Dynamic modelling of a railway wheelset based on Kane's method

Abstract

This study applies Kane's method to generate the equations of motion for a railway wheelset moving on a tangent track at a constant speed. Since the wheel and rail close contact conditions are used to obtain two nonholonomic constraint equations, the lateral vibration of the wheelset can be proven as a nonholonomic system possessing two degrees of freedom. Moreover, using Kane's approach to derive the linearised equations, we can take advantage of bypassing the full nonlinear equations and getting two equations with dynamic decoupling. When the set of equations in this work is compared with those in the literature, we found that two gyroscopic effect terms exist and yaw gravitational stiffness disappears, so that the critical speeds calculated in this work are always lower than those in the literature for the same numerical cases. At last, the contact conditions along with the creepages between wheels and rails can be directly expressed in terms of generalised speeds by using Kane's method. It shows that Kane's method focuses on motions rather than on configurations.