# Dynamic Train/Track Interaction: Simulation of Railhead Corrugation Growth under a Moving Bogie Using Mathematical Models Combined with Full-Scale Measurements

[Doktorsavhandling]

Heavier trains and higher speeds have increased the need for high-quality tracks and vehicles in order to fulfill safety and environmental requests. The phenomena involved in dynamic train/track interaction lead to noise radiation, induce ground-borne vibrations and degrade the track structure and the railcar wheels. Increased axle-loads and higher train speeds also accentuate the influence on the dynamic train/track interaction of imperfections appearing in the track structure and on the wheel tread. A special type of track imperfection is the so-called rail corrugation, which is a periodic vertical irregularity on the railhead.

The present thesis is concerned with the vertical dynamic interaction between the moving train and the track, and, in particular, with the modelling of corrugation growth on tangent tracks. Models of increasing complexity are developed, in-field measurements are performed, and realistic track parameters are sought for. The influence of different imperfections, such as rail corrugation, a hung sleeper or a wheelflat, on the wheel/rail contact force and on the track response is investigated. Physical explanations of the calculated interaction behaviour are given. The importance of including both of the two wheelsets in the bogie model is demonstrated and clarified. By use of factorial design methods, the influences of changes in some track parameters on the wheel/rail contact force when a wheelset passes a track having a random railhead irregularity are studied. The calculated results are compared to experimental results from full-scale measurements. A new ballast/subgrade model is suggested where measured frequency response functions together with an optimization routine are used to find the best values of the track parameters.

The corrugation growth model is based on the assumption that, on tangent tracks, the damage mechanism is wear from longitudinal slip due to driven, or braked, wheels. Setting out from an initial random railhead irregularity distribution, the corrugation growth is calculated as a function of the wave number of the irregularity. The results clearly show that, for a fixed train speed, the amplitude of irregularities of certain wavelengths will grow while the amplitudes of other irregularities will be smoothened. Comparisons between different corrugation models are carried out. The distribution of the wear within the contact area and also the shift of contact point is found to be important for the corrugation growth.

The track models used for the calculations are linear non-proportionally damped beam structures which are longitudinally rigid. Finite elements are employed and, in order to save computational time, the equations of motion for the track model are decoupled by use of complex-valued modal analysis. The vehicle is modelled as a discrete system of masses, springs and viscous dampers, which may be non-linear. Vertically, the wheel/rail contact is assumed to be Hertzian. The longitudinal contact is treated by use of a heuristic model for stationary rolling contact mechanics. The friction force influences the vertical dynamics of the track by applying a bending moment to the rail. Also, the longitudinal creepage depends on the rotation of the cross section of the rail and the angular velocity of the wheel. The friction law used is verified against the so-called exact theory for elastic stationary rolling contact. The system of equations governing the motion of the track, the motion of the vehicle, and the vertical and longitudinal wheel/rail contact is solved by use of a time stepping routine. The wear is taken as proportional to the frictional power and is assigned, at each time step, to the centroid of the wear distribution in the contact patch.

**Nyckelord: **train/track interaction, railway and track irregularities, railhead corrugation growth, railway dynamics and measurements, complex-valued modal analysis

Denna post skapades 2006-09-19. Senast ändrad 2013-09-25.

CPL Pubid: 1049