Skip to main content
Log in

A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems

  • Review
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This study is aimed at examining and comparing several friction force models dealing with different friction phenomena in the context of multibody system dynamics. For this purpose, a comprehensive review of present literature in this field of investigation is first presented. In this process, the main aspects related to friction are discussed, with particular emphasis on the pure dry sliding friction, stick–slip effect, viscous friction and Stribeck effect. In a simple and general way, the friction force models can be classified into two main groups, namely the static friction approaches and the dynamic friction models. The former group mainly describes the steady-state behavior of friction force, while the latter allows capturing more properties by using extra state variables. In the present study, a total of 21 different friction force models are described and their fundamental physical and computational characteristics are discussed and compared in details. The application of those friction models in multibody system dynamic modeling and simulation is then investigated. Two multibody mechanical systems are utilized as demonstrative application examples with the purpose of illustrating the influence of the various frictional approaches on the dynamic response of the systems. From the results obtained, it can be stated that both the choice of the friction force model and friction parameters involved can significantly affect the simulated/modeled dynamic response of mechanical systems with friction.

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

Access this article

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
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36
Fig. 37
Fig. 38
Fig. 39

Similar content being viewed by others

References

  1. Amontons, G.: De la resistance cause’e dans les machines. Mémoires de l’Academie Royale des Sciences. 206–226 (1699)

  2. Coulomb, C.A.: Théorie des machines simples, en ayant égard au frottement de leurs parties, et à la roideur des cordages. Mémoire de Mathématique et de Physique, Paris, France (1785)

  3. Morin, A.J.: New friction experiments carried out at Metz in 1831–1833. Proc. Fr. R. Acad. Sci. 4, 1–128 (1833)

    Google Scholar 

  4. Rabinowicz, E.: The nature of the static and kinetic coefficients of friction. J. Appl. Phys. 22, 1373–1379 (1951)

    Article  Google Scholar 

  5. Ścieszka, S.F., Jankowski, A.: The importance of static friction characteristics of brake friction couple, and methods of testing. Tribotest 3, 137–148 (1996)

    Article  Google Scholar 

  6. Rabinowicz, E.: Stick and slip. Sci. Am. 194, 109–118 (1956)

    Article  Google Scholar 

  7. Dieterich, J.: Time-dependent friction and the mechanics of stick-slip. Pure Appl. Geophys. 116, 790–806 (1978)

    Article  Google Scholar 

  8. Awrejcewicz, J., Olejnik, P.: Occurrence of stick-slip phenomenon. J. Theor. Appl. Mech. 35, 33–40 (2007)

    Google Scholar 

  9. Chatelet, E., Michon, G., Manin, L., Jacquet, G.: Stick/slip phenomena in dynamics: choice of contact model. Numerical predictions & experiments. Mech. Mach. Theory 43, 1211–1224 (2008)

    Article  MATH  Google Scholar 

  10. Berger, E.J., Mackin, T.J.: On the walking stick-slip problem. Tribol. Int. 75, 51–60 (2014)

    Article  Google Scholar 

  11. Zeitschrift des Vereines Deutscher Ingenieure Die wesentlichen Eigenschaften der Gleitund Rollenlager. 46, 1342–1348 (1903). (1432–1438, 1463–1470)

  12. Courtney-Pratt, J., Eisner, E.: The effect of a tangential force on the contact of metallic bodies. Proc. R. Soc. 238, 529–550 (1957)

    Article  Google Scholar 

  13. Hsieh, C., Pan, Y.-C.: Dynamic behavior and modelling of the pre-sliding static friction. Wear 242, 1–17 (2000)

    Article  Google Scholar 

  14. Bowden, F.P., Leben, L.: The nature of sliding and the analysis of friction. Proc. R. Soc. Lond., Ser. A, Math. Phys. Sci. 169, 371–391 (1939)

    Article  Google Scholar 

  15. Johannes, V.I., Green, M.A., Brockley, C.A.: The role of the rate of application of the tangential force in determining the static friction coefficient. Wear 24, 381–385 (1973)

    Article  Google Scholar 

  16. Awrejcewicz, J.: Chaotic motion in a nonlinear oscillator with friction. Korean Soc. Mech. Eng. J. 2(2), 104–109 (1988)

    Google Scholar 

  17. Awrejcewicz, J., Delfs, J.: Dynamics of a self-excited stick-slip oscillator with two degrees of freedom—Part I Investigation of equilibria. Eur. J. Mech. A/Solids 9(4), 269–282 (1990)

    MathSciNet  MATH  Google Scholar 

  18. Awrejcewicz, J., Delfs, J.: Dynamics of a self-excited stick-slip oscillator with two degrees of freedom—Part II Slip-stick, slip-slip, stick-slip transitions, periodic and chaotic orbits. Eur. J. Mech. A/Solids 9(5), 397–418 (1990)

    MathSciNet  MATH  Google Scholar 

  19. McMillan, A.J.: A non-linear friction model for self-excited vibrations. J. Sound Vib. 205(3), 323–335 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  20. Leine, R.I., van Campen, D.H., de Kraker, A., van den Steen, L.: Stick-slip vibrations induced by alternate friction models. Nonlinear Dyn. 16, 41–54 (1998)

    Article  MATH  Google Scholar 

  21. Awrejcewicz, J., Holicke, M.M.: Melnikov’s method and stick-slip chaotic oscillations in very weakly forced mechanical systems. Int. J. Bifurc. Chaos 9(3), 505–518 (1999)

  22. Awrejcewicz, J., Dzyubak, L., Grebogi, C.: Estimation of chaotic and regular (stick-slip and slip-slip) oscillations exhibited by coupled oscillators with dry friction. Nonlinear Dyn. 42, 383–394 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hetzler, H., Schwarzer, D., Seemann, W.: Analytical investigation of steady-state stability and Hopf-bifurcations occurring in sliding friction oscillators with application to low-frequency disc brake noise. Commun. Nonlinear Sci. Numer. Simul. 12, 83–99 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Fréne, J., Cicone, T.: Friction in Lubricated Contacts. Handbook of Material Behavior Models, pp. 760–767. Academic Press, Cambridge (2001)

    Book  Google Scholar 

  25. Hess, D.P., Soom, A.: Friction at a lubricated line contact operating at oscillating sliding velocities. J. Tribol. 112, 147–152 (1990)

    Article  Google Scholar 

  26. Dupont, P.E., Dunlap, E.P.: Friction modeling and control in boundary lubrication. In: Proceedings of the 1993 American Control Conference, San Francisco, California, pp. 1910–1914 (1993)

  27. Threlfall, D.C.: The inclusion of Coulomb friction in mechanisms programs with particular reference to DRAM au programme DRAM. Mech. Mach. Theory 13, 475–483 (1978)

  28. Ambrósio, J.A.C.: Impact of rigid and flexible multibody systems: deformation description and contact model. Virtual Nonlinear Multibody Syst. 103, 57–81 (2003)

    Article  MATH  Google Scholar 

  29. Andersson, S., Söderberg, A., Björklund, S.: Friction models for sliding dry, boundary and mixed lubricated contacts. Tribol. Int. 40, 580–587 (2007)

    Article  Google Scholar 

  30. Olsson, H., Åström, K.J., Canudas de Wit, C., Gäfvert, M., Lischinsky, P.: Friction models and friction compensation. Eur. J. Control 4, 176–195 (1998)

    Article  MATH  Google Scholar 

  31. Iurian, C., Ikhouane, F., Rodellar, J., Griñó, R.: Identification of a system with dry friction. Technical Report, Universitat Politècnica de Catalunya, Spain (2005)

  32. Marques, F., Flores, P., Lankarani, H.M.: On the frictional contacts in multibody system dynamics. Multibody Dyn. Comput. Methods Appl. Sci. 42, 67–91 (2016)

    Article  Google Scholar 

  33. Tustin, A.: The effects of backlash and of speed-dependent friction on the stability of closed-cycle control systems. J. Inst. Electr. Eng. 94, 143–151 (1947)

    Google Scholar 

  34. Popp, K., Stelter, P.: Nonlinear oscillations of structures induced by dry friction. In: Ing. W. Schiehlen (ed.) Nonlinear Dynamics in Engineering Systems, pp. 233–240. Springer, Berlin

  35. Armstrong-Hélouvry, B.: Control of Machines with Friction. Kluwer Academic Publishers, Norwell, Massachusetts (1991)

    Book  MATH  Google Scholar 

  36. Makkar, C., Dixon, W.E., Sawyer, W.G., Hu, G.: A new continuously differentiable friction model for control systems design. In: Proceedings of the 2005 IEEE/ASME, International Conference on Advanced Intelligent Mechatronics, pp. 600–605 (2005)

  37. Bo, L.C., Pavelescu, D.: The friction-speed relation and its influence on the critical velocity of stick-slip motion. Wear 82, 277–289 (1982)

    Article  Google Scholar 

  38. Karnopp, D.: Computer simulation of stick-slip friction in mechanical dynamic systems. J. Dyn. Syst., Measurement, Control 107, 100–103 (1985)

    Article  Google Scholar 

  39. Armstrong-Hélouvry, B., Dupont, P., Canudas de Wit, C.: A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica 30, 1083–1138 (1994)

    Article  MATH  Google Scholar 

  40. Wojewoda, J., Stefański, A., Wiercigroch, M., Kapitaniak, T.: Hysteretic effects of dry friction: modelling and experimental studies. Philos. Trans. R. Soc. A 366, 747–765 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  41. Awrejcewicz, J., Grzelczyk, D., Pyryev, Y.: A novel dry friction modeling and its impact on differential equations computation and Lyapunov exponents estimation. J. Vibroeng. 10, 475–482 (2008)

    MATH  Google Scholar 

  42. Dahl, P.R.: A solid friction model, Technical Report, The Aerospace Corporation, El Segundo, California (1968)

  43. Dahl, P.R.: Solid friction damping in mechanical vibrations. AIAA J. 14, 1675–1682 (1976)

    Article  Google Scholar 

  44. Pennestrì, E., Valentini, P.P., Vita, L.: Multibody dynamics simulation of planar linkages with Dahl friction. Multibody Syst. Dyn. 17, 321–347 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  45. Ksentini, O., Abbes, M.S., Abdessalem, J., Chaari, F., Haddar, M.: Study of mass spring system subjected to Dahl friction. Int. J. Mech. Syst. Eng. 2, 34–41 (2012)

    Google Scholar 

  46. Haessig, D.A., Friedland, B.: On the modeling and simulation of friction. J. Dyn. Syst. Measurement Control 113, 354–362 (1991)

    Article  Google Scholar 

  47. de Wit, Canudas, Canudas de Wit, C., Olsson, H., Åström, K.J., Lischinsky, P.: A new model for control of systems with friction. IEEETrans. Autom. Control 40, 419–425 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  48. Dupont, P., Armstrong, B., Hayward, V.: Elasto-plastic friction model: contact compliance and stiction. In: Proceedings of the 2000 American Control Conference, 2, 1072–1077 (2000)

  49. Swevers, J., Al-Bender, F., Ganseman, C.G., Projogo, T.: An integrated friction model structure with improved presliding behavior for accurate friction compensation. IEEE Trans. Autom. Control 45, 675–686 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  50. Lampaert, V., Al-Bender, F., Swevers, J.: A generalized maxwell-slip friction model appropriate for control purposes. In: Proceedings of IEEE International Conference on Physics and Control, St. Petersburg, Russia, pp. 1170–1178 (2003)

  51. Al-Bender, F., Lampaert, V., Swevers, J.: A novel generic model at asperity level for dry friction force dynamics. Tribol. Lett. 16, 81–93 (2004)

    Article  Google Scholar 

  52. Gonthier, Y., McPhee, J., Lange, C., Piedboeuf, J.-C.: A regularized contact model with asymmetric damping and dwell-time dependent friction. Multibody Syst. Dyn. 11, 209–233 (2004)

    Article  MATH  Google Scholar 

  53. De Moerlooze, K., Al-Bender, F., Van Brussel, H.: A generalised asperity-based friction model. tribol. lett. 40, 113–130 (2010)

    Article  Google Scholar 

  54. Oleksowicz, S., Mruk, A.: A basic theoretical model for friction process at microasperity level. Tribol. Trans. 54, 691–700 (2011)

    Article  Google Scholar 

  55. Liang, J., Fillmore, S., Ma, O.: An extended bristle friction force model with experimental validation. Mech. Mach. Theory 56, 123–137 (2012)

    Article  Google Scholar 

  56. Harnoy, A., Friedland, B.: Dynamic friction model of lubricated surfaces for precise motion control. Tribol. Trans. 37, 608–614 (1994)

    Article  Google Scholar 

  57. Contensou, P.: Couplage entre frottement de glissement et de pivotement dans la téorie de la toupe. In: Kreiselprobleme Gyrodynamics: IUTAM Symposium Calerina, 201–216 (1962)

  58. Zhuravlev, V.G.: The model of dry friction in the problem of the rolling of rigid bodies. J. Appl. Math. Mech. 62(5), 705–710 (1998)

    Article  MathSciNet  Google Scholar 

  59. Leine, R.I., Glocker, C.: A set-valued force law for spatial Coulomb–Contensou friction. Eur. J. Mech. A/Solids 22, 193–216 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  60. Kireenkov, A.A.: Combined model of sliding and rolling friction in dynamics of bodies on a rough plane. Mech. Solids 43(3), 412–425 (2008)

    Article  Google Scholar 

  61. Kosenko, I.I., Aleksandrov, E.B.: Implementation of the Contensou–Erismann tangent forces model in the Hertz contact problem. Multibody Syst. Dyn. 24, 281–301 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  62. Kudra, G., Awrejcewicz, J.: Tangens hyperbolicus approximations of the spatial model of friction coupled with rolling resistance. Int. J. Bifurcation Chaos 21(10), 2905–2917 (2011)

    Article  MATH  Google Scholar 

  63. Kudra, G., Awrejcewicz, J.: Bifurcational dynamics of a two-dimensional stick-slip system. Differ. Equ. Dyn. Syst. 20, 301–322 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  64. Kudra, G., Awrejcewicz, J.: Approximate modelling of resulting dry friction forces and rolling resistance for elliptic contact shape. Eur. J. Mech. A/Solids 42, 358–375 (2013)

    Article  MathSciNet  Google Scholar 

  65. Awrejcewicz, J., Kudra, G.: Celtic stone dynamics revisited using dry friction and rolling resistance. Shock Vib 19, 1115–1123 (2012)

    Article  Google Scholar 

  66. Awrejcewicz, J., Kudra, G.: Mathematical modelling and simulation of the bifurcational wobblestone dynamics. Discontin. Nonlinear. Complex. 3(2), 123–132 (2014)

    Article  Google Scholar 

  67. Dahl, P.R.: Measurement of solid friction parameters of ball bearings, Technical Report, The Aerospace Corporation, El Segundo, California (1977)

  68. Borsotto, B., Godoy, E., Beauvois, D., Devaud, E.: An identification method for static and coulomb friction coefficients. Int. J. Control Autom. Syst. 7(2), 305–310 (2009)

    Article  Google Scholar 

  69. Liu, L., Liu, H., Wu, Z., Yuan, D.: A new method for the determination of the zero velocity region of the Karnopp model based on the statistics theory. Mech. Syst. Signal Process. 23, 1696–1703 (2009)

    Article  Google Scholar 

  70. Bicakci, S., Akdas, D., Karaoglan, A.D.: Optimizing Karnopp friction model parameters of a pendulum using RSM. Eur. J. Control 20, 180–187 (2014)

    Article  MATH  Google Scholar 

  71. Wu, X.D., Zuo, S.G., Lei, L., Yang, X.W., Li, Y.: Parameter identification for a LuGre model based on steady-state tire conditions. Int. J. Autom. Technol. 12(5), 671–677 (2011)

  72. Piatkowski, T.: Dahl and LuGre dynamic friction models—The analysis of selected properties. Mech. Mach. Theory 73, 91–100 (2014)

    Article  Google Scholar 

  73. Sun, Y.H., Chen, T., Wu, C.Q., Shafai, C.: A comprehensive experimental setup for identification of friction model parameters. Mech. Mach. Theory 100, 338–357 (2016)

    Article  Google Scholar 

  74. Awrejcewicz, J., Olejnik, P.: Analysis of dynamic systems with various friction laws. Appl. Mech. Rev. 58(6), 389–411 (2005)

    Article  Google Scholar 

  75. Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P.: Review and comparison of dry friction force models. Nonlinear Dyn. 83(4), 1785–1801 (2016)

    Article  Google Scholar 

  76. Haug, E.J., Wu, S.C., Yang, S.M.: Dynamics of mechanical systems with coulomb friction, stiction, impact, and constraints addition, deletion - I Theory. Mech. Mach. Theory 21(5), 401–406 (1986)

    Article  Google Scholar 

  77. Wu, S.C., Yang, S.M., Haug, E.J.: Dynamics of mechanical systems with coulomb friction, stiction, impact, and constraints addition, deletion - II Planar Systems. Mech. Mach. Theory 21(5), 407–416 (1986)

    Article  Google Scholar 

  78. Wu, S.C., Yang, S.M., Haug, E.J.: Dynamics of mechanical systems with coulomb friction, stiction, impact, and constraints addition, deletion - II Spatial Systems. Mech. Mach. Theory 21(5), 417–425 (1986)

    Article  Google Scholar 

  79. Piedbœuf, J.C., Carufel, J., Hurteau, R.: Friction and stick-slip in robots: simulation and experimentation. Multibody Syst. Dyn. 4, 341–354 (2000)

    Article  MATH  Google Scholar 

  80. Frøgonaczek, J., Wojtyra, M.: On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints. Mech. Mach. Theory 46(3), 312–334 (2011)

    Article  MATH  Google Scholar 

  81. Lampaert, V., Swevers, J., Al-Bender, F.: Experimental comparison of different friction models for accurate low-velocity tracking. In: Proceedings of the 10th Mediterranean Conference on Control and Automation - MED2002, Lisbon, Portugal, 9p (2002)

  82. Tjahjowidodo, T., Al-Bender, F., Van Brussel, H.: Friction identification and compensation in a DC motor. In: Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, 6p (2005)

  83. Liu, Y.F., Li, J., Zhang, Z.M., Hu, X.H., Zhang, W.J.: Experimental comparison of five friction models on the same test-bed of the micro stick-slip motion system. Mech. Sci. 6, 15–28 (2015)

    Article  Google Scholar 

  84. Bengisu, M.T., Akay, A.: Stability of friction-induced vibrations in multi-degree-of-freedom systems. J. Sound Vibr. 171, 557–570 (1994)

    Article  MATH  Google Scholar 

  85. Bliman, P.-A., Sorine, M.: Friction modelling by hysteresis operators: application to Dahl, stiction and Stribeck effects. In: Proceedings of the Conference “Models of Hysteresis”, Trento, Italy (1991)

  86. Bliman, P.-A., Sorine, M.: A system-theoretic approach of systems with hysteresis: Application to friction modelling and compensation. In: Proceedings of the second European Control Conference, Groningen, The Netherlands, pp. 1844–1849, (1993)

  87. Bliman, P.A., Sorine. M.: Easy-to-use realistic dry friction models for automatic control. In: Proceedings of 3rd European Control Conference, Rome, Italy, pp. 3788-3794. (1995)

  88. Dupont, P., Hayward, V., Armstrong, B., Altpeter, F.: Single state elasto-plastic friction models. IEEE Trans. Autom. Control 47, 787–792 (2002)

    Article  MathSciNet  Google Scholar 

  89. Lampaert, V., Swevers, J., Al-Bender, F.: Modification of the Leuven integrated friction model structure. IEEE Trans. Autom. Control 47, 683–687 (2002)

    Article  MathSciNet  Google Scholar 

  90. Al-Bender, F., Lampaert, V., Swevers, J.: The generalized Maxwell-Slip model: a novel model for friction simulation and compensation. IEEE Trans. Autom. Control 50, 1883–1887 (2005)

    Article  MathSciNet  Google Scholar 

  91. Piatkowski, T.: GMS friction model approximation. Mech. Mach. Theory 75, 1–11 (2014)

  92. Do, N.B., Ferri, A.A., Bauchau, O.A.: Efficient simulation of a dynamic system with LuGre friction. J. Comput. Nonlinear Dyn. 2, 281–289 (2007)

    Article  Google Scholar 

  93. Saha, A., Wiercigroch, M., Jankowski, K., Wahi, P., Stefański, A.: Investigation of two different friction models from the perspective of friction-induced vibrations. Tribol. Int. 90, 185–197 (2015)

    Article  Google Scholar 

  94. Marques, F., Flores, P., Lankarani, H.: Study of friction force model parameters in multibody dynamics. In: Proceedings of IMSD 2016, The \(4^{{\rm th}}\) Joint International Conference on Multibody System Dynamics, Montreal, Canada, 10p (2016)

  95. Nikravesh, P.E.: Computer Aided Analysis of Mechanical Systems. Prentice Hall, Englewood Cliffs, New Jersey (1988)

    Google Scholar 

  96. Marques, F.: Frictional contacts in multibody dynamics. Master Dissertation, University of Minho, Portugal (2015)

Download references

Acknowledgments

The first author expresses his gratitude to the Portuguese Foundation for Science and Technology through the PhD grant (PD/BD/114154/2016). This work has been supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020—Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Filipe Marques.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marques, F., Flores, P., Pimenta Claro, J.C. et al. A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dyn 86, 1407–1443 (2016). https://doi.org/10.1007/s11071-016-2999-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-2999-3

Keywords

Navigation