Abstract
It is well-known that classical Coulomb dry friction model does not portrays important physical phenomena occurring in the contact between mating surfaces. Moreover, the discontinuity of force at zero velocity has many drawbacks during numerical simulations. In the attempt of exploring alternatives to Coulomb friction model, this paper presents the application of the Dahl friction model in a multibody dynamics formulation. The analysis herein presented includes also the modeling of friction forces in lower pairs and some hints on the efficient computation of Lagrange parameters during the fixed-point iteration process. Two numerical examples are offered.
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Ahmed, S., Lankarani, H.M., Pereira, M.F.O.S.: Frictional impact analysis in open-loop multibody mechanical systems. ASME J. Mech. Des. 121, 119ȓ127 (1999)
Arabyan, A., Wu, F.: An improved formulation for constrained mechanical systems. Multibody Syst. Dyn. 2, 49ȓ69 (1998)
Armstrong-Hélouvry, B., Dupont, P., Canudas, C.: A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica 38, 1083ȓ1138 (1994)
Bagci, C.: Gross Motion Time Response Analysis of the Four-Bar Mechanism by the Method of Components with Coulomb and Viscous Damping in Pair Bearings, Linkage Design Monographs Ȕ Final Report on NSF Gk-36624 (1976)
Armstrong-Hélouvry, B.: Control of Machines with Friction. Kluwer Academic Publishers, Dordrecht (1991)
Centea, D., Rahnejat, H., Menday, M.T., Non-linear multi-body dynamic analysis for the study of clutch torsional vibrations (judder). Appl. Math. Modell. (25), 177ȓ192 (2001)
Cheli, F., Pennestrì, E. (eds): Kinematics and Dynamics of Multibody Systems. Casa Editrice Ambrosiana, Milano (2006) (in italian)
Dahl, P.R.: Solid friction damping in mechanical vibrations. AIAA J. 14, 1675ȓ1682 (1976)
de Falco, D., Pennestrì, E., Vita, L., The Udwadia-Kalaba Formulation: A Report on its Numerical Efficiency in Multibody Dynamics Simulations and on its Teaching Effectiveness. Multibody Dynamics 2005 Ȕ ECCOMAS Thematic Conference, Madrid, Spain (2005)
de Jalón, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems. Springer Verlag, Berlin, Heidelberg, New York (1999)
Dupont, P.E.: The effect of Coulomb friction on the existence and uniqueness of the forward dynamics problem. In: Proceedings of the 1992 IEEE International Conference on Robotics and Automation, pp. 1442ȓ1447. Nice, France (1992)
Dupont, P., Hayward, V., Armstrong-Hélouvry, B., Altpeter, F.: Single state elastoplastic friction models. IEEE Trans. Autom. Control 47(5), 787ȓ792 (2002)
Eich-Soellner, E., Führer, C.: Numerical Methods in Multibody Dynamics. B.G. Teubner, Stuttgart (1998)
Glocker, C.: Set-Valued Force Laws: Dynamics of Non Smooth Systems. Lectures Notes in Applied and Computational Mechanics. Springer Verlag, Berlin, Heidelberg, New York (2001)
Hall, A.S.: Notes on Mechanism Analysis. Waveland Press Inc., Long Grove, IL (1986)
Han, I., Gilmore, B.J.: Multi-body impact motion with friction-analysis, simulation and experimental validation. ASME J. Mech. Des. 115, 412ȓ422 (1993)
Haug, E.: Computer-Aided Kinematics and Dynamics of Mechanical Systems. Allyn and Bacon, Boston, MA (1989)
Haug, E.J., Wu, S.C., Yang, S.M.: Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion, Part I (Theory), Part II (Planar Systems). Mech. Mach. Theory 21(5), 401ȓ416 (1986)
Herrmann, G.: The Graphical Statics of Mechanisms. Van Nostrand Company, New York (1900)
Ibrahim, R.A., http://www.mi.uni-koeln.de/mi/Forschung/Kuepper/friction.html
Kermani, M.R., Pate, R.V.: Friction identification in robotic manipulators, case studies. In: Proceedings of the 2005 IEEE Conference on Control Applications, Toronto, Canada (2005)
Klepp, H.J.: The existence and uniqueness of solutions for the pendulum with friction. J. Sound Vib. 175, 138ȓ143 (1994)
Klepp, H.J.: Kinetic friction locking for multi-body systems with friction. Zeitschrift für Angewandte Mathematik 46, 693ȓ708 (1995)
Klepp, H.J.: The existence and uniqueness of solutions for a single-degree-of-freedom system with two friction-affected sliding joints. J. Sound Vib. 185(2), 364ȓ371 (1995)
Lankarani, H.M.: A poisson-based formulation for frictional impact analysis of multibody mechanical systems with open or closed kinematic chains. ASME J. Mech. Des. 122, 489ȓ497 (2000)
Lenoir, Y.: Identification des modèles tribologique par pendule. C.R. Academie des Sciences, Paris, t.327, Série IIb, 1259ȓ1264 (1999)
Leonard, N.E., Krishnaprasad, P.S.: Comparative Study of Friction-Compensating Control Strategies for Servomechanisms. University of Maryland Ȕ Systems Research Center, Report TR 91-88 (1991)
Lindelöf, M.E.: Sur l'application de la méthode des approximations successives aux équations différentielles ordinaires du premier ordre. Comptes rendus hebdomadaires des séances de l'Académie des sciences 114, 454ȓ457 (1894)
Lorenz, H.: Lehrbuch der Technischen Physik: Erster Band: Technische Mechanik starrer Gebilde. Verlag von julius. Springer, Berlin (1924)
Nikravesh, P.: Computer-Aided Analysis of Mechanical Systems. Prentice-Hall, Englewood Cliffs, NJ (1988)
Oh, J. et al.: Duhem models for hysteresis in sliding and presliding friction. In: Proceedings of the 44th Conference on Decision and Control, and the European Control Conference 2005, pp. 8132ȓ8137. Seville, Spain (2005)
Olsson, H., Å ström, K.J., Canudas de Wit, C., Gäfvert, M., Lischinsky, P.: Friction models and friction compensation. Eur. J. Control 4(3), 176ȓ195 (1998)
Painlevé, P.: Leçons sur le Frottement. Cours Complémentaire del Mécanique Rationelle, Librairie Scientifique A. Hermann, Paris (1895)
Painlevé, P.: Sur le lois du frottement de glissement. Different articles with the same title appered in Comptes rendus de l'Académie des sciences 140, 702ȓ707 (1905), 141, 401ȓ405, 546ȓ552 (1906)
Paul, B.: Kinematics and Dynamics of Planar Machinery. Prentice-Hall, Englewood Cliffs, NJ (1982)
Pfeiffer, F., Glocker, C.: Multibody Dynamics with Unilateral Contacts. Wiley, Hoboken, NJ (1996)
Song, P., Kraus, P., Kumar, V., Dupont, P.: Analysis of Rigid Body Dynamic Models for Simulation of Systems, Technical report, MS-CIS-00-08, University of Pennsylvania, Department of Computer Science (2000)
Stewart, D.E.: Rigid-body dynamics with friction and impact. SIAM Rev. 42(1), 3ȓ39 (2000)
Stronge, W.J.: Multi-body impact with friction. In: Rahnejat, H., Ebrahimi, M., Whalley, R. (eds.) Multi-body Dynamics: Monitoring and Simulation Techniques Ȕ II, pp. 15ȓ26. Professional Engineering Publishing, Suffolk, UK (2000)
Threlfal D.C.: The inclusion of Coulomb friction in mechanisms programs with particular reference to DRAM. Mech. Mach. Theory 13, 475ȓ483 (1978)
Turner, J.D.: On the simulation of discontinuous functions. ASME J. Appl. Mech. 68, 751ȓ757 (2001)
Udwadia, F.E., Kalaba, R.E.: Analytical Dynamics Ȕ A New Approach. Cambridge University Press, Cambridge, UK (1996)
Wang, Y.P, Liao, W.H., Lee, C.L.: A state approach for dynamic analysis of sliding structures. Earthquake Eng. Struct. Dyn. 23, 790ȓ801 (2001)
Wang, Y., Mason, M.T.: Two-dimensional rigid-body collisions with friction. ASME J. Appl. Mech. 59, 635ȓ642 (1992)
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Pennestrì, E., Valentini, P.P. & Vita, L. Multibody dynamics simulation of planar linkages with Dahl friction. Multibody Syst Dyn 17, 321–347 (2007). https://doi.org/10.1007/s11044-007-9047-5
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DOI: https://doi.org/10.1007/s11044-007-9047-5