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Lubricant oil is crucial to the rolling bearings as the main medium of lubricating, cooling, cleaning, and so on. The oil starvation in and around the contacts is harmful to the performance and fatigue life of rolling bearings. Therefore, it is of necessity to understand the behaviors of oil transfer and the patterns of air-oil two-phase flow in bearings, especially with the influence of different capillary properties. This work established a transient air-oil two-phase flow model in a ball bearing based on computational fluid dynamics (CFD). Groups of cases are implemented to investigate the behaviors of oil transfer and air-oil flow under different capillary conditions with speed, surface tension, and viscosity. Flow patterns are classified by the morphological features of the air-oil flow. Staged phenomena are analyzed with flow patterns and reach good agreements with the observations from experiments. It is found that the oil distribution and air-oil flow behaviors in a ball bearing are strongly related to the speed and the ratio of oil viscosity and air-oil surface tension (μoil/σ). The flow maps imply that the levels of capillary number (Ca) may be the boundaries and the critical points of flow pattern transition between the different flow patterns in bearing.

Multilayer coatings offer a possibility to design the surface according to the different requirements, which attracts intense attentions from engineering and research community. The coupled thermo-mechanical contact problem of a multilayered material is of great interest. This paper firstly derives the frequency response functions (FRF) of thermoelastic fields through thermoelastic governing equations. The unknown coefficients in the FRFs are assembled in a linear system of matrix equations according to the thermal and mechanical loadings on surface and continuity condition of heat flux, temperature, displacement and stresses at each interface; then the coefficients are solved and expressed recursively. Based on the closed-form solution of FRFs, a fast semi-analytical method (SAM) is developed to solve the three-dimensional thermoelastic contact problem involved in arbitrary multilayered materials. There are no limits on the number or the thickness of layers, and material parameters can be varied arbitrarily. The present model is verified by literature and FEM and shows a high robustness and efficiency. Thermoelastic contact of multilayered materials with different coating designs under friction heating is further studied and the thermal effect is explored.

Multilayer coatings have been widely using in a wide range of applications, including industrial, biological and electrical areas, and the thermal distribution in a multilayered material is of great interest. In present paper, the frequency response functions (FRFs) of temperature field under unit point heat flux are derived through thermal conduction equation. The unknown coefficients in the FRFs are assembled in a linear system of matrix equations according to the heat input and continuity condition of heat flux and temperature at each interface; then the coefficients are solved and expressed recursively. Based on the closed-form solution of FRFs, a fast semi-analytical method (SAM) is developed to solve the three-dimensional steady state heat conduction in arbitrary multilayered materials, and there are no limits on the number or the thickness of layers. The temperature fields under different kinds of heat flux in multilayered coatings are studied. Moving heat flux and convection on the surface are also considered.

To date few experimental studies of EHL film are at speed above 5 m/s, and most optical EHL experiment is based on classical ball-on-disc contact. This paper presents a newly developed optical EHL test rig in ball-on-ring contact for the investigation of film thickness at high speed. Tests are conducted under tractive rolling condition up to 52 m/s. Results show that, film thickness follows classical prediction at low speed, deviates but still increases at medium speed and finally decreases at very high speed; severe sliding occurs at high speed; the film thickness profile along motion direction changes from flat to wedge.

This paper presents a semi-analytical method (SAM) to solve sliding finite-length space contact problem with consideration of the effect of free end surface. The equation set based on the overlapping concept is analytically solved with tangential load considered and the explicit expressions for equivalent mirrored loads are obtained. Conjugate gradient method (CGM) is adopted to solve the pressure distribution and Fast Fourier transform (FFT) is used to speed up stress related calculation. The model is verified by FEM and shows a high conformity. Different line contact situations are discussed to explore the effect of free end surfaces.

This paper aims to investigate the effect of the hardness distribution by carburizing on the contact behaviors. A developed elastic–plastic contact model based on a semi-analytical method is used. The effect of hardness on elastic–plastic contact behaviors is considered by means of the linear hardness-yielding strength relationship. Different hardness distributions are considered to simulate the possible results obtained in heat treatment. The results show that the hardness distribution and carburizing time/case depth have different influence on the plastic strain under different loads and roughness, while its influence on the maximum contact pressure and contact area ratio is very limited.

This paper proposes a dynamic model to investigate skidding in angular contact ball-bearings with considering the interaction between balls and raceways, cage and lubricant. The differential equations governing the motions of bearing elements are established and solved using a fourth-order Runge–Kutta algorithm; traction forces between balls and raceways are evaluated based on elastohydrodynamic lubrication theory. The results show that the applied axial load significantly influences the behavior of skidding due to the changes of internal load, orbital and rotation speeds of ball under different operating conditions; appropriate axial load can be determined to avoid severe skidding.

Superlubricity of graphite and graphene has aroused increasing interest in recent years. Yet how to obtain a long-lasting superlubricity between graphene layers, under high applied normal load in ambient atmosphere still remains a challenge but is highly desirable. Here, we report a direct measurement of sliding friction between graphene and graphene, and graphene and hexagonal boron nitride (h-BN) under high contact pressures by employing graphene-coated microsphere (GMS) probe prepared by metal-catalyst-free chemical vapour deposition. The exceptionally low and robust friction coefficient of 0.003 is accomplished under local asperity contact pressure up to 1 GPa, at arbitrary relative surface rotation angles, which is insensitive to relative humidity up to 51% RH. This ultralow friction is attributed to the sustainable overall incommensurability due to the multi-asperity contact covered with randomly oriented graphene nanograins. This realization of microscale superlubricity can be extended to the sliding between a variety of two-dimensional (2D) layers., Superlubricity can be unstable in graphene systems, especially under high applied loads. Here the authors use microspheres uniformly coated by graphene to measure friction between 2D materials and show that superlow friction is preserved for long periods of time under high loads and various atmospheres.

Modeling study of angular contact ball bearing, which is subjected to a combined action of radial, axial and moment loads, is performed in this paper. The centrifugal force and the gyroscopic moment are especially considered. To analyze the spin-to-roll ratios at both ball-outer and ball-inner raceway contacts simultaneously, the model discards the hypothesis of “raceway control” by introducing a controlling equation of ball pitch angle. The method simplifies the solution procedure involved in determining ball equilibrium equations. Numerical examples verify the model and show its capabilities in predicting the bearing characteristic parameters such as contact angle, contact force and spin-to-roll ratio under various operating conditions. It is also shown that the effect of the centrifugal force is of significant importance that should not be neglected in the design and analysis of rolling bearings, especially at high-speed conditions.

Rough surface elastic–plastic contact performance is investigated in this paper. First, a computer program is developed to generate rough surfaces with given parameters; Then, the elastic–plastic contact model is developed based on minimization of complementary energy and semi-analytical method; finally, contact analysis for rough surfaces are conducted. The results show that kurtosis and skewness have significant effects on the contact performance under light-medium load; for heavy load condition and small skewness, the contact characteristic parameters change slightly along with kurtosis. Comparing with elastic contact, the low contact pressure and large contact area are predicted in elastic–plastic contacts.

In this paper, a method based on coordinate equivalence was presented to investigate the characteristic parameters of angular contact ball bearing such as contact angle and contact force between ball and raceways subjected to the combined radial, axial and moment loads, with considering the effects of centrifugal force and gyroscopic moment in high-speed conditions. The radial, axial and angular displacements are solved based on Newton–Raphson method rather than as the known variables. The method simplifies the procedure involved in determining derivatives for Newton–Raphson method. The results show good agreement with existent model and can be used to analyze the bearing performance, especially for high-speed condition. It was also shown that the inertial loads resulting from the high-speed condition have significant effect on the contact angle and contact force between ball and raceways and have to be considered in the bearing design and performance analysis.

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.

Oil–air lubrication is widely used in the high-speed rotary machines; the oil is usually in the form of discrete droplets. The lubrication behavior of the oil droplet is rarely investigated. This paper investigates the effect of the oil droplet on lubrication performance based on the developed transient lubrication model with consideration of starvation conditions. The oil droplet is modeled as spherical segment with different heights, base radius, and positions, which will change the inlet oil supply conditions. The results show that the oil droplet with large size can generate thick oil film which is close to the one in fully flooded condition and can remain long time; the position of the oil droplet entering the contact region also has significant effect on the lubrication performance.

This article presents a mixed lubrication model for point contacts with considering the inlet starvation and interasperity cavitations. The pressure distribution on the entire computational domain is obtained through solving a unified Reynolds equation system without identifying hydrodynamic or asperity contact regions. The Jacobsson–Floberg–Olsson mass-conservative boundary conditions are incorporated in the lubrication analysis based on Elrod’s algorithm. The inlet oil supply condition which may bring about starvation and local cavitation phenomenon is considered by defining the inlet lubricant thickness distribution. The fast Fourier transform based technique is employed to speed up the surface deformation calculation. A unique solution scheme is constructed to solve full film region, cavitation region, and contact region simultaneously. The model has been applied to the lubrication problems of textured surface under starved conditions. Numerical examples are analyzed and the results show that the present model can be used to investigate the lubrication performance under starved conditions, and that the solution methods are computationally efficient and robust.

Finite-length line contact conditions, existing in applications such as gears or roller bearings, lead to subsurface stress distribution influenced by the free boundaries. This paper presents a semi-analytical method (SAM) for the finite-length line contact problem, based on the overlapping concept and matrix formation, to consider the effect of two free-end surfaces. In order to obtain two free surfaces, three half-spaces with mirrored loads to be solved are overlapped to cancel out the stresses at expected surfaces. The error introduced by this method is analyzed and proven to be negligible. The conjugate gradient method (CGM) is used to solve the pressure distribution, and the fast Fourier transform (FFT) is used to speed up the elastic deformation and stress-related calculation. The model is verified by finite element method (FEM) and shows a high conformity and efficiency. Besides, the line contact situations are discussed to explore the effect of free surfaces.

This paper develops an analytical model to investigate the effect of inhomogeneity in races on the dynamic behaviors of rolling bearing. The governing differential equations are obtained based on the Hertz contact theory and bearing kinematic equations with the centrifugal force and frictions considered. The surface disturbed displacement caused by inhomogeneities is obtained by the semi-analytical method (SAM) and treated as local surface defect in equations of motion through load–deformation relation. For the first time, the effect of material inhomogeneity on dynamics of rolling bearing is explored. The result shows that the inhomogeneity can make the system motion more complicated. The inhomogeneity in the inner race has a greater influence than in the outer race.

Based on statistical analysis for reasons and impacts of oil-spill accident in ports and offshore areas in China, the possibility index system of oil-spill risk and impact assessment index system were set up, respectively. Take Tianjin Port for example, weight of each evaluation factor was determined by analytic hierarchy process (AHP), and the membership functions of evaluation factors were established by down semi-trapezoidal distribution. Then the possibility and impacts of oil spills were evaluated by multi-level fuzzy integrated evaluation model. And the overall effects of oil-spill risk in Tianjin Port were determined by two-dimensional risk matrix.