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

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.

[1]  F. P. Bowden,et al.  Nature of Sliding and the Analysis of Friction , 1938, Nature.

[2]  A. Tustin,et al.  The effects of backlash and of speed-dependent friction on the stability of closed-cycle control systems , 1947 .

[3]  E. Rabinowicz The Nature of the Static and Kinetic Coefficients of Friction , 1951 .

[4]  E. Rabinowicz Stick and Slip , 1956 .

[5]  J. S. Courtney‐Pratt,et al.  The effect of a tangential force on the contact of metallic bodies , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[6]  P. Contensou Couplage entre frottement de glissement et frottement de pivotement dans la théorie de la toupie , 1963 .

[7]  P. Dahl A Solid Friction Model , 1968 .

[8]  C. Coulomb Théorie des machines simples, en ayant égard au frottement de leurs parties et a la roideur des cordages , 1968 .

[9]  C. A. Brockley,et al.  The role of the rate of application of the tangential force in determining the static friction coefficient , 1973 .

[10]  P. Dahl Solid Friction Damping of Mechanical Vibrations , 1976 .

[11]  Phil R Dahl,et al.  Measurement of Solid Friction Parameters of Ball Bearings , 1977 .

[12]  J. Dieterich Time-dependent friction and the mechanics of stick-slip , 1978 .

[13]  D. C. Threlfall,et al.  The inclusion of Coulomb friction in mechanisms programs with particular reference to DRAM au programme DRAM , 1978 .

[14]  D. Pavelescu,et al.  The friction-speed relation and its influence on the critical velocity of stick-slip motion , 1982 .

[15]  Dean Karnopp,et al.  Computer simulation of stick-slip friction in mechanical dynamic systems , 1985 .

[16]  Edward J. Haug,et al.  Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion—III Spatial systems , 1986 .

[17]  E. Haug,et al.  Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion—I theory , 1986 .

[18]  Edward J. Haug,et al.  Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion—II Planar systems , 1986 .

[19]  Parviz E. Nikravesh,et al.  Computer-aided analysis of mechanical systems , 1988 .

[20]  J. Awrejcewicz Chaotic motion in a nonlinear oscillator with friction , 1988 .

[21]  Bernard Friedland,et al.  On the Modeling and Simulation of Friction , 1990, 1990 American Control Conference.

[22]  J. Awrejcewicz DYNAMICS OF A SELF-EXCITED STICK-SLIP OSCILLATOR , 1991 .

[23]  A. Soom,et al.  Friction at a Lubricated Line Contact Operating at Oscillating Sliding Velocities , 1990 .

[24]  Brian Armstrong-Hélouvry,et al.  Control of machines with friction , 1991, The Kluwer international series in engineering and computer science.

[25]  Karl Popp,et al.  Nonlinear Oscillations of Structures Induced by Dry Friction , 1992 .

[26]  Eric P. Dunlap,et al.  Friction Modeling and Control in Boundary Lubrication , 1993, 1993 American Control Conference.

[27]  Carlos Canudas de Wit,et al.  A survey of models, analysis tools and compensation methods for the control of machines with friction , 1994, Autom..

[28]  A. Akay,et al.  Stability of Friction-Induced Vibrations in Multi-Degree-of-Freedom Systems , 1994 .

[29]  Bernard Friedland,et al.  Dynamic Friction Model of Lubricated Surfaces for Precise Motion Control , 1994 .

[30]  Carlos Canudas de Wit,et al.  A new model for control of systems with friction , 1995, IEEE Trans. Autom. Control..

[31]  S. Scieszka,et al.  The Importance of Static Friction Characteristics of Brake Friction Couple, and Methods of Testing , 1996 .

[32]  M. A.J. A NON-LINEAR FRICTION MODEL FOR SELF-EXCITED VIBRATIONS , 1997 .

[33]  van Dh Dick Campen,et al.  Stick-Slip Vibrations Induced by Alternate Friction Models , 1998 .

[34]  V. Zhuravlev The model of dry friction in the problem of the rolling of rigid bodies , 1998 .

[35]  Carlos Canudas de Wit,et al.  Friction Models and Friction Compensation , 1998, Eur. J. Control.

[36]  Mariusz M Holicke,et al.  MELNIKOV'S METHOD AND STICK–SLIP CHAOTIC OSCILLATIONS IN VERY WEAKLY FORCED MECHANICAL SYSTEMS , 1999 .

[37]  Jan Swevers,et al.  An integrated friction model structure with improved presliding behavior for accurate friction compensation , 1998, IEEE Trans. Autom. Control..

[38]  C. Hsieh,et al.  Dynamic behavior and modelling of the pre-sliding static friction , 2000 .

[39]  P. Dupont,et al.  Elasto-plastic friction model: contact compliance and stiction , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[40]  Richard Hurteau,et al.  Friction and Stick-Slip in Robots: Simulation and Experimentation , 2000 .

[41]  J. Frěne,et al.  SECTION 8.4 – Friction in Lubricated Contacts , 2001 .

[42]  Vincent Hayward,et al.  Single state elastoplastic friction models , 2002, IEEE Trans. Autom. Control..

[43]  Jan Swevers,et al.  EXPERIMENTAL COMPARISON OF DIFFERENT FRICTION MODELS FOR ACCURATE LOW-VELOCITY TRACKING , 2002 .

[44]  P. Dupont,et al.  Single State Elasto-Plastic Friction Models , 2002 .

[45]  Jan Swevers,et al.  Modification of the Leuven integrated friction model structure , 2002, IEEE Trans. Autom. Control..

[46]  C. Glocker,et al.  A set-valued force law for spatial Coulomb-Contensou friction , 2003 .

[47]  Jorge Ambrósio,et al.  Impact of Rigid and Flexible Multibody Systems: Deformation Description and Contact Models , 2003 .

[48]  F. Al-Bender,et al.  A generalized Maxwell-slip friction model appropriate for control purposes , 2003, 2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775).

[49]  F. Al-Bender,et al.  A Novel Generic Model at Asperity Level for Dry Friction Force Dynamics , 2004 .

[50]  John McPhee,et al.  A Regularized Contact Model with Asymmetric Damping and Dwell-Time Dependent Friction , 2004 .

[51]  Fayçal Ikhouane,et al.  Identification of a system with dry friction , 2005 .

[52]  W.E. Dixon,et al.  A new continuously differentiable friction model for control systems design , 2005, Proceedings, 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics..

[53]  Olivier A. Bauchau,et al.  Efficient simulation of a dynamic system with LuGre friction , 2005 .

[54]  Farid Al-Bender,et al.  FRICTION IDENTIFICATION AND COMPENSATION IN A DC MOTOR , 2005 .

[55]  Jan Awrejcewicz,et al.  Analysis of Dynamic Systems With Various Friction Laws , 2005 .

[56]  Jan Swevers,et al.  The generalized Maxwell-slip model: a novel model for friction Simulation and compensation , 2005, IEEE Transactions on Automatic Control.

[57]  C. Grebogi,et al.  Estimation of Chaotic and Regular (Stick–Slip and Slip–Slip) Oscillations Exhibited by Coupled Oscillators with Dry Friction , 2005 .

[58]  Jan Awrejcewicz,et al.  OCCURRENCE OF STICK-SLIP PHENOMENON , 2007 .

[59]  M. Wiercigroch,et al.  Hysteretic effects of dry friction: modelling and experimental studies , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[60]  H. Hetzler,et al.  Analytical investigation of steady-state stability and Hopf-bifurcations occurring in sliding friction oscillators with application to low-frequency disc brake noise , 2007 .

[61]  Stefan Björklund,et al.  Friction models for sliding dry, boundary and mixed lubricated contacts , 2007 .

[62]  E. Pennestrì,et al.  Multibody dynamics simulation of planar linkages with Dahl friction , 2007 .

[63]  E. Chatelet,et al.  Stick/slip phenomena in dynamics: Choice of contact model. Numerical predictions & experiments , 2007 .

[64]  J. Awrejcewicz,et al.  A novel dry friction modeling and its impact on differential equations computation and Lyapunov exponents estimation , 2008 .

[65]  A. Kíreenkov Combined model of sliding and rolling friction in dynamics of bodies on a rough plane , 2008 .

[66]  B. Borsotto,et al.  An identification method for static and coulomb friction coefficients , 2009 .

[67]  Hongzhao Liu,et al.  A new method for the determination of the zero velocity region of the Karnopp model based on the statistics theory , 2009 .

[68]  J. Awrejcewicz,et al.  On a Novel Dry Friction Modeling: Differential Equations Computation and Lyapunov Exponent Estimation , 2009 .

[69]  I. Kosenko,et al.  Implementation of the Contensou–Erismann tangent forces model in the Hertz contact problem , 2010 .

[70]  F. Al-Bender,et al.  A Generalised Asperity-Based Friction Model , 2010 .

[71]  Lei Lei,et al.  Parameter identification for a LuGre model based on steady-state tire conditions , 2011 .

[72]  Jan Awrejcewicz,et al.  Tangens Hyperbolicus Approximations of the Spatial Model of Friction Coupled with Rolling Resistance , 2011, Int. J. Bifurc. Chaos.

[73]  J. Fraczek,et al.  On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints , 2011 .

[74]  S. Oleksowicz,et al.  A Basic Theoretical Model for Friction Process at Microasperity Level , 2011 .

[75]  J. Awrejcewicz,et al.  Celtic stone dynamics revisited using dry friction and rolling resistance , 2012 .

[76]  M. Haddar,et al.  Study of Mass Spring System Subjected to Dahl Friction , 2012 .

[77]  J. Awrejcewicz,et al.  Bifurcational Dynamics of a Two-Dimensional Stick-Slip System , 2012 .

[78]  Ou Ma,et al.  An extended bristle friction force model with experimental validation , 2012 .

[79]  J. Awrejcewicz,et al.  Approximate modelling of resulting dry friction forces and rolling resistance for elliptic contact shape , 2013 .

[80]  E. J. Berger,et al.  On the walking stick–slip problem , 2014 .

[81]  Jan Awrejcewicz,et al.  Mathematical Modelling and Simulation of the Bifurcational Wobblestone Dynamics , 2014 .

[82]  Aslan Deniz Karaoglan,et al.  Optimizing Karnopp friction model parameters of a pendulum using RSM , 2014, Eur. J. Control.

[83]  T. Piatkowski,et al.  Dahl and LuGre dynamic friction models — The analysis of selected properties , 2014 .

[84]  T. Piątkowski GMS friction model approximation , 2014 .

[85]  Pedro Filipe Lima Marques Frictional contacts in multibody dynamics , 2015 .

[86]  Pankaj Wahi,et al.  Investigation of two different friction models from the perspective of friction-induced vibrations , 2015 .

[87]  Y. F. Liu,et al.  Experimental comparison of five friction models on the same test-bed of the micro stick-slip motion system , 2015 .

[88]  Paulo Flores,et al.  On the frictional contacts in multibody system dynamics , 2015 .

[89]  Ettore Pennestrì,et al.  Review and comparison of dry friction force models , 2016 .

[90]  H. Lankarani,et al.  Study of Friction Force Model Parameters in Multibody Dynamics , 2016 .

[91]  Tao Chen,et al.  A comprehensive experimental setup for identification of friction model parameters , 2016 .