Abstract
A dicone moving on a pair of cylindrical rails can be considered as a simplified model of a railway wheelset. Taking into account the non-linear friction laws of rolling contact, the equations of motion for this non-linear mechanical system result in a set of differential-algebraic equations. Previous simulations performed with the differential-algebraic solver DASSL, [2], and experiments, [7], indicated non-linear phenomena such as limit-cycles, bifurcations as well as chaotic behaviour. In this paper the non-linear phenomena are investigated in more detail with the aid of special in-house software and the path-following algorithm PATH [10]. We apply Poincaré sections and Poincaré maps to describe the structure of periodic, quasiperiodic and chaotic motions. The analyses show that part of the chaotic behaviour of the non-linear system can be fully understood as a non-linear iterative process. The resulting stretching and folding processes are illustrated by series of Poincaré sections.
Similar content being viewed by others
Bibliography
Abel, S. G. and Cooperrider, N. K., ‘An equivalent linearization algorithm for nonlinear system limit cycle analysis’, Journal Dynamic Systems, Measurement and Control 107, 1985, 117–122.
Brenan, K. E., Campbell, S. L. and Petzold, L. R., Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, North-Holland, New York, Amsterdam, London, 1989.
Cvitanovic, P., Universality in Chaos, Hilger, London, 1984.
Duffek, W., Jaschinski, A., and Jochim, M., ‘Curving performance and tangent track behaviour of the German high speed train’, in Proceedings of the 11th IAVSD-Symposium on the Dynamics of Vehicles on Roads and on Tracks, Kingston, Canada, Aug. 21–25, 1989, 166–178.
Grebogi, C., Ott, E., and Yorke, J. A., ‘Chaotic attractors in crisis’, Physical Review Letters 48(22), 1982, 1507–1510.
Jaschinski, A., ‘Anwendung der Kalkerschen Rollreibungstheorie zur dynamischen Simulation von Schienenfahrzeugen’, Technical Report, DLR-Deutsche Forschungsanstalt für Luft- und Raumfahrt, DFVLR-FB 87-07, Oberpfaffenhofen, 1987.
Jaschinski, A., ‘On the application of similarity laws to a scaled railway bogie model’, Doctoral Thesis, Delft University of Technology, 1990.
Kaas-Petersen, C. and True, H., ‘Periodic, biperiodic and chaotic dynamical behaviour of railway vehicles’, in Proceedings of the 9th IAVSD-Symposium on the Dynamics of Vehicles on Roads and on Tracks, Linköping, Sweden, June 24–28, 1985, 208–221.
Kaas-Petersen, C., ‘Chaotic behaviour in a bogie model’, Acta Mechanica, Leipzig, 1987.
Kaas-Petersen, C., ‘PATH — user's guide’, Department of Applied Mathematical Studies and Centre for Nonlinear Studies, University of Leeds, Leeds LS2 0JT, United Kingdom, 1987.
Kalker, J. J. ‘On the rolling contact of two elastic bodies in the presence of dry friction’, Doctoral Thesis, Delft University of Technology, 1967.
Kalker, J. J., ‘Unilateral problems in structural analysis’, in CISM Course and Lectures No. 288, Springer, Wien, New York, 1985.
Mosekilde, E, Feldberg, R., Knudsen, C., and Hindsholm, M., ‘Mode-locking and spatio temporal chaos in periodically driven Gunn diodes’, Physical Review B41, 2298, 1990.
Thompson, J. M. T. and Stewart, H. B., Nonlinear Dynamics and Chaos, Wiley, Chichester, 1986.
True, H., ‘Chaotic motion of railway vehicles’, in Proceedings of the 11th IAVSD-Symposium on the Dynamics of Vehicles on Roads and on Tracks, Kingston, Canada, Aug. 21–25, 1989, 578–587.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Knudsen, C., Feldberg, R. & Jaschinski, A. Non-linear dynamic phenomena in the behaviour of a railway wheelset model. Nonlinear Dyn 2, 389–404 (1991). https://doi.org/10.1007/BF00045671
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00045671