Nonlinear dynamics of railway wheelsets incorporating randomness

The thesis is to investigate the dynamic behavior of a single-axle railway wheelset and identify its chaotic behavior by means of time history, phase portrait, Lyapunov exponents, information dimension, bifurcation diagram and control strategy.; The thesis has its analytical and computational components. For the analytical component, several mathematical models of a single-axle rail vehicle wheelset are presented in order to compare their features for similarities and differences. These models present different contact theories of creep force, and have different parametric values. In addition, Model III does not consider gravitational stiffnesses and gyroscopic couple. As a result, directly comparing simulation results of these models makes it difficult to interpret results and to draw conclusions. Therefore, these models need to be expanded so that issues can be isolated and investigated accordingly. Randomness is introduced and becomes an integral part of the models. The latter step is necessary because any physical system is realistically operating under stochastic conditions. Randomness is introduced by the means of pseudo-random numbers whose characteristic is also discussed. For the computational component, the time history and phase portrait of the wheelset models and their combinations are used to examine the models for similarities and differences. The focus, however, is to employ Lyapunov exponents, information dimensions and bifurcation diagrams to study the effect of randomness in forward speed, or lateral clearance (dead band), or both forward speed and dead band, on the chaotic behavior of the single-axle wheelset. Results obtained show that Model IIb is the best model; Model III is also a good choice, especially when lacking wheelset data. Numerical simulations indicate that chaotic motion depends upon forward speed, yaw stiffness and the level of randomness. Increasing forward speed and the level of randomness seem to lead to chaos in the wheelset which may further lead to chaos in the railway vehicle system. However, increasing yaw stiffness can suppress the chaotic oscillations.; Toward the goal of chaos suppression, two control strategies are investigated: semi-active control and active control. Simulation results show that both can suppress chaos and control bifurcation pattern of the wheelset. Finally, the thesis concludes with some recommendations for fixture work.