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As the companion paper of Part I, this paper aims to get more insight into the essence of lambda and to reveal its nature and role in the transition of lubrication states. Mixed lubrication (ML) model with micro-asperities contacts has been discussed in details in Part I.

Mimetic algorithm is used to get numerical solutions. Relationships between film thickness ratios and lubrication states transition with different external loads, rotating speeds, radial clearances, elastic modulus, surface hardness and roughness parameters are obtained.

The characteristic parameters of transitions from boundary lubrication (BL) to ML and ML to hydrodynamic lubrication (HL) are studied to determine how these parameters change with above factors. Finally, the essence and major influencing factors of lambda are summarized for such bearings.

In Part II, the authors believe that the paper presents for the first time: further insight into the essence of the lambda ratio, and its role in the lubrication states transition are given; the determinations of the characteristic parameters of transition from BL to ML and ML to HL are investigated for the first time; the characteristic parameters of transitions from BL to ML and ML to HL are also studied to determine how parameters (external load, rotating speed, radial clearance, elastic modulus, surface hardness and roughness parameter) change with above factors; a summary of the essence and major influencing factors of lambda for such bearings is given.

The purpose of this study is to solve this problem. Different lubrication states play a huge role in friction, wear and service life of parts. To ensure the reliability and power of the internal combustion engine, it is necessary to ensure that the friction pair has been in the best lubrication state. One of the key problems of lubrication state and transformation characteristics is to achieve real-time measurement of lubrication state.

Previous studies show that the contact resistance method is very effective in the qualitative analysis of lubrication state test. The circuit is simple and does not require expensive test equipment. But this method could not accurately reflect the film thickness ratio. Through a combination of experimental and theoretical analysis methods, the limitation of the contact resistance method could be overcome.

The relationship between the point contact film-thickness ratio and contact resistance was established, then the film-thickness ratio could be obtained through the contact resistance, thus providing the basis for determining the point contact lubrication state.

According to existing research, the lubrication state of the friction pair mainly was determined through two methods, the friction coefficient and film-thickness ratio. But there are limitations on either using Stribeck curves or optical interference methods. The method used in this paper not only provides a verified way of design theory and model, but is also beneficial to the formation of a new design theory.

A new real-time measurement method of lubrication state based on contact resistance is established and its practicability and veracity are verified by series experiments.

The aim of this paper is to study the effect of deterministic roughness and small elastic deformation of surface on flow rates, load capacity and coefficient of friction in Rayleigh step bearing under thin film lubrication.

Reynolds equation, pressure-density relationship, pressure-viscosity relationship and film thickness equation are discretized using finite difference method. Progressive mesh densification (PMD) method is applied to solve the related equations iteratively.

The nature and shape of roughness play a significant role in pressure generation. It has been observed that square roughness dominates the pressure generation for all values of minimum film thickness. Deformation more than 100 nm in bounding surfaces influences the film formation and pressure distribution greatly. Divergent shapes of film thickness in step zone causes a delay of pressure growth and reduces the load capacity with decreasing film thickness. The optimum value of film thickness ratio and step ratios have been found out for the maximum load capacity and minimum coefficient of friction, which are notably influenced by elastic deformation of the surface.

It is expected that these findings will help in analysing the performance parameters of a Rayleigh step bearing under thin film lubrication more accurately. It will also help the designers, researchers and manufacturers of bearings.

Most of the previous studies have been limited to sinusoidal roughness and thick film lubrication in Rayleigh step bearing. Effect of small surface deformation due to generated pressure in thin film lubrication is significant, as it influences the performance parameters of the bearing. Different wave forms such as triangular, sawtooth, sinusoidal and square formed during finishing operations behaves differently in pressure generation. The analysis of combined effect of roughness and small surface deformation has been performed under thin film lubrication for Rayleigh step bearing using PMD as improved methods for direct iterative approach.

This paper aims to provide efficient methods to calculate the friction coefficients and film thickness ratios in mixed lubrication (ML) regime for water lubricated bearings. Mathematical models consider influence of micro-asperities contacts which is based on the Gauss random distribution.

Effects of external loads, rotating speeds and radial clearances are obtained. Algorithm shown here is applied to a class of common industrial problems. Calculated Stribeck values are given and evaluated. The calculated and experimental results agree well which proves the correctness of the model.

In Part I, the authors believe that the paper presents the following for the first time: universal methods are developed for the calculation of friction coefficients and film thickness ratios (lambda) in ML regime; effects of different external loads, rotating speeds and radial clearances on friction coefficients and film thickness ratios are presented in detail; comparisons are made between the results predicted by the model and experimental results, and they agree rather well which proves the correctness of the model.

Present work successfully develops universal methods for predicting the friction coefficients and film thickness ratios.

The purpose of this paper is to explore the pure squeeze thin film elastohydrodynamic lubrication (TFEHL) motion of circular contacts with adsorption layers attached to each surface under constant load condition. The proposed model can reasonably calculate the pressure distributions, film thicknesses, normal squeeze velocities, and effective viscosities during the pure squeeze process under thin film lubrication.

The transient modified Reynolds equation is derived in polar coordinates using viscous adsorption theory. The finite difference method and the Gauss‐Seidel iteration method are used to solve the transient modified Reynolds equation, the elasticity deformation equation, load balance equation, and lubricant rheology equations simultaneously.

The simulation results reveal that the thickness of the adsorption layer and the viscosity ratio significantly influence the lubrication characteristics of the contact conjunction in the thin film regime. In additional, the turning points in the film thickness which distinguish thin film lubrication from elastohydrodynamic lubrication curve is found. In thin film region, the effective viscosity predicted by present model is better than that predicted by traditional elastohydrodynamic theory.

The paper develops a numerical method for general applications with adsorption layers attached to each surface to investigate the pure squeeze action in a TFEHL spherical conjunction under constant load condition.

The paper aims to determine whether the type selection and parameters determination of the compensation are most important for yielding the acceptable or optimized characteristics in design of hydrostatic bearings.

This paper utilizes the equations of flow equilibrium to determine the film thickness or displacement of worktable with respect to the recess pressure.

The stiffness due to compensation of constant‐flow pump increases monotonically as recess pressure increases. Also, the paper considers which is larger than that due to orifice compensation and capillary compensation at the same recess pressure ratio.

The findings show that the usage range of recess pressure and compensation parameters can be selected to correspond to the smallest gradient in variations of worktable displacement or film thickness.

The breakdown of laminar flow in the clearance space of a journal is considered, and the point of transition is considered in relation to experiments carried out with ‘bearings’ of large clearance. Experiments involving flow visualization with very large clearance ratios of 0.05 to 0.3 show that the laminar regime gives way to cellular or ring vertices at the critical Reynolds number predicted by G. I. Taylor for concentric cylinders even in the presence of an axial flow and at a rather higher Reynolds number in the case of eccentric cylinders. The effect of the transition on the axial flow between the cylinders is small. The critical speed for transition as deduced by Taylor, is little affected by moderate axial flows and is increased by eccentricity. The effect of critical condition on the axial‐flow characteristics of the bearing system appears to be negligible, again for moderate axial flows. Assuming that the results can be extrapolated to clearances applicable to bearing operation, the main conclusion of this paper is that the breakdown of laminar flow, which is a practical possibility in very high‐speed bearings, is delayed by eccentric operation.

Powder lubrication is widely used in industrial production, but most of the research that analyze the wear process and speculate on the wear mechanism of the tested specimens lacks reliability, and it is difficult to reveal the essence of the friction and wear process. The purpose of this paper is using the optical in situ observation method to observe the condition of the powder lubrication layer in real time and dynamically, and directly obtain the morphology change of the specimen during the whole wear process, which is helpful to the establishment of new tribological basic theories such as friction and wear mechanism and lubrication theory.

Mechanical model of powder lubrication is established considering asperity and powder layer, and the influence of adhesion effect on load and friction force is analyzed. The finite difference method is used to solve the above physical model, and the influence of the adhesion effect on load and friction force is analyzed. The total load and friction of the friction pair are composed of two parts: fluid and asperity. Based on the optical in situ observation method to build a test platform. The interface of the adhesion stage was observed by SEM.

When the film thickness ratio is less than 1, the local damage and diffusion of the powder layer are basically completed and the adhesion stage is entered. At this time, the asperity is not fully loaded, the powder layer is loaded by 50%, the asperity is less loaded, the deformation is small and the possibility of plastic flow is reduced. However, in the adhesion stage, the friction force is basically generated between asperity, and the friction force ratio of the asperity is 80%. Heavy load and surface roughness of the specimen are the necessary conditions for the powder adhesion period.

In this paper, the failure process of the powder layer at the friction interface with different roughness and load is studied based on the optical in situ observation method. Second, the contact surface with the micro-convex body and powder layer is simulated, and the influence of adhesion effect on the mechanical properties of the real contact surface in the process of powder lubrication is analyzed, thus providing theoretical guidance for mechanical processing, workpiece operation and lubrication design.

Mechanical model considering asperities and powder layer powder lubrication was established to analyze the influence of the adhesion effect on load and friction. Based on the optical in situ observation method to build a test platform. The tests found that the failure process of the powder lubricating layer includes five stages: powder complete stage, local failure stage, local failure diffusion stage, powder adhesion stage and complete failure stage.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2022-0322/

The analysis of lubricating properties and efficiency is important for aviation high-speed gear. So far, the project of lubricating properties and efficiency are processing under the condition of a given lubricating state, which is still depending on practical experience. This paper aims to mostly focus on the analysis of given lubricating state but lost sight of the relevance of lubrication parameters and lubricating state, which not only makes the analysis of aviation high-speed gear transmission and efficiency fail to trace to practical situation but also has an adverse effect on the reliance and validity of the project.

Based on this, the numerical model of spraying oil and oil film spreading is established, and the quantitative relationship between spray lubrication parameters and spreading characteristics of oil film is studied. According to the geometric and mechanical conditions of meshing points and taking the influence of rich-oil/starved-oil lubrication and roughness of teeth surface into consideration, corrected film thickness under condition of elasto-hydrodynamic lubrication and lubricating state of mesh points are analyzed. On this basis, power consumption and efficiency of gear transmission are also calculated by figuring out the solid friction and oil friction separately.

Through the research of this thesis, the effect of friction power consumption and efficiency with lubrication parameters is discussed. The effect of lubrication parameters on friction power consumption and efficiency of gear is complex. With the increase of spreading film thickness and film length, the frictional power consumption is less and the efficiency is higher.

This work provides a systematic technological approach to lubrication design and efficiency calculation of aviation high-speed gear transmission, which has remarkable engineering significance for the accurate lubrication design of the aviation mechanical parts.

The purpose of this paper is to propose a wheel/rail mixed lubrication model to study the water lubrication behavior of wheel/rail contact interface.

The numerical simulation method is applied in this paper. A deterministic mixed lubrication model considering surface roughness and transient state is established. The quasi-system numerical and finite difference method are used for numerical solution. The model is verified by comparing with the experimental data in the literature under the same conditions.

Under wet conditions, the change of train speed will change the lubrication state of the wheel/rail contact interface. With an increasing speed, the average film thickness and the film thickness ratio increase, while the adhesion coefficient, the contact load ratio and the contact area ratio decrease. When the creep ratio increases from 0% to 0.5%, the wheel/rail adhesion coefficient and subsurface stress increase sharply. With the increase of axle load, the average film thickness decreases and the adhesion coefficient increases.

This paper aims to improve the mixed lubrication theory by analyzing the characteristics of wheel/rail friction and lubrication, so as to provide some guidance and theory for train driving behavior.

Using the deterministic model, the lubrication state of the wheel/rail contact interface affected by various external factors and the adhesion behavior of wheel/rail progressive process from boundary lubrication to mixed lubrication are studied.