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In this study, a numerical model is developed for the analysis of elastohydrodynamic lubrication (EHL) at transient conditions during startup and shutdown processes. The time-dependent solutions are derived from an iterative algorithm with surface roughness involved, and the initial value is specified as the solution of the dry contact for the startup or steady-state solution of the lubrication contact at the starting velocity for the shutdown. The technique of discrete convolution and fast Fourier transform (DC-FFT) is employed to improve the computational efficiency. Solutions for smooth surfaces are compared with those obtained numerically and experimentally, and good consistency can be found. Profiles of pressure and film thickness and contours of subsurface stresses are analyzed to reveal the effects of acceleration/deceleration on the lubrication evolution. An isotropic roughness is then taken into account for the analysis. It is concluded that the coupling effects of the lubricant cavitation and oriented roughness would result in complex profiles of pressure and film thickness due to their disturbances to the lubrication film. A machined rough surface is presented to demonstrate the generality of the model. The analysis may potentially provide guidance to estimate the behavior of mechanical elements. [ABSTRACT FROM AUTHOR]

This study investigates the effects of the microdimple texture on the friction and surface temperature performances of a ball-on-disk contact, operating under the speed and load ranges that cover typical gearing applications. Circular-shaped microdimple arrays with different dimple center distances and dimple depths are implemented on the ball surface to quantify the impacts of these two parameters on the friction coefficient and the maximum ball surface temperature. In addition, the contacts of three surface texture combinations, namely microdimpled and polished ball surface versus polished disk surface, polished ball surface versus polished disk surface, and ground ball surface versus ground disk surface, are compared to demonstrate any beneficial or detrimental effect of microdimples in heavily loaded high-speed applications. This study adopts a thermal mixed EHL point contact model, whose capability and accuracy have been well demonstrated by comparing to the experimental measurements, to quantify the deterministic tribological behavior within the contact, allowing the exploration of the underlying mechanism that governs the role of microdimples in the elastohydrodynamic lubrication (EHL). [ABSTRACT FROM AUTHOR]

Soft elastohydrodynamic lubrication (soft-EHL) is an important mechanism in biotribological systems. The soft-EHL has some distinct differences from the traditional hard-EHL, and a systematic analysis factoring in key features of the “softness” appears to be lacking. In this paper, a complete soft-EHL line-contact model is developed. In the model, the half-space approximation is replaced by the finite thickness analysis; the geometrical and material nonlinearity due to finite deformation is factored in; the surface velocities altered by the curvature effect are considered, and the load balance equation is formulated based on the deformed configuration. Solutions are obtained using a finite element method (FEM). The film thickness, pressure distributions, and material deformation are analyzed and discussed under various entraining velocities, elastic modulus, and material thickness of the soft layer. Comparisons are made between soft-EHL and hard-EHL modeling assumptions. The analyses show that the classical EHL modeling is not suitable for soft materials with high loads. The results show that the finite deformation (Green strain) should be considered in soft-EHL analysis. In the contact region, the hard EHL solver overestimates the pressure distribution and underestimates the film thickness and deformation. [ABSTRACT FROM AUTHOR]

The paper deals with an experimental study of an elastohydrodynamic contact under insufficient lubricant supply. Theoretical studies published in this research area focus mainly on the development of theoretical models, and there is a lack of experimental validation of the theoretical models. This paper presents original experimental results and aims to describe the starvation severity level as a function of the inlet film thickness and contact geometry. Experimental data are compared with an analytical model for point contacts published by Chevalier. The study was also extended to elliptical contacts to achieve a comparison with the different parameters of the side-flow resistance used by Damiens. Both models agree well with the experiments. [ABSTRACT FROM AUTHOR]

Transient thermal elastohydrodynamic lubrication (EHL) line contact simulations are carried out to study the traction behavior during accelerated motion considering realistic shear-thinning behavior. Using three lubricants with different inlet viscosity and shear-thinning parameters, the application of present analysis for lubricant selection is demonstrated. Owing to squeeze film action, the film evolution is delayed, and EHL traction during acceleration is found to increase much above the designed value. This effect decreases with increasing starting speed. The most shear-thinning test oil considered here yields the lowest traction coefficient with minimum variation in its value desirable for smooth and vibration-free operation. [ABSTRACT FROM AUTHOR]

This work presents an exact and general model order reduction (MOR) technique for a fast finite element resolution of elastohydrodynamic lubrication (EHL) problems. The reduction technique is based on the static condensation principle. As such, it is exact and it preserves the generality of the solution scheme while reducing the size of its corresponding model and, consequently, the associated computational overhead. The technique is complemented with a splitting algorithm to alleviate the hurdle of solving an arising semidense matrix system. The proposed reduced model offers computational time speed-ups compared to the full model ranging between a factor of at least three and at best 15 depending on operating conditions. The results also reveal the robustness of the proposed methodology which allows the resolution of very highly loaded contacts with Hertzian pressures reaching several GPa. Such cases are known to be a numerical challenge in the EHL literature. [ABSTRACT FROM AUTHOR]

This paper investigates coupling strategies for finite element modeling (FEM) of thermal elastohydrodynamic lubrication (TEHL) problems. The TEHL problem involves a strong coupling between several physics: solid mechanics, fluid mechanics, and heat transfer. Customarily, this problem is split into two parts (elastohydrodynamic (EHD) and thermal) and the two problems are solved separately while an iterative procedure is established between their respective solutions. This weak coupling strategy involves a loss of information, as each problem is not made intimately aware of the evolution of the other problem s solution during the resolution procedure. This typically leads tc slow convergence rates. The current work offers a full coupling strategy for the TEHL problem, i.e., both the EHD and thermal parts are solved simultaneously in a monolithic system. The system of equations is generated from a finite element discretization of the governing field variables: hydrodynamic pressure, solids elastic deformation, and temperature. The full coupling strategy prevents any loss of information during the resolution procedure leading to very fast convergence rates (solution is attained within a few iterations only). The performance of the full coupling strategy is compared to that of different weak coupling strategies. Out of simplicity, only steady-state line contacts are considered in this work. Nevertheless, the proposed methodology, results, and findings are of a general nature and may be extrapolated to circular or elliptical contacts under steady-stare or transient conditions. [ABSTRACT FROM AUTHOR]

Ball piston is an essential design element in eccentric ball piston pump. The objective of this paper is to investigate the dynamic force and lubrication characteristics of the ball piston. In this study, a tribodynamic model of the ball piston is proposed. The model couples the elastohydrodynamic lubrication model of ball-ring pair and the elastohydrodynamic model of ball-cylinder pair with the dynamic model of the ball piston. The interaction between tribological behavior and dynamic performance and the effects of centrifugation and structural deformation of the ball piston are considered. The pressure distributions and film profiles of the ball-ring pair and ball-cylinder pair are calculated. The dynamic normal contact forces and friction forces are analyzed. The friction torque loss and mechanical efficiency of the whole pump are obtained by combing the tribodynamic model of the ball piston with a simplified friction torque model of cylinder-valve shaft pair. A test bench is established for validating the simulation resu'ts. The results show that the normal contact force of the ball-ring pair waves in each stroke, and in discharge stroke, the contact force is much bigger than that in suction stoke because of loading force, while the friction force changes very little for the ball sliding in the outer ring. Comparing with the average friction force of the ball-ring pair, the average friction force of the ball-cylinder pair is small, which reflects that the ball-ring pair is more prone to wear. For the ball-ring friction pair, when the load increases, the secondary contact pressure peak appears, the profile of film presents a horseshoe shape, and the classical shrinkage appears at the outlet of contact region. For the ball-cylinder pair, the film pits and the contact pressure jumps at the entrance of contact region for the heavy load and the high shear stain of film. In addition, the friction torque presents a nonlinear growth trend with the increasing working pressure. [ABSTRACT FROM AUTHOR]

A thermal elastohydrodynamic lubrication (TEHL) model is developed for a coated spur gear pair to investigate the effect of soft coatings and hard coatings on the tribological behavior of such a gear pair during meshing. The coating properties, i.e., the ratio of the Young's modulus between the coating and the substrate, and the coating thickness, are represented in the calculation of the elastic deformation. Discrete convolution, fast Fourier transform (DC-FFT) is utilized for the fast calculation of the surface deformation. The variation of the radius of curvature, the rolling speed, the slide-to-roll ratio, and the tooth load along the line of action (LOA) during meshing is taken into account and the transient squeeze effect is considered in the Reynolds equation. Energy equations of the solids and the oil film are derived. The temperature field and the pressure field are solved iteratively. The tribological behavior is evaluated in terms of the minimum film thickness, the maximum pressure, the temperature rise, the coefficient of friction, and the frictional power loss of the tooth contact during meshing. The results show discrepancies between the soft coating results and hard coating results. [ABSTRACT FROM AUTHOR]

The behavior of roughness features under rolling-sliding inside highly loaded elastohydrodynamically lubricated (EHL) contacts is studied in detail for many years now. In particular, the roughness deformation was subject to different theoretical analyses as well as experiments. A recent experimental work developed by Šperka et al. (2016, "Experimental Study of Roughness Effects in a Rolling-Sliding EHL Contact--Part I: Roughness Deformation," Tribol. Trans., 59(2), pp. 267-276) studied the effect of kinematic operating conditions (mean velocity and slide to roll ratio) on the deformed profile of a ridge. The current paper presents results of full numerical simulations and their direct comparison to experiments in order to study the dependency of roughness deformation on the operating conditions. The assumption of non-Newtonian lubricant behavior seems to have a significant influence on the results as well. Results indicate that, in agreement with experiments, the variation of mean velocity causes changes in the deformed profiles of roughness while, on the other hand, the magnitude of slide to roll ratio (for sliding larger than ±50%) does not have influence on the size of the deformation. [ABSTRACT FROM AUTHOR]

Elastohydrodynamic lubrication (EHL) analysis in finite line contacts is usually modeled by a finite-length roller contacting with a half-space, which ignores effect of the two free boundaries existing in many applications such as gears or roller bearings. This paper presents a semi-analytical method, involving the overlapping method and matrix formation, for EHL analysis in the finite line contact problem to consider the effect of two free end surfaces. Three half-spaces with mirrored loads to be solved are overlapped to cancel out the stresses at expected surfaces, and three matrices can be obtained and reused for the same finite-length space. The isothermal Reynolds equation is solved to obtain the pressure distribution and the fast Fourier transform (FFT) is used to speed up the elastic deformation and stress related calculation. Different line contact situations, including straight rollers, tapered rollers, and Lundberg profile rollers, are discussed to explore the effect of free end surfaces. [ABSTRACT FROM AUTHOR]

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]

In contacts of functionally graded elastic solids, the conditions produced are significantly different from the ones in similar contacts of homogeneous elastic materials. Especially it is true for heavily loaded lubricated contacts. The situation is even more diverse due to different dependences of the material elastic parameters on material depth. In the previous papers, the cases of lubricated contacts with coatings made of homogeneous materials are considered using asymptotic and semi-analytical methods. The goal of the paper is to determine the behavior of the coating effectiveness criteria in heavily loaded elastohydrodynamically lubricated (EHL) contacts for coatings with elastic modulus varying linearly and exponentially across the coating thickness as well as to compare the results with the case of coatings made of homogeneous materials. The above criteria include the criteria on the lubrication film thickness and friction force. The approach used for analyzing the influence of functionally graded elastic materials on parameters of heavily loaded line EHL contacts is based on the asymptotic methods earlier developed by the authors. The analysis is based on splitting the problem into two distinct parts: the problem for dry (nonlubricated) contacts and a problem for lubricated contacts. The bridge between the two problems is the asymptotic behavior of pressure in the vicinity of the end points of the contacts. More specifically, in the central part of the contact the solution of the EHL problem for functionally graded materials is close to the one for the dry contact of these materials while in the narrow zones near the inlet and exit points of the contact the lubrication effects become comparable to the effects due to the elasticity of the solids. This approach to the EHL problem solution reveals its structure. [ABSTRACT FROM AUTHOR]

This work investigates the sensitivity of the surface roughness lubricant life adjustment factor for rolling-element bearings to variations in measured roughness. Roughness measurement results using different values of stylus tip dimension and short wavelength cutoff filter were obtained for several bearing raceway surfaces and used as the inputs for a lubricant life adjustment factor based on the lambda ratio-the ratio of elastohydrodynamic lubrication (EHL) film thickness to the composite surface roughness. The effect on predicted bearing life is shown to be significant. As one means of verification of surface roughness measurements, an ISO type D random!repeating precision roughness specimen was also investigated and shown to have excellent sensitivity to stylus tip dimension, demonstrating its effectiveness as a tool for assessment of stylus radius and condition. [ABSTRACT FROM AUTHOR]

The experimental observation of the inlet dimple of the elastohydrodynamic lubrication (EHL)film was carried out in point and elliptical contacts, respectively, and then, the numerical analysis under point contacts was conducted. The inlet dimple appears and then moves upstream toward the inlet and finally disappears with the increase of the entrainment speed. In the meantime, the dimple depth increases at the beginning and then decreases. The high load leads to a wide entrainment speed range where dimple exists. The varying range of the entrainment speed corresponding to the dimple appearance is smaller at a smaller included angle between the minor axis of elliptical contact and the entrainment direction. [ABSTRACT FROM AUTHOR]

Surface plastic deformation due to contact (lubricated or dry) widely exists in many mechanical components, as subsuiface stress caused by high-pressure concentrated in the contact zone often exceeds the material yielding limit, and the plastic strain accumulates when the load is increased and/or repeatedly applied to the swface in a rolling contact. However, previous plasto-elastohydrodynamic lubrication (PEHL) studies were mainly for the preliminary case of having a rigid ball (or roller) rotating on a stationary elastic-plastic flat with a fixed contact center, for which the numerical simulation is relatively simple. This paper presents an efficient method for simulating PEHL in a rolling contact. The von Mises yield criteria are used for determining the plastic zone, and the total computation domain is discretized into a number of cuboidal elements underneath the contacting swface, each one is considered as a cuboid with uniform plastic strain inside. The residual stress and sutface plastic deformation resulted from the plastic strain can be solved as a half-space eigenstrain-eigenstress problem. A combination of threedimensional (3D) and two-dimensional (2D) discrete convolution and fast Fourier transform (DC-FFT) techniques is used for accelerating the computation. It is observed that if a rigid ball rolls on an elastic-plastic swface. the characteristics of PEHL lubricant film thickness and pressure distribution are different from those of PEHL in the preliminary cases previously investigated. It is also found that with the increase of rolling cycles, the increment of plastic strain accumulation gradually approaches a stable value or drops down to zero, determined by the applied load and the material hardening properties, eventually causing a groove along the rolling direction. Simulation results for different material hardening properties are also compared to reveal the effect of body materials on the PEHL behaviors. [ABSTRACT FROM AUTHOR]

By coupling the equations of the modified Reynolds equation with the anisotropic slip effect, the piezoviscosity and piezodensity relations, the elasticity deformation equation, and the load equilibrium equation are solved simultaneously using the finite element method (FEM) for the elastohydrodynamic lubrication (EHL) of circular contact problems under constant load conditions. Results show that the film thickness is more sensitive to the slip length in a sliding direction (x-direction) than to the slip length in a transverse direction (y-direction). A slip in the y-direction concentrates the pressure toward the center region, and the film collects toward the central region and possesses a deeper dimple. The central pressure and coefficient of friction (COF) increase as the slip length in the ydirection increases. On the contrary, the central pressure and COF decrease as the slip length in the x-direction increases. Detailed results and animations for film thicknesses and pressure distributions are available under the ''Supplemental Data tab for this paper on the ASME Digital Collection. [ABSTRACT FROM AUTHOR]

Numerical solution of mixed elastohydrodynamic lubrication (EHL) is of great importance for the study of lubrication formation and breakdown, as well as surface failures of mechanical components. However, converged and accurate numerical solutions become more difficult, and solution process with a fixed single discretization mesh for the solution domain appears to be quite slow, especially when the lubricant films and sutface contacts coexist with real-machined roughness involved. Also, the effect of computational mesh density is found to be more significant if the average film thickness is small. In the present study, a set of sample cases with and without machined sutface roughness are analyzed through the progressive mesh densification (PMD) method, and the obtained results are compared with those from the direct iteration method with a single fixed mesh. Besides, more numerical analyses with and without surface roughness in a wide range of operating conditions are conducted to investigate the influence of different compound modes in order to optimize the PMD procedure. In addition, different initial conditions are used to study the effect of initial value on the behaviors of this transient solution. It is observed that, no matter with or without sutface roughness considered, the PMD method is stable for transient mixed EHL problems and capable of significantly accelerating the EHL solution process while ensuring numerical accuracy. [ABSTRACT FROM AUTHOR]

A high-order polynomial gas distribution cam mechanism is investigated theoretically from the viewpoint of thermal elastohydrodynamic lubrication (EHL). First, a cam with a larger base circle radius is employed, which results in slide-roll ratio 2.0 < S <9.0 when the two surfaces move oppositely. The pressure, film thickness, and temperature profiles at a number of angular positions of the cam are presented, together with the isothermal results. The comparison between thermal and isothermal oil characteristics is also shown. It is revealed that the isothermal analysis partly overestimates the actual film thickness and it also misses some essential local phenomena. Second, a cam with a smaller base circle radius is studied, which leads to drastic variations in the slide-roll ratio which encounters four times' occurrences of infinity in one working period. The pressure, film thickness, and temperature profiles at some angular cam positions together with the oil characteristics are given, showing much dramatic variations. A very small film thickness is observed at the contact of the tappet with the start of the cam basic segment, which suggests a possible risk of direct contact of both surfaces. [ABSTRACT FROM AUTHOR]

In Older to obtain a fast solution scheme, the trajectory piecewise linear (TPWL) method is applied to the transient elastohydrodynamic (EHD) line contact problem for the first time. TPWL approximates the nonlinearity of a dynamical system by a weighted superposition of reduced linearized systems along specified trajectories. The method is compared to another reduced order model (ROM), based on Galerkin projection, Newton-Raphson scheme and an approximation of the nonlinear reduced system functions. The TPWL model provides further speed-up compared to the Newton-Raphson based method at a high accuracy. [ABSTRACT FROM AUTHOR]

An analysis of the classic friction modeling in lubricated contacts is conducted. Its major deficiency for soft materials (low-elastic moduli) leading to significant overstating of friction in heavily loaded isothermal and thermal lubricated contacts is revealed. An improved model of friction in a heavily loaded lubricated contact is proposed. The model is based on incorporating the tangential displacements of the solid surfaces in contact, leading to a significant reduction of the frictional stress due to the decrease of the actual sliding of lubricated surfaces. Generally, this frictional stress reduction increases with the slideto- roll ratio, and it is extremely important for high slide-to-roll ratios for which classic approaches lead to unrealistically overestimated values of frictional stresses. The high slide-to-roll ratio values can be found in many practical applications, such as clutches. Several examples of the frictional stress calculated based on this model as well as the comparison with the classical results are given for the case of smooth solid surfaces and lubricants with Newtonian rheology. Also, the results allow to take a look at the role and the necessity of considering thermal and lubricant non-Newtonian effects on solution of various EHL problems for such heavily loaded contacts. [ABSTRACT FROM AUTHOR]

Line contact is common in many machine components, such as various gears, roller and needle bearings, and cams and followers. Traditionally, line contact is modeled as a two-dimensional (2D) problem when the surfaces are assumed to be smooth or treated stochastically. In reality, however, surface roughness is usually three-dimensional (3D) in nature, so that a 3D model is needed when analyzing contact and lubrication deterministically. Moreover, contact length is often finite, and realistic geometry may possibly include a crowning in the axial direction and round corners or chamfers at two ends. In the present study, plasto-elastohydrodynamic lubrication (PEHL) simulations for line contacts of both infinite and finite length have been conducted, taking into account the effects of surface roughness and possible plastic deformation, with a 3D model that is needed when taking into account the realistic contact geometry and the 3D surface topography. With this newly developed PEHL model, numerical cases are analyzed in order to reveal the PEHL characteristics in different types of line contact. [ABSTRACT FROM AUTHOR]

This paper provides the first cross-comparison of three established elastohydrodynamic computational methods to investigate the conformal long-bearing pure squeeze cylindrical bearing problem with rigid journal and elastic sleeve. The benefits of each analysis method in addressing both theoretical and practical issues in problem formulation and application are discussed. A set of nondimensional design charts for minimum film thickness and maximum film pressure under a step load are presented. With a judicious choice of load and sleeve geometry, it is found that a uniform film pressure can develop over a large film pocket in the limit of conformal journal and sleeve contact even with relatively high modulus materials such as steel. [ABSTRACT FROM AUTHOR]

In the design of cylindrical roller bearings (CRBs), a long life is one of the most essential criteria. However, the life of bearings depends on the multitude of factors that includes the fatigue, lubrication, and thermal characteristics in bearings. In the present work, three primary objectives namely, the dynamic capacity, the elastohydrodynamic lubrication (EHL) minimum film-thickness, and the maximum temperature have been optimized, sequentially. Some of these objectives may be contradicting to each other. The optimum bearing design has been attempted by first deriving a constrained nonlinear formulation and then optimizing it with an evolutionary algorithm. Constraint violations study has been performed to have assessment of the effectiveness of each of the constraints. A convergence study has been carried out to ensure the near global optimum point in the design. In terms of the basic dynamic capacity of the bearing, there is an excellent conformity among the optimized and customary bearings. A sensitivity study of various geometric design variables has been performed to see changes in objective functions and results show that geometric variables have hardly any undesirable influence. [ABSTRACT FROM AUTHOR]

Spiral bevel and hypoid gears are key components widely used for transmitting significant power in various types of vehicles and engineering machineries. In reality, these gear surfaces are quite rough with three-dimensional (3D) topography that may significantly influence the lubrication formation and breakdown as well as components failures. Previous spiral bevel and hypoid gears lubrication studies, however, were limited mostly to cases under the full-film lubrication condition with smooth surfaces. In the present study, a comprehensive analysis for gearing geometry, kinematics, mixed lubrication performance, and friction and interfacial flash temperature in spiral bevel and hypoid gears is developed based on a recently developed mixed elastohydrodynamic lubrication (EHL) model that is capable of handling practical cases with 3D machined roughness under severe operating conditions and considering the effect of arbitrary entrainment angle. Obtained results from sample cases show that the simulation model developed can be used as an engineering tool for spiral bevel and hypoid gears design optimization and strength prediction. [ABSTRACT FROM AUTHOR]

Soft elastohydrodynamic lubrication (EHL) problems widely exist in hydraulic reciprocating rod seals and pose great challenges because of high nonlinearity and strong coupling effects, especially when the EHL problems are of high dimensions. In this paper, a strongly coupled fluid structure interaction (FSI) model is proposed to solve the transient soft EHL problems in U-cup hydraulic reciprocating rod seals. The Navier-Stokes equations, rather than the Reynolds equation, are employed to govern the whole fluid field in the soft EHL problems, with the nonlinearity of the solid taken into consideration. The governing equations of the fluid and solid fields are combined into one equation system and solved monolithically. To determine the displacements of nodes of the fluid field, a new moving mesh method based on the combination of the Laplace equation and the leader-follower methods is put forward. At last, the proposed FSI model runs successfully with the moving mesh method, and the boundaries of the hydrodynamic lubrication zones and the hydrostatic zones are formed automatically and change dynamically during the coupling process. The results are as follows: The soft EHL problems show typical characteristics, like the constriction effects of the lubricating films, and the law of dynamic development of the lubricating films and the fluid pressures is revealed. The minimum stroke lengths needed to generate complete lubricating films vary with the rod speeds and movement directions, so the design of the rod seals should be paid close attention to, in particular the rod seals of short stroke lengths. Furthermore, along with the dynamic development processes of the fluid pressures during the instroke of U-cup seals, the lubricating film humps expand and locate between the fluid pressure abrupt points and the outlet zones. After the U-cup seals reach the steady-states, the fluid abrupt points disappear and no changes of the film humps are observed. Theoretically, the proposed method can be popularized to solve similar soft EHL problems. [ABSTRACT FROM AUTHOR]

Elastohydrodynamic lubrication (EHL) film thickness and rolling resistance play a critical role in determining friction, wear, life, and other tribological characteristics of rolling bearings. Although film thickness formulas are widely used and experimentally verified, accurate prediction of the film thickness is still difficult under starved conditions. This paper presents a numerical study of starved EHL point contacts using a nonuniform inlet film thickness obtained from a modified Coyne-Elrod boundary condition. An experimental verification of the numerical results is also presented. Based on the results of a parametric study, inlet distance formulas are obtained as a function of the initial film thickness, the fully flooded central film thickness, and the capillary number. By using the inlet distance formulas and the Hamrock-Dowson formulas, the central film thickness, the minimum film thickness, and the viscous rolling resistance can be calculated. [ABSTRACT FROM AUTHOR]

A transient lubrication model has been developed for the sliding interface between the slipper and swashplate in axial piston hydraulic pumps and motors. The model considers a nonisothermal fluid model, microdynamic motion of the slipper, as well as pressure and thermal deformations of the bounding solid bodies through a partitioned solution scheme. The separate contributions of elastohydrostatic and elastohydrodynamic lubrication are studied. Although hydrostatic deformation dominates, hydrodynamic effects are crucial for actual operation. Finally, the impact of transient deformation on lubricant pressure is explored, with its consideration necessary for accurate analysis. [ABSTRACT FROM AUTHOR]

In a series of publications, the author has shown that the passage of ductile microparticles through elastohydrodynamic (EHD) contacts results in frictional heating that can greatly affect suiface damage. The thermoviscoplastic numerical mode! built for those studies is extended in the present article. A more rigorous analysis of dynamic (strainrate) effects is performed and a new element of heating is introduced, namely, that owed to plastic work of the surfaces being indented. The model is then quantitatively validated against experimental data on soft and hard particles extruded in rolling and rolling-sliding contacts. It is also compared to past numerical predictions of the author. Following its validation, the model is further expanded to predict the formation of dark and white tribochemical layers of overtempered and untempered martensite, respectively, on steel surfaces, caused by the particle-induced frictional heating. Such layers are wellknown in machining processes of hardened steels as being the result of phase transformations and play a critical role in contact fatigue. The debris model in this article is used to predict the layer thickness and relative hardness for a variety of operating conditions. Layers of micrometric thickness are typically found and graphic examples are presented, linking their location to that of debris dents. A parametric study examines the role of particle size and hardness, Coulomb friction coefficient, and contact rolling velocity on dark and white layer thickness and relative hardness. The layers are zones of great inhomogeneity and thermomechanical anisotropy, increasing the risk of spalling by delamination as they are potential sources of crack initiation, particularly in sliding contacts. However, white layers in particular may actually be beneficial to contact fatigue in rolling contacts because of their substantially increased hardness. The conclusion of the study is that debris-driven suiface indentation and abrasion should no longer be viewed from a purely mechanistic or geometrical perspective but has to consider the tribochemical or microstructural-modification factor for the correct evaluation of the remaining useful life of a dented or abraded contact. [ABSTRACT FROM AUTHOR]

Siloxane-based polymers (polysiloxanes) are susceptible to temporary shear-thinning that manifests as a reduction of elastohydrodynamic film thickness with increasing entrainment speed or effective shear rate. The departure from Newtonian film thickness can be predicted with the power-law exponent ns, an indicator of the severity of shear-thinning in a polymeric fluid that is influenced by the macromolecular structure. In this paper, a combination of extant rheological and tribological models is applied to determine the power-law exponent of several polysiloxanes using film thickness measurements. Film thickness data at several temperatures and slide-to-roll ratios are used to validate the methodology for several siloxane-based polymers with alkyl and aryl branches. [ABSTRACT FROM AUTHOR]

A novel nano-to-elastohydrodynamic lubrication (EHL) multiscale approach, developed to integrate molecular-scale phenomena into macroscopic lubrication models based on the continuum hypothesis, is applied to a lubricated contact problem with a ceramic-steel interface and a nanometric film thickness. Molecular dynamics (MD) simulations are used to quantify wall slip occurring under severe confinement. Its dependence on the sliding velocity, film thickness, pressure, and different wall materials is described through representative analytical laws. These are then coupled to a modified Reynolds equation, where a no-slip condition applies to the ceramic suiface and slip occurring on the steel wall is described through a Navier-type boundary condition. The results of this nano-to-EHL approach can contradict the well-established lubrication theory for thin films. In fact, slip can occur over the whole contact length, leading to a significant modification of the lubricant flow and consequently of the film thickness. If both walls move at the same velocity, the flow is reduced at the contact inlet and the film thickness decreases. I f the nonslipping wall entrains the fluid, this one is accelerated resulting in a larger mass flow; nevertheless, the suiface separation is reduced as the lubricant flows even faster in the contact center. The opposite effect occurs if the slipping suiface entrains the fluid, causing a lower mass flow hut higher film thickness. Finally, friction is generally smallei compared to the classical no-slip case and becomes independent of the sliding velocity as total slip is approached. [ABSTRACT FROM AUTHOR]

Transient film thickness behavior is investigated using full elastohydrodynamic lubrication (EHL) line contact simulations during film collapse due to sudden halt and impact loading. Due attention is given to realistic shear-thinning behavior and comparisons are made with a largely ignored class of EHL lubricants that exhibit linear pressureviscosity dependence at low pressures. The EHL film collapse is found to be governed by the piezoviscous response and the linear P-V oils exhibit rapidly collapsing EHL entrapment. Under impact loading, the transient film thickness deviates markedly from the corresponding steady-state behavior and this departure is a function of lubricant rheology. [ABSTRACT FROM AUTHOR]

Heavily loaded point elastohydrodynamically lubricated (EHL) contacts involved in steady purely transitional, skewed transitional, and transitional with spinning motions are considered. It is shown that in the central parts of the inlet and exit zones of such heavily loaded point EHL contacts the asymptotic equations governing the EHL problem along the lubricant flow streamlines for the above types of contact motions can be reduced to two sets of asymptotic equations: one in the inlet and one in the exit zones. The latter sets of equations are identical to the asymptotic equations describing lubrication process in the inlet and exit zones of the corresponding heavily loaded line EHL contact (Kudish, I. I., 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC). For each specific motion of a point contact, a separate set of formulas for the lubrication film thickness is obtained. For different types of contact motions, these film thickness formulas differ significantly (Kudish, I. L, 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC). For heavily loaded contacts, the discovered relationship between point and line EHL problems allows to apply to point contacts most of the results obtained for line contacts (Kudish, I. L, 2013, Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches, Chapman and Hall/CRC: Kudish, I. I., and Covitch, M. J., 2010, Modeling and Analytical Methods in Tribology, Chapman and Hall/CRC). [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]

A rigid sphere approaching a lubricated flat surface with a layer of elastic coating on the elastic substrate is explored under constant load conditions. The transient pressure profiles, film shapes, elastic deformation, von Mises stress σvon) during the pure squeeze process under various operating conditions in the elastohydrodynamic lubrication (EHL) regime are discussed. The simulation results reveal that the greater the Young's modulus of coating is, the greater the pressure distribution is, the smaller the contact area is, and the greater the maximum stress (avon) value is. Ai the Young's modulus of coating decreases, the central elastic deformation at the surface (Z = 0) increases and the deformation at the interface of coating! substrate (Z=--l) decreases. For hard coating cases, the maximum central pressure increases to an asymptotic value and minimum film thickness decreases to an asymptotic value as the coating thickness increases. For soft coating cases, this phenomenon reverses. A thicker and stiff er coating leads to a higher maximum stress. At the deformation recovery stage, the positions of the maximum stress would begin to offset downwards and closer to the coating!substrate interface. Moreover, the position of maximum stress varies from the coating to the subsurface as the Young's modulus of coating increases. The EHL with stress analysis can prevent the chance of fracture in coating or substrate. These characteristics are important for the lubrication design of mechanical elements with coatings. [ABSTRACT FROM AUTHOR]

The numerical simulations of surface textures in point-contact lubrication are conducted based on the unified Reynolds equation model. The textures are numerically produced on one of the interacting surfaces. The lubricant t heological parameters used in the simulations are calibrated by experiments. The numerical results show good agreements with those from experiments. The friction reduction mechanism is investigated by systemiCally analyzing the periodic change of friction coefficient of textures. It is illustrated that the transient friction coefficient is minimal when the dent moves to the front boundary edge of the Hertzian contact zone. A local film enhancement region will be formed on the trail of the dent within the Hertzian contact region. The results suggest that a bigger local film enhancement area will offer stronger film thickness enhancement as welt as a lower friction coefficient. Different pattern distributions are also studied to find the optimal distribution of patterned textures, which not only achieves a lower friction coefficient, but also offers stronger film thickness enhancement; moreover, the optimal distribution is numerically proved to be applicable for a wide range of working conditions. [ [ABSTRACT FROM AUTHOR]

A novel model is constructed for solving elastohydrodynamic lubrication (EHL) of multilayered materials. Because the film thickness equation needs the term of the deformation caused by pressure, the key problem for the EHL of elastic multilayered materials is to develop a method for calculating their surface deformations, or displacements, caused by pressure. The elastic displacements and stresses can be calculated by employing the discrete-convolution and fast Fourier transform (DC-FFT) method with influence coefficients. For the contact of layered materials, the frequency response functions (FRFs), relating pressure to suiface displacements and stress components, derived from the Papkovich-Neuber potentials are applied. The influence coefficients can be obtained by employing FRFs. The EHL of functionally graded material (FGM) can also be well solved using a multilayer material system. The effects of material layers and property gradient on EHL film thickness and pressure are further investigated [ABSTRACT FROM AUTHOR]

A new structural stiffness model for the compliant structure in foil gas bearings is intro-duced in the first part of this work. The model investigates the possibility that the flat seg-ment between bumps, in bump foil strip, may deflect laterally and separate from the rigid bearing suiface, and it also considers the interaction between bumps in the bump foil strip, the friction between the bump foil, and the surrounding structure. The validity of the analytical solution was verified through direct comparison with previous numerical and analytical models. In the second part of this work, the introduced bump foil model is used to investigate the static characteristics of generation II gas foil thrust bearing. The numerical simulations of the coupled fluid-structure interactions revealed that the foil thrust bearings share many features with their rigid bearing counterpart and the results showed clearly that the load carrying capacity of foil thrust bearings increases nonli-nearly with the rotation speed and is expected to reach an asymptote as the rotation speed exceeds a certain value. The effects of ramp height and interface friction (i.e., fric-tion at bump foil/rigid bearing interface and bump foil/top foil interface) on the static characteristics of generation II foil thrust bearings are investigated. [ABSTRACT FROM AUTHOR]

Numerical simulations of the elastohydrodynamic lubrication (EHL) have been con-ducted by many researchers, in which the entrainment velocity is usually parallel to one of the axes of Hertzian contact ellipse. However, in some engineering applications, such as the counteiformal contacts in spiral bevel and hypoid gears, entraining velocity vector may have an oblique angle that could possibly influence the lubrication characteristics significantly. Also, a vast majority of gears operate in mixed EHL mode in which the rough sui face asperity contacts and lubricant films coexist. These gears are key elements widely used for transmitting significant power in various types of vehicles and engineer-ing machinery. Therefore, model development for the mixed EHL in elliptical contacts with an arbitrary entrainment angle is of great importance. In the present paper, a recently developed mixed EHL model is modified to consider the effect of arbitrary entraining velocity angle, and the model is validated by comparing its results with avail-able experimental data and previous numerical analyses found in literature. Based on this, numerical simulations are conducted to systematically study the influence of entrain-ment angle on lubricant film thickness in wide ranges of speed, load, and contact elliptic-ity. The obtained results cover the entire lubrication spectrum from thick-film and thin-film lubrication all the way down to mixed and boundary lubrication. In addition, minimum film thickness prediction formula is also developed through curve-fitting of the numerical results. [ABSTRACT FROM AUTHOR]

This paper offers central film thickness formula pertaining to shear-thinning lubricants under rolling!sliding point contact conditions. The shear-thinning behavior of the lubri-cants is modeled using Carreau viscosity equation and the piezo-viscous response employed herein is the free-volume based Doolittle equation in conjunction with Tait' s equation of state for lubricant compressibility. The present formulation is based on recip-rocal asymptotic isoviscous piezo-viscous coefficient as it is a more accurate measure of the high pressure piezo-viscous response of elastohydrodynamic lubricated (EHL) lubri-cants compared to the conventional pressure-viscosity coefficient. Comparisons between simulated, cwve-fitted values, and experimental results validate both the employed numerical approach and rheological model. [ABSTRACT FROM AUTHOR]

The transient film thickness and pressure distributions in point elastohydrodynamic lubri-cation (EHL) contacts during start-stop-start motion are discussed based on experimen-tal and numerical analyses. When the machine element starts to move after the stopping, where the oil is entrapped between two surfaces, the pressure at the exit area increases very much. The pressure increase depends markedly on the overall film thickness before the stopping of the motion, but is hardly controlled by the acceleration after the stopping. It can be considered that this phenomenon affects the rolling contact fatigue damage. [ABSTRACT FROM AUTHOR]

Inhomogeneities in matrix may significantly affect the performance of mechanical ele-ments, such as possible fatigue life reduction for rolling bearing due to stress concentra-tion induced by inhomogeneities; on the other hand, most components operate under lubrication environment. So far the numerical algorithms to solve lubrication problems without the consideration of inhomogeneities or inclusions are well developed. In this pa-per, the combination of elastohydrodynamic lubrication (EHL) and inclusion problem is realized to consider the effect of material inhomogeneity on the lubrication performance and subsurface stress distribution, etc. The matrix inhomogeneity will induce disturbed displacement, which will modify the film thickness and consequently result in the change of lubricated contact pressure distribution, etc. The matrix inhomogeneity is treated as the homogeneous inclusion with equivalent eigenstrain according to equivalent inclusion method (EIM), and the disturbed displacement is calculated by semi-analytical method (SAM). While the pressure and film thickness distributions are obtained by solving Reyn-olds equation. The iterative process is realized to consider the interaction between lubri-cation behavior and material response. The results show the inhomogeneity in contacting body will greatly influence the lubricated contact peiformance. The influences are differ-ent between compliant and stiff inhomogeneity. It is also found that different sizes and positions of inhomogeneity can significantly affect the contact characteristic parameters. [ABSTRACT FROM AUTHOR]

Efficiency and durability are among the top concerns in mechanical design to minimize environmental impact and conserve natural resources while fulfilling performance requirements. Today mechanical systems are more compact, lightweight, and transmit more power than ever before, which imposes great challenges to designers. Under the circumstances, some simplified analyses may no longer be satisfactory, and in-depth studies on mixed lubrication characteristics, taking into account the effects of 3D surface roughness and possible plastic deformation, are certainly needed. In this paper, the recently developed plasto-elastohydrodynamic lubrication (PEHL) model is employed, and numerous cases with both sinusoidal waviness and real machined roughness are analyzed. It is observed that plastic deformation may occur due to localized high pressure peaks caused by the rough surface asperity contacts, even though the external load is still considerably below the critical load determined at the onset of plastic deformation in the corresponding smooth surface contact. It is also found, based on a series of cases analyzed, that the roughness height, wavelength, material hardening property, and operating conditions may all have significant influences on the PEHL performance, subsurface von Mises stress field, residual stresses, and plastic strains. Generally, the presence of plastic deformation may significan tly reduce some of the pressure spikes and peak values of subsurface stresses and make the load support more evenly distributed among all the rough surface asperities in contact. [ABSTRACT FROM AUTHOR]

The numerical studies on the influences of surface parameters skewness and kurtosis on tribological characteristics under mixed elastohydrodynamic lubrication (mixed EHL) conditions are extended to fatigue life. Non-Gaussian rough surfaces are generated numerically with given autocorrelation function, skewness, and kurtosis. The results show that the maximum pressure increases as the skewness increases, however its variation with kurtosis is closely related to skewness. Similar trends to that of the maximum pressure are obseiyed for the maximum von Mises stress. The fatigue life decreases as the skewness increases, however it undergoes apparent fluctuations with the increase of kurtosis. As the kurtosis increases, the influence of skewness on fatigue life becomes more significant, and vice versa. [ABSTRACT FROM AUTHOR]

The effects of the transversely isotropic coating layer on the elastohydrodynamic lubrication (EHL) circular contact problems are analyzed and discussed under constant load condition. The equivalent elastic modulus for an equivalent isotropic half-space problem is applied to simplify the present transversely isotropic coating. The finite element method (FEM) is utilized to solve the Reynolds equation, the load balance equation, the rheology equations, and the elastic deformation equation simultaneously. The simulation results of the present equivalent model are compared with those of an anisotropic material elasticity matrix to evaluate the applicable range of coating thickness under a fixed relative error. The pressure distribution tends to gradually escalating and concentrating toward the center with increasing longitudinal Young's modulus. The variations of pressure and film thickness become significant as the coating thickness becomes thinner. The deformations of inteiface are smaller than the deformations of the surface. The film thickness and pressure characteristics of the lubricant are discussed for various parameters. These characteristics are important for the design of the mechanical element with coating layer. [ABSTRACT FROM AUTHOR]

The effects of nanotexturing on oil film thickness and shape under pointcontact elastohydrodynamic lubrication (EHL) conditions were experimentally investigated. A diskonball friction tester with an optical interferometer was used to measure oil film thickness and to observe the oil film shape. Periodic groove structures with a spiral, perpendicular, or parallel shape and with various groove depths and distances were formed by irradiation of a femtosecond laser onto the surface of steel balls. These nanotextured balls were tested under a load of 20 N and at rotational speeds from 1.0 to 3.Omis. Most of the balls with nanotexturing had a thicker oil film than those without texturing. The groove depth and angle were the key parameters determining the thickness of the oil film as they controlled the amount of side leakage of oil from the contact point. Optimization of these parameters resulted in an oil film that was almost twice as thick as that on the ball without texturing. [ABSTRACT FROM AUTHOR]

A mathematical model is presented in this paper for rolling-sliding contacts operating in a mixed regime of elastohydrodynamic lubrication and boundary lubrication. The model is based on the framework of Johnson et al. (1972, "A Simple Theory of Asperity Con-tacts in Elastohydrodynamic Lubrication," Wear, 19, pp. 91-108). It incorporates into this framework a number of important asperity-level variables including asperity friction, friction-induced plastic flow, flash temperature, and boundary-film tribo-chemistry. The model yields a number of variables useful for the assessment of the state of the mixed lubrication. They include the load sharing between fluid and asperities, area of asperity contacts, and fraction area of asperity contacts undergoing plastic flow along with exper-imentally measurable variables such as the traction coefficient, friction power intensity, and temperature of the overall contact. The model is limited to mixed-lubrication prob-lems in which the load is mainly carried by the fluid pressure and the total area of asper-ity contacts is a small percentage of the Hertz area. Further development is possible to formulate a model into a wider mixed-lubrication regime using some modeling concepts developed in this paper in conjunction with other modeling techniques. [ABSTRACT FROM AUTHOR]

In this paper, a nonisothermal fluid-structure interaction mathematical model for the pis-ton/cylinder interface leakage is presented. Full account is taken of the piston eccentric-ity, elastic deformations of the piston pair, the nonisothermal flow in the interface, and the physical properties of the fluid such as the pressure-viscosity and temperature-viscosity effects. The numerical method for the solution of the model is given, which can simultaneously solve for the fluid pressure distribution and leakage rate in the inteiface. The model is validated by comparing the calculated leakage rates with the measurements. Results show the good accuracy of the model. The impacts of parameters such as the pis-ton diameter, the initial clearance between the piston pair, and the piston velocity on the leakage rate are discussed. Some of the conclusions provide good guidance for the design of high-pressure fuel pumps. [ABSTRACT FROM AUTHOR]

This paper addresses a largely ignored aspect pertaining to the elastohydrodynamic lubri-cation (EHL) traction behavior of fragile lubricants which undergo transition to glassy state at typical EHL contact zone pressures. For such lubricants, a conventional EHL model predicts extremely high and unrealistic values of traction coefficient, especially under near pure rolling conditions where thermal effect is negligible. Therefore, an EHL model incorporating the effect of limiting shear stress and the associated wall slip phenom-enon is presented herein. Unlike the other such investigations involving limiting shear stress behavior, the present model employs Carreau-type power-law based models to describe the rheology of lubricants below the limiting shear stress along with realistic pressure-viscosity relationships (WLF and Doolittle-Tait). The use of Carreau-type shear-thinning model in this analysis allows the simultaneous prediction of minimum film thick-ness and traction coefficient for lubricants which shear-thin in the inlet zone and exhibit limiting shear stress behavior in the contact zone, a feature absent in the existing EHL models utilizing ideal visco-plastic or some other unrealistic rheological model. Using pub-lished experimental data pertaining to the shear-thinning and pressure-viscosity response of two fragile lubricants (L100 and LVI260), it has been demonstrated that the present model can explain the appearance of plateau in the experimental traction curve. Also, the influence of shear-thinning parameters and the pressure-viscosity coefficient on the predicted limiting shear stress ¿one has been studied. [ABSTRACT FROM AUTHOR]