Three-dimensional Rolling Contact Research Articles

A Numerical Model for Solving Three-Dimensional Rolling Contact Problems with Elastic Coating Layers

In this work, a numerical model is proposed for three-dimensional rolling contact problems with one or two elastic layers, and the tangential contact solution is emphasized. Previous works on this topic have mostly been two-dimensional, in which only longitudinal creepage has been considered. With the three-dimensional model presented in this work, all possible creepages, such as the longitudinal, lateral and spin creepages are taken into account. In order to improve the calculation efficiency, the conjugate gradient method and the FFT technique are employed. The influence coefficients for displacement and stress are obtained from the corresponding frequency response functions. The numerical results are validated against existing results and good agreement can be found. The effects of the different layers’ thicknesses and elastic moduli under different creepage combinations on the traction distribution and stick/slip results are investigated. It can be seen that by adjusting the layer parameters the traction and stick/slip results can be modified significantly, and it may, therefore, be very useful information for improving the rolling contact fatigue and mitigating wear problems in various mechanical systems.Graphical

Numerical analysis of three-dimensional thermo-elastic rolling contact under steady-state conditions

In this study, a three-dimensional thermo-elastic model that considers the interaction of mechanical and thermal deformation is developed using a semi-analytic method for steady-state rolling contact. Creepage types in all directions are considered in this model. For verification, the numerical analysis results of shear traction and temperature increase are compared separately with existing numerical results, and the consistency is confirmed. The analysis results include heat flux, temperature increase, contact pressure, and shear traction. Under severe rolling conditions, the thermal effect changes the behavior of the contact interface significantly. Furthermore, the effects of creepage, rolling speed, and conformity under different rolling and creep conditions are investigated.

Wheel wear comparison between motor car and trailer of intercity train

To analyze wheel wear discrepancy between motor car and trailer of an intercity train, a novel wheel wear rates calculation model was proposed, which was composed of the intercity train dynamics model, wheel-rail three-dimensional rolling contact FEM model and the wear model. The simulated results were contrasted with measured results in field test. The simulated results showed the motor car wheels had larger rotation rate and longitudinal creepage than the trailer wheels. Meanwhile, the motor car wheels encountered larger vertical forces and longitudinal forces from bogie because of the heavier car body and the impact of traction torque. The traction torque acting on motor car wheel could increase the slip rates in the rear part of wheel contact patch and weaken the spinning phenomenon of relative slip. Larger contact pressure and slip rates caused the higher wear rates of motor car wheel than those of trailer wheel. The overall trends of wheel wear depth in simulated and tested results were similar. And they both showed the motor car wheel encountered the more serious wear than the trailer wheel. These models can be used to study the effect of the traction characteristics curves on the wear of wheel.

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.

Numerical simulation of wheel wear evolution for heavy haul railway

The prediction of the wheel wear is a fundamental problem in heavy haul railway. A numerical methodology is introduced to simulate the wheel wear evolution of heavy haul freight car. The methodology includes the spatial coupling dynamics of vehicle and track, the three-dimensional rolling contact analysis of wheel-rail, the Specht’s material wear model, and the strategy for reproducing the actual operation conditions of railway. The freight vehicle is treated as a full 3D rigid multi-body model. Every component is built detailedly and various contact interactions between parts are accurately simulated, taking into account the real clearances. The wheel-rail rolling contact calculation is carried out based on Hertz’s theory and Kalker’s FASTSIM algorithm. The track model is built based on field measurements. The material loss due to wear is evaluated according to the Specht’s model in which the wear coefficient varies with the wear intensity. In order to exactly reproduce the actual operating conditions of railway, dynamic simulations are performed separately for all possible track conditions and running velocities in each iterative step. Dimensionless weight coefficients are introduced that determine the ratios of different cases and are obtained through site survey. For the wheel profile updating, an adaptive step strategy based on the wear depth is introduced, which can effectively improve the reliability and stability of numerical calculation. At last, the wear evolution laws are studied by the numerical model for different wheels of heavy haul freight vehicle running in curves. The results show that the wear of the front wheelset is more serious than that of the rear wheelset for one bogie, and the difference is more obvious for the outer wheels. The wear of the outer wheels is severer than that of the inner wheels. The wear of outer wheels mainly distributes near the flange and the root; while the wear of inner wheels mainly distributes around the nominal rolling circle. For the outer wheel of front wheelset of each bogie, the development of wear is gradually concentrated on the flange and the developing speed increases continually with the increase of traveled distance.

Numerical investigation of the spall opening angle of surface initiated rolling contact fatigue

The spall opening angle was studied for surface initiated rolling contact fatigue with the purpose to allow assessment of the volume of detached material. The influence of friction and the crack inclination angle on the damage spread in the contact surface was investigated with the asperity point load mechanism and a simplified three-dimensional rolling contact fatigue load. Crack arrest due to crack closure was proposed as explaining mechanism for the spall opening angle of the typical v-shaped or arrowhead crack configurations. A new three-dimensional crack geometry was presented allowing the study of the spalling surface morphology in a gear application. Stress intensity factors along the crack front were computed using the eXtended Finite Element Method (XFEM) implemented in Abaqus (6.12). Both low crack inclination angles and increased friction resulted in larger spall opening angles. For cracks with small inclination angles the effects of increased friction on the spall opening angle appeared however very little. The findings increase understanding of the surface morphology and the damage process and further motivate the asperity point load mechanism as an important source for surface initiated RCF damage.

Three-dimensional elastic–plastic stress analysis of wheel–rail rolling contact

Abstract A finite element model with the implementation of an advanced cyclic plasticity theory was used to study the three-dimensional elastic–plastic rolling contact stresses of wheel and rail. Three-dimensional rolling contact was simulated by multiple translations of the normal pressure and tangential tractions across the rail surface. The contact area, normal contact pressure and tangential tractions were calculated by the Kalker's program CONTACT. The finite element simulations were conducted to investigate the influence of partial slip condition and varying contact load on the rolling contact stresses and deformations. The results show that the partial slip condition or the creepage has a greater effect on the residual strains than on the residual stresses. While the residual strains and surface displacements increase at a reduced rate with increasing rolling passes, the residual stresses stabilize after a limited number of rolling passes. The present simulation results also indicate that a varying normal contact force results in a plastic deformation induced wavy rolling contact surface profile. Such a wavy surface profile evolves with rolling history and tends to stabilize due to the decaying ratchetting rate. The residual stresses and strains near the wave trough of the residual wavy deformation are higher than those near the wave crest of the residual wavy deformation. The wave depth of the residual wavy deformation increases with an increase of creepage.

On the application of Dang Van criterion to rolling contact fatigue

In this note, the problem of the calibration of the Dang Van multiaxial fatigue criterion is addressed. The discussion is based on uniaxial fatigue tests performed with different stress ratios. Results show that the usual technique for calibrating the constants of the Dang Van criterion does not agree with experimental evidence, especially for negative stress ratios. For this reason, a different fatigue failure locus made of two straight line segments is proposed and typical three-dimensional rolling contact stress histories are analyzed using the traditional and proposed methods. Results show that the conventional technique does not agree with knowledge coming from shakedown approaches of rolling contact while the proposed method seems to constitute a more appropriate limit.

Three-Dimensional Elastic-Plastic Stress Analysis of Rolling Contact

Three-dimensional elastic-plastic rolling contact stress analysis was conducted incorporating elastic and plastic shakedown concepts. The Hertzian distribution was assumed for the normal surface contact load over a circular contact area. The tangential forces in both the rolling and lateral directions were considered and were assumed to be proportional to the Hertzian pressure. The elastic and plastic shakedown limits obtained for the three-dimensional contact problem revealed the role of both longitudinal and lateral shear traction on the shakedown results. An advanced cyclic plasticity model was implemented into a finite element code via the material subroutine. Finite element simulations were conducted to study the influences of the tangential surface forces in the two shear directions on residual stresses and residual strains. For all the cases simulated, the p0/k ratio (p0 is the maximum Hertzian pressure and k is the yield stress in shear) was 6.0. The Qx/P ratio, where Qx is the total tangential force on the contact surface in the rolling direction and P is the total normal surface pressure, ranged from 0 to 0.6. The Qy/P ratio (Qy is the total tangential force in the lateral direction) was either zero or 0.25. Residual stresses increase with increasing rolling passes but tend to stabilize. Residual strains also increase but the increase in residual strain per rolling pass (ratchetting rate) decays with rolling cycles. Residual stress levels can be as high as 2k when the Qx/P ratio is 0.6. Local accumulated shear strains can exceed 20 times the yield strain in shear after six rolling passes under extreme conditions. Comparisons of the two-dimensional and three-dimensional rolling contact results were provided to elucidate the differences in residual stresses and ratchetting strain predictions.

A Polynominal Approach For The Three-Dimensional Wheel-Rail Rolling Contact

SUMMARYThe elastic three-dimensional rolling contact of quasi-identical bodies is a common contact situation in railway dynamics.This article proposes a new fast calculation method for the three-dimensional normal pressure and tangential traction distribution. It consists of the combination of strip theory and the general polynominal approach for the two-dimensional solutions developped by Nielson.The calculation effort is expected to be of the same order of magnitude as Le-The's program, however thereby covering a large class of railway contact situations with increased precision.The proposed method allows for parametric studies and is therefore helpful in getting more insight into the phenomenon of contact mechanics. One possible application is the simulation of the formation of rail corrugation with an improved formulation of the contact mechanics.

Numerical Analysis of Viscous Lubricating Oil Penetrating into a Three-Dimensional Rolling Contact Fatigue Crack

The penetration of a viscous lubricating oil into a three-dimensional surface crack under a rolling contact stress was calculated. The finite element method was applied to solve the Reynolds equation coupled with the elastic deformation of the crack. The process of penetration is roughly the same as in the two-dimensional model. The lubricating oil begin to flow into the crack when the contact pressure passes the crack mouth. The lubricating oil enters the crack tip and increases the stress intensity factor when nondimensional viscosity β=ηvE2/(ap03) is small. The crack is not open when β is large, because the contact pressure passes before the lubricating oil flows into the crack. The critical value of β was calculated. The penetration of the lubricating oil in the three-dimensional model is not easy as compared with the two-dimensional model.

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

A novel treatment of a direct procedure for elastic-plastic analysis and shakedown is presented and its application to problems in three-dimensional rolling contact with or without case-hardened layers 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. These eigenstrains are determined using an incremental projection method based on the purely elastic solution and a special representation of the yield condition for a linear-kinematic hardening material. The three-dimensional residual problem is then further split into a plane problem and an anti-plane problem which are readily solved using the finite element method. A significant advantage of the present analysis over the alternative approach of simulating repeated rolling until shakedown occurs is that in the present analysis, the final shakedown solution is obtained directly by solving three elasticity problems. Results are compared with full elastic-plastic finite element calculations available from the literature and good agreement is observed. The effects of surface hardened layers on the distributions of residual stress and displacement are investigated for both two- and three-dimensional contact. The direct approach is shown to be a straightforward and efficient method for obtaining the steady state solution in the analysis of three-dimensional problems in rolling and/or sliding contact.

Elasto-Plastic Finite Element Analysis of Repeated Three-Dimensional, Elliptical Rolling Contact With Rail Wheel Properties

This paper presents an elasto-plastic analysis of the repeated, frictionless, three-dimensional rolling contact similar to the ones produced by the rail-wheel geometry. This paper treats an elliptical contact rolling across a semi-infinite half space. The contact shape and loading: semi-major axis (in the rolling direction), w1 = 8 mm, and semi-minor axis, w2 = 5.88 mm, reflect standard rail and wheel curvatures and a wheel load of 149 KN (33,000 lb). A three-dimensional, elasto-plastic finite element model, developed earlier, is employed together with the elastic-linear-kinematic-hardening-plastic (ELKP) idealization of the cyclic plastic behaviour of a material similar to rail and wheel steels. The calculations present the displacements, the stress-strain distributions, stress-plastic strain histories and the plastic strain ranges in the half-space. The cyclic plasticity approaches a steady state after one contact with further contacts producing open but fully reversed stress-strain hysteresis loops, i.e., plastic shakedown.

Elasto-Plastic Finite Element Analysis of Three-Dimensional Pure Rolling Contact Above the Shakedown Limit

This paper describes calculations for repeated, frictionless, three-dimensional rolling contact, for a relative peak pressure (po/k) of 6.0 (above the shakedown limit) for a circular contact patch. This analysis was carried out for two material responses, elastic-perfectly plastic (EPP) and elastic-linear-kinematic-hardening plastic (ELKP), using the elasto-plastic finite element model developed earlier. The ELKP material parameters are those appropriate for hardened bearing steel. Frictionless three-dimensional rolling contact is simulated by repeatedly translating a Hertzian pressure distribution across the surface of an elasto-plastic half space. The half space is represented by a finite mesh with elastic boundaries. The paper describes the complex stress state existing in the half space and the attending plasticity, as the load translates. The calculations present the distortion of the rim, the residual stress-strain distributions, stress-strain histories, and the cyclic plastic strain increments in the vicinity of the contact. Compared with the analyses at the shakedown limit, higher residual stresses and strains are observed.

Elastoplastic Finite Element Analysis of Three-Dimensional, Pure Rolling Contact at the Shakedown Limit

This paper describes a three-dimensional elastoplastic finite element model of repeated, frictionless rolling contact. The model treats a sphere rolling on an elastic-perfectly plastic and an elastic-linear-kinematic-hardening plastic, semi-infinite half space. The calculations are for a relative peak pressure (po/k) = 4.68 (the theoretical shakedown limit for perfect plasticity). Three-dimensional rolling contact is simulated by repeatedly translating a hemispherical (Hertzian) pressure distribution across an elastoplastic semi-infinite half space. The semi-infinite half space is represented by a finite mesh with elastic boundaries. The calculations describe the distortion of the rim, the residual stress-strain distributions, stress-strain histories, and the cyclic plastic strain ranges in the vicinity of the contact.

Rolling Contact With Friction and Non-Hertzian Pressure Distribution

A numerical technique has been developed to deal with three-dimensional rolling contact problems with an arbitrary contact region under an arbitrary pressure. Results of this technique are checked against existing solutions for cases of Hertzian contact. A solution for a case of non-Hertzian contact is also presented. This numerical technique works satisfactorily for cases with small spin creepage. For cases of large spin creepage, we utilize a recent work (by the authors) for the limiting case of fully developed sliding contact.

A Three-Dimensional Rolling Contact Model for a Reinforced Rubber Tire

Abstract A steady state formulation of the rolling contact problem with friction that allows the analysis of free rolling, cornering, acceleration, and braking is presented. This formulation is applied to the finite element analysis of tires. A layered shell finite element with shear deformation that allows for large deflection and rotation is developed. In each layer, orthotropic Hookean materials or Mooney-Rivlin type materials with fiber reinforcements can be used and the incompressibility constraint is enforced with Lagrange multipliers. The contact constraint is enforced with a penalty and the friction term, instead of the usual Coulomb friction, is regularized by a differentiable form that makes it more suitable for numerical analysis. A numerical example for a typical tire is also given.

Three-dimensional finite deformation, rolling contact of a hyperelastic cylinder: Formulation of the problem and computational results

In this paper, a general class of three-dimensional rolling contact problems is analyzed by finite element methods. Finite deformations and frictional contact are considered. The results of several numerical experiments are also presented.