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Elastohydrodynamic lubrication (EHL) is an important branch of the lubrication theory, describing lubrication mechanisms in nonconformal contacts widely found in many mechanical components such as various gears, rolling bearings, cams and followers, metal-rolling tools, traction drives, and continuous variable transmissions. These components often transmit substantial power under heavy loading conditions. Also, the roughness of machined surfaces is usually of the same order of magnitude as, or greater than, the estimated average EHL film thickness. Consequently, most components operate in mixed lubrication regime with significant asperity contacts. Due to very high pressure concentrated in small areas, resulted from either heavy external loading or severe asperity contacts, or often a combination of both, subsurface stresses may exceed the material yield limit, causing considerable plastic deformation, which may not only permanently change the surface profiles and contact geometry but also alter material properties through work hardening as well. In the present study, a three-dimensional plastoelastohydrodynamic lubrication (PEHL) model has been developed by taking into account plastic deformation and material work-hardening. The effects of surface/subsurface plastic deformation on lubricant film thickness, surface pressure distribution, and subsurface stress field have been investigated. This paper briefly describes the newly developed PEHL model and presents preliminary results and observed basic behavior of the PEHL in smooth-surface point contacts, in comparison with those from corresponding EHL solutions under the same conditions. The results indicate that plastic deformation may greatly affect contact and lubrication characteristics, resulting in significant reductions in lubricant film thickness, peak surface pressure and maximum subsurface stresses. [DOI: 10.1115/1.4001813] Keywords: plasto-elastohydrodynamic lubrication (PEHL), elastohydrodynamic lubrication, plastic deformation, elastic-plastic contact, plastic deformation, tribology

The average flow model proposed by Patir and Cheng offers a great convenience for the analysis of rough surfaces in lubrication. The contact factor introduced by Wu and Zheng helps to solve a difficulty in local film evaluation using the average flow model. This paper reports a simple method to calculate the contact factor. Method validation is demonstrated by the comparison of the contact factors for Gaussian surfaces obtained with the present method and the fitting formula of Wu and Zheng. The proposed method cannot only easily compute the contact factor values for Gaussian surfaces; it can also be used for those of non-Gaussian and measured surfaces, especially those with unknown probability density distribution of the roughness height. [DOI: 10.1115/1.4001195] Keywords: contact factor, probability density function, surface orientation, Gaussian and non-Gaussian surfaces, measured surfaces

A compliance operator is often utilized to evaluate the elastic displacement of surfaces in the simulation of transient and steady-state elastohydrodynamic lubrication of conformal-contact systems. The values of the compliance operator represent the elastic responses of all nodes when only one node is under a unit load. The accuracy of compliance operator values, computational cost, and storage size are important issues. Our study of steady-state conformal-contact elastohydrodynamic lubrication analyses suggests a method of selective-fine-mesh with selective-storage, as well as a special technique of the combined selective-fine-mesh with selective-storage mapping. These two techniques enable an efficient elasticity procedure for the simulation of steady-state and transient conformal-contact elastohydrodynamic lubrication systems by means of the finite element method. [DOI: 10.1115/1.4001120] Keywords: conformal-contact elastohydrodynamic lubrication, finite element, transient

Modifying the surface topography of tribological interfaces has the potential to improve the friction performance of certain mechanical components that experience sliding contact. Vibromechanical texturing (VMT), an improved texturing method based on the convenient turning process, is introduced. This process is performed on a standard computer numeric controlled (CNC) lathe, which is retrofitted with a piezoelectric-actuated tool positioning stage. Controlled vibratory, motion of the tool is used to cut microsized dimples into the surface of the workpiece. Two types of workpiece materials are used: aluminum and hardened steel with three forms of workpiece geometries: outer cylinder, inner cylinder; and flat/end face. The accuracy of the texturing method is compared with a basic surface topography model, which predicts texture dimensions within an 11% error for aluminum and up to 90% error for hardened steel using the current open-loop control system. Further analysis of the textured samples shows no significant signs of process-induced damage. It is demonstrated that this VMT method is a versatile, accurate technique that has potential to be a cost-effective means for surface texturing of tribological components. [DOI: 10.1115/1.4000418]

This paper discussed the computational accuracy of roughsurface point-contact isothermal elastohydrodynamic lubrication (EHL) analysis by investigating the effects of differential scheme, viscosity-pressure, and shear-thinning models. An EHL experiment with multitransverse ridges was employed as simulated target. Four differential schemes, including the combined and the separate first-order and second-order backward schemes, were investigated. It is found that the separate second-order backward scheme offers the best results based on the comparison with the experimental data, with which two roughness derivatives may be fully or partially canceled each other; thus, the discretization error induced by roughness can be reduced. The consistency of differential schemes is an important issue for the separate schemes. The Yasutomi free-volume viscosity-pressure model and the Eyring rheological model are found to yield the numerical simulations the closest to experimental results. [DOI: 10.1115/1.2842245] Keywords: EHL, differential schemes, viscosity-pressure models, rheological models

Surface pitting due to contact fatigue is a major failure mode of many mechanical components, such as various gears and rolling-element bearings. Pitting life prediction, therefore, is vital to design and performance/reliability improvements. Conventional prediction methods, commonly found in industrial standards, are based on the Hertzian contact theory, under the assumptions that surfaces are ideally smooth with no lubrication. Today, the trend of high power density, high reliability, compact design requires the life prediction to consider severe operation conditions in mixed lubrication, and the effect of surface roughness and topography. Also, it has been well known that ductile material failures in concentrated contacts are better correlated with the subsurface yon Mises stress, rather than the normal Hertzian pressure. The present study aims to develop a pitting life prediction approach for line-contact components based on a 3D line-contact mixed elastohydrodynamic lubrication (EHL) model recently developed by Ren et al. (2009, 'A Three-Dimensional Deterministic Model.for Rough Surface Line-Contact EHL Problems,' ASME J. Tribol., 131, p. 011501), which is capable of simulating the entire transition from full-film and mixed EHL down to dry contact of real machined rough surfaces under severe operating conditions. The pitting life evaluation employs the fatigue life model developed by Zaretsky (1987, 'Fatigue Criterion to System Design, Life and Reliability,' J. Propul. Power, 3(1), pp. 76-83) and extended by Epstein et al. (2003, 'Effect of Surface Topography on Contact Fatigue in Mixed Lubrication, ' Tribol. Trans., 46, pp. 506-513) using the yon Mises stress field calculated based on the rough surface mixed-EHL results. Sample cases are analyzed for 15 sets of transmission gears, and the life prediction results are compared with available experimental data. With optimized material constants in the life model, predicted pitting life results well agree with the test data. [DOI: 10.1115/1.3195040] Keywords: pitting, contact fatigue, failure analysis, life prediction, mixed lubrication, elastohydrodynamic lubrication (EHL), gear failures, gear lubrication

Sliding electrical contacts are found in many electromechanical devices, such as relays, switches, and resistance spot welding. Temperature rise due to sliding friction and electrical current may be the major source of sliding electrical contact deterioration. This paper reports the development of a three-dimensional thermo-elasto-plastic contact model of counterformal bodies, which takes into account transient heat flux, temperature-dependent strain hardening behavior, and a realistic heat partition between surfaces. Transient contact simulations induce a significant increase in computational burden. The discrete convolution and fast Fourier transform and the conjugate gradient method are utilized to improve the computation efficiency. The present model is used to study the case of a half-space sliding over a stationary sphere, and both are made of 7075 aluminum alloy; the contact resistance is considered mainly due to the surface oxide film. The simulation results indicate that the transient contact model is able to capture the history of plastic deformation accumulation and the material melting inception. [DOI: 10.1115/1.3084214] Keywords: sliding electrical contact, elastoplasticity, thermal softening

Elastic-plastic contact of a smooth sphere and a half-space with a real machined surface is simulated using an integration-based multilevel contact model. The total surface deflection is composed of bulk and asperity deformations. They are calculated at the global and the asperity level, respectively, which are connected through the asperity-supporting load. With this new model, the accurate contact area and contact pressure under a given load are quickly predicted using a relatively coarse grid system. The calculated load-area curve shows good agreement with the experimental data. Finally, the effects of the surface topography, including roughness and the asperity radius, upon the real contact area are analyzed. [DOI: 10.1115/1.3085944] Keywords: multilevel, elastic-plastic contact, rough surface

The relative motion between two surfaces under a normal load is impeded by friction. Interfacial junctions are formed between surfaces of asperities, and sliding inception occurs when shear tractions in the entire contact area reach the shear strength of the weaker material and junctions are about to be separated. Such a process is known as a static friction mechanism. The numerical contact model of dissimilar materials developed by the authors is extended to evaluate the maximum tangential force (in terms of the static friction coefficient) that can be sustained by a rough surface contact. This model is based on the Boussinesq-Cerruti integral equations, which relate surface tractions to displacements. The materials are assumed to respond elastic perfectly plastically for simplicity, and the localized hardness and shear strength are set as the upper limits of contact pressure and shear traction, respectively. Comparisons of the numerical analysis results with published experimental data provide a validation of this model. Static friction coefficients are predicted for various material pairs in contact first, and then the behaviors of static friction involving rough surfaces are extensively investigated. [DOI: 10.1115/1.3063814] Keywords: static friction, dissimilar-material contact, roughness

This paper reports the development of a novel three-dimensional (3D) deterministic model (3D L-EHL) for rough surface line-contact mixed-elastohydrodynamic lubrication (EHL) problems. This model is highly demanded because line contacts are found between many mechanical components, such as various gears, roller and needle bearings, cams and followers, and work rolls and backup rolls in metal-forming equipment. The macro aspects of a line-contact problem can be simplified into a two-dimensional (2D) model; however, the topography of contacting rough surfaces, microasperity contacts, and lubricant flows around asperities are often three-dimensionaL The present model is based on Hu and Zhu's unified 3D mixed-EHL model (Hu and Zhu, 2000, 'Full Numerical Solution to the Mixed Lubrication in Point Contacts,' ASME J. Tribol., 122(1), pp. 1-9) originally developed for point contacts and the mixed fast Fourier transform (FFT)-based approach for deformation calculation formulated by Chen et al. (2008, 'Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts With Normally Flat Surface,' ASME J. Appl. Mech., 75(1), 011022-1-11). It is numerically verified through comparisons with results from the line-contact Hertzian theory and the conventional 2D line-contact smooth-surface EHL formulas. Numerical examples involving 3D sinusoidal and digitized machined surfaces are also analyzed. Sample cases indicate that transverse roughness may yield greater film thickness than longitudinal roughness. This observation is qualitatively in agreement with the trend predicted by Patir and Cheng's stochastic model (1978, 'Effect of Surface Roughness on the Central Film Thickness in EHL Contacts,' Proceedings of the Fifth Leeds-Lyon Symposium on Tribology, London, pp. 15-21). However, the roughness orientation effect does not appear to be quantitatively as great as that shown in the work of Patir and Cheng for the same range of h ratio. Keywords: three-dimensional line-contact, mixed elastohydrodynamic lubrication, deterministic modeling, rough surface contact, surface topography, tribology

A thermomechanical analysis of elasto-plastic bodies is a necessary step toward the understanding of tribological behaviors of machine components subjected to both mechanical loading and frictional heating. A three-dimensional thermoelastoplastic contact model for counterformal bodies has been developed, which takes into account steady state heat flux, temperature-dependent strain hardening behavior, and interaction of mechanical and thermal loads. The fast Fourier transform and conjugate gradient method are the underlying numerical algorithms used in this model. Sliding of a half-space over a stationary sphere is simulated with this model. The friction-induced heat is partitioned into two bodies based on surface temperature distributions. In the simulation, the sphere is considered to be fully thermoelastoplastic, while the half-space is treated to be thermoelastic. Simulation results include surface pressure, temperature rise, and subsurface stress and plastic strain fields. The paper also studies the influences of sliding speed and thermal softening on contact behaviors for sliding speed ranging three orders of magnitude. Keywords: elasto-plastic contact, thermal softening, heat partition

Lubricant base oils are often blends of different molecular weight cuts to arrive at a specified ambient pressure viscosity and, to improve the temperature-viscosity behavior or to simply increase the viscosity, viscosity-modifying polymer additives are often added to the base oil. This paper investigates the effect of mixture rheology on elastohydrodynamic lubrication (EHL) film thickness using EHL contact measurements and a full numerical analysis for three synthetic lubricants including two single-component lubricants PAO650 and PAO100 and a mixture of these. The pressure and shear dependences of the viscosity of these lubricants were measured with high-pressure viscometers; viscosities were not adjusted to fit experiment. The point contact film thicknesses for these lubricants in pure rolling were measured using a thin-film colorimetric interferometry apparatus. Numerical simulations based on the measured rheology show very good agreement with the measurements of film thickness while the Newtonian prediction is up to twice the measurement. These results validate the use of realistic shear-thinning and pressure-viscosity models, which originate from viscosity measurements. It is conceivable that simulation may provide a means to 'engineer' lubricants with the optimum balance of film thickness and friction through intelligent mixing of components. Keywords: EHL, elastohydrodynamics, rheology, film thickness, shear thinning, non-Newtonian, viscosity

Accumulative plastic deformation due to repeated loading is crucial to the lives of many mechanical components, such as gears, stamping dies, and rails in rail-wheel contacts. This paper presents a three-dimensional numerical model for simulating the repeated rolling or sliding contact of a rigid sphere over an elasto-plastic half-space. This model is a semi-analytical model based on the discrete convolution and fast Fourier transform algorithm. The half-space behaves either elastic-perfectly plastically or kinematic plastically. The analyses using this model result in histories of stress, strain, residual displacement, and plastic strain volume integral (PV) in the half-space. The model is examined through comparisons of the current results with those from the finite element method for a simple indentation test. The results of rolling contact obtained from four different hardening laws are presented when the load exceeds the theoretical shakedown limit. Shakedown and ratchetting behaviors are discussed in terms of the PV variation. The effect of friction coefficient on material responses to repeated sliding contacts is also investigated. [DOI: 10.1115/1.2755171]

Sliding wear is a significant surface failure mode in many mechanical components. The magnitude of changes in surface topography due to wear may be comparable to or larger than the original surface roughness and elastic deformation. However, wear has rarely been incorporated into the numerical models used as predictive tools in engineering practice. This paper presents a numerical approach to simulate the wear process based on the deterministic mixed elastohydrodynamic lubrication (EHL) model developed and modified by Zhu and Hu (2001, Tribol. Trans., 44, pp. 383-398). It is assumed that wear takes place at locations where the surfaces are in direct contact, and the wear rate at those local contact spots is proportional to the relative sliding speed, the local contact pressure, and inversely proportional to the hardness of the surface. At each simulation cycle, the distributions of lubricant film thickness and contact pressure are calculated by using the mixed EHL model. The material removal at each contact location is evaluated and the surface topography modified correspondingly. The renewed surface topography is then used for the next cycle. The model is formulated such that any mathematically expressed wear law can be implemented, and therefore, the simulation can be applied to a wide variety of engineering applications. [DOI: 10.1115/1.2736439] Keywords: sliding wear, mixed EHL simulation

An elastohydrodynamic lubrication (EHL) model for coated surfaces in point contacts has been developed by combining the elastic deformation formulation for the coated surfaces with an EHL model. Inverse fast Fourier transform (IFFT) is employed first to obtain the influence coefficients (ICs) from the frequency response function (FRF). The subsequent calculation of elastic deformation is performed using the efficient algorithm of discrete convolution and fast Fourier transform (DC-FFT). The coating EHL model is verified by the comparison to available numerical results. The effects of coating on lubrication under various loads, speeds, rheological models, and pressure-viscosity behaviors are numerically investigated. Similar to the observations from dry contact, stiffer coatings in EHL tend to reduce the nominal contact radius but increase the maximum contact pressure, and vice versa for more compliant coatings. However; as coating thickness increases, the influence of coatings on film thickness, including the central and the minimum film thicknesses, does not follow a monotonic variation, and therefore, cannot be predicted by any simple film thickness equation. The reason for that is the pressure viscosity effect which tends to counterbalance the effect of coating. The average friction coefficient in lubricant film increases in stiff coating cases but decreases for compliant coating cases. Furthermore, two possible approaches to improving the minimum film thickness thus reducing friction and wear in mixed lubrication are indicated: a thin stiff coating for conventional EHL and a thick compliant coating for soft EHL. [DOI: 10.1115/1.2736433] Keywords: EHL, coating, FFT

When contact problems are solved by numerical approaches, a surface profile is usually described by a series of discrete nodes with the same intervals along a coordinate axis. Contact computation based on roughness datum mesh may be time consuming. An adaptive-surface elasto-plastic asperity contact model is presented in this paper. Such a model is developed in order to reduce the computing time by removing the surface nodes that have little influence on the contact behavior of rough surfaces. The nodes to be removed are determined by a prescribed threshold. The adaptive-surface asperity contact model is solved by means of the element-free Galerkin-finite element coupling method because of its flexibility in domain discretization and versatility in node arrangements. The effects of different thresholds on contact pressure distribution, real contact area, and elasto-plastic stress fields in contacting bodies are investigated and discussed. The results show that this model can help reduce about 48% computational time when the relative errors are about 5%. [DOI: 10.1115/1.2345418] Keywords: elasto-plastic, contact, adaptive, rough surface, threshold

This paper investigates the effects of differential scheme and mesh density on elastohydrodynamic lubrication (EHL) film thickness based on a full numerical solution with a semi-system approach. The solution variation with different schemes and mesh sizes is revealed based on a set of numerical cases in a wide range of central film thickness from several hundred nanometers down to a few nanometers. It is observed that when the film is thick, the effects of differential schemes and mesh density are not significant. However, if the film becomes ultra-thin, e.g., below 10-20 nanometers, the influence of mesh density and differential schemes becomes more significant, and a proper dense mesh and differential scheme may be highly desirable. The present study also indicates that the solutions from the 1st-order backward scheme give the largest film thickness among all the solutions from different schemes at the same mesh size. [DOI: 10.1115/1.2194916] Keywords: elastohydrodynamic lubrication, thin-film EHL behavior, numerical methods

There has been a long-standing need for a piezoviscous parameter [[alpha].sub.film] that, together with the ambient viscosity [[micro].sub.0], will completely quantify the Newtonian rheology so that the film thickness for liquids that do not shear-thin in the inlet may be calculated as h = h([[micro].sub.0], [[alpha].sub.film], ...), regardless of the details of the pressure-viscosity response. It seems that Blok's reciprocal asymptotic isoviscous pressure has certain advantages over the conventional pressure-viscosity coefficient, which is poorly suited for this purpose. The first detailed review of piezoviscous models for low pressures is provided. A simulation code that is apparently stable for all realistic pressure-viscosity response was utilized with diverse piezoviscous models and model liquids to develop a satisfactory definition of [[alpha].sub.film] that reads [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; 1/[[alpha].sup.*] = [[integral].sup.[infinity].sub.0] [micro](0)dp/[micro](p). In the case of [micro] = [[micro].sub.0] exp ([[alpha]p]), [[alpha].sub.film] = [alpha] and formulas are provided for other models. [DOI: 10.1115/1.2197846] Keywords: pressure-viscosity coefficient, Newtonian, piezoviscous, film thickness, elastohydrodynamics

An elastic adhesive contact model based on the element-free Galerkin-finite element (EFG-FE) coupling method is presented in this paper. The model is first validated though comparison to theoretical solutions. A numerical simulation of the adhesive contact between a microelastic cylinder and a rigid half-space is then conducted. The adhesive contact characteristics of three metals (Al, Cu, and Fe) are studied at different Tabor parameters. The relationships of the applied load and contact half-width of the adhesive contacts are analyzed. Contact pressures, stress contours and deformed profiles of different cylinder sizes and applied loads are illustrated and discussed. The results are compared to published solutions, and good agreements are observed. [DOI: 10.1115/1.2114931] Keywords: adhesive contact, meshless methods

The element-free Galerkin-finite element (EFG-FE) coupling method, combined with the linear mathematical programming technique, is utilized to solve two-dimensional elastoplastic contact problems. Two discretized models for an elastic cylinder contacting with a rigid plane are used to investigate the boundary effects in a contact problem when using the EFG-FE coupling method under symmetric conditions. The influences of the number of Gauss integration points and the size supporting the weight function in the meshless region on the contact pressure and stress distributions are studied and discussed by comparing the numerical results with the theoretical ones. Furthermore, the elasto-plastic contact problems of a smooth cylinder with a plane and a rough surface with a plane are analyzed by means of the EFG-FE method and different elasto-plasticity models. [DOI: 10.1115/1.1843134]

In tribological contact, frictional heating may lead to temperature rise, which in turn may result in thermal displacement of the contacting bodies. The quantification of these effects is desirable in order to more accurately predict wear and failure of contacting surfaces. The change in temperature at a contact area may be attributed to the combined effects of frictional heating and convective cooling. This paper presents a transient, three-dimensional solution for the normal surface displacement of an elastic half-space due to an arbitrarily distributed, moving heat source and surface convection. [DOI: 10.1115/1.1924574]

Engineering practices and analyses have indicated that surface textures and topography may significantly affect the tribological performance of contact interfaces. Such an influence may be complicated and difficult to be captured with only a few statistic surface parameters. The need for further improvement of the performance and life of machine elements requires that surface topography and textures be optimized. The utilization of a numerical tool to determine the basic geometric aspects of surface textures may be named a virtual texturing technology, with which surface optimization may start from patterned surfaces where topography can be precisely quantified and the relationship between textures and lubrication performance can be numerically established. Presented in this paper are the concept of the virtual texturing technology, models involved, and a preliminary exploration of the relationship between a dimpled texture design and the mixed lubrication characteristics for a typical counterformal contact. The dimple influence area and the number of interruption are found to be two key factors for designing dimpled surfaces for counterformal contact lubrication. It is demonstrated that virtual texturing is able to provide comparative information and directions for innovative surface design and optimization. [DOI: 10.1115/1.2000273]

The stress field within machine components is an important indicator for contact failures. Since both thermal stresses due to frictional heating and plasticity are significant in engineering application, it is critical to predict the total stress field. In this work, the steady-state thermal effect is considered and a thermo-elastic--plastic contact model is developed. The model is applicable for rolling and/or sliding contact problem, as far as small equivalent plastic strain hypothesis is respected. Influence coefficients for surface normal displacement, temperature, and strain and stress tensors are used with the discrete convolution and fast Fourier transform algorithm. The single-loop conjugate gradient iteration scheme is also applied to achieve fast convergence speed. Simulations are presented for several academic examples ranging from elastic to thermo-elastic--plastic. The thermo-elastic--plastic analyses show that the heat factor in a contact situation has significant effect not only on the critical Hertzian pressure and on the pressure distribution, but also on the magnitude and depth of the maximum von Mises stress during loading and the residual ones found after unloading. [DOI: 10.1115/1.1843851]

This paper presents a concise boundary integral equation framework for relating the thermal-mechanical surface load (the three traction components and the normal heat flux) to the thermal-mechanical response (the three quasi-static displacement components and the steady-state temperature). This uncoupled thermoelastic framework allows the simultaneous calculation of displacement and temperature--without subsurface discretization--because it is based on classical Green's functions for displacement and for temperature and on newly derived Green's functions for thermoelastic displacement. In general the boundary element method (BEM) can be applied with this framework to finite geometry problems of steady-state thermal-mechanical contact. Here, example calculations are performed for counterformal contact problems, which can be modeled as contact on a halfspace. A linear element BEM is developed and compared with the constant element BEM for speed and accuracy. The linear element BEM uses newly derived influence coefficients for constant loads over an arbitrary triangular element, and these closed form expressions are used to improve the accuracy of the numerical algorithm. The constant element BEM uses the discrete convolution fast Fourier transform (DC-FFT) algorithm, which is based on influence coefficients for constant loads over rectangular elements. The quasi-static surface displacements and the steady-state surface temperature are calculated from an applied semi-ellipsoidal pressure with accompanying frictional heating effects. The surface thermal-mechanical behavior of the counterformal contact is shown in graphs vs. the radius, and the deviations from axisymmetry are highlighted. [DOI: 10.1115/1.1757492]

This paper presents an improvement of a simplified approach, namely, the macro-micro approach, used to model the mixed elastohydrodynamic lubrication problems in counter-formal contacts, and its comparison with Zhu and Hu's full-scale mixed-EHL model. In this approach, Patir and Cheng's average flow model is employed to obtain the distribution of piecewise average pressure. A contact-embedment method that incorporates the detail of asperity contact pressure into the overall pressure distribution is utilized to reveal the severity of surface interaction. Numerical experiments are conducted, and the results are compared with those obtained by means of the full-scale mixed-EHL. The regime of the application of this macro-micro approach is explored. [DOI: 10.1115/1.1631017]

A mixed lubrication model is developed to investigate the lubrication of coupled journal-thrust-bearing systems. The governing equations are mapped into a computational domain with a conformal mapping technique developed in a previous study by Wang et al. (2002). In order to study the influence of the boundary conditions on the performance of the bearing system, either the Reynolds boundary conditions or the JFO's mass conserving conditions are applied to the governing Reynolds equations. The performance of a typical coupled journal-thrust bearing system is numerically investigated and the effects of viscosity, misalignment angle and feeding scheme are discussed. [DOI: 10.1115/1.1574519]

The Stribeck curve is an important means to demonstrate the frictional behavior of a lubricated interface during the entire transition from boundary and mixed to full-film lubrication. In the present study, a new test apparatus has been built that can operate under rolling-sliding conditions at a continuously variable speed in an extremely wide range, approximately from 0.00006 to 60 m/s, covering six orders of magnitude. Hence, a complete Stribeck curve can be measured to reveal its basic characteristics for lubricated counterformal contacts. The measured curves are compared with numerical simulation results obtained from an available unified mixed elastohydrodynamic lubrication (EHL) model that is also capable of handling cases during the entire transition. A modified empirical model for the limiting shear stress of lubricant is obtained, and a good agreement between the measured and calculated Stribeck curves is achieved for the tested base oils in all the three lubrication regimes, which thus well validates the simulation methods employed. Both the experimental and numerical results indicate that the Stribeck curves for counterformal contact interfaces behave differently from those for conformal contacts. When the rolling speed increases at a fixed slide-to-roll ratio, the friction continuously decreases even in the full-film lubrication regime due to the reduction of the lubricant limiting shear stress caused mainly by the rise of the surface flash temperature. In addition, the test results indicate that the boundary additives in a commodity lubricant may have considerable influence on the boundary lubrication friction but that on the friction in the mixed and full-film lubrication appears to be limited. [ABSTRACT FROM AUTHOR]

Steady-state mixed hydrodynamic lubrication of rigid journal bearing is investigated by using a finite difference form of the Patir-Cheng average Reynolds equation under the Reynolds boundary condition. Two sets of discretization meshes. the rectangular and nonorthogonal herringbone meshes, are considered. A virtual-mesli approach is suggested to resolve the problem due to the singularities of pressure derivatives at the turning point of the herringbone mesh. The effectiveness of the new approach is examined by comparing the predicted load with that found in the literature for a smooth-surface case solved in the conventional rectangular mesh. The effects of the skewness angles of symmetric and asymmetric herringbone meshes on the predicted parameters, such as load, friction coefficient, attitude angle, and maximum pressure, are investigated for smooth, rough, and herringbone-grooved bearing surfaces. It is found that the new approach helps to improve the computational accuracy significantly, as demonstrated by comparing the results with and without the treatment of the pressure derivative discontinuity although the latter costs slightly less computational time. [ABSTRACT FROM AUTHOR]

The "Stribeck curve" is a well-known concept, describing the frictional behavior of a lubricated inteiface during the transition from boundary and mixed lubrication up to full-film hydrodynamic!elastohydrodynamic lubrication. It can be found in nearly every tribology textbook!handbook and many articles and technical papers. However, the majority of the published Stribeck curves are only conceptual without real data from either experiments or numerical solutions. The limited number of published ones with real data is often incomplete, covering only a portion of the entire transition. This is because generating a complete Stribeck curve requires experimental or numerical results in an extremely wide range of operating conditions, which has been a great challenge. Also, numerically calculating a Stribeck cun'e requires a unified model with robust algorithms that is capable of handling the entire spectrum of lubrication status. In the present study, numerical solutions in counterformal contacts of rough surfaces are obtained by using the unified deterministic mixed elastohydrodynamic lubrication (EHL) model recently developed. Stribeck curves are plotted in a wide range of speed and lubricant film thickness based on the simulation results with various types of contact geometry using machined rough surfaces of different orientations. Surface flash temperature is also analyzed during the friction calculation considering the mutual dependence between friction and interfacial temperature. Obtained results show that in lubricated concentrated contacts, friction continuously decreases as speed and film thickness increase even in the full-film regime until extremely high speeds are reached. This is mainly due to the reduction of lubricant limiting shear stress caused by flash temperature rise. The results also reveal that contact ellipticity and roughness orientation have limited influence on frictional behaviors, especially in the full-film and boundary lubrication regimes. [ABSTRACT FROM AUTHOR]

This paper presents a novel method to compute the lubricant pressure distribution between a rough and a smooth surface in relative motion. The originality of this method is to combine a deterministic approach for the large scales and a stochastic model for the small scales of the problem. Ai a result, the new method allows a significant mesh reduction while maintaining an accurate prediction of the generated load. [ABSTRACT FROM AUTHOR]

Effect of roughness orientation on lubricant film thickness has been an important issue of surface design, attracting much attention since the 1970s. A systematical study, however, is still needed for various contact types in an extended range of operating conditions, especially in mixed lubrication cases with film thickness to roughness ratio (λ ratio) smaller than 0.5. The present study employs a deterministic mixed elastohydrodynamic lubrication (EHL) model to investigate the performance of lubricating films in different types of contact geometry, including the line contact, circular contact, and elliptical contacts of various ellipticity ratios. The speed range for analyzed cases covers 11 orders of magnitude so that the entire transition from full-film and mixed EHL down to dry contact (corresponding λ ratio from about 3.5 down to 0.001 or so) is simulated. Three types of machined surfaces are used, representing transverse, longitudinal, and isotropic roughness, respectively. The line contact results are compared with those from the stochastic models by Patir and Cheng ("Effect of Surface Roughness Orientation on the Central Film Thickness in EHD Contacts," Proc. 5th Leeds-Lyon Symp. on Tribol., 1978, pp. 15-21) and the influence of roughness orientation predicted by the deterministic model is found to be less significant than that by the stochastic models, although the basic trends are about the same when λ>0.5. The orientation effect for circular or elliptical contact problems appears to be more complicated than that for line contacts due to the existence of significant lateral flows. In circular contacts, or elliptical contacts with the ellipticity ratio smaller than one, the longitudinal roughness may become more favorable than the isotropic and transverse. Overall, the orientation effect is significant in the mixed EHL regime where theXratio is roughly in the range from 0.05 to 1.0. It is relatively insignificant for both the full-film EHL (λ > 1.2 or so) and the boundary lubrication/dry contact (λ < 0.025 ∼ 0.05). [ABSTRACT FROM AUTHOR]

Steady-state smooth surface hydrodynamic lubrications of a pocketed pad bearing, an angularly grooved thrust bearing, and a plain journal bearing are simulated with the mass-conservation model proposed by Payvar and Salant. Three different finite difference schemes, i.e., the harmonic mean scheme, arithmetic mean scheme, and middle point scheme, of the interfacial diffusion coefficients for the Poiseuille terms are investigated by using a uniform and nonuniform set of meshes. The research suggests that for the problems with continuous film thickness and pressure distributions, the results obtained with these numerical schemes generally well agree with those found in the literatures. However, if the film thickness is discontinuous while the pressure is continuous, there may be an obvious deviation. Compared with both the analytical solution and other two schemes, the harmonic mean scheme may overestimate or underestimate the pressure. In order to overcome this problem artificial nodes should be inserted along the wall of the bearings where discontinuous film thickness appears. Moreover, the computation effi-ciency of the three solvers, i.e., the direct solver, the line-by-line the tridiagonal matrix algorithm (TDMA) solver, and the global successive over-relaxation (SOR) solver, are investigated. The results indicate that the direct solver has the best computational effi-ciency for a small-scale lubrication problem (around 40 thousand nodes). TDMA solver is more robust and requires the least storage, but the SOR solver may work faster than TDMA solver for thrust bearing lubrication problems. Numerical simulations of a group of grooved thrust bearings were conducted for the cases of different outer and inner radii, groove depth and width, velocity, viscosity, and reference film thickness. A curve fitting formula has been obtained from the numerical results to express the correlation of load, maximum pressure, and friction of an angularly grooved thrust bearing in lubrication. [ABSTRACT FROM AUTHOR]

Contact of viscoelastic materials with complicated properties and surface topography require numerical solution approaches. This paper presents a 3-D senuanalytical contact model for viscoelastic materials. With the hereditary integral operator and elastic-viscoelastic correspondence principle, surface displacement is expressed in terms of viscoelastic creep compliance and contact pressure distribution history in the course of a contact process. Through discretizing the contact equations in both spatial and temporal dimensions, a numerical algorithm based on the robust Conjugate Gradient method and Fast Fourier transform has been developed to solve the normal approach, contact pressure, and real contact area simultaneously. The transient contact analysis in the time domain is computationally expensive. The fast Fourier transform algorithm can help reduce the computation cost significantly. The comparisons of the new numerical results with an analytical viscoelastic contact solution for Maxwell materials and with an indentation test measurement reported in the literature has validated and demonstrated the accuracy of the proposed model. Moreover, the present model has been used to simulate the contact between a polymethyl methaciylate (PMMA) substrate and a rigid sphere driven by step, ramped, and harmonic normal loads. The validated model and numerical method can successfully compute the viiscoelastic contact responses of polymer-based materials with time-dependent properties and surface roughness subjected to complicated loading profiles. [ABSTRACT FROM AUTHOR]

Elastohvdrodvnaniic Lubrication (EHL) is commonly known as a mode of fluid-film lubrication in which the mechanism of hydrodynamic film formation is enhanced by surface elastic deformation and lubricant viscosity increase due to high pressure. It has been an active and challenging field of research since the 1950s. Significant breakthroughs achieved in the last 10-15 years are largely in the area of mixed EHL, in which surface asperity contact and hydrodynamic lubricant film coexist. Mixed EHL is of the utmost importance not only because most power-transmitting components operate in this regime, hut also due to its theoretical universality that dry contact and full-film lubrication are in fact its special cases under extreme conditions. In principle, mixed EHL has included the basic physical elements for modeling contact, or hydrodynamic lubrication, or both together. The unified mixed lubrication models that have recently been developed are now capable of simulating the entire transition of interfacial status from full-film and mixed lubrication down to dry contact with an integrated mathematic formulation and numerical approach. This has indeed bridged the two branches of engineering science, contact mechanics, and hydrodynamic lubrication theory, which hare been traditionally separate since the 1880s mainly due to the lack of powerful analytical and numerical tools. The recent advancement in mixed EHL begins to bring contact and lubrication together, and tlnis an evolving concept of "Interfacial Mechanics" can be proposed in order to describe interfacial phenomena more precisely and collaborate with research in other related fields, such as interfacial physics and chemistry, more closely. This review paper briefly presents snapshots of the history of EHL research. and also expresses the authors' opinions about its further development as a gateway to interfacial mechanics. [ABSTRACT FROM AUTHOR]

Elastohydrodynamic lubrication (EHL) is an important branch of the lubrication theory, describing lubrication mechanisms in nonconformal contacts widely found in many mechanical components such as various gears, rolling bearings, cams and followers, metal-rolling tools, traction drives, and continuous variable transmissions. These components often transmit substantial power under heavy loading conditions. Also, the roughness of machined surfaces is usually of the same order of magnitude as, or greater than, the estimated average EHL film thickness. Consequently, most components operate in mixed lubrication regime with significant asperity contacts. Due to very high pressure concentrated in small areas, resulted from either heavy external loading or severe asperity contacts, or often a combination of both, subsurface stresses may exceed the material yield limit, causing considerable plastic deformation, which may not only permanently change the surface profiles and contact geometry but also alter material properties through work hardening as well. In the present study, a three-dimensional plastoelastohydrodynamic lubrication (PEHL) model has been developed by taking into account plastic deformation and material work-hardening. The effects of surface/subsurface plastic deformation on lubricant film thickness, surface pressure distribution, and subsurface stress field have been investigated. This paper briefly describes the newly developed PEHL model and presents preliminary results and observed basic behavior of the PEHL in smooth-surface point contacts, in comparison with those from corresponding EHL solutions under the same conditions. The results indicate that plastic deformation may greatly affect contact and lubrication characteristics, resulting in significant reductions in lubricant film thickness, peak surface pressure and maximum subsurface stresses. [ABSTRACT FROM AUTHOR]

The average flow model proposed by Patir and Cheng offers a great convenience for the analysis of rough surfaces in lubrication. The contact factor introduced by Wu and Zheng helps to solve a difficulty in local film evaluation using the average flow model This paper reports a simple method to calculate the contact factor Method validation is demonstrated by the comparison of the contact factors for Gaussian surfaces obtained with the present method and the fitting formula of Wu and Zheng. The proposed method cannot only easily compute the contact factor values for Gaussian surfaces; it can also be used for those of non-Gaussian and measured surfaces, especially those with unknown probability density distribution of the roughness height. [ABSTRACT FROM AUTHOR]

This paper discussed the computational accuracy of rough-surface point-contact isothermal elastohydrodynamic lubrication (EHL) analysis by investigating the effects of differential scheme, viscosity-pressure, and shear-thinning models. An EHL experiment with multitransverse ridges was employed as simulated target. Four differential schemes, including the combined and the separate first-order and second-order backward schemes, were investigated. It is found that the separate second-order backward scheme offers the best results based on the comparison with the experimental data, with which two roughness derivatives may be fully or partially canceled each other; thus, the discretization error induced by roughness can be reduced. The consistency of differential schemes is an important issue for the separate schemes. The Yasutomi free-volume viscosity-pressure model and the Eyring rheological model are found to yield the numerical simulations the closest to experimental results. [ABSTRACT FROM AUTHOR]

Surface pitting due to contact fatigue is a major failure mode of many mechanical components, such its various gears and rolling-element bearings. Pitting life prediction, therefore, is vital to design and performance/reliability improvements. Conventional prediction methods, commonly found in industrial standards, are based on the Hertzian contact theory under the assumptions that surfaces are ideally smooth with no lubrication. Today, the trend of high power density, high reliability compact design requires the life prediction to consider severe operation conditions in mixed lubrication, and the effect of surface roughness and topography. Also, it has been well known that ductile material failures in concentrated contacts are better correlated with the subsurface von Mises stress, rather than the normal Hertzian pressure. The present study aims to develop a pitting life prediction approach for line-contact "components based on a 3D line-contact mixed elastohydrodynamic lubrication (EHL) model recently developed by Ren et al. (2009, "A Three-Dimensional Deterministic Model for Rough Surface Line-Contact EHL Problems," ASME J. Tribol., 131, p. 011501), which is capable of simulating the entire transition from full-film and mixed EHL down to dry contact of real machined rough surfaces under severe operating conditions. The pitting life evaluation employs the fatigue life model developed by Zaretsky (1987, "Fatigue Criterion to System Design, Life and Reliability," J. Propul. Power, 3(1), pp. 76-83) and extended by Epstein et al. (2003, "Effect of Surface Topography on Contact Fatigue in Mixed Lubrication,". Tribol. Trans., 46, pp. 506-513) using the yon Mises stress field calculated based on the rough surface mixed-EHL results. Sample cases are analyzed for 15 sets of transmission gears, and the life prediction results are compared with available experimental data. With optimized material constants in the life model, predicted pitting life results well agree with the test data. [ABSTRACT FROM AUTHOR]

This paper reports the development of a novel three-dimensional (3D) deterministic model (3D L-EHL) for rough surface line-contact mixed-elastohydrodynamic lubrication (EHL) problems. This model is highly demanded because line contacts are found between many mechanical components, such as various gears, roller and needle bearings, cams and followers, and work rolls and backup rolls in metal-forming equipment. The macro aspects of a line-contact problem can be simplified into a two-dimensional (2D) model; however, the topography of contacting rough surfaces, microasperity contacts, and lubricant flows around asperities are often three-dimensional. The present model is based on Hu and Zhu's unified 3D mixed-EHL model (Hu and Zhu, 2000, "Full Numerical Solution to the Mixed Lubrication in Point Contacts," ASME J. Tribol., 122(1), pp. 1-9) originally developed for point contacts and the mixed fast Fourier transform (FFT)-based approach for deformation calculation formulated by Chen et al. (2008, "Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts With Normally Flat Surface," ASME J. Appl. Mech., 75(1), 011022-1-11). It is numerically verified through comparisons with results from the line-contact Hertzian theory and the conventional 2D line-contact smooth-surface EHL formulas. Numerical examples involving 3D sinusoidal and digitized machined surfaces are also analyzed. Sample cases indicate that transverse roughness may yield greater film thickness than longitudinal roughness. This observation is qualitatively in agreement with the trend predicted by Patir and Cheng's stochastic model (1978, "Effect of Surface Roughness on the Central Film Thickness in EHL Contacts," Proceedings of the Fifth Leeds-Lyon Symposium on Tribology, London, pp. 15-21). However, the roughness orientation effect does not appear to be quantitatively as great as that shown in the work of Patir and Cheng for the same range of λ ratio. [ABSTRACT FROM AUTHOR]

Coatings are widely used for interface performance enhancement and component life improvement, as well as for corrosion prevention and surface decoration. More and more mechanical components, especially those working under severe conditions, are coated with stiff (hard) thin coatings. However, the effects of coatings on lubrication characteristics, such as film thickness and friction, have not been well understood, and designing coating for optimal tribological performance is a grand challenge. In this paper, the influences of coating material properties and coating thickness on lubricant film thickness are investigated based on a point-contact isothermal elastohydrodynamic lubrication (EHL) model developed recently by the authors. The results present the trend of minimum film thickness variation as a function of coating thickness and elastic modulus under a wide range of working conditions. Curve fitting of numerical results indicates that the maximum increase in minimum film thickness, Imax, and the corresponding optimal dimensionless coating thickness, H2max, can be expressed in the following forms: Imax =0.769M0.0238R20.0297L0.1376 exp(-0.0243 ln² L) and H2max =0.049M0.4557R2-0.1722L0.7611 exp(-0.0504 ln² M -0.0921 ln² L). These formulas can be used to estimate the effect of coatings on film thickness for EHL applications. [ABSTRACT FROM AUTHOR]

Lubricant base oils are often blends of different molecular weight cuts to arrive at a specified ambient pressure viscosity and, to improve the temperature-viscosity behavior or to simply increase the viscosity, viscosity-modifying polymer additives are often added to the base oil. This paper investigates the effect of mixture rheology on elastohydrodynamic lubrication (EHL) film thickness using EHL contact measurements and a full numerical analysis for three synthetic lubricants including two single-component lubricants PA0650 and PAOIO0 and a mixture of these. The pressure and shear dependences of the viscosity of these lubricants were measured with high-pressure viscometers; viscosities were not adjusted to fit experiment. The point contact film thicknesses for these lubricants in pure rolling were measured using a thin-fihn colorimetric interferometry apparatus. Numerical simulations based on the measured rheology show very good agreement with the measurements of film thickness while the Newtonian prediction is up to twice the measurement. These results validate the use of realistic shear-thinning and pressure-viscosity models, which originate from viscosity measurements. It is conceivable that simulation may provide a means to "engineer", lubricants with the optimum balance of film thickness and friction through intelligent mixing of components. [ABSTRACT FROM AUTHOR]

Sliding wear is a significant surface failure mode in many mechanical components. The magnitude of changes in surface topography due to wear may be comparable to or larger than the original surface roughness and elastic deformation. However, wear has rarely been incorporated into the numerical models used as predictive tools in engineering practice. This paper presents a numerical approach to simulate the wear process based on the deterministic mixed elastohydrodynamic lubrication (EHL) model developed and modified by Zhu and Hu (2001, Tribol. Trans., 44, pp. 383-398). It is assumed that wear takes place at locations where the surfaces are in direct contact, and the wear rate at those local contact spots is proportional to the relative sliding speed, the local contact pressure, and inversely proportional to the hardness of the surface. At each simulation cycle, the distributions of lubricant film thickness and contact pressure are calculated by using the mixed EHL model. The material removal at each contact location is evaluated and the surface topography modified correspondingly. The renewed surface topography is then used for the next cycle. The model is formulated such that any mathematically expressed wear law can be implemented, and therefore, the simulation can be applied to a wide variety of engineering application. [ABSTRACT FROM AUTHOR]

An elastohydrodynamic lubrication (EHL) model for coated surfaces in point contacts has been developed by combining the elastic deformation formulation for the coated surfaces with an EHL model. Inverse fast Fourier transform (IFFT) is employed first to obtain the influence coefficients (ICs) from the frequency response function (FRF). The subsequent calculation of elastic deformation is performed using the efficient algorithm of discrete convolution and fast Fourier transform (DC-FFT). The coating EHL model is verified by the comparison to available numerical results. The effects of coating on lubrication under various loads, speeds, rheological models, and pressure-viscosity behaviors are numerically investigated. Similar to the observations from dry contact, stiffer coatings in EHL tend to reduce the nominal contact radius but increase the maximum contact pressure, and vice versa for more compliant coatings. However, as coating thickness increases, the influence of coatings on film thickness, including the central and the minimum film thicknesses, does not follow a monotonic variation, and therefore, cannot be predicted by any simple film thickness equation. The reason for that is the pressure viscosity effect which tends to counterbalance the effect of coating. The average friction coefficient in lubricant film increases in stiff coating cases but decreases for compliant coating cases. Furthermore, two possible approaches to improving the minimum film thickness thus reducing friction and wear in mixed lubrication are indicated: a thin stiff coating for conventional EHL and a thick compliant coating for soft EHL. [ABSTRACT FROM AUTHOR]

This paper presents a three-dimensional numerical elasto-plastic model for the contact of nominally fiat surfaces based on the periodic expandability of surface topography. This model is built on two algorithms: the continuous convolution and Fourier transform (CC-FT) and discrete convolution and fast Fourier transform (DC-FFT), modified with duplicated padding. This model considers the effect of asperity interactions and gives a detailed description of subsurface stress and strain fields caused by the contact of elasto-plastic solids with rough surfaces. Formulas of the frequency response functions (FRF) for elastic/plastic stresses and residual displacement are given in this paper. The model is verified by comparing the numerical results to several analytical solutions. The model is utilized to simulate the contacts involving a two-dimensional wavy surface and an engineering rough surface in order to examine its capability of evaluating the elasto-plastic contact behaviors of nominally flat surfaces. [ABSTRACT FROM AUTHOR]