Skip to main content
SpringerLink
Log in

A Stick-Slip Model Based on Granular Flow Theory

  • Original Paper
  • Published:
Tribology Letters Aims and scope Submit manuscript

Abstract

It is well known that stick-slip phenomena are prevalent in all types of mechanical systems and present one of the greater challenges to tribology. Stick-slip is widely studied and occurs at length scales from kilometers in techtonic movements to nanometers in MEMS applications. Granular flows are likewise widely studied and are known to exhibit stick-slip behavior. The purpose of this paper is to extract a straightforward result from the continuum granular flow theory due to Aranson and Tsimring (Phys Rev E 65:0161303, 2002) to obtain a simple and accessible model which can predict, or at least describe, stick-slip. A relatively simple formula for effective viscosity is provided and some typical results portrayed. The perspective of the paper is that a continuum stick-slip model which incorporates some basic principles may be useful in the modeling of real engineering systems.

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
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Aranson, I.S., Tsimring, L.S.: Continuum theory of partially fluidized granular flows. Phys. Rev. E 65, 0161303 (2002)

    Article  Google Scholar 

  2. Cao, M., Wang, K.W., Fujii, Y., Tobler, W.E.: Advanced hybrid neural network automotive friction component model for powertrain system dynamic analysis. Part 1: model development. Proc. Inst. Mech. Eng. D 218(8), 831 (2004)

    Article  Google Scholar 

  3. Verstraten, T., Furnédmont, R., Lopez-Garcia, P., Rodriguez-Cianca, D., Cao, H.L., Vanderborght, B., Lefeber, D.: Modeling and design of an energy-efficient dual-motor actuation unit with a planetary differential and holding brakes. Mechatronics 49, 134 (2018)

    Article  Google Scholar 

  4. Yu, C.M., Craig, K., Tichy, J.A.: Granular collision lubrication. J. Rheol. 38, 921 (1994)

    Article  CAS  Google Scholar 

  5. Haff, P.K.: Grain flow as a fluid mechanical phenomenon. J. Fluid Mech. 134, 401 (1983)

    Article  Google Scholar 

  6. Elkholy, K.N., Khonsari, M.M.: Experimental investigation on the stick-slip phenomenon in granular collision lubrication. ASME J. Tribol. 130(3), 021302 (2008)

    Article  Google Scholar 

  7. Tichy, J., Berthier, Y., Iordanoff, I.: A continuum model for granular contact lubricationand interactions with discrete simulations. ASME J. Tribol. 130(3), 031301 (2008)

    Article  Google Scholar 

  8. Khomenko, A.V., Lyashenko, I.A.: A stochastic model of stick-slip boundary friction with account for the deformation effect of the shear modulus of the lubricant. J. Frict. Wear 31(4), 308 (2010)

    Article  Google Scholar 

  9. Braun, O.M., Tosatti, E.: Kinetics of stick-slip friction in boundary lubrication. Europhys. Lett. 88(4), 48003 (2009)

    Article  Google Scholar 

  10. Filippov, A.E., Klafter, J., Urbakh, M.: Friction through dynamical formation and rupture of molecular bonds. Phys. Rev. Lett. B 92(13), 135503 (2004)

    Article  CAS  Google Scholar 

  11. Wornyoh, E.Y.A., Jasti, V.K., Higgs, C.F.: A review of dry particulate lubrication: powder and granular materials. ASME J. Tribol. 129(2), 438 (2007)

    Article  CAS  Google Scholar 

  12. Elkholy, K.N., Khonsari, M.M.: On the effect of enduring contact on the flow and thermal characteristics in powder lubrication. Proc. Inst. Mech. Eng. J 222(J6), 741 (2008)

    Article  CAS  Google Scholar 

  13. Kabir, M.A., Lovell, M.R., Higgs, C.R.: Utilizing the explicit finite element method for studying granular flows. Tribol. Lett. 29(2), 85 (2008)

    Article  Google Scholar 

  14. Sawyer, G.W., Tichy, J.A.: Lubrication with granular flow: continuum theory, particle simulations, comparison with experiment. ASME J. Tribol. 123(4), 777 (2001)

    Article  Google Scholar 

  15. Midi, G.D.R.: On dense granular flows. Eur. Phys. J. E 14, 341 (2004)

    Article  CAS  Google Scholar 

  16. Smart, A.G.: A thermodynamic theory of granular material endures. Phys. Today 70, 20 (2017)

    Google Scholar 

  17. Landau, L.D., Lifshitz, E.M.: Statistical Physics. Pergamon Press, New York (1980)

    Google Scholar 

  18. Nedderman, R.M.: Statics and Kinematics of Granular Materials. Cambridge University Press, Cambridge (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    John Tichy

  2. Laboratoire de Mécanique des Contacts et des Solides, Institut National des Sciences Appliquées de Lyon, 69621, Villeurbanne, France

    Benyebka Bou-Saïd

Authors
  1. John Tichy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benyebka Bou-Saïd
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to John Tichy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tichy, J., Bou-Saïd, B. A Stick-Slip Model Based on Granular Flow Theory. Tribol Lett 67, 14 (2019). https://doi.org/10.1007/s11249-018-1119-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11249-018-1119-6

Keywords

Search

Navigation