Modelling and Test Verification of Suspension Optimal Damping Ratio for Electric Vehicles Considering Occupant-cushion and In-wheel Motor Effects

Authors

School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo, China

Abstract

The damping ratio of chassis suspension is a key parameter for damping matching of in-wheel motor vehicles (IWMVs). Because the motor is attached to the driving wheel, the initial design method of the damping ratio for traditional cars is not entirely suitable for IWMVs. This paper proposes an innovative initial design method of the damping ratio for IWMVs. Firstly, a traveling vibration model of occupant-vehicle-road (OVR) for IWMVs is established. The model involves the occupant, cushion, suspension, in-wheel motor, road, and running speed. Secondly, on the basis of the model, using a special form of infinite integral, a mathematical expression of the occupant root-mean-square (RMS) acceleration is derived. Thirdly, based on the RMS optimization criterion for ride comfort, an 8 order polynomial equation about the suspension optimal damping ratio is deduced. Subsequently, through factors analysis, the change principles of the optimal damping ratio versus vehicle parameters are unveiled. Finally, the reliability of the optimal damping ratio is validated by test. The relative deviation of the calculated optimal damping ratio and the tested damping ratio is 5.4%. The results show that the proposed optimal damping ratio can effectively guide the suspension damping matching for IWMVs.

Keywords


1.     Hung, Y.-H. and Wu, C.-H., "A combined optimal sizing and energy management approach for hybrid in-wheel motors of evs", Applied Energy,  Vol. 139, (2015), 260-271.

2.     Li, X.H. and Qian, H., "The present status and future trends of in-wheel motors for electric vehicles", in Advanced Materials Research, Trans Tech Publ. Vol. 433, (2012), 6943-6950.

3.     Chen, Y. and Wang, J., "Design and evaluation on electric differentials for overactuated electric ground vehicles with four independent in-wheel motors", IEEE Transactions on Vehicular Technology,  Vol. 61, No. 4, (2012), 1534-1542.

4.     Nam, K., Fujimoto, H. and Hori, Y., "Lateral stability control of in-wheel-motor-driven electric vehicles based on sideslip angle estimation using lateral tire force sensors", IEEE Transactions on Vehicular Technology,  Vol. 61, No. 5, (2012), 1972-1985.

5.     Katsuyama, E. and Omae, A., "Improvement of ride comfort by unsprung negative skyhook damper control using in-wheel motors", SAE International Journal of Alternative Powertrains,  Vol. 5, No. 2016-01-1678, (2016), 214-221.

6.     Wei, T. and Zhichao, H., "Analyses on the vertical characeristics and motor vibraiton of an electric vehicle with motor-in-wheel drive [j]", Automotive Engineering,  Vol. 3, No. 4, (2014), 398-403.

7.     Solmaz, S., Afatsun, A.C. and Baslamish, S.Ç., "Parametric analysis and compensation of ride comfort for electric drivetrains utilizing in-wheel electric motors", in Modelling Symposium (EMS), 2015 IEEE European, (2015), 219-224.

8.     Wang, R., Jing, H., Yan, F., Karimi, H.R. and Chen, N., "Optimization and finite-frequency h∞ control of active suspensions in in-wheel motor driven electric ground vehicles", Journal of the Franklin Institute,  Vol. 352, No. 2, (2015), 468-484.

9.     Shao, X., Naghdy, F. and Du, H., "Reliable fuzzy h∞ control for active suspension of in-wheel motor driven electric vehicles with dynamic damping", Mechanical Systems and Signal Processing,  Vol. 87, (2017), 365-383.

10.   Nakhaie Jazar, G., Alkhatib, R. and Golnaraghi, M., "Root mean square optimization criterion for vibration behaviour of linear quarter car using analytical methods", Vehicle System Dynamics,  Vol. 44, No. 06, (2006), 477-512.

11.   Yin, Z., Khajepour, A., Cao, D., Ebrahimi, B. and Guo, K., "Pneumatic suspension damping characterisation with equivalent damping ratio", International Journal of Heavy Vehicle Systems,  Vol. 19, No. 3, (2012), 314-332.

12.   Yu, Z., "Automobile theory", Machinery Industry Press: Beijing,  (2009).

13.   Zhao, L., Zhou, C., Yu, Y. and Yang, F., "Hybrid modelling and damping collaborative optimisation of five-suspensions for coupling driver-seat-cab system", Vehicle System Dynamics,  Vol. 54, No. 5, (2016), 667-688.

14.   Dong, X.M., Yu, M., Liao, C.R. and Chen, W.M., "Pareto optimization of a two-degree of freedom passive linear suspension using a new multi objective genetic algorithm", International Journal of Engineering, Transactions A: Basics,  Vol. 24, No. 3, (2011), 291-299.

15.   Moghadam-Fard, H. and Samadi, F., "Active suspension system control using adaptive neuro fuzzy (ANFIS) controller", International Journal of Engineering-Transactions C: Aspects,  Vol. 28, No. 3, (2014), 396-402.

16.   Mastinu, G., Gobbi, M. and Pace, G., "Analytical formulae for the design of a railway vehicle suspension system", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science,  Vol. 215, No. 6, (2001), 683-698.

17.   Zhao, L., Zhou, C. and Yu, Y., "Comfort improvement of a novel nonlinear suspension for a seat system based on field measurements", Strojniski vestnik-Journal of Mechanical Engineering,  Vol. 63, No. 2, (2017), 129-137.

18.   Rezaiee Pajand, M., Aftabi Sani, A. and Hozhabrossadati, S.M., "Free vibration analysis of a six-degree-of-freedom mass-spring system suitable for dynamic vibration absorbing of space frames", International Journal of Engineering,  Vol. 30, (2017).

19.   Gao, W., Zhang, N. and Dai, J., "A stochastic quarter-car model for dynamic analysis of vehicles with uncertain parameters", Vehicle System Dynamics,  Vol. 46, No. 12, (2008), 1159-1169.

20.   Yu, F., Li, D.-F. and Crolla, D., "Integrated vehicle dynamics control—state-of-the art review", in Vehicle Power and Propulsion Conference, 2008. VPPC'08. IEEE, (2008), 1-6.

21.   Beardon, A.F., "Complex analysis: The argument principle in analysis and topology, Wiley-Interscience,  (1979).