Rolling Contact Stresses Research Articles

Effect of Track Structure Parameters on Rolling Contact Stresses of Wheel-rail

The effects of rail base slope, rail gauge and curve radius on the rolling contact stresses and wear index of JM3 wheelset and track in static rolling contact are analyzed by using the rolling contact theory of three-dimensional elastic bodies with non-Hertz form, numerical program of CONTACT and Bossinesq-Cerruti force/displacement formula and the Gaussian numerical integration. The numerical results indicate that the stresses, wear index and normal pressure will achieve the minimal value when the rail base slope is 1/20. The maximal shear stress and equivalent stress can decrease by 40.15% and 39.37% respectively when the rail base slope changes from 1/40 to 1/20. It is suggested that the profile of worn tread is optimized due to bigger contact stresses when the rail base slope is 1/40. The appropriate augment of rail gauge can decrease the maximal shear stress, equivalent stress and normal pressure on the contact patch of wheel-rail. The maximal stress of contact patch under the curve track condition will increase evidently comparing to the tangent track. Moreover, the curve radius will change the distributing of stick-slip area and decreasing curve radius will increase total slip of the contact patch and wear index of wheel-rail.

Full Two-Dimensional Model for Rolling Resistance. II: Viscoelastic Cylinders on Rigid Ground

Following the previous paper, “Full two-dimensional model for rolling resistance: Hard cylinder on viscoelastic foundation of finite thickness,” addressing modeling of rigid cylinder rolling against viscoelastic foundation of finite thickness, this paper focuses on the development of a rigorous full two-dimensional semianalytical model for viscoelastic rollers with layered structure rolling against a rigid ground. In this model, the polar coordinate system is used, the solution is expanded into a set of Fourier series corresponding to the angular coordinate, the frequency domain master curves of G′ and G″ characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special condensed structure model based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. Examples are given to show the model capabilities to efficiently handle rolling resistance and contact stresses, and capture major characteristics of standing-wave phenomenon, such as sharp rise of rolling resistance, emergence of standing waves and material dynamic softening as the rolling speed approaches a critical value. The methodology may be of interest to industrial roller designers.

Tensile stress life model for rolling contact fatigue of silicon nitride ceramic balls

The relation expression between failure probability and rolling contact fatigue life is deduced with WEIBULL fracture statistic method for the silicon nitride ceramic ball in ball-cylinder geometric model. The tensile stress life model about silicon nitride ceramic balls is set up between rolling contact fatigue life and contact stress on the basis of the correlative numerical solution between the rating life and the maximum contact stress. The tensile stress life model is conceived basing on maximum principal tensile stress. It is indicated that the tensile stress life model is feasible through rolling contact fatigue test with different stress level. It is verified by the tensile stress life model that silicon nitride ceramic balls failed by the maximum principal tensile stress, not by the maximum shear stress. In comparison with the L-P shear stress life model, the tensile stress life model is reasonable for rolling con-tact fatigue life prediction of silicon nitride ceramic balls.

Contact stresses in conical rollers

In this paper, the pure rolling contact stresses in conical rollers under normal loading are studied. The existing analytical expression for pure rolling contact pressure in uniform cross-section cylinders is modified to determine the contact area, the contact pressure, and its distribution in conical rollers under normal loading. The Hertzian contact stresses are determined for the modified pure rolling contact pressure distribution. The theoretical results are compared with the finite element analysis using ABAQUS, for different vertex angles, materials, and loads. The results of the theoretical model are found to be consistent with the finite element simulations in predicting the contact pressure, the distribution, and the contact stresses in conical rollers.

Elastic-Plastic Finite Element Analysis of Nonsteady State Partial Slip Wheel-Rail Rolling Contact

A finite element analysis with the implementation of an advanced cyclic plasticity theory was conducted to study the elastic-plastic deformation under the nonsteady state rolling contact between a wheel and a rail. The consideration of nonsteady state rolling contact was restricted to a harmonic variation of the wheel-rail normal contact force. The normal contact pressure was idealized as the Hertzian distribution, and the tangential force presented by Carter was used. Detailed rolling contact stresses and strains were obtained for repeated rolling contact. The harmonic variation of the normal (vertical) contact force results in a wavy rolling contact surface profile. The results can help understand the influence of plastic deformation on the rail corrugation initiation and growth. The creepage or stick-slip condition greatly influences the residual stresses and strains. While the residual strains and surface displacements increased at a reduced rate with increasing rolling passes, the residual stresses stabilize after a limited number of rolling passes. The residual stresses and strains near the wave trough of the residual wavy deformation are higher than those near the wave crest.

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.

Numerical Investigation on the Effects of Machining-Induced White Layer during Rolling Contact

It is well known that a thin phase-transformed white layer can be formed on component surfaces produced by hard machining. However, it is not clear as to how the white layer affects component performance, for example, in rolling contact fatigue. This study aims to determine the effects of white layer and associated residual stress on rolling contact stresses and strains. It is nearly impossible for an experimental study to identify the effects of white layer alone on rolling contact. Furthermore, small-scale contact stresses and strains (less than 30 μm) of the phase-transformed region are difficult to measure using the current experimental techniques. Therefore, a finite element analysis simulation model of rolling contact incorporating machining-induced surface integrity has been developed in this study. Three cases were investigated to decouple the effects of surface integrity factors: surface with white layer only, surface with residual stress only, and surface with white layer and residual stress. The simulation results show that distinct material properties of the white layer significantly influence the magnitudes and distributions of near-surface stresses and strains instead of those in the subsurface. Furthermore, it can be inferred that the white layer would affect near-surface fatigue damage instead of subsurface fatigue damage. The simulated near-surface fatigue damage mechanisms have been substantiated by the fatigue test data.

FE-simulation of the effects of machining-induced residual stress profile on rolling contact of hard machined components

Compared with grinding, hard turning may induce a relatively deep compressive residual stress. However, the interactions between the residual stress profile and applied load and their effects on rolling contact stresses and strains are poorly understood, and are difficult to measure using the current experimental techniques due to the small-scale of the phenomena. A new 2-D finite element simulation model of bearing rolling contact has been developed, for the first time, to incorporate the machining-induced residual stress profile instead of only surface residual stresses. Three cases using the simulation model were assessed: (a) measured residual stress by hard turning, (b) measured residual stress by grinding, and (c) free of residual stress. It was found that distinct residual stress patterns hardly affect neither the magnitudes nor the locations of peak stresses and strains below the surface. However, they have a significant influence on surface deformations. The slope and depth of a compressive residual stress profile are key factors for rolling contact fatigue damage, which was substantiated by the available experimental data. Equivalent plastic strain could be a parameter to characterize the relative fatigue damage. The magnitudes of machining-induced residual stress are reduced in rolling contact. The predicted residual stress pattern and magnitude agree with the test data in general. In addition, rolling contact is more sensitive to normal load and residual stress pattern than tangential load.

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.

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.

Fatigue Limit Concept and Life Prediction Model for Rolling Contact Machine Elements

The weakness of the present method of fatigue limit assessment is discussed and a new approach to fatigue limit assessment using a three-parameter log-log and Weibull plot is proposed. With this new approach to the analysis of alternating fatigue test data, it is confirmed that hearing steel does not show any fatigue limit, whereas structural steel does have a distinct fatigue limit. In absence of a fatigue limit for hearing steel, a minimum life or a minimum number of stress cycles prior to failure is proposed for the analysis of fatigue life behavior under a given rolling contact fatigue load or stress, leading to a three-parameter Weibull life distribution function. The experimental data is found to fit very well to this distribution. A comparison of the stress-life exponents estimated for the structural steel and bearing steel using three methods of analysis shows the values to be very close indicating similarity in their fatigue behaviors. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference in San Francisco, CA October 21–24, 2001

Elastic-Plastic Finite Element Analysis of Partial Slip Rolling Contact

The finite element model with the implementation of a robust cyclic plasticity theory was used to simulate the elastic-plastic stresses for the partial slip (stick-slip) line rolling contact. Detailed rolling contact stresses and strains were obtained for up to 40 rolling passes. The partial slip condition greatly affects the residual stress in the rolling direction and the residual shear strain within a thin layer of material near the contact surface. The residual stress in the axial direction was not significantly influenced by the partial slip condition. An increase in friction coefficient drives the location of maximum shear strain to the contact surface. In addition, a comparison was made between the finite element results and the results obtained from an approximate method.

Experimental analysis of rolling contact stresses in a viscoelastic strip

An experimental approach to two-dimensional, viscoelastic, steadily moving rolling contact is described. The photoviscoelastic technique is employed for the analysis of rolling contact stresses between a viscoelastic plate and a rigid rolling cylinder in which the principal axes of stress, strain and birefringence are not coincident with each other. Using an elliptically polarized white light, the distribution of isochromatic fringe order and the principal axes of birefringence at an instant are determined from a single photoviscoelastic image. The time variations of the differences of the principal stresses and strains, as well as their directions, are obtained by use of the optical constitutive equations of photoviscoelasticity. The experimental results involving the time variation of the stresses around the contact surface and their distributions are analyzed.

Analysis of Viscous Lubricant Penetrating into Rolling Contact Fatigue Crack.

The penetration of a viscous lubricant 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 the two dimensional model. The lubricant begin to flow into the crack when the contact pressure is passing the crack mouth. The lubricant enters to the crack tip and increases the stress intensity factor, when a nondimensional parameter β=ηυE2/(ap30)is small. The crack does not open when β is large, because the contact pressure has passed before the lubricant flows into the crack. The critical value of β was calculated. The penetration of the lubricant is not easy as compared with the two dimensional model.

A model for rolling contact failure

Rolling contact stress and failure analyses were conducted for the Hadfield steel (manganese steel) and the Bainitic alloy (J7). The first alloy is used in diamond crossings and frogs in the railroad industry while the second alloy is a candidate for such applications. A series of fatigue experiments were conducted on these alloys to establish the damage parameters. The proposed fatigue damage parameter incorporated the role of both shear and normal stress ranges on the `critical' plane upon surveying all planes at a material point. Maximum local plastic strains, accumulated strains, and three-dimensional residual stresses were computed under pure rolling conditions for p o/ k (Hertzian pressure normalized by yield stress in shear) values in the range 4.0 to 8.0 using a semi-analytical approach. A multiaxial stress–strain plasticity model developed by the authors was used in the calculations of the contact stress and strain fields. The advantage of this model over the previous models is that it predicts the correct trends in the material ratchetting rate and non-proportional loading response. For life prediction, a new combined ratchetting–multiaxial fatigue damage model was presented. The damage at different depths below the surface was interrogated with this model to determine the location where failure will originate. The results show that the Bainitic alloy exhibits longer lives under the same Hertzian pressure and for both materials the life is finite when the normalized pressure, p o/ k ratio, exceeded 4.0.

Analysis of Rolling Contact Fatigue Crack Filled with Viscous Lublicating Oil.

The penetration of a viscous lubricant into a two 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 lubricant begins to flow into the crack when the contact pressure is passing the crack mouth. The lubricant enters to the crack tip and increases the stress intensity factor, when a nondimensional parameter β=ηνE2/(ap30) is small. The crack does not open when β is large, because the contact pressure has passed before the lubricant flows into crack. The critical values of β were calculated. The penetration of the lubricant becomes easy when a frictional stress acts as the crack opening.

Orthogonal Shear Stress Amplitude as a Function of Rolling Contact Ellipticity and Depth

A simple and convenient computational algorithm has been derived and demonstrated for the orthogonal shear stress amplitude as a function of rolling contact ellipticity and depth. This solution extends the early rolling contact stress analysis of Lundberg and Palmgren beyond the unique level where the maximum occurs and to a broader range of contact ellipticities to includes contact ellipses with major axes in the rolling direction

Rolling contact stress analysis with the application of a new plasticity model

Previous elastic-plastic stress analyses of rolling contact have not produced accurate results of shear strain accumulation because the plasticity models applied in contact analysis were not designed to handle long term ratchetting behavior of a material. In this work, we studied the residual stresses and progressive shear strain ratchetting for the line rolling contact problems utilizing a recently developed semi-analytical approach in conjunction with a new plasticity model. The p 0/ k ratio ranges from 5.0 to 9.0 and the Q P ratio ranges from -0.3 to 0.3, where p 0 is the maximum Hertzian pressure, k is the yield stress in shear of the material, Q represents the total tangential force, and P is the total normal load. The material properties used in the simulations are those of 1070 steel with a pearlitic microstructure. It was found that the ratchetting rate of rolling surface movement rapidly decreases with increasing number of rolling passages (cycles) and ratchetting continues for many cycles. The simulations confirm that a driven wheel undergoes enhanced fatigue damage compared with a driving wheel. It is concluded that the pure rolling contact ( Q P = 0 ) produces “forward” surface movement. The tangential force plays a considerable role in the surface ratchetting but its influence on the residual stresses is insignificant. The overall residual stresses are mainly determined by the p 0/ k ratio. Calculations were also conducted to simulate multiple passes of trains over a rail and the ratchetting in a locomotive driving wheel. A locomotive driving wheel produces “forward” surface ratchetting on the rail and car wheels following the driving wheels produce “backward” surface ratchetting on the rail. Most existing plasticity theorems are not capable of predicting this change in ratchetting direction. In the presence of multiple block loading histories a steady state ratchetting may not be reached.

Stress Analysis for Rolling Contact Between Two Viscoelastic Cylinders

The two-dimensional viscoelastic rolling contact with Coulomb’s dry friction is considered for steady-state rolling. A so-called standard linear solid (three parameter model) is used to characterize the viscoelastic material behavior. Rolling contact stresses between two rolling cylinders are investigated by a boundary element method, based on the half-space theory. Numerical results are presented including the stress distribution at the contact surfaces and in viscoelastic bodies as well as rolling resistance.

Approximate crack growth estimate of railway wheel influenced by normal and shear action

An elastic-plastic analysis of railway wheel life prediction is made for obtaining the residual stresses due to braking and alternating rolling contact stresses between the wheel and rail. These stresses are then used to obtain approximate crack border stress intensity factors K I, K II, and K III such that an equivalent combined load stress intensity factor can be derived by application of the strain energy density criterion. By including the effect of both the normal and shear action on the locomotive wheel, the results are indicative of those observed in service. While cracks may nucleate from thermal fatigue, it suffices to consider the cyclic load due to rolling contact for estimating the fatigue lives of locomotoive wheels.