Dynamic Wheel/Rail Rolling Contact at Singular Defects with Application to Squats

Abstract

Squats, as a kind of short wavelength rail surface defects, have become one of the main rolling contact fatigue problems in railways worldwide. The purpose of this work is to better understand the squatting phenomenon, contribute to reduction and even prevention of squat occurrence, and thereby reduce the related costs. To such an end, a new modeling approach has been developed in this dissertation, i.e. a three-dimensional finite element (FE) model of the vehicle–track interaction. Both wheel set and rail are simulated as three-dimensional continua. A detailed surface-to-surface contact algorithm is integrated within the FE model in order to solve the frictional rolling contact between the wheel and rail. Different traction/braking efforts are simulated. Detailed modeling of the wheel and rail ensures the consideration of important eigen-modes related to squats, mainly in the high frequency range. Other structures of the vehicle–track system are also modeled to appropriate extents. An estimate of contact stresses with sufficient accuracy is the basis of further dynamic, stress, and fatigue analyses of squats. The FE model has been validated for both normal and tangential contact solutions by comparing it to the widely accepted Hertz theory and Kalker’s CONTACT program. Due to the fact that Hertz theory and CONTACT are only applicable to static contact problems, the steady-state rolling contact between smooth wheels and smooth rails, with the contact occurring in the middle of the rail top, is simulated by the FE model for the purpose of validation. The results show that the FE model is reliable for the solution of frictional rolling contact. On the other hand, the FE model can also take into account actual contact geometry, material non-linearity, and transient effects, which are required for more complicated cases like the wheel–rail rolling contact at a squat. Therefore, the newly developed modeling approach provides a valid and promising tool to solve the problem of rolling contact in the presence of friction. With the validated FE model, the influence of plastic deformation on the solution of frictional wheel–rail rolling contact is further investigated. A bi-linear elasto-plastic material model is employed. It is found that the contact geometry change caused by plastic deformation can significantly modify both the normal and the tangential solutions. When squat type defects are added to the rail top, the calculated dynamic contact forces show a good agreement in wavelength with observed squats in the field. This means that vibrations related to squats are captured by the FE model, proving the applicability of the FE modeling in treating the high frequency dynamics of a system containing rolling contact. Furthermore, based on the simulations and field observations, a growth process of squats from light to mature state has been postulated. This postulation has been validated by track monitoring conducted in the Netherlands. Further analyses of the FE simulations show that squats mainly excite the vehicle–track system at two frequencies. The vibration component with the lower frequency can transfer down to the ballast layer, especially at the support close to the squat. The high frequency vibration component has similar magnitude at several fastenings near the squat and is negligible at the ballast layer. For the investigated rolling speed range between 40 and 140 km/h, both two vibration components increase in magnitude and wavelength with the rolling speed. The vibration component at the higher frequency can be absent when the rolling speed is sufficiently low, e.g. at 40 km/h for the simulated system. By evaluating the stress under rolling contact and comparing it with material strength, it is derived that an initial rail surface defect such as an indentation can only grow into a mature squat when it is over a critical size of 6–8 mm under the typical Dutch railway condition. This critical size has also been verified by monitoring tests. The work of this dissertation formed the basis for a ‘Guideline to Best Practice of Squat Treatment’, written upon invitation by the International Union of Railways.