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The purpose of this paper is to discuss the combined effects of the deterministic surface roughness and porous structure on the lubrication property of the multi-layer bearing.

Digital filtering technique and Kozeny-Carman equation are used to simulate the random Gauss surface and the internal pore structure of the porous bearing, respectively. Effects of surface morphology, structure and pores on the lubrication property are discussed by using the finite difference method.

Results show that the lubrication performance of the multi-layer bearing increased with the increase of the surface roughness. Also, the transverse surface is better than that of the longitudinal surface. Moreover, lubricating property is getting worse with the increase of the height of each layer and the porosity. The lower permeability surface is beneficial to improve the lubrication performance when the total porosity is certain.

The effect of the Gauss roughness parameters on the detail of lubrication performance are analysed, such as the migration of the oil film rupture point position, the expansion of the pressure distribution region and the fluctuation of the pressure distribution curve with the roughness parameters. The combined effects of surface roughness, multi-layer structure and the internal pore parameters on the hydrodynamic behaviours of multi-layer porous bearing are analysed. This work is beneficial for the analysis of the tribological property and the structural design of multi-layer bearing.

The purpose of this paper is to explore the pure squeeze elastohydrodynamic lubrication motion of circular contacts with surface roughness under constant load conditions. The proposed model can reasonably calculate the effects of surface roughness on the transient pressure profiles, film shapes, and normal squeeze velocities during the pure squeeze process.

Based on Christensen's stochastic theory, the transient modified Reynolds equation is derived in polar coordinates to consider the effects of surface roughness. 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 circular type roughness possesses storage oil capacity. Comparatively, the radial type roughness possesses leak oil capacity. Therefore, the film thickness is found with circular type roughness, followed by smooth, and then radial type roughness. In additional, the central dimensionless pressure is found with radial type roughness, followed by smooth, and then circular type roughness.

A numerical method for general applications with surface roughness was developed to investigate the pure squeeze action in an isothermal EHL spherical conjunction under constant load conditions, but without asperities contact.

The purpose of this paper is to analyze and discuss the coupled effects of surface roughness and flow rheology for a homogeneous mixture of Newtonian base oil and power law fluids on the performance of elastohydrodynamic lubrication (EHL) circular contact problems.

The average flow model is adapted for the interaction of the flow rheology of lubricant and surface roughness. The average Reynolds type equation (ARTE) and the related flow factors (which describes the coupled effects of surface roughness and flow rheology of a mixture), the viscosity‐pressure and density‐pressure relations equations, the elastic deformation equation, and the force balance equation are then solved simultaneously. The multilevel multi‐integration algorithm and Gauss‐Seidel iteration method are utilized to calculate the film thickness and pressure distributions of the EHL circular contact problems effectively.

The effects of volume fraction, flow index of power law fluid, and surface roughness parameters (Peklenik number, standard deviation of composite surface roughness) on the film thickness and pressure distributions are discussed. The results show that the effects of surface roughness should be considered especially in EHL contact problems.

The EHL of circular contacts lubricating with mixture of two lubricants is first analyzed. The coupling effects of surface roughness and flow rheology of mixture (a Newtonian fluid and a power‐law fluid) on the EHL performance are first discussed in this paper.

This study aims to present a numerical solution for the analysis of the influence of surface roughness as presented by a sinusoidal ripple of different amplitude and wavelength on the performance of transient elastohydrodynamic lubrication at motion start-up under different operational parameters of entraining speed and load as well as different acceleration rates.

A statistical asperity micro-contact model represented by a sinusoidal ripple expressed by two parameters (wavelength and undeformed amplitude) is considered. The ball equation of motion is used to calculate the force on the ball as it starts to move. The time-dependent Reynolds equation is solved together with surface deformation and statistical asperity models using the Newton–Raphson technique with the Gauss–Seidel iteration method.

The behaviour of the film thickness was found to be strongly influenced by the acceleration rate for different ripple amplitude and wavelength parameters. The effect of increasing the final entraining speed will eventually lead to rapid film thickness build-up and increase the film thickness jump at the moment of motion start-up. The effect of increasing applied load is to reduce the deviation of the minimum film thickness jump at the start-up of motion, making its value approximately equal to the steady-state value over the entire run-time period.

Influence of surface roughness for various wavelength and undeformed amplitude on the performance of transient elastohydrodynamic lubrication at motion start-up is presented at different acceleration rates as well as for different operating parameters of entraining speed and load. Ball equation of motion is used to calculate the force on the ball as it starts to move.

The purpose of this paper is to investigate the effects of surface topography, including surface roughness, circumferential waviness and radial taper, on hydrodynamic performance of liquid film seals considering cavitation.

A mathematical model of liquid film seals with surface topography was established based on the mass-conservative algorithm. Liquid film governing equation was discretized by the finite control volume method and solved by the Gauss–Seidel relaxation iterative algorithm, and the hydrodynamic performance parameters of liquid film seals were obtained considering surface roughness, circumferential waviness and radial taper separately.

The results indicate that the values of load-carrying capacity and frication torque are affected by the surface topography in varying degrees, but the effect is limited.

The results presented in the study are expected to aid in determining the optimum value of structural parameters for the optimum seal performance because of the realistic model which considers both surface topography and cavitation.

This paper aims to investigate the effect of surface roughness (radial and azimuthal) and viscosity variation on a squeeze film of a conical bearing with a non-Newtonian lubricant by using Rabinowitsch fluid model.

The main objective is to determine the stochastic nonlinear modified Reynolds equation for rough conical bearing. Later, first-order closed-form solutions are obtained using a small perturbation method and are numerically solved using the Gauss quadrature method.

The findings of this paper, numerical calculations, are analyzed for pressure, load carrying capacity and response time. The simulated results indicate that the influence of surface roughness increases the pressure, load carrying capacity and response time, whereas the viscosity variation factor decreases the pressure, load and response time.

According to both types of surface roughness with viscosity variation, the performance of a squeeze film rough conical bearing was improved by using Rabinowitsch fluid model. As it is inevitable to consider viscosity variation for bearing designer, it leads to a long life period of conical bearing.

The purpose of this study is to investigate the combined effect of surface force, solvation and Van der Waals forces and surface topography parameters of amplitude and wavelength on the formation of ultrathin films for elastohydrodynamic lubrication of point contact problems.

The Newton–Raphson technique is used to simultaneously solve the Reynolds’ film thickness including surface roughness and elastic deformation, surface force of solvation and Van der Waals forces and load balance equations. Different values of surface amplitude and wavelength were simulated in addition to the load variation.

The simulation results revealed that roughness effects are important as the film thickness decreases. The oscillation in the pressure and film thickness is due to the combined action of the solvation force and surface topography parameters. The limiting values of the surface topography parameters of the amplitude and wavelength varied and depended on the load. For different values of wavelength and load, amplitude values up to 0.25 nm have no effect on ultrathin film formation.

The combined effect of the surface force and surface roughness on the formation of ultrathin films was evaluated for elastohydrodynamic lubrication of point contact problems under different operating conditions of load and surface topography parameters of amplitude and wavelength. The limited surface topography parameters of the amplitude and wavelength are shown and analyzed.

The purpose of this paper is to investigate the effects of surface topography, including surface roughness, waviness and taper, on the cavitation of liquid film lubricated mechanical seals (LFL-MS).

A universal governing equation considering cavitation is established, and an equivalent relative density is defined to characterize the cavitation degree. The equation is discretized by the finite volume method and solved by the Gauss–Seidel relaxation scheme.

Results indicate that both radial length and a circumferential width of the cavitation zone and cavitation degree are affected significantly by the waviness amplitude and taper, but the effect of surface roughness is limited.

Effect mechanism of surface topography on the cavitation of LFL-MS is investigated and cavitation degree is reflected by an equivalent relative density. The results further help to comprehensively explore the cavitation mechanism.

The purpose of this paper is to focus on the creation of an isothermal elastic ring-liner model to highlight, through stresses, the occurrence of the plastic deformation in certain crank angles under extreme dry lubrication conditions.

The stresses that are exported from this analysis are pointing out not only the necessity for an elastoplastic model to be created, but also the importance of predicting the correct friction coefficient, as pointed out by both the contact surface stress and that in depth of the two bodies in contact.

The comparison between the finite element model and the adhesion mathematical model of Johnson, Kendall and Roberts seals the importance to calculate the interaction forces, acting on the common solid surface, in the pursuit of defining a propriate contact patch. Additionally, a three-dimensional ring model is built, highlighting the importance of the modeling surface’s micro asperities for a solid stress analysis. Also, numerical experiments are conducted, in contact with the cylinder and a piston ring made of an iron alloy and of two different plating materials, such us Chromium (Cr) and Chromium‒Nickel Alloy (CrN). The ability to calculate the stress concentration factor is also described.

A three-dimensional ring model is built, highlighting the importance of the modeling surface’s micro asperities for a solid stress analysis. Also, numerical experiments are conducted, in contact with the cylinder and a piston ring made of an iron alloy and of two different plating materials, such us Chromium (Cr) and Chromium‒Nickel Alloy (CrN). The ability to calculate the stress concentration factor is also described.

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.