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The adhesion at the wheel-rail contact is critical in train operation. Low adhesion leads to a longer distance for a train to accelerate and brake, and this may cause serious accidents. Sand particles are applied onboard trains at the wheel-rail contact to enhance the adhesion level. In this study, a finite element model is developed to investigate the mechanical behaviour of sand particles in a wheel-rail contact and how they affect the adhesion level. The acceleration and braking events using rolling/slipping and sliding contacts are simulated. Morphological properties of sand particles such as size and aspect ratio are considered. The adhesion enhancement is quantified from each simulation for comparison. The results indicate that the adhesion enhancement during the first contact between the wheel and sand particles is negligible and starts to increase when the wheel is rolling on the fragments. Its magnitude is controlled by the new third-body layers generated during the particle breakage under both rolling and sliding contacts. However, under sliding contact, when a similar amount of fragments is considered, the coarser particles with a larger aspect ratio tend to produce a higher adhesion enhancement. • Adhesion enhancement by sand can be correlated to newly generated surface area of third body. • Sand provide a higher adhesion enhancement during the acceleration compared to the braking. • During traction, the adhesion enhancement is influenced by the number of fragments. • During braking, the coarser and elongated particle generates a higher adhesion enhancement. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to develop a full Finite Element (FE) computational method for the dynamics of unstable frictional rolling contact systems in order to calculate reference solutions in many applications, especially curve squeal for railway transportation but also roller bearing or metal cutting. The proposed method is characterized by the use of a fine FE discretization of the contact surface in a Eulerian frame, nonlinear frictional contact laws and model reduction techniques. An application to the frictional rolling contact between two annular cylinders is presented in both quasi-static and dynamic cases with mode coupling instabilities. The validation of the approach in quasi-static conditions is carried out by comparison with CONTACT software. Stability and transient results show that the technique is able to simulate friction-induced vibrations at high frequencies. Reduced models are tested and show a good agreement with the full model. [ABSTRACT FROM AUTHOR]

Abstract 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. Graphical abstract Image 1 Highlights • Systematically explore the core procedure for solution of dynamic rolling contact. • Dynamic analyses with nonlinearities in material, geometry and boundary conditions. • Couple calculation of friction rolling with calculation of structural dynamics. • Apply the procedure to the modeling of nonlinear wheel-rail dynamic interactions. [ABSTRACT FROM AUTHOR]

The paper analyzes applicability of rolling contact simulation in low speed and adhesion conditions. Additionally, transition zone of the coefficient of friction (COF) is implemented. Effects of the COF are examined to the forces which are normal and tangential components. Various comparative studies are also computed. Differences between numerical results and results of the comparative studies are observed for validation. The results show that outputs of developed FEM model are compatible with comparative studies. Transition zone of the COF directly affects the traction force at low speed conditions. [ABSTRACT FROM AUTHOR]

A three-dimensional finite element rolling contact model between wheel and rail with increased spin effect is developed in this paper to study the normal and the tangential contact problems, as well as the creep force characteristics in elasticity and in elasto-plasticity. Three finite element analyzes using the explicit and the implicit integration scheme are employed and the finite element solution is compared to the solution of the CONTACT software in elasticity. The elastic solution with the implicit methods is sensitive to the energy dissipation related to the time increment size. The optimum time increment size is found as a compromise between computational efficiency and calculation accuracy. The numerical results show a good agreement between the finite element methods and CONTACT for the normal and the tangential contact solution. The initial slopes of the creep force characteristics in the longitudinal and the lateral direction from the implicit solution are slightly lower than the results from CONTACT. When the elasto-plastic material behavior is applied, the maximum contact pressure and the von Mises stresses are reduced for both explicit and implicit methods and the plastic deformation occurs in all the contact area. The contact patch becomes egg shaped instead of the elliptic and the area of stick zone area increases. In addition, the initial slopes of the creepage-creep force curves are reduced by 15% in the longitudinal direction and by 13% in the lateral direction. [ABSTRACT FROM AUTHOR]

The aim of this work is to assess the effects of conformity on local contact related quantities at the wheel–rail interface such as traction distributions, subsurface stresses and frictional work distributions. For this purpose conformal contact analyses are carried out by means of Finite Element (FE) models, and also with the exact rolling contact theory approach developed by Kalker, which has been appropriately adapted by the authors in order to take into account some of the effects of conformity. On the other hand, equivalent cases are analysed without taking into account the effects of conformity. In this way, the validity of the hypothesis of non-conformity is evaluated in different cases with varying degrees of conformity. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to develop a numerical approach to solve the transient rolling contact problem with the consideration of velocity dependent friction. Design/methodology/approach – A three dimensional (3D) transient FE model is developed in elasticity by the explicit finite element method. Contact solutions with a velocity dependent friction law are compared in detail to those with the Coulomb’s friction law (i.e. a constant coefficient of friction). Findings – The FE solutions confirm the negligible influence of the dependence on the normal contact. Hence, analysis is focussed on the tangential solutions under different friction exploitation levels. In the trailing part of the contact patch where micro-slip occurs, very high-frequency oscillations are excited in the tangential plane by the velocity dependent friction. This is similar to the non-uniform sliding or tangential oscillations observed in sliding contact. Consequently, the micro-slip distribution varies greatly with time. However, the surface shear stress distribution is quite stable at different instants, even though it significantly changes with the employed friction model. Originality/value – This paper proposes an approach to solve the transient rolling contact problem with the consideration of velocity dependent friction. Such a problem was usually solved in the literature by the simplified contact algorithms, with which detailed contact solutions could not be obtained, or with the assumption of steady rolling. [ABSTRACT FROM AUTHOR]

Spin in frictional rolling contact can cause significant stress, which is the key to understanding and predicting the wear and fatigue behavior of contact components, such as wheels, rails, and rolling bearings. The lateral creep force arising from spin influences the kinematics of a wheelset and thus of vehicles. The solution that is currently employed in the field of elasticity and continuum statics was developed by Kalker and uses a boundary element method (BEM). In this paper, a new approach based on Lagrangian explicit finite element (FE) analysis is employed. This approach is able to consider arbitrary geometric profiles of rails and wheels, complex material behavior and dynamic effects, and some other factors. The new approach is demonstrated using a three-dimensional (3D) model of a wheel with a coned profile rolling along a quarter cylinder and can be easily adapted to apply to wheels and rails of arbitrary profiles. The 3D FE model is configured with elastic material properties and is used to obtain both normal and tangential solutions. The results are compared with those of the Hertz theory and the Kalker's model. The 3D FE model is then configured with elastoplastic material properties to study the spin-rolling contact with plasticity. The continuum dynamics phenomenon is captured by the FE model, which enhances the ability of the model to mimic reality. This improvement considerably extends the applicability of the FE model. The model can be applied to fatigue and wear analyses at gauge corners or rails as well as to deep groove bearings, where a large geometrical spin is present and plastic deformation may be of importance. [ABSTRACT FROM AUTHOR]

A theoretical and computational framework for the analysis of thermomechanically coupled, frictional, stationary (steady-state) rolling contact based on an Arbitrary Lagrangian–Eulerian (ALE) kinematical description is presented. The finite element method is employed in a numerical implementation featuring two-dimensional cylinder–plate rolling contact, with a contact formulation incorporating mechanical and thermal frictional interaction. The ALE formulation is noted to allow for linearization of the governing equations, localized mesh refinement, a time-independent description of stationary dynamics, velocity-independent contact interface modelling and so on. Numerical simulations show the model to be able to capture, for example, stick/slip behaviour and a range of thermal phenomena, including the effect of convective cooling of the cylinder due to the contact with the plate. [ABSTRACT FROM PUBLISHER]

Wear, rolling contact fatigue, and plastic deformation are the major failure modes of railway wheels and rails. Proper analyses of the failure mechanisms as well as improvement in design and maintenance require an accurate evaluation of the stress and strain states. Solution of frictional rolling contact between wheel and rail in elasto-plasticity seems, however, still to lack in the literature. This paper presents a model for such a solution. A 3D finite element model is built up to simulate the rolling contact. The focus is on the tangential problem, namely the distributions of surface shear stress and micro-slip as well as the distinction of areas of adhesion and slip in the contact patch. With the presented model the assumptions of half space, linear elasticity and quasi-static or steady state, which are often employed in existing solution of rolling contact, are dropped. A bilinear elasto-plastic material with isotropic hardening is employed to examine the effects of plasticity on frictional rolling. It is found that when plastic flow occurs, the contact patch in the rail top changes from an ellipse into an egg shape; the cross influence between the normal and tangential contact problems become stronger: the normal solution is not independent of the tangential solution any more, and the tangential solution is greatly affected by the normal solution. The model can be applied to investigation of the relationships between material properties, plastic deformation, frictional work, wear, and crack initiation. Such relationships may help in better understanding the occurrence of corrugation, head checks, and squats, and may further be used for design of fatigue resistant materials and profiles of wheel and rail. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper mixed finite element methods of higher-order for time-dependent contact problems are discussed. The mixed methods are based on resolving the contact conditions by the introduction of Lagrange multipliers. Dynamic Signorini problems with and without friction are considered involving thermomechanical and rolling contact. Rothe’s method is used to provide a suitable time and space discretization. To discretize in time, a stabilized Newmark method is applied as an adequate time stepping scheme. The space discretization relies on finite elements of higher-order. In each time step the resulting problems are solved by Uzawa‘s method or, alternatively, by methods of quadratic programming via a suitable formulation in terms of the Lagrange multipliers. Numerical results are presented towards an application in production engineering. The results illustrate the performance of the presented techniques for a variety of problem formulations. [Copyright &y& Elsevier]

To simulate the contact and separation of wheels and rails accurately, the stiffness between them should be correct. This paper developed a nonlinear moving wheel element based on a simple point contact scheme to simulate moving train problems, where the element stiffness is set to a power function directly fitted from the finite-element result of the wheel and rail contact analysis. The finite-element result of the wheel/rail contact analysis indicates that the changes in vertical stiffness with changing contact forces can be accurately fitted by using the proposed power function, and the horizontal stiffness can be simply regressed using a constant. The validated example in this paper shows that the nonlinear moving wheel element can simulate the complicated contact and separation problem correctly, both in the displacement and contact force fields, and the major advantage is that a fine mesh is not necessary in the moving train contact analysis. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents simple, yet robust and efficient algorithms for solving steady-state, frictional, rolling/sliding contact problems, in two and three dimensions. These are alternatives to powerful, well established, but in particular instances, possibly ‘cumbersome’ general-purpose numerical techniques, such as finite-element approaches based on constrained optimization. The cores of the solvers rely on very general principles: (i) resolving motional conflicts, and (ii) eliminating unacceptable surface tractions. The proposed algorithms are formulated in the context of small deformations and applied to the cases of a rigid cylinder and a rigid sphere rolling on a linear viscoelastic layer of finite thickness, in two and three dimensions, respectively. The underlying principles are elucidated, relevant mathematical expressions derived and details given about corresponding implementation techniques. The proposed contact algorithms can be extended to more general settings involving a deformable indenter, material nonlinearities and large deformations. [Copyright &y& Elsevier]

Abstract: Superior physical properties of engineering ceramics are well recognized in modern technology. However, high brittleness is typical for these materials, which leads to low resistance to crack initiation and propagation. In the silicon nitride (Si3N4) balls, whose failure is studied here, the most dangerous pre-existing defect is the so called C-crack – the circumferential surface crack of conical shape, formed during the ball manufacturing process. The finite elements method is used for the simulation of rolling of the cracked ball. By applying the linear elastic fracture mechanics approach, the crack criticality in terms of the stress intensity factors is identified. The parametric study regarding the levels of the contact load, crack shape, depth and friction coefficient between crack''s surfaces is presented. [Copyright &y& Elsevier]

Abstract: We revisit the classical creep theory for a belt drive system as a rolling contact problem between a rubber ring and rigid cylinders to evaluate the effects of linear viscoelasticity and large strain of the belt on the system in a steady state. We first construct the general theory of belt mechanics for a multi-pulley system by dimensional reduction from 3D extensible, unshearable rod. We then develop the belt mechanics for a linear viscoelastic belt and show that the effect of retardation time can be involved in the effective friction coefficient: the classical Euler''s belt formula can be recovered. Next, we assume that the belt is a neo-Hookean material and examine the effect of large strain of the belt on the contact pressure distribution. We compare the theory with the results by finite element analysis and show that the theory provides good quality. [Copyright &y& Elsevier]

Abstract: Wheel–rail frictional rolling contact has been solved for linear elasticity and statics and with the half-space assumption in three dimensions. In recent years, the normal contact problem has also been treated in elasticity and elasto-plasticity with the finite element (FE) method; the half-space assumption is dropped. In this paper, a 3D transient FE model is presented to solve both the normal and the tangential contact problems simultaneously for arbitrary geometry. The explicit time integration scheme employed renders it intrinsically suitable for transient analysis of high frequency dynamic processes. The model is first validated with Hertz theory and Kalker''s computer program CONTACT for the normal solution and with CONTACT for the tangential solution, for the case of wheel tread–rail top contact. Subsequently, the influence of element size on solution accuracy is examined by comparing the results of different element sizes. The analyses show that the presented model is valid for the solution of frictional rolling. [Copyright &y& Elsevier]

Two-dimensional elastic contact problems, including normal, tangential, and rolling contacts are treated with the finite element method in this study. Stress boundary conditions and kinematic conditions are transformed into multiple point constraints for nodal displacements in the finite element method. Upon imposing these constraints into the finite element system equations, the calculated nodal stresses and nodal displacements satisfy stress and displacement contact conditions exactly. Frictional and frictionless contacts between elastically identical as well as elastically dissimilar materials are treated in this study. The contact lengths, sizes of slip and stick regions, the normal and the shear stresses can be found. [ABSTRACT FROM AUTHOR]

Abstract: Uncertainty analysis and parametric studies are presented for estimating the fatigue failure probability of surface cracks in silicon nitride ball bearings subjected to rolling contact fatigue. Uncertainty quantification of input parameters are presented first based on experimental data, inspection capability, and geometric reasoning. Surrogate models for equivalent stress intensity factors are then used for uncertainty propagation, which are built upon high fidelity finite element modeling with half-penny-shaped surface cracks. Instead of black-box type surrogate modeling, physical observations are employed to decompose the high dimensional surrogate model into multiple one-dimensional models. The cross-validation technique is used to find the best surrogate that has the smallest prediction variance. The probability of failure is estimated using Monte Carlo simulation and surrogate models. The parametric studies show that reducing the maximum crack size (by limiting inspection threshold) and increasing the fatigue threshold (by improving fracture toughness of a material) are the most effective ways of reducing the probability of failure. For example, decreasing the maximum crack size by 4.4% and increasing the lowest fracture threshold by 2.8% results in the reduction of probability of failure by 40%. Ball survivability increases with decreasing ball diameter, for a given peak Hertzian stress. In order to apply the current study to hybrid ball bearing design, the survivability results are generalized through non-dimensionalization. [Copyright &y& Elsevier]

Abstract: Fatigue life investigations have been made for cylindrical hollow rollers in pure rolling contact. In addition to normal loading, the rollers have been subjected to tangential loading of 1/3rd the normal load value. Sufficient coefficient of friction has been used to ensure no slipping occurs. Two main models were built with different hollowness percentages to investigate the hollowness percentage that gives the longest fatigue life. The first model consists of two cylindrical rollers of same size, while the second model consists of two rollers of different sizes. Two cases have been studied, when both rollers are hollow and when only one roller is hollow. The stress distribution in the roller body and the resulting deformation has been investigated using the finite element package, ABAQUS. Then the Ioannides–Harris (IH) theory was used to predict the fatigue life of the hollow rollers in pure rolling contact. Investigations have been made for five different materials, CVD 52100, Carburized steel, VIMVAR M50, M50NiL and Induction-hardened steel. It has been found that the optimum hollowness percentage with the longest fatigue life ranges is around 50%. Many factors affect the optimum hollowness percentage, like the kind of the material used for the cylindrical roller, whether the rollers in contact are of the same size or different size and whether the hollow roller is in contact with another hollow roller or in contact with solid roller. [Copyright &y& Elsevier]

Dynamic behaviors of the contact surface between ball and raceway in a guideway mechanism vary with the applied loads and hence affect the mechanical responses of machine tools. The study aims to investigate the nonlinear characteristics of dynamic behaviors at the rolling contact interface in linear guideway mechanisms. Firstly, analytical method was introduced to understand the contact behaviors based on Hertz, contact theory in a point-to-point way. Then, the finite element approach with a three-dimensional surface-to-surface contact model and appropriate contact stiffness was developed to study the dynamic characteristics of such linear guideways. Finally, experiments with modal test were conducted to verify the significance of both the analytical and the numerical results. Results told that the finite element approach may provide significant predictions. The study results also concluded that the current nonlinear models based on Hertz's contact theory may accurately describe the contact characteristic of a linear guideway mechanism. In the modal analysis, it was told that the natural frequencies vary a little with different loading conditions; however, the mode shapes are changed obviously with the magnitude of applied loads. Therefore, the stiffness of contact interface needs to be properly adjusted during simulation which may affect the dynamic characteristics of the machine tools. [ABSTRACT FROM AUTHOR]

Abstract: The influence of the size of material defects on rolling contact fatigue of railway wheels is investigated. To study differences between uniaxial tensile loading and rolling contact loading, finite element simulations of a defected component are carried out. The results show that stress and strain fields (as quantified by the Jiang–Sehitouglu multiaxial fatigue criterion) in the vicinity of a defect differ between these two cases. It is concluded that semi-empirical methods derived for uniaxial loading are doubtful for rolling contact applications. Instead, an elasto-plastic finite element based model is designed and employed to compare fatigue impact of defects of different sizes subjected to rolling contact loading. [Copyright &y& Elsevier]