Nonlinear Analysis of Hunting Motion by Focusing on Non-selfadjointness

摘要

When the running speed of railway vehicles exceeds critical limits, they begin to suffer from hunting motion that can affect ride comfort and threaten their safety. Even below such critical speeds, which can be obtained by linear analysis, such vehicles can experience hunting motions because their wheel systems have nonlinear characteristics. In this study, by taking into consideration the non-selfadjointness of such systems, we derive the normal form of the equation of motion for a single wheel set under the relevant cubic and quintic nonlinearities. Equations for the different orders that arise due to those nonlinearities are then derived from an original equation using a method of multiple scales, and an adjoint linear operator is used to obtain the equation governing the dynamics with a slower timescale. Additionally, a normal form with two unknown coefficients was obtained, after which we identify the nonlinear coefficients of the normal form using the experimental method proposed in our previous research. We also obtain a subcritical Hopf bifurcation diagram from the normal form, the theoretical results of which agree well with our experimental results.