Modelling of rail track dynamics and wheel/rail interaction

A theoretical computer model for analyzing vertical dynamic responses of railway tracks and irregular wheel/rail interactions is developed. The model is capable of investigating four general areas of railway track dynamics. These are: (1) Natural vibration characteristics; (2) Dynamic track responses in the frequency domain (dynamic compliance); (3) Dynamic track responses under a stationary impact, load; and (4) Dynamic track/wheelset responses to moving wheel/rail interaction.; The track model is formulated by treating the infinitely long track as a finite length of a periodic structural system resting on a Winkler foundation. Only transversely (cross-track) symmetric dynamic responses are considered. Both the rail and the ties are described as elastic beams of either the Bernoulli-Euler type or the Timoshenko type. The ties may also be treated as discrete rigid masses. The rail is discretely supported on the ties with an intermediate spring and dashpot unit simulating the vibration attenuating effects of the fastening mechanisms and the rail pads (for concrete-tie tracks). The ties are underlaid by a distributed array of springs and dashpots representing the resilience and vibration absorbing effects of the ballast and subgrade which constitutes the track bed.; For track dynamic responses to irregular wheel/rail interactions, a wheelset model is incorporated. The wheelset model is a four degree of freedom lumped mass/spring system consisting of a two-axle truck with two wheel unsprung masses (including axle masses), the truck side frame mass and its pitch moment of inertia. For high frequency track responses and wheel/rail interaction, the vehicle components above the truck side frame are represented by a static load. The commonly used non-linear Hertzian contact model couples the wheelset and the track systems at the wheel/rail interfaces. Various types of wheel tread or rail profile shapes may be input as an excitation source to the wheel/rail interfaces as the wheels travel along on the rail at any speed.; The general equations of motion of the track system are established directly according to the Newton's law applied to a continuous structural system. The free vibrational characteristics of individual track components are obtained by using basic principles of beam vibrations. For the free vibrational analysis of the whole track as an integral structural system, the track models is divided into identical elements consisting of one rail span between two adjacent ties complete with the equivalent, frequency-dependent stiffness of the rail support. The method of exact dynamic stiffness matrix, applied to the discretized track element, is used to formulate the eigenvalue problem of the track structure. Method of solution to the eigenvalue problem is developed by incorporating the Gaussian elimination method with maximum pivoting.; The general solutions to the equations of motion of the track system are obtained by using the classical technique of modal analysis. The frequency domain solutions involve Fourier transformation and time domain solutions involve the Range-Kutta numerical routine or the Gaussian-Quadrature integration procedure. Applications of the solutions include the dynamic compliance analysis in the frequency domain, dynamic track responses to a stationary impact force, and dynamic track and wheelset responses under irregular wheel/rail interactions. Dynamic track responses include stresses/strains, displacements, accelerations, rail seat forces and ballast pressure. Wheel/rail interaction responses include wheel/rail impact forces due to various wheel tread and rail profile irregularities, wheel vertical trajectory and accelerations. A large number of numerical examples are presented and corresponding conclusions are made under a wide range of dynamic scenarios.