 216.
Johnson, D. B. and Huston, J. C. (1984). Nonlinear lateral stability analysis of road vehicles using Liapunov’s second method. SAE Trans., 798–805.
Karnopp, D. (2004). Vehicle Stability. CRC Press. Boca Raton, Florida, USA.
Kathleen, T. A., Tim, D. S. and James, A. Y. (1997). Chaos: An Introduction to Dynamical Systems. Springer. New York, NY, USA.
Ko, Y. E. and Lee, J. M. (2002). Estimation of the stability region of a vehicle in plane motion using a topological approach. Int. J. Vehicle Design 30, 3, 181–192.
Kondepudi, D. and Prigogine, I. (2014). Modern Thermodynamics: From Heat Engines to Dissipative Structures. 2nd edn. John Wiley & Sons Ltd. Chichester, UK.
Meng, F., Shi, S., Bai, M., Zhang, B., Li, Y. and Lin, N. (2021). Dissipation of energy analysis approach for vehicle plane motion stability. Vehicle System Dynamics, 1–24.
Mitschke, M. and Wallentowitz, H. (1972). Dynamik der Kraftfahrzeuge (Vol. 4). Springer. Berlin, Germany.
Mu, Y., Li, L. and Shi, S. (2018). Modified tire-slip-angle model for chaotic vehicle steering motion. Automotive Innovation 1, 2, 177–186.
Olson, B. J., Shaw, S. W. and Stépán, G. (2005). Stability and bifurcation of longitudinal vehicle braking. Nonlinear Dynamics 40, 4, 339–365.
Ono, E., Hosoe, S., Tuan, H. D. and Doi, S. I. (1998). Bifurcation in vehicle dynamics and robust front wheel steering control. IEEE Trans. Control Systems Technology 6, 3, 412–420.
Prigogine, I. (2017). Non-Equilibrium Statistical Mechanics. Dover Publications Inc.. Mineola, NY, USA.
Sadri, S. and Wu, C. (2013). Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents. Vehicle System Dynamics 51, 6, 906–924.
Sadri, S. and Wu, C. Q. (2012). Lateral stability analysis of on-road vehicles using Lyapunov’s direct method. IEEE Intelligent Vehicles Symp. (IV), Madrid, Spain.
Samsundar, J. and Huston, J. C. (1998). Estimating lateral stability region of a nonlinear 2 degree-of-freedom vehicle. SAE Trans., 1791–1797.
Shen, S., Wang, J., Shi, P. and Premier, G. (2007). Nonlinear dynamics and stability analysis of vehicle plane motions. Vehicle System Dynamics 45, 1, 15–35.
Shi, S., Li, L., Wang, X., Liu, H. and Wang, Y. (2017). Analysis of the vehicle driving stability region based on the bifurcation of the driving torque and the steering angle. Proc. Institution of Mechanical Engineers, Part D: J. Automobile Engineering 231, 7, 984–998.
Slotine, J. J. E. and Li, W. (1991). Applied Nonlinear Control. Prentice Hall. Englewood Cliffs, New Jeersey, USA.
Steindl, A., Edelmann, J. and Plöchl, M. (2020). Limit cycles at oversteer vehicle. Nonlinear Dynamics 99, 1, 313–321.
Wang, X. and Shi, S. (2021). Vehicle coupled bifurcation analysis of steering angle and driving torque. Proc. Institution of Mechanical Engineers, Part D: J. Automobile Engineering 235, 7, 1864–1875.
Wang, X., Shi, S., Liu, L. and Jin, L. (2013). Analysis of driving mode effect on vehicle stability. Int. J. Automotive Technology, 14,3, 363–373.
Wolf, A., Swift, J. B., Swinney, H. L. and Vastano, J. A. (1985). Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena 16, 3, 285–317.
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Acknowledge the funding from National Natural Science Foundation of China (grant number 51975242 and U1964202) for theory research and experiment.
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Meng, F., Shi, S., Zhang, B. et al. Global Characteristics Analysis for Vehicle System with Driving Torque Based on Dissipation of Energy. Int.J Automot. Technol. 23, 1609–1619 (2022). https://doi.org/10.1007/s12239-022-0140-9
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DOI: https://doi.org/10.1007/s12239-022-0140-9