Skip to main content
SpringerLink
Log in

Analytical description of ride comfort and optimal damping of cushion-suspension for wheel-drive electric vehicles

  • Published:
International Journal of Automotive Technology Aims and scope Submit manuscript

Abstract

To provide initial design values of seat cushion and chassis suspension damping for wheel-drive electric vehicles (WDEVs), this paper presents an analytical estimation method and a practical damping parameters design method. Firstly, two formulae of the human body vertical acceleration in terms of the power spectrum density (PSD) and the root mean square (RMS) are deduced for WDEVs. Then, the coupling effects of the key vehicle parameters on ride comfort are revealed. Finally, with a practical example, the damping parameters of the cushion and the suspension are initially designed and analyzed. The results show that when every 10.0 kg increases for motor mass, the optimal damping values of the cushion and the suspension should be reduced by about 15.0 Ns/m and 50.0 Ns/m, respectively. However, the RMS acceleration increases 0.017 m/s2 with a decrease of 2.5 % for ride comfort.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

WDEVs:

wheel-drive electric vehicles

RMS:

root mean square

PSD:

power spectrum density, m2/s3

m 3 :

human body mass, kg

m 2 :

vehicle body mass, kg

m 1 :

tire system mass, kg

m 0 :

motor mass, kg

K 3 :

cushion stiffness, N/m

K 2 :

suspension stiffness, N/m

K 1 :

tire stiffness, N/m

C 3 :

cushion damping, N·s/m

C 2 :

suspension damping, N·s/m

x 3 :

human body bounce, m

x 2 :

vehicle body bounce, m

x 1 :

wheel hop, m

q :

road excitation, m

ω 3 :

approximate natural angular frequency of human body system, rad/s

ω 2 :

approximate natural angular frequency of vehicle body system, rad/s

ω 1 :

approximate natural angular frequency of tire system, rad/s

f 3 :

approximate natural frequency of human body system, Hz

f 2 :

approximate natural frequency of vehicle body system, Hz

f 1 :

approximate natural frequency of tire system, Hz

ξ 3 :

damping ratio of cushion system

ξ 2 :

damping ratio of chassis suspension system

r 2 :

mass ratio of human body and vehicle body

r 1 :

mass ratio of vehicle body and unsprung mass

η 1 :

stiffness ratio of cushion and chassis suspension

η 2 :

stiffness ratio of tire and chassis suspension

α 2 :

frequency ratio of human body system and vehicle body

α 1 :

frequency ratio of tire system and vehicle body

a(t):

human body vertical acceleration, m/s2

σ a :

human body vertical RMS acceleration, m/s2

References

  • Beardon, A. F. (1979). Complex Analysis. 1st edn. Wiley. New York, USA.

    MATH  Google Scholar 

  • Chen, L., Bian, M. Y., Luo, Y. G. and Li, K. Q. (2016). Tire-road friction coefficient estimation based on the resonance frequency of in-wheel motor drive system. Vehicle System Dynamics 54, 1, 1–19.

    Article  Google Scholar 

  • Chen, Y. and Wang, J. M. (2012). Design and evaluation on electric differentials for overactuated electric ground vehicles with four independent in-wheel motors. IEEE Trans. Vehicular Technology 61, 4, 1534–1542.

    Article  MathSciNet  Google Scholar 

  • Etsuo, K. and Ayana, O. (2016). Improvement of ride comfort by unsprung negative skyhook damper control using in-wheel motors. SAE Int. J. Alternative Powertrains 5, 1, 214–221.

    Google Scholar 

  • Hung, Y. H. and Wu, C. H. (2015). A combined optimal sizing and energy management approach for hybrid inwheel motors of EVs. Applied Energy, 139, 260–271.

    Article  Google Scholar 

  • Nam, K. N., Fujimoto, H. and Hori, Y. (2012). Lateral stability control of in-wheel-motor-driven electric vehicles based on sideslip angle estimation using lateral tire force sensors. IEEE Trans. Vehicular Technology 61, 5, 1972–1985.

    Article  Google Scholar 

  • Li, X. H. and Qian, H. (2012). The present status and future trends of in-wheel motors for electric vehicles. Materials Science and Information Technology, 433-440, 6943–6950.

    Google Scholar 

  • Mastinu, G. R. M., Gobbi, M. and Pace, G. D. (2001). Analytical formulae for the design of a railway vehicle suspension system. Proc. Institution of Mechanical Engineers, Part C: J. Mechanical Engineering Science 215, 6, 683–698.

    Google Scholar 

  • Nakhaie, J. C., Alkhatib, R. and Golnaraghi, M. F. (2006). Root mean square optimization criterion for vibration behavior of linear quarter car using analytical methods. Vehicle System Dynamics 44, 6, 477–512.

    Article  Google Scholar 

  • Selim, S., Can, A. A. and Çaglar, B. S. (2016). Parametric analysis and compensation of ride comfort for electric drivetrains utilizing in-wheel electric motors. Int. J. Simulation: Systems, Science and Technology 17, 33, 7.1–7.8.

    Google Scholar 

  • Sun, W., Li, Y. N., Huang, J. Y. and Zhang, N. (2015). Vibration effect and control of in-wheel switched reluctance motor for electric vehicle. J. Sound and Vibration, 338, 105–120.

    Article  Google Scholar 

  • Tang, L., Shangguan, W. B. and Dai, L. (2012). A calculation method of joint forces for a suspension considering nonlinear elasticity of bushings. Proc. Institution of Mechanical Engineers, Part K: J. Multibody Dynamics 226, 4, 281–297.

    Google Scholar 

  • Tong, W. and Hou, Z. C. (2014). Analyses on the vertical characteristics and motor vibration of an electric vehicle with motor-in-wheel drive. Automotive Engineering 36, 4, 398–403.

    Google Scholar 

  • Yu, F. and Lin, Y. (2005). Vehicle System Dynamics. 1st edn. China Machine Press. Beijing, China.

    Google Scholar 

  • Yu, Z. S. (2009). Automobile Theory. 5th edn. China Machine Press. Beijing, China.

    Google Scholar 

  • Zhao, L. L., Zhou, C. C. and Yu, Y. W. (2016). Hybrid modeling of seat-cab coupled system for truck. Int. J. Automotive Technology 17, 5, 769–776.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Fuxing Yang & Leilei Zhao

  2. School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo, 255049, China

    Yuewei Yu & Changcheng Zhou

Authors
  1. Fuxing Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leilei Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuewei Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Changcheng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leilei Zhao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, F., Zhao, L., Yu, Y. et al. Analytical description of ride comfort and optimal damping of cushion-suspension for wheel-drive electric vehicles. Int.J Automot. Technol. 18, 1121–1129 (2017). https://doi.org/10.1007/s12239-017-0109-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12239-017-0109-2

Key words

Search

Navigation