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A smooth model of the resultant friction force on a plane contact area

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Języki publikacji
EN
Abstrakty
EN
A class of smooth approximations of the total friction force occurring on a plane finite contact surface is presented. It is assumed that the classical Coulomb friction law is valid on any infinitesimal element of the contact region. The models describe the stick phase, the fully developed sliding and the transition between these two modes. They take into account different values of static and dynamic friction coefficients. The models are applied in simulation of a dynamical system performing translational and rotational stick-slip oscillations, and then they are verified by comparison with the corresponding results in which an event-driven discontinuous model of friction is used.
Rocznik
Strony
909--919
Opis fizyczny
Bibliogr. 33 poz., rys.
Twórcy
autor
  • Lodz University of Technology, Department of Automation, Biomechanics and Mechatronics, Łódź, Poland
  • Lodz University of Technology, Department of Automation, Biomechanics and Mechatronics, Łódź, Poland
Bibliografia
  • 1. Acary V., Brogliato, B., 2010, Numerical Methods for Nonsmooth Dynamical Systems, Springer
  • 2. Awrejcewicz J., Lamarque C.-H., 2003, Bifurcation and Chaos in Nonsmooth Mechanical Systems, World Scientific, Singapore
  • 3. Awrejcewicz J., Olejnik P., 2003, Stick-slip dynamics of a two-degree-of-freedom system, International Journal of Bifurcation and Chaos, 13, 4, 843-861
  • 4. Awrejcewicz J., Supeł B., Lamarque C.-H., Kudra G., Wasilewski G., Olejnik P., 2008, Numerical and experimental study of regular and chaotic motion of triple physical pendulum, International Journal of Bifurcation and Chaos, 18, 10, 2883-2915
  • 5. Bogacz, R., Sikora, J., 1990, On stability of periodic solutions of a discrete system with many degrees of freedom and dry friction, Proceedings of the Vibrations in Physical Systems, 57-59, Poznan, Poland
  • 6. Contensou P., 1963,Couplage entre frottement de glissement et de pivotement dans la th´eorie de la toupe, [In:] Kreiselprobleme Gyrodynamic, Ziegler H. (Ed.), IUTAM Symposium, Celerina, 1962, Springer-Verlag, Berlin, 201-216
  • 7. Do N.B., Ferri A.A., Bauchau O.A., 2007, Efficient simulation of a dynamic system with LuGre friction, Journal of Computational and Nonlinear Dynamics, 2, 4, 281-289
  • 8. Filippov A.F., 1964, Differential equations with discontinuous right-hand side, American Mathematical Society Translations, 42, 199-231
  • 9. Filippov A.F., 1988, Differential Equations with Discontinuous Right-Hand Sides, Kluwer Academic, Dordrecht
  • 10. G´enot F., Brogliato B., 1999, New results on Painlev´e Paradoxes, European Journal of Mechanics – A/Solids, 18, 653-677
  • 11. Howe R.D., Cutkosky M.R., 1996, Practical force-motion models for sliding manipulation, International Journal of Robotics Research, 15, 6, 557-572
  • 12. Jean M., 1999, The non-smooth contact dynamics method, Computer Methods in Applied Mechanics and Engineering, 177, 235-257
  • 13. Jellet J.H., 1872, Treatise on the Theory of Friction, Hodges, Foster and Co, Dublin
  • 14. Kireenkov A.A., 2008, Combined model of sliding and rolling friction in dynamics of bodies on a rough plane, Mechanicsof Solids, 43, 3, 412-425
  • 15. Kosenko I., Aleksandrov E., 2009, Implementation of the Contensou-Erisman model of friction in frame of the Hertz contact problem on Modelica, 7th Modelica Conference, Como, Italy, 288-298
  • 16. Kudra G., Awrejcewicz J., 2011a, Regularized model of coupled friction force and torque for circularly-symmetric contact pressure distribution, Proceedings of the 11th Conference on Dynamical Systems – Theory and Applications, 353-358
  • 17. Kudra G., Awrejcewicz J., 2011b, Tangenshyperbolicus approximations of the spatial model of friction coupled with rolling resistance, International Journal of Bifurcation and Chaos, 21, 10, 2905-2917
  • 18. Kudra G., Awrejcewicz J., 2012a, Bifurcational dynamics of a two-dimensional stick-slip system, Differential Equations and Dynamical Systems, 20, 3, 301-322
  • 19. Kudra G., Awrejcewicz J., 2012b, Celtic stone dynamics revisited using dry friction and rolling resistance, Shock and Vibration, 19, 5, 1115-1123
  • 20. Kudra G., Awrejcewicz J., 2013, Approximate modelling of resulting dry friction forces and rolling resistance for elliptic contact shape, European Journal of Mechanics – A/Solids, 42, 358-375
  • 21. Leine R.I., van Campen D.H., Van De Vrande B.L., 2000, Bifurcations in nonlinear discontinuous systems, Nonlinear Dynamics, 23, 2, 105-164
  • 22. Leine R.I., Glocker Ch., 2003, A set-valued force law for spatial Coulomb-Contensou friction, European Journal of Mechanics – A/Solids, 22, 2, 193-216
  • 23. Leine R.I., Nijmeijer H., 2004, Dynamics and Bifurcations of Non-smooth Mechanical Systems, Springer
  • 24. Moreau J.J., 1988, Unilateral contact and dry friction in finite freedom dynamics, Nonsmooth Mechanics and Applications, 1-82, Springer-Verlag, Wien
  • 25. Moller M., Leine R.I., Glocker Ch., 2009, An efficient approximation of orthotropic setvalued laws of normal cone type, Proceedings of the 7th EUROMECH Solid Mechanics Conference, Lisbon, Portugal
  • 26. Painlev´e P., 1895, Le¸con sur le frottement, Hermann, Paris
  • 27. Pilipchuk V.N., Tan C.A., 2004, Creep-slip capture as a possible source of squeal during decelerated sliding, Nonlinear Dynamics, 35, 259-285
  • 28. Sikora, J., Bogacz, R., 1993, On dynamics of several degrees of freedom system, ZAMM – Journal of Applied Mathematics and Mechanics, 73, T118-T122
  • 29. Stamm W., Fidlin A., 2007, Regularization of 2D frictional contacts for rigid body dynamics, IUTAM Symposium on Multiscale Problems in Multibody System Contacts, 291-300, Springer
  • 30. Stamm W., Fidlin A., 2008, Radial dynamics of rigid friction disks with alternating sticking and sliding, Proceedings of the 6th EUROMECH Nonlinear Dynamics Conference, Saint Perersburg
  • 31. Stewart D., Trinkle J.C., 1996, An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and Coulomb friction, International Journal of Numerical Methods in Engineering, 39, 2673-2691
  • 32. Zhuravlev V.P., 1998, The model of dry friction in the problem of the rolling of rigid bodies, Journal of Applied Mathematics and Mechanics, 62, 5, 705-710
  • 33. Zhuravlev V.P., Kireenkov A.A., 2005, Pad´e expansions in the two-dimensional model of Coulomb friction, Mechanics of Solids, 40, 2, 1-10
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniajacą naukę.
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Bibliografia
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