A singular rail or wheel surface irregularity, such as a squat, insulation joint or wheel flat, can cause large wheelrail impact force. Both the magnitude and frequency content of the impact force need to be correctly modelledbecause they are closely related to the formation, deterioration and detection of such irregularities. In this paper,we compare two types of commonly used wheel-track interaction models for wheel-rail impact problems, i.e., abeam and a continuum finite element model. We first reveal the differences between the impact forces predictedby the two models due to a typical rail squat using a time-frequency analysis. Subsequently, we identify thecauses for the differences by evaluating the effects of different model assumptions, as well as different modelparameters. Results show that the impact force consists of a forced vibration peak M1 followed by free vibrationrelated oscillations with three dominant frequencies: f1 (340 Hz), f2 (890 Hz) and f3 (1120 Hz). Compared withthe continuum model, the beam model with a Hertzian contact spring overestimates the M1 peak force. Thediscrepancy can be reduced by using a Winkler bedding contact model. For the track model, the beam model iscomparable to the continuum model up to about 800 Hz, beyond which the track damping starts to deviate. As aresult, above 500 Hz, the contact forces dominate at f2 for the beam while at f3 for the continuum model. Finally,we show that the continuum model is more accurate than the beam model by comparing to field observations.The effects of stress wave propagation on the differences are also discussed.@en

One goal of this thesis is to study the performance and accuracy of an explicit finite element (FE) method for frictional rolling contact in a wider-range of conditions. The other goal is to reveal the physical phenomena of squats and the mechanisms behind, such as cracking mechanisms and development process. The first part studies the applicability of half-space-based methods in non-conforming contact problems and their accuracy by comparing a validated implicit FE method in terms of their solutions. In the second part, spin-rolling contact is analyzed using the explicit FE method for frictional rolling contact, and the solution is verified against two half-space-based methods, i.e., the Hertz theory and the Kalker’s variational theory. The third part of the thesis studies a five-year continual field monitoring on a large number of squats induced by corrugation. Various stages of the life cycle of corrugation-induced squats, from small black depressions without cracks to mature two-lung shaped squats accompanied by Y-shaped and I-shaped cracks, were revealed. Their corresponding mechanisms were also provided. Finally, in the fourth part of this thesis, weld-induced squats are studied based on the five-year continual field monitoring and numerical simulations. Based on the observations, a hypothesis of the formation and development process of squats at welds is proposed. Afterwards, a 3D FE model is built to verify the hypothesis .@en

Weld-induced squats are a major damage type in high-speed railways as well as in conventional railways. They incur high maintenance costs and endanger operational safety. This paper first presents and analyzes five-year continual field monitoring observations and measurements of squats at rail welds. A hypothesis of the formation and development process of the squats is proposed, which includes three steps. Steps 1 and 2 are pre-cracking, and Step 3 is post-cracking. To verify the pre-cracking process, a three-dimensional (3D) finite element (FE) model is then built up to simulate the vehicle-track interaction with detailed consideration of the local wheel-rail frictional rolling contact. Not only dynamic contact forces but also plastic deformation and wear are calculated. Starting from a smooth rail surface with varying yield stress derived from field-measured hardness, the numerical analysis confirms the hypothesis that the varying hardness at heat-affected zones (HAZs) leads to initial V-shaped irregularities due to differential plastic deformation. Afterward, the surface irregularities excite the dynamic longitudinal contact force, which in turn produces a W-shaped surface pattern through further differential plastic deformation. The growth of the W-shaped pattern leads to the formation of squats. This work provides insight into the squat formation process at rail welds and suggests that welding quality control in terms of hardness variation in the HAZs could reduce or even avoid squats. Early detection of squats with dynamics-based methods is possible.@en

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.

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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.

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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.

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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.

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