Bifurcation Behavior and Attractors in Vehicle Dynamics

• Autorzy: Hochlenert, D. , Von Wagner, U. , Hornig, S.
• Konferencja: German-Polish Workshop Dynamical Problems in Mechanical Systems (11 ; 23-28.08.2009 ; Sarbinowo, Poland)
• Języki publikacji: EN

Abstrakty

EN

Nonlinear self-excited systems in vehicle dynamics are discussed using the examples of squealing automotive disk brakes and the stability behavior of a railway wheelset. Both systems show self-excited vibrations for specific operation states. The self-excited vibrations are due to friction forces between pad and disk in the case of the automotive disk and due to contact forces in the case of the railway wheelset respectively. The analysis of the nonlinear equations of motion shows that the trivial solution looses stability either through a sub- or through a supercritical Hopf bifurcation depending on the system's parameters. In the case of a subcritical Hopf bifurcation two stable solutions coexist and the initial conditions determine which solution emerges. The properties of the nonlinear systems such as critical velocities, limit cycle amplitudes and attractors of coexisting solutions are calculated using center manifold reduction and normal form theory.

Słowa kluczowe

EN

self-excited vibrations; brake squeal; railway wheelset; Hopf bifurcation; center manifold; domains of attraction

• Czasopismo: Machine Dynamics Problems
• Rocznik: 2009
• Tom: Vol. 33, No. 2
• Strony: 57-73
• Opis fizyczny: Bibliogr. 16 poz., wykr.

Twórcy

autor

Hochlenert, D.

autor

Von Wagner, U.

autor

Hornig, S.

• Technical University of Berlin. Institute of Mechanics, Chair of Mechatronics and Machine Dynamics,

Bibliografia

• Bellmann, L., Stolz, U., Wallaschek, J., 2007, Zum belastungsabhängigen mechanischen Verhalten von Bremsbelagwerkstoffen während des Bremsenquietschens, Nichtlineare Schwingungen - Reibung und Kontaktmechanik (VDI-Berichte, 2022), 207-223, VDI Verlag, Dusseldorf.
• Hayashi, C., 1964, Nonlinear Oscillations in Physical Systems, McGraw-Hill.
• Hochlenert, D., 2006, Selbsterregte Schwingungen in Scheibenbremsen: Mathematische Modellbildung und aktive Unterdrückung von Bremsenquietschen, Ph.D. thesis, Technische Universität Darmstadt.
• Hochlenert, D., 2009, Nonlinear Stability Analysis of a Disk Brake Model, Nonlinear Dynamics, 58(1), 63-73.
• Hochlenert, D., Spelsberg-Korspeter, G., Hagedorn, P., 2007, Friction Induced Vibrations in Moving Continua and Their Application to Brake Squeal, ASME Journal of Applied Mechanics, 74, 542-549.
• Kinkaid, N. M., O'Reilly, O. M., Papadopoulos, P., 2003, Automotive Disc Brake Squeal, Journal of Sound and Vibration, 267, 105-166.
• Knothe, K., Böhm, F., 1999, History of stability of railway vehicles and road vehicles, Vehicle System Dynamics, 31, 283-323.
• Popp, K., Schiehlen, W., 1993, Fahrzeugdynamik, Teubner, Stuttgart.
• Rand, R., Armbruster, D., 1988, Perturbation methods, bifurcation theory and computer algebra, Springer Verlag, New York.
• Seyranian, A.P., Mailybaev, A.A., 2003, Multiparameter Stability Theory with Mechanical Applications, World Scientific, Singapore.
• Spelsberg-Korspeter, G., 2007, Self-excited vibrations in gyroscopic systems, Ph.D. thesis, Technische Universität Darmstadt.
• Troger, H., Steindl, H., 1991, Nonlinear Stability and Bifurcation Theory, Springer Verlag, Wien.
• von Wagner, U., 2009, Nonlinear dynamic behaviour of a railway wheelset, Vehicle System Dynamics, 47(5), 627-640.
• von Wagner, U., Hochlenert, D., Hagedorn, P., 2007, Minimal Models for Disk Brake Squeal, Journal of Sound and Vibration, 302, 527-539.
• Xu, G., Troger, H., Steindl, A., 1990, Global Analysis of the Loss of Stability of a Special Railway Bogie, W. Schiehlen (Editor), Nonlinear Dynamics in Engineering Systems, Springer Verlag, Berlin.
• Yuhas, D., Ding, J., Venkatesan, S., 2006, Non-linear Aspects of Friction Material Elastic Constants, Proceedings of the SAE 24th annual Brake Colloquium & Exhibition, SAE Paper 2006-01-3193.