Skip to main content
SpringerLink
Log in

Qualitative Analysis of the Traction Force of a Rotating Drive Wheel with a Weightless Tire

  • Research Articles
  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

A plane problem of controlled rotation of a wheel with a weightless tire is considered. The wheel is placed on a fixed base and is equipped with a shock absorber to damp vertical vibrations. For simplicity, horizontal motions of the rotation axis are not admitted. It is required to maximize the average traction force on a sufficiently long time interval by applying a bounded control torque on the rotation axis. A nonlinear mathematical model of the system is developed, with the tire modeled by a weightless solid hollow cylinder connected to the wheel disk by numerous weightless springs that are in a pretensioned state. Equations of motion are derived with the use of the quasistatic condition. The dynamics of the process and the maximum traction force are analyzed.

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

Fig. 1.

Similar content being viewed by others

References

  1. D. Hao, C. Zhao, and Y. Huang, “A reduced-order model for active suppression control of vehicle longitudinal low-frequency vibration,” Shock Vib. 2018, 5731347 (2018).

    Google Scholar 

  2. I. V. Meshcherskii, Collection of Problems in Theoretical Mechanics, 34th ed. (Nauka, Moscow, 1975) [in Russian].

    Google Scholar 

  3. K. Popp and W. Schiehlen, Ground Vehicle Dynamics (Springer, Berlin, 2010).

    Book  Google Scholar 

  4. S. A. Reshmin, “The effect of loss of traction under asymmetric vibrations of the drive wheels of the vehicle,” in Proc. 14th Int. Conf. “Stability and Oscillations of Nonlinear Control Systems” (Pyatnitskiy’s Conference) (STAB), Moscow, 2018 (IEEE, Piscataway, NJ, 2018), pp. 1–2.

    Google Scholar 

  5. S. A. Reshmin, “Qualitative analysis of the undesirable effect of loss of traction force of a vehicle during an intense start,” Dokl. Phys. 64 (1), 30–33 (2019) [transl. from Dokl. Akad. Nauk 484 (3), 289–293 (2019)].

    Article  Google Scholar 

  6. S. A. Reshmin, “The analysis of the loss of the traction effect during an intensive start of a vehicle,” J. Comput. Syst. Sci. Int. 58 (3), 349–359 (2019) [transl. from Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 3, 24–33 (2019)].

    Article  MathSciNet  Google Scholar 

  7. W. Schiehlen and P. Eberhard, Applied Dynamics (Springer, Cham, 2014).

    MATH  Google Scholar 

  8. V. Ph. Zhuravlev, “On plane self-excited vibrations of a cantilever suspended wheel,” Mech. Solids 47 (2), 155–159 (2012) [transl. from Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 3–8 (2012)].

    Article  Google Scholar 

  9. V. Ph. Zhuravlev, D. M. Klimov, and P. K. Plotnikov, “A new model of shimmy,” Mech. Solids 48 (5), 490–499 (2013) [transl. from Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 5, 13–23 (2013)].

    Article  Google Scholar 

  10. V. F. Zhuravlev and G. M. Rozenblat, “On vibrations of a wheel carriage in the presence of friction,” Dokl. Phys. 56 (2), 118–121 (2011) [transl. from Dokl. Akad. Nauk 436 (5), 627–630 (2011)].

    Article  Google Scholar 

  11. V. Ph. Zhuravlev and G. M. Rozenblat, “On the instability of a car in the vertical plane under rectilinear motion with friction forces taken into account,” Mech. Solids 46 (4), 495–507 (2011) [transl. from Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 3–17 (2011)].

    Article  Google Scholar 

Download references

Funding

This work is supported by the Russian Science Foundation under grant 18-11-00307.

Author information

Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia

    S. A. Reshmin

Authors
  1. S. A. Reshmin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. A. Reshmin.

Additional information

Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 315, pp. 211–221 https://doi.org/10.4213/tm4222.

Translated by I. Nikitin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Reshmin, S.A. Qualitative Analysis of the Traction Force of a Rotating Drive Wheel with a Weightless Tire. Proc. Steklov Inst. Math. 315, 198–208 (2021). https://doi.org/10.1134/S0081543821050151

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543821050151

Search

Navigation