ABSTRACT
The basic physical phenomena involved in the dynamics of railway vehicles have been described in Chapter 1. Equations of motion governing the stability and dynamic response of vehicles will now be derived which encompass the essential features of the wheel-rail geometry, the frictional forces acting between wheel and rail and the elastic and damping forces generated by the suspension. As attention will be confined to the dynamics at low frequencies, the wheelset and track are assumed to be rigid apart from local elasticity in the contact patch between wheel and rail, and the contributions of the local deflections near the contact patch to the overall motion of the wheelset are neglected. The wheelset, which is assumed to be axisymmetric about the axle centreline, is considered to be constrained to run along the track at constant speed. The track is arbitrarily curved in plan view and may be canted. The kinematics of the wheelset is considered first, and this is followed by a discussion of wheel rail geometry. An evaluation of the creep forces acting between wheel and rail makes it possible to formulate equations of motion of a freely running wheelset. This is followed by the derivation of the equations of motion of a complete two-axle vehicle in which the action of the suspension is taken into account.
