Temperature rise and film thickness reduction are the most important factors in elastohydrodynamic lubrication (EHL). In the EHL contact area, interfacial resistances (velocity/thermal slips) induced by the molecular interaction between lubricant and solid become significant due to the large surface/volume ratio. Although the velocity slip has been investigated extensively, less attention has been paid on the thermal slip in the EHL regime. In this study, numerical simulations were conducted by applying three cases of boundary slips to surfaces under sliding/rolling contacts moving in the same direction for the Newtonian thermal EHL. We found that the coupled velocity/thermal slips lead the most significant temperature rise and film thickness reduction among the three cases. The velocity slip results in a lower temperature in the lubricant and solids, whereas the thermal slip causes a temperature rise in the entire contact area in the lubricant as the film thickness decreases simultaneously. Furthermore, the effect of thermal slip on lubrication is more dominant than that of velocity slip, which increases the entrainment velocity or slide–roll ratio.

This study allows contact models based on semi-analytical methods including the impacts of thermoelastic deformations in contacts of finite dimension bodies. The proposed method controls heat flows crossing free boundaries. A comparison with FEA reveals that the proposed method can reduce the calculation times by more than 98%. The paper introduces the thermoelasticity effects into thermal-elastohydrodynamic lubrication (TEHL) modeling of line contact problems. The analysis reveals that including thermoelastic deformations changes the pressure profile and tends to localize the pressure close to the distribution center. Compared to TEHL simulations, the examined configurations caused an overall increase in the maximum pressure by about 9%, an overall film thickness reduction of about 7%, and an overall temperature increase of about 2 K.

The effects of thermal conductivity, heat capacity, thermal inertia, and slide-roll ratio (SRR) on point elastohydrodynamic lubrication (EHL) are discussed with engineering ceramics and steel by a non-Newtonian thermal EHL analysis. When the thermal conductivities of contacting materials are significantly different, the film thickness is greatly affected by which material has the higher velocity. However, the film thickness is dominated by the heat capacity when the difference in thermal conductivity is not large. In contact of materials with the same mechanical and thermal properties, the film thickness and friction coefficient are influenced by the thermal inertia.

This work presents a comprehensive numerical study of thermal elastohydrodynamic lubrication performance in axially crowned rollers, based on a full-system finite element approach. Axial crowning has always been introduced to finite line contacts, as a mean for improving film thickness. Its influence on friction has often been overlooked though. The current work reveals that axial crowning has a negative influence on friction, increasing it significantly with respect to the reference case of straight rollers. It is shown that, with increased crowning height (or reduced crowning radius), minimum film thickness is increased, but so is friction. Therefore, film thickness enhancement comes at the expense of a deterioration in friction. Besides, achieving sufficient enhancements in minimum film thickness would require using relatively low crowning radii, which would lead to a substantial increase in friction. The frictional increase is traced back to an overall increase in contact pressures and effective contact area within the lubricating conjunction. It is also shown that, when film thickness is the most critical design parameter, the best compromise between enhanced film thickness and deteriorated friction would be to combine axial crowning with roller-end profiling. However, when friction is the most critical design parameter, a simple roller-end profiling would offer the best compromise.

A computational fluid dynamics analysis of two-phase flow was used to obtain the distribution of lubricant in a journal bearing, including inlet tube and groove. It was found that for an incomplete starting film, the oil spread-length varies along the groove depth and film thickness. The magnitude of variation was found to be independent of the inlet mass flowrate. Numerical simulations of the proposed model show that in the cavitation region, the streamlets do not fill the entire film thickness. The present numerical model agrees with experimental observations.

The third particle occurred at the interface of contacting surfaces is common situations in relative motion part. This study involved developing an analysis framework to investigate the contact characteristics in the full range of 3-body mixed lubrication. Conventional 2-body mixed lubrication is a special case of 3-body mixed lubrication analysis with particle size of zero. This study revealed that the values of real contact area, film thickness, contact mode, and the solid contact load in 3-body contact were larger than those in ideal 2-body contact in mixed lubrication, and they increased with an increasing particle size or density under the study conditions. The initial stages and transition processes of four types of 3-body contact modes under mixed lubrication were significantly different for different particle sizes and densities. The size of the third particle increased the values of both minimum and maximum values, λ min and λ max , of film parameter in the mixed lubrication regime. The particle density did not have a significant effect on the λ max value in mixed lubrication. Higher particle density led to a larger λ min value in mixed lubrication. The conventional film parameter, λ, was not a sufficient indicator of the different lubrication regimes in 3-body contact.

Gear pumps are largely employed in aero-engine fuel systems to provide the combustor with fuel at adequate pressure and flowrate. The radial load applied on the gears, as a consequence of the pump pressure rise, is entirely supported by the hybrid journal bearings. Lubrication of these is accomplished using low viscosity aviation fuel, which makes the design and analysis of journal bearings particularly challenging. Furthermore, considering the operating conditions of these journal bearings, elastic deformations play a significant role on their performance and equilibrium location. A numerical model has been developed to support the analysis and future design of hybrid journal bearings for fuel pump applications. The primary objective of the tool is to characterize the equilibrium position of the journal during steady-state operation at part and full load, where the resultant elastic displacements are more significantly affecting the pressure distribution of the lubrication film. The developed method effectively combines Elrod’s cavitation algorithm with the dimensionless pressure definition known as the Vogelpohl parameter, resulting in a simple and robust methodology to characterize the pressure distribution within the lubricant for different bearing designs and operating conditions. Six different multidimensional root-finding solvers have been implemented and their performance evaluated against robustness, accuracy and computational speed requirements. Newton–Raphson based methods have shown promising tradeoffs for the problem at hand. Validation of the tool has been made comparing experimental film thickness measurements, performed on a fuel pump from a modern turbofan engine, with predicted data from the numerical model.

The relative sliding at the meshing point directly affects the contact and lubrication characteristics of the gear pair, and is the main cause of gear wear and power loss. In this research, for investigation of a new type of low sliding ratio (LSR) gear pair whose tooth profile is constructed by a cubic function, a Three-dimensional (3D) mixed EHL line contact model was established with consideration of the effect of tooth profile geometry, transient motion characteristics, load distribution and machining roughness. The distribution of the center film thickness of the LSR gear along the meshing line was predicted through an example the result of which was compared with a typical line contact EHL formula to verify the model. In addition, the difference was investigated in film thickness distribution, of friction coefficient and temperature rise between LSR spur gears and involute spur gears. Basing on above, there was discussion about the effect of 3D rough tooth surface on the contact lubrication characteristics of LSR gears. The results demonstrated that the minimum center film thickness of the LSR gear appeared at the alternating point of the concave and convex tooth surfaces. At the same time, compared with the involute gear, the LSR gear significantly increased the film thickness at the start and ending points of the meshing, and reduced the friction coefficient and the flash temperature rise.

This paper provides the main causes of asymmetric or directional deformation of surface roughness based on a transient non-Newtonian thermal elastohydrodynamic lubrication (EHL) model, where the contact materials have different thermal conductivities and elastic moduli. In order to obtain the actual shape of the surface asperity, the surface shapes of contact bodies are evaluated separately. It is clarified that the asymmetric deformation of the asperities appears due to two causes. One depends on the slide-roll ratio (SRR) and the difference in thermal conductivity between contact materials, and the other is caused by the contact pressure between the asperities through the oil film.

The purpose of this study is to investigate the role of the misalignment journal, caused by linear shaft misalignment, on the transient wear and mixed lubrication performances using a numerical model. In the numerical model, the transient geometry lubrication clearance considering the journal misalignment, the transient elastic deformation, and the transient wear depth of the bearing are incorporated to evaluate the transient film thickness during the wear process. The evolutions, under different external loads, of the wear depth of the bearing, wear-rate, elastic deformation of the bearing, film thickness, fluid pressure, and contact pressure are calculated by the numerical model. Furthermore, the calculated results of the misaligned journal bearing are compared with those of the aligned journal bearing. The results show that the distributions of the wear depth of the bearing, film pressure, and elastic deformation of the bearing are asymmetric along the axial direction and the peak values of them shift toward the back end when the journal misalignment is considered. The maximum wear depth, maximum fluid pressure, maximum contact pressure, and maximum bearing’s elastic deformation of the misaligned journal condition are significantly larger than those of the aligned journal condition.

This article investigates the static and dynamic performances of bionic textures fused micro-pocketed journal bearing considering cavitation. The new bionic textures placed inside the micro-pocket toward the trailing side has been conceived inspired from the skins of freshwater fish. The mass conservation satisfying partial differential lubrication equations for the static and dynamic pressures are discretized using the finite volume method (FVM) followed by simultaneous solution of the system equations using the Fischer–Burmeister–Newton–Schur (FBNS) and the Broyden’s method with Sherman–Morrison formula. The minimum film thickness, friction force, temperature rise, dynamic coefficients, effective damping and stiffness, critical mass, and system characteristic roots have been explored with new conceived bores, and the numerical results have also been compared with conventional plain and conventional pocketed bore bearings. Significant static and dynamic performance improvements have been found in the presence of bionic textures fused micro-pocketed bores in comparison to conventional bores.

Elastohydrodynamic lubrication (EHL) in point contacts can be numerically solved with various iteration methods, but so far the flow continuity of such solutions has not been explicitly verified. A series of closed regions with the same inlet side boundary is defined, and two treatments to total all flows related to the other boundaries of the closed regions are defined to enable flow-continuity verifications. The multigrid method and the traditional single mesh method with different relaxation configurations are utilized to solve different cases to evaluate computation efficiencies. For the multigrid method, the combination of a pointwise solver together with hybrid-relaxation factors is identified to perform better than other combinations. The single mesh method has inferior degrees of flow continuity than the multigrid method and needs much smaller error control values of pressure to achieve a decent level of flow continuity. Because flow continuity has a physical meaning, its verifications should be routinely included in any self-validation process for any EHL results. Effects of control errors of pressure, mesh sizes, differential schemes, and operating conditions on flow continuities are studied. Then, trends of film thickness with respect to speed are briefly discussed with meshes up to 4097 by 4097.

Utilizing a computational approach, this study quantifies the onset of lubrication starvation for line contacts of rough surfaces operating under typical ranges of automotive gearing applications. The response parameter is selected as the critical film thickness supply, at which starvation initiates. The potential influential parameters (predictors) considered include normal force density, rolling velocity, sliding, lubricant viscosity, and surface roughness amplitude. A non-Newtonian thermal mixed lubrication model is employed to determine the critical lubricant supply under various operating and surface roughness conditions. General linear regression is implemented to reach an easy-to-use equation (R-squared value higher than 97%), facilitating the quantification of starvation dependence on the predictors that are statistically significant.

In designing any machine element, we need to optimize the design to attain its maximum utilization. Herein, deep-groove ball bearings have been chosen for optimization. Optimization has been done in such a way that the design is robust so that manufacturing tolerances can be considered in the design. Robust design ensures that changes in design variables due to manufacturing tolerances have a minimum effect on the objective function, i.e., its performance. Robustness is achieved by maximizing the mean value of the objective function and minimizing its deviation. For rolling element bearings, its life is one of the most crucial considerations. The rolling bearing rating life depends on dynamic capacity, lubrication conditions, contamination, mounting, manufacturing accuracy, and material quality, and thus, the dynamic capacity and elasto-hydrodynamic minimum film thickness have been taken as objective functions for the current problem. Rolling element bearings have standard boundary dimensions, which include the outer diameter, inner diameter, and bearing width for the case of deep-groove ball bearings. So the performance can be improved by changing internal dimensions, which are the bearing pitch diameter, ball diameter, the inner and outer raceway groove curvature coefficients, and the number of rolling elements. These five internal geometrical parameters are taken as design variables; moreover, five design constraint factors are also included. Thirty-six constraint equations are considered, which are mainly based on geometry and strength considerations. In the present work, the objective functions are optimized individually (i.e., the single-objective optimization) and then simultaneously (i.e., the multi-objective optimization). Nondominated sorting genetic algorithm (NSGA-II) has been used as the optimization tool. Pareto-optimal fronts are obtained for one of the bearings. Of many points on the Pareto-front, only the knee solutions have been presented . This paper shows that geometrically feasible bearings can be designed by optimizing multiple-objective functions simultaneously and by also incorporating the variations in dimensions, which occur due to manufacturing tolerance.

The tribological properties of gear interface have been widely concerned in the past decades. In this study, based on the local involute profile and crown modification, a thermal elastohydrodynamic lubrication model is proposed for a helical gear pair. To discuss the influences of dynamic load on the tribological properties of helical gear pair, the dynamic mesh force of tooth surface is obtained by torsional vibration model. The influences of working conditions and surface roughness on the tribological properties of helical gear pair are investigated. The tribological properties are evaluated in terms of the average film thickness, friction coefficient, mechanical power loss etc. Results show that the dynamic effect of gears has a significant effect on the tribological properties, especially at a specific speed, such as resonance speed. In order to simulate gear lubrication accurately, it is recommended to adopt local involute tooth profile and consider tooth profile modification to calculate geometric clearance. The influence of input rotation speed on the dynamic characteristics and tribological properties of gear is more significant than that of input torque. The surface roughness significantly changes the distribution of interface pressure and film thickness. With the increase of roughness amplitude, the local fluctuation amplitude of pressure and film thickness increase and the dry contact occurs at the end of contact line. Meanwhile, the maximum subsurface stress moves toward the tooth surface, especial for the high frequency engineering roughness. This local stress concentration is harmful to the fatigue life of gear meshing process.

In sliding-rolling concentrated contacts, the grease film is subjected to shear action. In this study, grease film behaviors have been observed under different sliding-rolling ratios (SRRs) by measuring film thickness and friction coefficient simultaneously. The evolution patterns of the grease films with disc revolutions are affected by SRR, entrainment speed, and grease consistency. The severe starvation due to film decay at low shear and the film recovery at high shear has been recognized. The grease with low consistency is in a fully flooded state due to improvement in lubricant replenishment. In addition, the corresponding friction coefficient tends to increase or be constant in terms of contact states. The mechanisms of the grease behavior related to shear actions and grease properties are analyzed.

This study presents a finite-element-based numerical investigation of the influence of roller-end axial profiling type on the lubrication performance of thermal elastohydrodynamic finite line contacts. Performance is evaluated with respect to the reference case of straight rollers. The two most commonly used profiling types (i.e., dub-off and logarithmic) are compared under similar profiling length and height. It is found that a logarithmic profile outperforms a dub-off one by all accounts (i.e., frictional dissipation, lubricant film thickness, pressure buildup, and temperature rise), unless an extremely steep logarithmic shape is adopted. In the latter case, lubricant film thickness and pressure buildup may end up being negatively affected.

Due to high efficiency, multigrid (MG) algorithms developed by Lubrecht and Venner or others have been widely applied to solve the Reynolds equation in lubrication simulations. However, such algorithms are complex in nature and in-depth understandings and further development are of interest. This work proposes a new restriction operator of pressure to simplify the relaxation of the load balance equation and constructs several new relaxation processes based on key options of relaxations when either pressures or changes of pressure are evaluated from the Reynolds equation. In addition, effects of cycle types, treatments of cavitation boundary, line-solvers, relaxation factors, and differential schemes are revealed. This paper further implements a mass conservation algorithm into the MG code in order to deal with micro-cavitations. Characteristics of film thickness, pressure, flow continuity, and residuals, resulting from smooth, wavy, or rough surfaces are discussed. Finally, the results from the last correction cycles at various levels are recommended to be used for better accuracy.

The integration of foil bearing technology into high-speed oil-free machines has been slow in progress, in part, due to the low load-carrying capacity of the foil thrust bearing. It is crucial this issue is addressed through innovative solutions without overcomplicating the bearing design because simplicity is one of the attractive features of the foil bearing. This work presents novel thrust foil bearing with taper-flat configuration and pocket grooves on the bearing top foil as a secondary pressure boosting mechanism. Parametric study of the pocket dimensions on a rigid bearing reveals that the bearing static performance is the most sensitive to the pocket angular span. Further two-dimensional fluid–structure interaction analyses on foil thrust bearing predict a reduction of power loss by 10% with increased average film thickness. Minimum film thickness also increases when the bearing is lightly loaded but it is reduced 20% at the taper-flat transition area under high loading condition. This issue can be overcome by using stiffer bump foil; however, this is not implemented in this work due to other design constraints. Test results at 90,000 rpm and 140,000 rpm show, by adding the pocket groove pattern on the top foil, the power loss is reduced by 16% compared to the traditional taper-flat configuration.

Hydro-viscous drive has gained extensive application in fans, pumps, belt conveyors, and scraper conveyors for step-less speed regulating, soft starting, and overload protection. In the mixed friction stage, the state of contact and load-bearing capacity are always changing with the pressure of control oil. In order to predict the load-bearing capacity of friction pairs, a description of the frictional and hydrodynamic lubrication states was first made. Oil film’s pressure distribution and load-bearing capacity were analyzed with the average flow model. The fractal contact model of the asperity surface was proposed for simulating mutual contact state and contact load between the asperities. The influences of fractal parameters on the contact performance of friction pairs were conducted. Eventually, test rig of load-bearing capacity was established. As indicated by the experiment, asperity contact area and load-bearing capacity of the asperity contact increase slowly at first and then rapidly with reduced film thickness ratio. Correspondingly, oil film load-bearing capacity progressively reduces. Due to the reduction of film thickness ratio, friction pairs’ load-bearing capacity increases gradually. The load-bearing capacity of friction pairs is affected by the fractal dimension and scale factor. Results of the experiment well conform to the theoretical values, which illustrates that friction pairs’ load-bearing capacity can be accurately predicted and computed using the average flow model and M-B fractal contact model. The calculation offers a theoretical reference to the survey about friction and torque properties of the hydro-viscous drive.