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

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

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)

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

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

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

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

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

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

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)

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

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

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

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

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)

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)

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

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)

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)

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

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)

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)

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)

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)

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

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

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)

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)

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

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

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)

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

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)

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)

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

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

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)

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)

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

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)

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)

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)

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

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

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

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)

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

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)

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)

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)

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)

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)

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)

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

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

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

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

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)

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)

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

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)

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)

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)

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

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)

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

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

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

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)

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)

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

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)

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

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)

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

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

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)

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)

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)

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

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)

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)

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)

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)

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

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)

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)

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)

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

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

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)

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

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)

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)

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

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

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