Two-dimensional Rolling Contact Research Articles

Power Dissipation and Wear Modeling in Wheel–Rail Contact

This paper is concerned with the modeling of power dissipation due to friction and its relation with wear estimation in wheel–rail contact. Wear is a complex multi-scale and multi-physical phenomenon appearing in rolling contact. Wear is generated by high contact stress and the work of friction forces. This phenomenon leads to the appearing of the worn material in the form of wear debris between contacting surfaces. In contact models, wear is usually described in terms of the wear depth function. This function modifies the gap between the contacting bodies as well as the shape of the surfaces of the wheel and rail in contact. In this paper, besides the wear depth function, the dissipated energy, rather than the contact stress, is taken into account to evaluate the wear impact on rail or wheel surfaces. The dissipated energy allows us to more precisely evaluate the wear debris amount as well as the depth of wear and its distribution along the contact interface. A two-dimensional rolling contact problem with frictional heat flow is considered. The elasto-plastic deformation of the rail is considered. This contact problem is governed by a coupled system of mechanical and thermal equations in terms of generalized stresses, displacement and temperature. The finite element method is used to discretize this problem. A discretized system of equations with nonpenetration and friction conditions is transformed and formulated as a nonlinear complementarity problem. The generalized Newton method is applied to numerically solve this mechanical subproblem. The Cholesky method is used to find the solution of the heat-conductive problem. The dissipated power is evaluated based on the resultant force and slip at a reference point. Numerical results including the distribution of slip velocity, power factor and wear rate are provided and discussed.

Nonlocal thermomechanical coupled modeling method for two-dimensional rolling contact using a peridynamic approach

The development of thermomechanical coupled simulations for rolling contacts is challenging when the adjacent material is temperature-dependent or when there are cracks or other discontinuities on the contact surface. This paper proposes a novel thermomechanical coupled modeling method for rolling contacts using a nonlocal peridynamic (PD) approach. Fully coupled, ordinary state-based PD thermomechanical equations for the plane strain and plane stress cases are derived based on the strain-energy density, including thermal coupling terms, and detailed information on each parameter is provided. Subsequently, an algorithm for rolling thermal contacts in PD is proposed based on the penalty method. This study further provides a detailed modeling process and an algorithm for the proposed method based on a multi-rate time-integration scheme for numerical implementation. A typical two-dimensional (2D) wheel–rail rolling contact model is established to evaluate the performance of the proposed contact modeling method in wheel–rail thermal contact and to analyze the influence of temperature-dependent material and rail-surface cracks on the thermomechanical response. It is found that the contact stress and rail-surface temperature rise in the case of small creepages and temperature-independent materials are in good agreement with the analytical solution. In the case of large creepages, the mechanical and temperature results of using temperature-dependent materials and temperature-independent materials are quite different, and the frictional heat generated can cause martensitic transformation of adjacent materials. Rail-surface cracks cause a sharp increase in the contact stress and temperature rise near the cracks, and the high temperature also promotes crack growth.

An alternative to FASTSIM for tangential solution of the wheel–rail contact

ABSTRACTIn most rail vehicle dynamics simulation packages, tangential solution of the wheel–rail contact is gained by means of Kalker's FASTSIM algorithm. While 5–25% error is expected for creep force estimation, the errors of shear stress distribution, needed for wheel–rail damage analysis, may rise above 30% due to the parabolic traction bound. Therefore, a novel algorithm named FaStrip is proposed as an alternative to FASTSIM. It is based on the strip theory which extends the two-dimensional rolling contact solution to three-dimensional contacts. To form FaStrip, the original strip theory is amended to obtain accurate estimations for any contact ellipse size and it is combined by a numerical algorithm to handle spin. The comparison between the two algorithms shows that using FaStrip improves the accuracy of the estimated shear stress distribution and the creep force estimation in all studied cases. In combined lateral creepage and spin cases, for instance, the error in force estimation reduces from 18% to less than 2%. The estimation of the slip velocities in the slip zone, needed for wear analysis, is also studied. Since FaStrip is as fast as FASTSIM, it can be an alternative for tangential solution of the wheel–rail contact in simulation packages.

Analysis and numerical simulation of rolling contact between sphere and cone

In non-conforming rolling contact, the contact stress is highly concentrated in the contact area. However, there are some limitations of the special contact model and stress model used for the theoretical study of the phenomenon, and this has prevented in-depth analysis of the associated friction, wear, and failure. This paper is particularly aimed at investigating the area of rolling contact between a sphere and a cone, for which purpose the boundary is determined by the Hertz theory and the geometries of the non-conforming surfaces. The phenomenon of stick-slip contact is observed to occur in the contact area under the condition of no-full-slip (Q < μ · P). Using the two-dimensional rolling contact theory developed by CARTER, the relative positions of the stick and slip regions and the distribution of the tangential force over the contact area are analyzed. Furthermore, each stress component is calculated based on the McEwen theory and the idea of narrow band. The stress equations for the three-dimensional rolling contact between the sphere and the cone are obtained by the principle of superposition, and are used to perform some numerical simulations. The results show that the stress components have a large gradient along the boundary between the stick and slip regions, and that the maximum stress is inversely proportional to the contact coefficient and proportional to the friction coefficient. A new method for investigating the stress during non-classical three-dimensional rolling contact is proposed as a theoretical foundation for the analysis of the associated friction, wear, and failure.

Quasi-static analysis of two-dimensional rolling contact with slip-velocity dependent friction

In this paper the influence of a velocity-dependent friction law on the interactions inside the contact patch between a rolling wheel and a rail is presented, assuming that the quasi-static approach is still applicable. In the model, traction builds up until a critical configuration is reached, after which an instantaneous reset occurs. The system jumps from one state to another in a discontinuous way. This suggests that the true elastic field, including dynamical effects, is adjusted in a very short time span, which is not resolved in the quasi-static approach. Inside the contact patch much higher and swiftly changing micro-slip velocities may occur than were anticipated previously, which are not well-described by friction laws that use an instantaneous relation between sliding velocity v(t) and coefficient of friction μ(t).

Effect of small harmonic oscillations during the steady rolling of a cylinder on a plane

If a wheel rolling over a rail transmits a tangential traction, frictional microslip occurs in part of the contact area, resulting in energy dissipation and localized wear. If the applied forces oscillate in time, the resulting wear will be non-uniform, resulting in ‘corrugations’ that can grow with progressive passes, depending on the dynamics of the overall system. In this paper, a linear perturbation method is used to obtain closed-form expressions for the receptance of a two-dimensional rolling contact subjected to small oscillations in normal force and rotational speed superposed on a mean value in the limit of large coefficient of friction. Corresponding expressions are also obtained for the amplitude and phase of the energy dissipation in the contact, which is expected to correlate with the local wear rate. The results are compared with a simpler Winkler model of the contact and with other models that have been used for the analysis of rail corrugation. Surprisingly good agreement is obtained with numerical results due to Gross-Thebing for the receptances due to oscillations in rotational speed.

Numerical simulation of wheel rolling over rail at high-speeds

In the paper, a contact element method was used to analyze a wheel rolling over a rail at high-speeds. The rolling contact of the wheel and rail was considered as a two-dimensional rolling contact in a pure rolling and steady state. The loads applied to the wheel are the different axle-loads of train and the inertia forces caused by accelerations of the wheel in its pure rolling state. The convergence of non-linear numerical analysis on frictional contact was reached through repeated contact calculations. The normal contact pressure and tangential traction on wheel/rail contact surface were obtained for the different axle-loads and the different rolling speeds. The highest rolling speed in the numerical simulation is 400 km/h. Through the detailed numerical simulation and analysis, it was found that there exist some differences between the traditional Hertzian contact pressure and the present normal pressure. With the speed increasing the normal contact pressure becomes larger in the leading area of the contact surface, and becomes smaller in the trailing area of the contact surface. However, in the trailing area the tangential traction become larger, and in the leading area becomes smaller with the speed increasing.

Elastic-Plastic Finite-Element Analysis of Repeated, Two-Dimensional Wheel-Rail Rolling Contact under Time-Dependent Load

A study was performed using a finite-element model to obtain stresses, strains, and deformations for repeated, two-dimensional rolling contact of a locomotive driving wheel and a rail under time-dependent load. An advanced cyclic plasticity model was used with a commercial finite element code via a material subroutine. The time-dependent load was considered a harmonic variation of the wheel-rail normal contact force. The normal contact pressure was assumed to follow the Hertzian distribution and the tangential force followed the Carter distribution. A wavy profile is formed on the running surface of the rail subjected to the harmonic variation of the normal (vertical) contact force. The developed wavelength of the profile corresponds to the frequency of the normal contact force for the actual train speed. The creepage or rolling-sliding condition plays an important role in the residual strains and deformations, but its influence on the residual stresses is insignificant. The residual stresses at the surface decrease with increasing rolling passes and gradually tend to stabilize. The residual strains and surface displacements increase with increasing rolling cycle, but the increases in residual strain and surface displacement per rolling pass (ratchetting rate) decay. The residual stresses, strains, and deformations near the wave trough of the residual wavy deformation are larger than those near the wave crest. For any given creepage including zero value, when the number of rolling passes increases, the surface depth of the wavy-deformed surface increases but the ratchetting rate decays. The results are useful in investigating the influence of plastic deformation on rail corrugation.

Crack Face Friction Effects on Mode II Stress Intensities for a Surface-Cracked Coating in Two-Dimensional Rolling Contact

This work focuses on the effects of crack free friction on Mode II stress intensity factors, KII, for a vertical surface crack in a two-dimensional finite element model of TiN/steel subject to rolling line contact. Second-order extrapolation of KI and KII from nodal stresses ahead of the crack tip is found to be a more consistent technique than linear extrapolation. Results indicate that maximum KJJ values, which occur when the load is adjacent to the crack, may be significantly reduced in the presence of crack face friction. The reduction is more significant for thick coatings than for thin. Crack extension and increased layer thickness result in increased KII values. The effect of crack face friction on compressive KI values appears negligible. Comparative results are presented for MoS2/steel and diamond-like carbon/Ti systems. Presented at the 51st Annual Meeting in Cincinnati, Ohio May 19–23, 1996

Influence of Indent Geometry on Repeated Two-Dimensional Rolling Contact

A “two-body,” elasto-plastic finite element model is employed to simulate repeated rolling contact in the presence of a surface irregularity. It is shown that the maximum Mises stress and equivalent plastic strain values in the substrate are related to the height of the pressure spikes. The results of the finite element calculations are used to derive generalizations about the influence of the indent geometry on the pressure spikes, peak cyclic plastic strains and their location below the surface. These relations can serve as guidelines for designing the depth and properties of surface coatings and modified layers.

A Direct Analysis of Two-Dimensional Elastic-Plastic Rolling Contact

A direct approach for elastic-plastic analysis and shakedown is presented and its application to a two-dimensional rolling contact problem is demonstrated. The direct approach consists of an operator split technique, which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains. The eigenstrains are determined using an incremental projection method which is valid for nonproportional loading and both elastic and plastic shakedown. The residual problem is solved analytically and also by using a finite element procedure which can be readily generalized to more difficult problems such as three-dimensional rolling point contact. The direct analysis employs linear-kinematic-hardening plastic behavior and thus either elastic or plastic shakedown is assured, however, the phenomenon of ratchetting which can lead to incremental collapse, cannot be treated within the present framework. Results are compared with full elastic-plastic finite element calculations and a step-by-step numerical scheme for elastic-plastic analysis. Good agreement between the methods is observed. Furthermore, the direct method results in substantial savings in computational effort over full elastic-plastic finite element calculations and is shown to be a straightforward and efficient method for obtaining the steady state (shakedown) solution in the analysis of rolling and/or sliding contact.

Analysis of rolling contact with kinematic hardening for rail steel properties

This study presents calculations of two-dimensional rolling contact deformation for rail steel properties. Finite element analyses, previously carried out for perfect plasticity, are extended to the kinematic hardening behavior of rail steel. A three-parameter elastic-linear-kinematic-hardeningplastic description of the cyclic stress-strain behavior of rail steel is inserted in the finite element model. Steady state results are obtained after two translations. The effects of the kinematic hardening at three relative peak pressures p o k k = 4.0, 4.5 and 5.0 are examined. The calculations evaluate the rim distortion, the cyclic plastic strains and the residual stresses, the shakedown limit for kinematic hardening and the effects of strain-amplitudedependent kinematic properties. The calculations reveal that the kinematic hardening of rail steel produces substantial alterations relative to the deformation and residual stresses associated with perfect plasticity. Cyclic strains are an order of magnitude smaller and the residual stresses are about half the value of comparable relative contact pressures. While the relative elastic shakedown limit, p o k k = 4 , is the same as for perfect plasticity, absolute values of wheel load at shakedown are modest because of the relatively low value of the kinematic yield strength of rail steel. Accordingly, a 33000 lbf (146.7 KN) wheel load applied to a new rail produces a relative peak contact pressure p o k k = 6.2 which exceeds the corresponding shakedown limit.