Hertz Contact Problem between Wheel and Rail

2013 ◽  
Vol 837 ◽  
pp. 733-738 ◽  
Author(s):  
Tiberiu Axinte
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Contact Problem ◽  
Contact Pressure ◽  
Three Dimensional ◽  
Contact Problems ◽  
Rolling Contact ◽  
Hertz Contact ◽  
Shakedown Limit ◽  
Plastic Shakedown

Rail-wheel contact problems have been analyzed by the use of the three-dimensional finite element models. Based on these models, the paper presents a study regarding the applicability of the Hertz contact to rail-wheel contact problems. Beside a standard rail, the study also considers a crane rail and a switching component. The bodies of the contact problem are the standard rail UIC60 and the standard wheel UICORE. The maximum contact pressure which the material can support in the elastic range in steady state conditions is known as the shakedown limit. With an operating contact pressure below the shakedown limit the rail would be expected to remain elastic a long period of its lifecycle. However, examination of rail cross-sections shows severe plastic deformation in a sub-surface layer of a few tens of microns thickness; the contact patch size is in tens of millimeters. 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 in order to study the influences of the tangential surface forces in the two shear directions on residual stresses and residual strains. The Hertz theory is restricted to frictionless surfaces and perfectly elastic solids, but it is the best method for determining deformations and stress from pitch of contact. Form change due to wear and plastic deformation of a rail can reduce the service life of a track. The purpose of this investigation was to study the development of these damage mechanisms on new and three years old rails in a commuter track over a period of two years.

Analysis of Wheel-Rail Elasto-Plastic Contact Problem

2002 ◽  
Author(s):  
Jun Zhang ◽  
Yingxi Liu ◽  
Changhua Wu
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Contact Problems ◽  
Internal Force ◽  
Rolling Contact ◽  
Tractive Force ◽  
Parametric Quadratic Programming ◽  
Friction Factors ◽  
Quadratic Programming Method ◽  
Parametric Quadratic Programming Method

Using the finite element parametric quadratic programming method, computation of Elastic and Elastic-plastic rolling contact problems between wheel and rail is carried out for various cases such as different wheel diameters, different axle loads, different tractive force and different friction factors. The contact states and the contact internal force between wheel and rail are obtained, and their changing laws corresponding with every above-mentioned parameter are analyzed in this paper.

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

1991 ◽  
Vol 58 (2) ◽  
pp. 347-353 ◽  
Author(s):  
S. M. Kulkarni ◽  
G. T. Hahn ◽  
C. A. Rubin ◽  
V. Bhargava
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Kinematic Hardening ◽  
Three Dimensional ◽  
Bearing Steel ◽  
Complex Stress State ◽  
Rolling Contact ◽  
Stress Strain ◽  
Element Analysis ◽  
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.

Three-Dimensional Elastic-Plastic Stress Analysis of Rolling Contact

2002 ◽  
Vol 124 (4) ◽  
pp. 699-708 ◽  
Author(s):  
Yanyao Jiang ◽  
Biqiang Xu ◽  
Huseyin Sehitoglu
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Stress Analysis ◽  
Tangential Force ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Normal Surface ◽  
Elastic Plastic ◽  
Residual Strains ◽  
Plastic Shakedown

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.

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

1990 ◽  
Vol 57 (1) ◽  
pp. 57-65 ◽  
Author(s):  
S. M. Kulkarni ◽  
G. T. Hahn ◽  
C. A. Rubin ◽  
V. Bhargava
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Kinematic Hardening ◽  
Three Dimensional ◽  
Element Model ◽  
Rolling Contact ◽  
Stress Strain ◽  
Element Analysis ◽  
Perfectly Plastic ◽  
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.

A Shakedown Limit under Hertz Contact Pressure

2011 ◽  
Vol 291-294 ◽  
pp. 1506-1510
Author(s):  
Jim S. Shiau
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Mathematical Programming ◽  
Contact Mechanics ◽  
Contact Pressure ◽  
Hertz Contact ◽  
Moving Surface ◽  
Load Limit ◽  
Shakedown Limit ◽  
Surface Loads

In his "Contact Mechanics" book, Professor K. L. Johnson described an analytical lower bound shakedown approach to predict the shakedown load limit under repeated Hertz moving surface loads. Based on Bleich-Melan shakedown theorem, this problem will be revisited in this paper using finite element techniques and mathematical programming.

scholarly journals The Indentation Rolling Resistance in Belt Conveyors: A Model for the Viscoelastic Friction

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 58 ◽  
Author(s):  
Nicola Menga ◽  
Francesco Bottiglione ◽  
Giuseppe Carbone
Keyword(s):  
Contact Problem ◽  
Finite Thickness ◽  
Numerical Procedure ◽  
Contact Problems ◽  
Accurate Solution ◽  
Rolling Contact ◽  
Viscoelastic Layer ◽  
Force Coefficient ◽  
Belt Conveyors ◽  
Energy Dissipated

In this paper, we study the steady-state rolling contact of a linear viscoelastic layer of finite thickness and a rigid indenter made of a periodic array of equally spaced rigid cylinders. The viscoelastic contact model is derived by means of Green’s function approach, which allows solving the contact problem with the sliding velocity as a control parameter. The contact problem is solved by means of an accurate numerical procedure developed for general two-dimensional contact geometries. The effect of geometrical quantities (layer thickness, cylinders radii, and cylinders spacing), material properties (viscoelastic moduli, relaxation time) and operative conditions (load, velocity) are all investigated. Physical quantities typical of contact problems (contact areas, deformed profiles, etc.) are calculated and discussed. Special emphasis is dedicated to the viscoelastic friction force coefficient and to the energy dissipated per unit time. The discussion is focused on the role played by the deformation localized at the contact spots and the one in the bulk of the thin layer, due to layer bending. The model is proposed as an accurate solution for engineering applications such as belt conveyors, in which the energy dissipated on the rolling contact of idle rollers can, in some cases, be by far the most important contribution to their energy consumption.

3-D Elasto-Plastic Contact Finite Element Analysis for Bearings Design

1990 ◽  
Author(s):  
Wang Shigang ◽  
Yu Jun ◽  
Zhou Ji ◽  
Li Mingzhang
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Geometrical Nonlinearity ◽  
Contact Problems ◽  
Plastic State ◽  
Element Analysis ◽  
Surface Pressure Distribution ◽  
Tangential Stiffness ◽  
Stiffness Method ◽  
Error Method

Abstract In this paper, A 3-D elasto-plastic contact problem in bearings is studied by Finite Element Method (FEM). A computer program has been developed for this purpose. A trial-error method is employed to cope with the geometrical nonlinearity and a tangential stiffness method is employed to tackle the material nonlinearity appeared in elasto-plastic contact problems. A frictionless contact problem of roller bearings is analysed, the result reveals that in 3-D elasto-plastic state the trend of the contact surface pressure distribution is similar to Hertz problem’s but flater.

scholarly journals Elasto-plastic analysis of the contact region between a rigid ellipsoid and a semi-flat surface

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879739 ◽  
Author(s):  
Pengyang Li ◽  
Lingxia Zhou ◽  
Fangyuan Cui ◽  
Quandai Wang ◽  
Meiling Guo ◽  
...  
Keyword(s):  
Residual Stress ◽  
Plastic Deformation ◽  
Plastic Strain ◽  
Contact Pressure ◽  
Contact Region ◽  
Three Dimensional ◽  
Von Mises Stress ◽  
Effective Plastic Strain ◽  
Normal Forces ◽  
Von Mises

When the load acting on a mechanical structure is greater than the yield strength of the material, the contact surface will undergo plastic deformation. Cumulative plastic deformation has an important influence on the lifespan of mechanical parts. This article presents a three-dimensional semi-analytical model based on the conjugate gradient method and fast Fourier transform algorithm, with the aim of studying the characteristic parameters of the contact region between a rigid ellipsoid and elasto-plastic half-space. Moreover, normal forces and tangential traction were considered, as well as the contact pressure resulting from various sliding speeds and friction coefficients. The contact pressure, effective plastic strain, von Mises stress, and residual stress were measured and shown to increase with increasing sliding velocity. Finally, when the friction coefficient, contact pressure, and effective plastic strain are increased, the von Mises stress is also shown to increase, whereas the residual stress decreases.

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