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The objective of this research is to conduct a finite element analysis to better understand the effects of induction hardening on rolling contact fatigue (RCF). The finite element analysis was developed in three-dimensional to estimate the maximal loading and the positions of the crack nucleation sites in the case of cylinder contact rolling. Rolling contact with or without surface compressive residual stress (RS) were studied and compared. The RS profile was chosen to simulate the effects of an induction hardening treatment on a 48 HRC tempered AISI4340 steel component. As this hardening process not only generates a RS gradient in the treated component but also a hardness gradient (called over-tempered region), both types of gradients were introduced in the present model. RSs in compression were generated in the hard case (about 60 HRC); tension values were introduced in the over-tempered region, where hardness as low as 38 HRC were set. In order to estimate the maximal allowable loadings in the rotating cylinders to target a life of 106 cycles, a multiaxial Dang Van criterion and a shear stress fatigue limit were used in the positive and negative hydrostatic conditions, respectively. With the proposed approach, the induction hardened component was found to have a maximal allowable loading significantly higher than that obtained with a nontreated one, and it was observed that the residual tensile stress peak found in the over-tempered region could become a limiting factor for fatigue rolling contact life. [ABSTRACT FROM AUTHOR]

A theoretical and computational framework for the analysis of fully transient, thermome-chanically coupled, frictional rolling contact based on an arbitrary Lagrangian-Eulerian (ALE) kinematical description is presented. In particular, a computationally efficient methodology for mixed control between the ALE referential velocities and their corresponding driving forces is developed and discussed in depth. Numerical examples involving two-dimensional (2D) cylinder-plate rolling contact are presented, covering a range of transient, thermomechanically coupled rolling contact phenomena, taking place on a broad range of time scales. Here, particular points of emphasis include dynamical effects in the vicinity of the contact region and the time scales on which mechanical and thermal mechanisms operate. [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 comprehensive numerical model is developed using Lagrangian finite element (FE) formulation for investigating the steady-state viscoelastic (VE) rolling contact response. Schapery's nonlinear viscoelastic (NVE) model is adopted to simulate the VE behavior. The model accounts for large displacements and rotations. A spatially dependent incremental form of the VE constitutive equations is derived. The dependence on the histoiy of the strain rate is expressed in terms of the spatial variation of the strain. The Lagrange multiplier approach is employed. The classical Coulomb's friction law is used. The developed model is verified and its applicability is demonstrated. [ABSTRACT FROM AUTHOR]

The complexities of analyzing rolling element bearings vary. Vendors offer cataloged solutions comprised of limiting loads and speeds, bearing life, and lubricant recommendations. These guidelines meet the needs of most customers; however, more demanding applications warrant advanced analyses. This work focuses on thermal management. Current literature offers system level solutions using either resistance methods or finite element analysis (FEA). Resistance methods have rapid computation time, yet lack accuracy. Finite element methods improve the accuracy, but are computationally cumbersome. This work proposes an integral transform method. The rapidly computed solution yields accurate results. The methodology and results of this work are presented in a three-part series. Part I details existing literature and provides the framework for a new heat transfer model. This model describes rolling-element bearing systems containing a shaft, housing, and numerous bearing raceways. It also includes gears, cooling jackets, and is applicable for several methods of lubrication. The model consists of solid component partial differential equations (PDEs) in conjunction with analytic expressions for fluid temperatures, convection equation, and mass flow. Part II presents the housing, shaft, and bearing raceway PDE solutions. Part III offers experimental validation, as well as observations from experiments on fluid flow within the bearing. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a three-dimensional finite element model of rigid hemisphere repeatedly rolling over a rough flat surface under constant normal load is discussed. The aim of this research is to study the von Mises residual stress and plastic strain distribution and to determine the steady-state phase of the repeated rolling contacts. The results show that the change of residual stress distribution takes place in the first-two rolling cycles and there is no significant change for the residual stress from the second to third rolling cycle, i.e. the surface is run-in after a few cycles. The increase of the contact load affects the area of the von Mises residual stress at the surface and subsurface and also the number of the deforming asperities. The residual stress distribution is getting wider as the normal force increases. The plastic strain is captured after the third cycle of rolling. Small area of plastic strain is found for the rough surface for the low forces applied which indicates the surface deformed mainly elastically. The rough surface is predicted to be plastically deformed for the highest force applied. [Copyright &y& Elsevier]

Abstract: Current work presents Finite Elements study of hydrogen diffusion into a metal substrate loaded by rolling contact. The main goal of the presented study is to investigate stress effect on hydrogen transport in rolling contact conditions. In this work, rolling contact is defined by the Hertzian pressure, moving along the bearing ring. Although, hydrogen diffusion with respect to bearing is studied here, very similar approach can be used for other components of machinery subjected to rolling contact. Governing equations are given in the current study in dimensionless form, and parametric study, analyzing influence of different dimensionless parameters on subsurface concentration of hydrogen, is presented. [Copyright &y& Elsevier]

The background of the present study is the rolling contact fatigue (RCF) in a brittle polymer disk. The disk has been tested on a two disk machine, under controlled normal and tangential loads, with no global slip. After several million cycles and under different operating conditions, it has been observed that (1) the tangential load highly influences the RCF phenomenon, (2) a network of regularly spaced cracks appears,, and (3) in the driving position, the RCF phenomenon develops faster. To explain these observations, a numerical model based on the finite element method (FEM) has been built: the cracks have been quite simply modeled, stick-slip has been chosen as the friction model, and the disk-on -disk contact has been replaced by a disk-on-plane contact. To study tile influence of same of the operating conditions, the design of experiments (DOE) techniques has been used. The statistical postprocessing associated to DOE has confirmed the experimental observations with a good reliability. In addition, with some mechanical considerations, scenarios of what experimentally happens arc proposed. The association FEM/ DOE is an original and efficient way to explain phenomena in the field of RCF: the accuracy of the FEM coupled with DOE statistical treatments make it possible to have a good predictabilitt despite some uncontrolled parameters. [ABSTRACT FROM AUTHOR]

Abstract: Because most fatigue cracks in wheel and rail take place by rolling contact between wheel and rail in railway industry, it is critical to understand the rolling contact phenomena, especially for the three-dimensional situation. In this paper the steady-state and transient rolling contact problem of three-dimensional elastic bodies has been studied. The transient conditions were controlled by the applied relative slip. The variation of tangential traction and stick-slip region on rolling contact surface were obtained using the finite element method. The three-dimensional distribution of tangential traction and contact stresses on the contact surface are investigated. Results show that the distribution of tangential traction and contact stresses on the contact surface varies rapidly as a result of the variation of stick-slip region. The tangential traction is very close in form to Carter''s distribution that contact region divided into stick and slip region. The contact stress at the leading edge is greater than at the trailing edge and the transient distance increases with small slip. [Copyright &y& Elsevier]

Abstract: Because most fatigue cracks in wheel and rail take place by rolling contact between wheel and rail in railway industry, it is critical to understand the rolling contact phenomena, especially for the three-dimensional situation. In this paper the steady-state and transient rolling contact problem of three-dimensional elastic bodies has been studied. The transient conditions were controlled by the applied relative slip. The variation of tangential traction and stick-slip region on rolling contact surface were obtained using the finite element method. The three-dimensional distribution of tangential traction and contact stresses on the contact surface are investigated. Results show that the distribution of tangential traction and contact stresses on the contact surface varies rapidly as a result of the variation of stick-slip region. The tangential traction is very close in form to Carter''s distribution that contact region divided into stick and slip region. The contact stress at the leading edge is greater than at the trailing edge and the transient distance increases with small slip. [Copyright &y& Elsevier]

The continuum theory of elasticity and/or homogeneously discretized finite element models have been commonly used to investigate and analyze subsurface stresses in Hertzian contacts. These approaches, however, do not effectively capture the influence of the random microstructure topology on subsurface stress distributions in Hertzian contacts. In this paper, a finite element model for analyzing subsurface stresses in an elastic half-space subjected to a general Hertzian contact load with explicit consideration of the material microstructure topology is presented. The random internal geometry of polycrystalline microstructures is modeled using a 3D Voronoi tessellation, where each Voronoi cell represents a distinct material grain. The grains are then meshed using finite elements, and an algorithm was developed to eliminate poorly shaped elements resulting from "near degeneracy" in the Voronoi tessellations. Hertzian point and line contacts loads are applied as distributed surface loads, and the model's response is evaluated with commercial finite element software ABAQUS. Internal stress results obtained from the current model compare well with analytical solutions from theory of elasticity. The influence of the internal microstructure topology on the subsurface stresses is demonstrated by analyzing the model's response to an over rolling element using a critical plane approach. [ABSTRACT FROM AUTHOR]

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]

A previously published model for plasticity assessment in rolling contact, based on a simplification of the non- linear kinematic and isotropic hardening model of Chaboche and Lemaitre, is discussed, and an update is introduced in order to improve its accuracy in the plastic strain prediction within the region just underneath the contact surface. The update is based on a correction of the yield limit and of the strain rate as a function of the load ratio of the tensile stress in the direction parallel to the contact surface. The effectiveness and the accuracy of the updated model in not too severe conditions are demonstrated through comparisons with results obtained by finite element model (FEM) analyses. An application of the model to some experimental results obtained on rail and railway wheel steels is also carried out, and quite good agreement is found in plastic strain prediction, although some discrepancies are found. The method appears to be a valid tool for practical application, especially for its ability of combining the effects of different phenomena and of simulating a number of cycles of the order of millions in a reasonable time. [ABSTRACT FROM AUTHOR]

Fault diagnosis of the low-speed rolling bearings is difficult, due to the reasons of the special structure, the peculiar working condition and the complex fault mechanism. Due to the fault features of the low-speed rolling bearings, in this paper, by applying stress waves and wavelet analysis, a new method for the fault diagnosis of those rolling bearings was presented. Firstly, the 01B65EX Cooper rolling bearing with low speed is taken as an example, and the three-dimension contact models for the good and inner race fault bearings were set up, which is studied through finite element method, and then the stress, the strain and the contact stress distribution are then given. The stress and strain distribution law of the outer race and the contact stress distribution law of the interface on good and fault bearing were compared. Then on the basis of the stress wave analysis, the wavelet transform of data signals that are collected in the experiments are carried out, for which the db6 wavelet with 4 scales is employed. Finally the characteristic frequencies of the stress waves with the simulative faults are extracted. The fault of low-speed rolling bearing is well diagnosed. Results show that stress wave and wavelet analysis is an effective method for diagnosing the fault of low-speed machinery. [ABSTRACT FROM AUTHOR]

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]

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. [ABSTRACT FROM AUTHOR]

The rolling contact of a case study is discussed. A method for describing the contact of the two rolls of a calender unit is presented. Firstly, the rotor dynamics system of a roll is described by expressing the kinetic energy in a global non-rotating coordinate frame and the strain energy in a rotating frame by using a finite element (FE) mesh and then by deriving the rotor dynamical matrix equations accordingly. The contact of the two rolls is then defined as a line contact moving on the roll surfaces according to the rotation movements. A procedure for determining the movement on the surface of FE mesh is presented. The contact stiffness function between the rolls is described. The aim of this study is to create a cost effective simulation approach for numerical time domain analyses. An example simulation is illustrated. [ABSTRACT FROM AUTHOR]

In order to evaluate the surface durability of sintered machine elements, the fatigue lives of 28 kinds of sintered roller under a sliding/rolling contact condition were estimated using Paris's law based on linear fracture mechanics. The fatigue tests were conducted using a two-cylinder testing machine. The stress intensity factor for the mode II under the Hertzian contact condition was calculated using the finite element model. The value of the stress intensity factor became larger as the crack length became longer to the contact surface, and the value of the stress intensity factor range was independent of the crack angle. It could be clarified that the fatigue lives of the sintered rollers depended on the pore diameter and the hardness. It was obvious that the pore distribution has to be taken into consideration to estimate the fatigue lives of the sintered rollers more precisely. [ABSTRACT FROM AUTHOR]