Advertisement

Interaction between asymmetrical damping and geometrical nonlinearity in vehicle suspension systems improves comfort

  • J. C. M. Fernandes
  • P. J. P. Gonçalves
  • M. SilveiraEmail author
Original paper
  • 119 Downloads

Abstract

This work explores the role of asymmetrical damping and geometrical nonlinearities in the suspension system of a simplified vehicle model in order to improve comfort. Improving comfort for passengers is a constant challenge for the automotive industry. Although technologies have been introduced for this purpose, many vehicles still use suspension systems which are less effective in vibration isolation due to cost restrictions. To improve comfort at relatively low cost, the use of asymmetrical suspension dampers has been explored. It has been shown that different asymmetry ratios can be advantageous to improve comfort at different frequency ranges. Models which include the suspension geometry can help to better understand the vehicle dynamical response, as it also depends on the geometrical arrangement of its components. As a contribution to the current literature, this paper proposes a study on asymmetrical damping considering a Double Wishbone suspension geometry. A nonlinear single-degree-of-freedom system subject to harmonic base excitation is used. The combination of asymmetry and geometry nonlinearities is investigated for varying asymmetry ratio, geometrical parameters and vehicle velocity. The numerical and experimental results show that the geometrical nonlinearity induces changes in the spring and damping forces because of different inclinations of the spring–damper assembly during expansion and compression, resulting in changes in acceleration amplitude and resonance frequency. This effect is superimposed on the effect of asymmetrical damping coefficient alone, ultimately influencing the acceleration of the suspended mass. Therefore, these two effects must be considered carefully when designing a suspension system with comfort criteria.

Keywords

Asymmetrical damping Geometrical nonlinearity Vehicle dynamics Comfort 

Notes

Acknowledgements

J.C.M. Fernandes received funding from the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 1571870.

Compliance with ethical standards

Conflict of Interest

P.J.P. Gonçalves and M. Silveira declare that they have no conflict of interest.

Supplementary material

11071_2019_5374_MOESM1_ESM.mp4 (3 mb)
Supplementary material 1 (mp4 3088 KB)
11071_2019_5374_MOESM2_ESM.mp4 (7.6 mb)
Supplementary material 2 (mp4 7829 KB)

References

  1. 1.
    Arana, C., Evangelou, S.A., Dini, D.: Series active variable geometry suspension application to comfort enhancement. Control Eng. Pract. 59, 111–126 (2017).  https://doi.org/10.1016/j.conengprac.2016.11.011 CrossRefGoogle Scholar
  2. 2.
    Armstrong-Helouvry, B.: Control of Machines with Friction, vol. 128. Springer, New York (2012).  https://doi.org/10.1007/978-1-4615-3972-8 CrossRefzbMATHGoogle Scholar
  3. 3.
    Attia, H.A.: Dynamic modelling of the double wishbone motor-vehicle suspension system. Eur. J. Mech. A Solids 21(1), 167–174 (2002).  https://doi.org/10.1016/S0997-7538(01)01178-0 CrossRefzbMATHGoogle Scholar
  4. 4.
    Berger, E.: Friction modeling for dynamic system simulation. Appl. Mech. Rev. 55(6), 535–577 (2002).  https://doi.org/10.1115/1.1501080 CrossRefGoogle Scholar
  5. 5.
    Chandra Shekhar, N., Hatwal, H., Mallik, A.: Response of non-linear dissipative shock isolators. J. Sound Vib. 214(4), 589–603 (1998).  https://doi.org/10.1006/jsvi.1997.1468 CrossRefGoogle Scholar
  6. 6.
    Cherian, V., Jalili, N., Ayglon, V.: Modelling, simulation, and experimental verification of the kinematics and dynamics of a double wishbone suspension configuration. Proceed. Inst. Mech. Eng. Part D J. Automob. Eng. 223(10), 1239–1262 (2009).  https://doi.org/10.1243/09544070JAUTO1153 CrossRefGoogle Scholar
  7. 7.
    De Wit, C.C., Olsson, H., Astrom, K.J., Lischinsky, P.: A new model for control of systems with friction. IEEE Trans. Autom. Control 40(3), 419–425 (1995).  https://doi.org/10.1109/9.376053 MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Dixon, J.: Suspension Analysis and Computational Geometry. Wiley, New York (2009).  https://doi.org/10.1002/9780470682906 CrossRefzbMATHGoogle Scholar
  9. 9.
    Eckert, M.: Der sommerfeld-effekt: theorie und geschichte eines bemerkenswerten resonanzphanomens. Eur. J. Phys. 17(5), 285 (1996).  https://doi.org/10.1088/0143-0807/17/5/007 CrossRefGoogle Scholar
  10. 10.
    Fernandes, J.C.M., Silveira, M., Pontes Junior, B.R., Balthazar, J.M.: Effects of asymmetrical damping ratio and damper inclination on vertical dynamics of a suspension system. Math. Eng. Sci. Aerosp. (MESA) 6(3), 391–398 (2015)Google Scholar
  11. 11.
    Gaul, L., Nitsche, R.: The role of friction in mechanical joints. Appl. Mech. Rev. 54(2), 93–106 (2001).  https://doi.org/10.1115/1.3097294 CrossRefGoogle Scholar
  12. 12.
    Gonçalves, P., Silveira, M., Junior, B.P., Balthazar, J.: The dynamic behavior of a cantilever beam coupled to a non-ideal unbalanced motor through numerical and experimental analysis. J. Sound Vib. 333(20), 5115–5129 (2014).  https://doi.org/10.1016/j.jsv.2014.05.039 CrossRefGoogle Scholar
  13. 13.
    Gonçalves, P.J.P., Silveira, M., Petrocino, E., Balthazar, J.: Double resonance capture of a two-degree-of-freedom oscillator coupled to a non-ideal motor. Meccanica 51(9), 2203–2214 (2016).  https://doi.org/10.1007/s11012-015-0349-z MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gonçalves, J.P.C., Ambrósio, J.A.C.: Optimization of vehicle suspension systems for improved comfort of road vehicles using flexible multibody dynamics. Nonlinear Dyn. 34, 113–131 (2003).  https://doi.org/10.1023/B:NODY.0000014555.46533.82 CrossRefzbMATHGoogle Scholar
  15. 15.
    Guglielmino, E., Sireteanu, T., Stammers, C.W., Ghita, G., Giuclea, M.: Semi-active Suspension Control: Improved Vehicle Ride and Road Friendliness. Springer, London (2008).  https://doi.org/10.1007/978-1-84800-231-9 CrossRefzbMATHGoogle Scholar
  16. 16.
    Guntur, H.L., Setiawan, L.F.: The influence of asymmetry ratio and average of the damping force on the performance and ride comfort of a vehicle. Int. J. Veh. Syst. Model. Test. 11(2), 97–115 (2016).  https://doi.org/10.1504/IJVSMT.2016.077924 CrossRefGoogle Scholar
  17. 17.
    Holen, P.: Experimental evaluation of modally distributed damping in heavy vehicles. Veh. Syst. Dyn. 46(6), 521–539 (2008).  https://doi.org/10.1080/00423110701496461 CrossRefGoogle Scholar
  18. 18.
    Hrovat, D.: Survey of advanced suspension developments and related optimal control applications. Automatica 33(10), 1781–1817 (1997).  https://doi.org/10.1016/S0005-1098(97)00101-5 MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    ISO 2631-1: Mechanical Vibration and Shock: Evaluation of Human Exposure to Whole-body Vibration. Part 1, General Requirements: International Standard ISO 2631-1: 1997 (E). ISO (1997)Google Scholar
  20. 20.
    Jazar, R.N.: Vehicle Dynamics: Theory and Application. Springer, Berlin (2017).  https://doi.org/10.1007/978-3-319-53441-1 CrossRefGoogle Scholar
  21. 21.
    Karnopp, D.: Active and semi-active vibration isolation. In: Elarabi, M.E., Wifi, A.S. (eds.) Current Advances in Mechanical Design and Production VI, pp. 409–423. Elsevier, Amsterdam (1995).  https://doi.org/10.1016/B978-008042140-7/50037-8 CrossRefGoogle Scholar
  22. 22.
    Li, Z., Zuo, L., Luhrs, G., Lin, L., Qin, Y.X.: Electromagnetic energy-harvesting shock absorbers: design, modeling, and road tests. IEEE Trans. Veh. Technol. 62(3), 1065–1074 (2013).  https://doi.org/10.1109/TVT.2012.2229308 CrossRefGoogle Scholar
  23. 23.
    Lindvai-Soos, D., Horn, M.: New level of vehicle comfort and vehicle stability via utilisation of the suspensions anti-dive and anti-squat geometry. Veh. Syst. Dyn. 56(7), 1002–1027 (2018).  https://doi.org/10.1080/00423114.2017.1378818 CrossRefGoogle Scholar
  24. 24.
    Lotus, C.: Lotus Elan Owner’s Workshop Manual. Marston Book Services Ltd, Abingdon (1974)Google Scholar
  25. 25.
    Maher, D., Young, P.: An insight into linear quarter car model accuracy. Veh. Syst. Dyn. 49(3), 463–480 (2011).  https://doi.org/10.1080/00423111003631946 CrossRefGoogle Scholar
  26. 26.
    Mastinu, G., Ploechl, M.: Road and Off-road Vehicle System Dynamics Handbook. CRC Press, London (2014). ISBN 9781138075290Google Scholar
  27. 27.
    Norton, R.L.: Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines. McGraw-Hill Higher Education, Boston (2004)Google Scholar
  28. 28.
    Rajalingham, C., Rakheja, S.: Influence of suspension damper asymmetry on vehicle vibration response to ground excitation. J. Sound Vib. 266(5), 1117–1129 (2003).  https://doi.org/10.1016/S0022-460X(03)00054-3 CrossRefGoogle Scholar
  29. 29.
    Rill, G.: Road Vehicle Dynamics: Fundamentals and Modeling. Ground vehicle engineering series. Taylor & Francis, London (2011). ISBN 9781439838983 - CAT# K11773CrossRefGoogle Scholar
  30. 30.
    Sengijpta, S.K.: Fundamentals of Statistical Signal Processing: Estimation Theory. Taylor & Francis Group, London (1995)Google Scholar
  31. 31.
    Shojaeefard, M.H., Khalkhali, A., Yarmohammadisatri, S.: An efficient sensitivity analysis method for modified geometry of macpherson suspension based on pearson correlation coefficient. Veh. Syst. Dyn. 55(6), 827–852 (2017).  https://doi.org/10.1080/00423114.2017.1283046 CrossRefGoogle Scholar
  32. 32.
    Silveira, M., Pontes Junior, B.R., Balthazar, J.M.: Reducing vertical and angular accelerations with nonlinear asymmetrical shock absorber in passenger vehicles. In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (2013).  https://doi.org/10.1115/DETC2013-12241
  33. 33.
    Silveira, M., Pontes Junior, B.R., Balthazar, J.M.: Use of nonlinear asymmetrical shock absorber to improve comfort on passenger vehicles. J. Sound Vib. 333(7), 2114–2129 (2014).  https://doi.org/10.1016/j.jsv.2013.12.001 CrossRefGoogle Scholar
  34. 34.
    Silveira, M., Wahi, P., Fernandes, J.: Effects of asymmetrical damping on a 2 dof quarter-car model under harmonic excitation. Commun. Nonlinear Sci. Numer. Simul. 43, 14–24 (2017).  https://doi.org/10.1016/j.cnsns.2016.06.029 MathSciNetCrossRefGoogle Scholar
  35. 35.
    Silveira, M., Wahi, P., Fernandes, J.: Exact and approximate analytical solutions of oscillator with piecewise linear asymmetrical damping. Int. J. Non Linear Mech. (2019).  https://doi.org/10.1016/j.ijnonlinmec.2018.12.007 CrossRefGoogle Scholar
  36. 36.
    Verros, G., Natsiavas, S., Stepan, G.: Control and dynamics of quarter-car models with dual-rate damping. J. Vib. Control 6(7), 1045–1063 (2000).  https://doi.org/10.1177/107754630000600706 CrossRefGoogle Scholar
  37. 37.
    Zhang, Y., Zhang, X., Zhan, M., Guo, K., Zhao, F., Liu, Z.: Study on a novel hydraulic pumping regenerative suspension for vehicles. J. Frankl. Inst. 352(2), 485–499 (2015).  https://doi.org/10.1016/j.jfranklin.2014.06.005 CrossRefzbMATHGoogle Scholar
  38. 38.
    Zhao, L., Yu, Y., Zhou, C., Mao, S., Yang, F.: Simulation of vertical characteristics and in-wheel motor vibration of electric vehicles with asymmetric suspension damper under road impact. Int. J. Model. Simul. 39(1), 14–20 (2019).  https://doi.org/10.1080/02286203.2018.1468991 CrossRefGoogle Scholar
  39. 39.
    Zhou, G., Kim, H.S., Choi, Y.J.: A new method of identification of equivalent suspension and damping rates of full-vehicle model. Veh. Syst. Dyn. 57, 1573–1600 (2018).  https://doi.org/10.1080/00423114.2018.1531135 CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, School of EngineeringSão Paulo State University (UNESP)BauruBrazil

Personalised recommendations