The modeling of dynamic frictional rolling contact is crucial for accurately predicting behavior and deterioration of structures under dynamic interactions such as wheel/rail, tire/road, bearings and gears. However, reliable modeling of dynamic frictional rolling contact is challenging, because it requires a careful treatment of friction and a proper consideration of the dynamic effects of the structures on the contact. This study takes the wheel-rail dynamic interaction as an example to systematically explore the core algorithms for the modeling of dynamic frictional rolling contact by way of explicit finite element analyses. The study also theoretically demonstrates that the explicit finite element method handles nonlinearities in friction, material properties, arbitrary contact geometries and boundary conditions, and fully couples the calculation of frictional rolling contact with the calculation of high-frequency structural dynamics. An indirect validation method for dynamic contact solutions is proposed. To promote the broad use of the method, this paper proposes a detailed procedure for establishing robust wheel-rail dynamic interact tion models and obtaining dynamic contact responses. The proposed procedure can also be applied to the modeling of dynamic interactions occurring to tire-road, bearings and gears.

Rail squats originate from a number of sources, such as corrugations, indentations and welds. A five-year continual field monitoring study was performed on squats induced by corrugations. This study indicated that a small black depression formed at the corrugation under wheel-rail dynamic forces, and then, a primary crack typically initiated on the gauge side edge of the depression. Subsequently, the crack began to propagate in the rail surface in a U shape toward the gauge side in both the traffic direction and the opposite-traffic direction and into the rail toward the field side at an angle of approximately 20°. Rail inclination could influence the crack initiation location and propagation path. The geometry of the black squat depression was initially elliptical, and then, its edge followed the U-shaped cracking path as it grew. The squats turned into a kidney-like shape, typically with a U-shaped crack. Tensile stress likely led to the squat crack initiation and propagation. This cracking phenomenon and mechanism are analogous to the ring/cone crack formation of brittle materials under sphere-sliding contact. As the squats grew further, a ridge formed in the middle part of the depression, and an I-shaped crack appeared at this ridge due to the impact of the wheels. This process eventually led to two-lung-shaped mature squats, typically with a Y-shaped crack. The findings of this paper provide insight into the formation of rail squats.

In light of two wheel-rail contact relations, i.e., displacement compatibility and force equilibrium, a newly developed three-dimensional (3D) model for vehicle-track interactions is presented in this paper. This model is founded on the basis of an assumption: wheel-rail rigid contact. Unlike most of the dynamic models, where the interconnections between the vehicle and the track entirely depend on the wheel-rail contact forces, the subsystems of the vehicle and the tracks in the present study are effectively united as an entire system with interactive matrices of stiffness, damping and mass by the energy-variational principle and wheel-rail contact geometry. With wheel-rail nonlinear creepage/equivalent stiffness, this proposed model can derive dynamic results approaching to those of vehicle-track coupled dynamics. However, it is possible to apply a relatively large time integral step with numerical stability in computations. By simplifying into a linearized model, pseudo-excitation method (PEM) can be theoretically implemented to characterize the dominant vibration frequencies of vehicle-track systems due to random excitations. Finally, a trail method is designed to achieve the wheel climbing derailment process and a full derailment case where the bottom of the wheel flange has completely reached the rail top to form a complete derailment is presented.

The half-space assumption has been employed in many solution methods for non-conforming contact problems in elasticity such as the Hertz theory and the Kalker's variational theory. It is generally believed that to guarantee acceptable accuracy in these half-space-based methods, the characteristic size (twice length of one semi-axis) of the contact patch should be much smaller than the significant dimensions (i.e. the height, width, length and the principal radii of curvature) of each body in contact. In engineering practice, the 3x rule is often employed, which requires that the significant dimensions be at least three times as large as the characteristic size. However, this requirement has not been justified. In this paper, the applicability of half-space-based methods is investigated by comparing the solutions obtained using the Hertz theory and the Kalker's theory with those of the Finite Element (FE) method which is not limited to the half-space assumption. Different combinations of significant dimensions in terms of height, width and length are studied. Various contact patch eccentricities and contact body shapes are considered. It is found that the half-space-based methods yield high-accuracy calculation for non-conforming contact problems. Even when the significant dimensions are as small as 1.1x the characteristic size, the differences between the solutions of the half-space-based methods and the FE method are within 9%. The findings of this paper indicate that the typically assumed 3x restriction can be greatly relaxed. Since a clear estimation of the deviation of the results of half-space-based methods from those of the FE method is provided, the applicability of half-space-based methods in mechanical engineering can be much better understood.