Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

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

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

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.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  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

    Article  Google Scholar 

  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

    Book  MATH  Google Scholar 

  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

    Article  MATH  Google Scholar 

  4. Berger, E.: Friction modeling for dynamic system simulation. Appl. Mech. Rev. 55(6), 535–577 (2002). https://doi.org/10.1115/1.1501080

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

  8. Dixon, J.: Suspension Analysis and Computational Geometry. Wiley, New York (2009). https://doi.org/10.1002/9780470682906

    Book  MATH  Google Scholar 

  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

    Article  Google Scholar 

  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. 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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

  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

    Article  MATH  Google Scholar 

  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

    Book  MATH  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

  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)

  20. Jazar, R.N.: Vehicle Dynamics: Theory and Application. Springer, Berlin (2017). https://doi.org/10.1007/978-3-319-53441-1

    Book  Google Scholar 

  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

    Chapter  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  24. Lotus, C.: Lotus Elan Owner’s Workshop Manual. Marston Book Services Ltd, Abingdon (1974)

    Google Scholar 

  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

    Article  Google Scholar 

  26. Mastinu, G., Ploechl, M.: Road and Off-road Vehicle System Dynamics Handbook. CRC Press, London (2014). ISBN 9781138075290

    Google Scholar 

  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. 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

    Article  Google Scholar 

  29. Rill, G.: Road Vehicle Dynamics: Fundamentals and Modeling. Ground vehicle engineering series. Taylor & Francis, London (2011). ISBN 9781439838983 - CAT# K11773

    Book  Google Scholar 

  30. Sengijpta, S.K.: Fundamentals of Statistical Signal Processing: Estimation Theory. Taylor & Francis Group, London (1995)

    Google Scholar 

  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

    Article  Google Scholar 

  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. 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

    Article  Google Scholar 

  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

    Article  MathSciNet  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  MATH  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Silveira.

Ethics declarations

Conflict of Interest

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

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 3088 KB)

Supplementary material 2 (mp4 7829 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fernandes, J.C.M., Gonçalves, P.J.P. & Silveira, M. Interaction between asymmetrical damping and geometrical nonlinearity in vehicle suspension systems improves comfort. Nonlinear Dyn 99, 1561–1576 (2020). https://doi.org/10.1007/s11071-019-05374-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-05374-y

Keywords