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To form and develop a new mode of mixed elastohydrodynamic lubrication (mixed EHL) which is more realistic and of more application values to a practical elastohydrodynamic contact on gears, cams and roller bearings than the previous and current existing mixed EHL models.

The representative theoretical and experimental studies on elastohydrodynamic lubrication (EHL) and mixed EHL carried out in the previous and recent time, including those of the author, are reviewed. The obtained results on EHL and mixed EHL in those studies and the viewpoints on the mode of mixed EHL based on those results developed in those studies are compared and evaluated. Strong proves are formed on the new mode of mixed EHL proposed in the present paper based on these comparisons and evaluations.

Strong viewpoints are formed on the mode of the occurrence of dry contact in EHL in a practical concentrated contact. A new mode of mixed EHL is proposed by incorporating this mode of the occurrence of dry contact in EHL. Also, comments and evaluations on the previous researches on mixed EHL are made.

A very useful material for the engineers who are engaged in the design of EHL on gears, cams and roller bearings, and for the tribology scientists who thrust efforts in studying EHL and mixed EHL both by theoretical modeling and by experiments.

A new mode of mixed EHL is originally proposed by incorporating the finding of a more realistic mode of the occurrence of dry contact in EHL. This new mode of mixed EHL should become the direction of the theoretical research of mixed EHL in the future time. It provides a clearer way to this research.

To develop a fairly different EHL inlet zone analysis for investigating the contact‐lubricant interfacial limiting shear stress effect on line contact EHL film thickness in isothermal conditions. This analysis is purposed to give fast and qualitatively correct results.

A Grubin‐like EHL inlet zone analysis is derived with closed form of the analytical results of the EHL film thickness, the EHL film pressure, the contact‐lubricant interfacial shear stress and the contact‐lubricant interfacial slipping velocity in the EHL inlet zone based on the assumption of the contact‐lubricant interfacial limiting shear stress in the EHL inlet zone. In this analysis, the lubricant is allowed to slip at the contact surface; The inlet contact surface shape is known from results referenced in this paper; The physical condition for the presence of the film slippage is incorporated; The lubricated area is divided into different kinds of film slippage zones where are, respectively, applied different governing equations. Three deterministic equations in this analysis are obtained and solving these coupled equations gives the solutions of the boundaries of the slip zone and the percentage reduction of the central film thickness by the contact‐lubricant interfacial limiting shear stress effect in this EHL.

Compared with the earlier approaches to the present problem, the present analysis has the advantage of giving fast and qualitatively correct solutions. The results obtained from the present analysis show that the contact‐lubricant interfacial limiting shear stress effect on EHL film thickness is usually strong when the contact‐lubricant interfacial limiting shear stress in the EHL inlet zone is low; This effect can greatly reduce the global EHL film thickness especially in severe operating conditions.

A very useful material for the academic researcher and the engineer who are engaged in the study and measurement of the effect of the contact‐lubricant interfacial limiting shear stress on EHL film thickness and EHL film pressure.

A fairly different EHL inlet zone analysis is originally developed based on the assumption of the contact‐lubricant interfacial limiting shear stress in the EHL inlet zone. The physical condition for the contact‐lubricant interfacial slippage is first incorporated in this analysis. Deterministic governing equations in this analysis are derived and solving these coupled equations gives the final solutions of the present problem. This analysis has the advantage of giving fast and qualitatively correct solutions. It convincible shows the contact‐lubricant interfacial limiting shear stress effect on EHL film thickness and EHL film pressure in the present EHL.

To make a derivation of the load‐carrying capacity of elastohydrodynamic lubrication for special operating conditions, i.e. extremely heavy loads or extremely low rolling speeds based on the Newtonian fluid model by taking the Grubin‐type EHL inlet zone analysis, justify the load‐carrying capacity of elastohydrodynamic lubrication film in these operating conditions, and propose future trends of the research in EHL and mixed EHL based on the obtained results in the present paper.

A Grubin‐type EHL inlet zone analysis is carried out for the isothermal EHL of line contacts in special operating conditions, i.e. extremely heavy loads or extremely low rolling speeds based on the Newtonian fluid model. Comparison is made between the central EHL film thickness in line contacts, respectively, predicted by conventional EHL theories and accurately predicted from the present analysis for these operating conditions. An interpretation is made for the EHL film thickness in these operating conditions by taking the approach of the transportation and flow of the fluid through elastohydrodynamic contact when the EHL film is, respectively, thick and molecularly thin in the Hertzian zone. Conclusions are drawn on the load‐carrying capacity of EHL, EHL contact regimes and mixed EHL regimes in these operating conditions.

The present EHL inlet zone analysis shows that the EHL film thickness in the Hertzian zone is on the nanometer scale and the lubricant is non‐continuum across the film thickness in the Hertzian zone at relatively heavy loads in line contact EHL when the dimensionless rolling speed is lower than the dimensionless characteristic rolling speed U_ch=0.0372W^1.50/G. In this case, the central EHL film thickness in line contact EHL predicted by the conventional EHL theory may be several orders of magnitudes higher than that accurately predicted. This difference may be greater for heavier loads.The present results for line contact EHL based on the Newtonian fluid model show that in line contact EHL, for relatively heavy loads and the dimensionless rolling speed lower than the dimensionless characteristic rolling speed U_ch=0.0372W^1.50/G, the EHL analysis needs to further incorporate the lubricant non‐continuum effect across the film thickness in part of the lubricated area to investigate the EHL film thickness and the EHL film pressure in the contact in this very low film thickness condition; only the results based on such an analysis are believable for the EHL stage where the lubricant film thickness in the Hertzian zone approaches to zero and then vanishes; the results for EHL based on the Newtonian fluid model is unable to conclude that the EHL film thickness in the Hertzian zone is zero and dry contact occurs between the contact surfaces in EHL in any operating condition for ignoring the lubricant non‐continuum regime governing the EHL stage preceding the occurrence of the zero lubricant film thickness in EHL.

A very useful source of information for academic scientists, engineers and tribologists who are engaged in the study and application of the theory of elastohydrodynamic lubrication.

A derivation is first carried out for the isothermal EHL of line contacts in extremely heavy loads or extremely low rolling speeds by taking the Grubin‐type EHL inlet zone analysis by the present paper. Results and conclusions on the load‐carrying capacity of EHL in these operating conditions are first strict and thus convincing. These results are also original in clarifying the future trends of the researches in EHL and mixed EHL.

Internal gearings are commonly used in transmissions due to their advantages like high-power density. To ensure high efficiency, load-carrying capacity and good noise behavior, a profound knowledge of the local gear mesh is essential. The tooth contact of internal gears relates to a convex and concave surface that form a conformal contact. This is in contrast to external gears, where two convex surfaces form a contraformal contact. This paper aims at a better understanding of conformal contacts under elastohydrodynamic lubrication (EHL) to improve the design of internal gearings.

An existing numerical EHL model is used for studying the characteristic properties of a hard conformal EHL line contact. A hard contraformal EHL line contact is studied as reference. Non-Newtonian fluid behavior and thermal effects are considered. By taking into account the local contact conformity and kinematics, the effects and relevance of the curvature of the lubricant gap and micro-slip are analyzed. In a parameter study, scale effects of the contact radii on film thickness, temperature rise and friction are examined.

The curvature of the lubricant gap and effects of micro-slip are small in hard conformal EHL line contacts. For high micro-slip, it can be neglected. Hence, the modeling of conformal contacts using an equivalent geometry of the contact problem is reasonable. The parameter study shows beneficial tribological aspects of the conformal contact compared to the contraformal contact. Higher film thickness and lower fluid coefficient of friction are observed for conformal contacts, which can be attributed to lower pressures for the case of the same external normal force, or to a higher contact temperature rise for the case of equivalent contact pressure.

Despite its widespread existence, the local geometry and kinematics in hard conformal EHL line contacts like in internal gearings have been rarely studied. The findings help for a better understanding of local contact characteristics and its relevance. The quantified scale effects help to improve the efficiency and load-carrying capacity of machine elements with hard conformal EHL contacts, like internal gearings.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2022-0366/

This paper studies elastohydrodynamic lubrication (EHL) of line contacts for the slide‐roll ratios 0‐2 based on the assumptions of interfacial shear strength and interfacial slip. It is shown that the viscoelastic, viscoplastic and non‐continuum fluids distribute from the inlet zone to the Hertzian contact zone in order for a given operating condition when the load and rolling speed exceed critical values. For the rolling speed below the critical, the distributing fluids from the inlet zone to the Hertzian contact zone in order are viscoelastic and non‐continuum when the load exceeds a critical value. These show a multirheological behavior EHL film, formed in a contact, which may represent a mode of mixed lubrication. For this mode of lubrication, the fluid model should handle both inlet and Hertzian contact zones where the fluids are, respectively, continuum and non‐continuum. A new EHL analysis and theory, therefore needs to be established.

To review, analyze and present the effects of the contact‐fluid interfacial shear strength and contact‐fluid interfacial slippage and the critical importance of these effects in elastohydrodynamic lubrication (EHL).

The experimental and theoretical research results of the contact‐fluid interfacial shear strength and its caused contact‐fluid interfacial slippage in hydrodynamic lubrication and especially in EHL obtained in the past decades and progressed in recent years by the present author and by others are reviewed. Analysis and presentation are made on both the contact‐fluid interfacial shear strength versus fluid pressure curve for a given bulk fluid temperature in an isothermal EHL and the influence of the bulk fluid temperature on this curve.

It is very clearly and well understood from the present paper that the value of the contact‐fluid interfacial shear strength in the inlet zone in an EHL contact, i.e. at low EHL fluid film pressures is usually low and usually has rather a weak dependence on the EHL fluid film pressure. This proves the correctness of the EHL theories previously developed by the author based on the assumption of this low value and dependence on the EHL fluid film pressure of the contact‐fluid interfacial shear strength. It is also very clearly understood that the bulk fluid temperature usually has a strong influence on the value of the contact‐fluid interfacial shear strength in EHL and the increase of this temperature usually significantly reduces the value of the contact‐fluid interfacial shear strength in EHL.

A very useful material for the engineers who are engaged in the design of EHL on gears, cams and roller bearings, and for the tribology scientists who thrust efforts in studying EHL and mixed EHL both by theoretical modeling and by experiments.

A new and generalized mode of mixed EHL is originally proposed by incorporating the finding of a more realistic mode of the contact regimes in a practical mixed EHL based on the contact‐fluid interfacial shear strength and contact‐fluid interfacial slippage effects. This mode of mixed EHL should become the direction of the theoretical research of mixed EHL in the future.

After working through and discussing this case, learners should be able to:1. evaluate the financial condition of Ellerine Holdings Limited (EHL) at the time of the merger proposal and use it to make inferences about the company’s ability, at that time, to function effectively as a going concern;2. identify the conditions within EHL and in the operating environment that may have made it necessary for EHL to seek to change its business strategy;3. determine whether the acquisition price offered to EHL by African Bank Investments Limited (ABIL) was fair; and4. compute the value accretion/loss expected to be realised by the existing shareholders of ABIL and EHL under the merger proposal.

This case situates the directors of Ellerine Holdings, a furniture retail company that merged with African Bank Limited in 2007, reflecting on the events that led up to both entities being placed into business rescue in 2014 and asking whether the merger was the cause of the demise. If they had chosen an alternative partner, would the results have been different?

Masters Level students – MBA or Masters in Finance.

For instructors.The following material has been provided with the teaching note for instructors:- Teaching Note.- Johannesburg Stock Exchange News System (SENS) extract of related original filing.For students.The following supplementary material has been provided to accompany the case:- Financial information on the two companies (Excel spreadsheet).- Johannesburg SENS extract of related original filing.

CSS 1: Accounting and Finance.

The purpose of this study is to investigate the influence of surface texture on the subsurface characteristics of contact interfaces under elastohydrodynamic lubrication condition. As a typical contact form of gears and bearings, the optimization of friction characteristics at the elastohydrodynamic lubrication (EHL) interface has attracted the attention of scholars. Laser surface texturing is a feasible optimization solution, but there have been concerns about whether the surface texture of high-pair parts will affect their fatigue life.

To examine the impact of texture preparation on the subsurface characteristics of high-pair interfaces under EHL conditions, a point contact EHL model is developed that takes into account the effect of textured surface topography. The pressure and thickness of the oil film are calculated as input parameters under different loads and entrainment velocities. The finite element method is used to simulate the impact of textures with varying diameters, densities and depths on the subsurface characteristics of the elastohydrodynamic interface. According to ISO 25178, analyze the relationship between 3D topography parameters and subsurface characteristics and study the trend of friction characteristics and subsurface characteristics based on the results of the ball on disc friction tests.

The outcomes suggest that under different rotational velocity and load conditions, the textured surfaces exhibit improved friction reduction effects; however, the creation of textures can result in significant subsurface plastic deformation and local peeling. The existence of texture makes the larger stress zone in the subsurface layer closer to the surface, leading to fatigue failure near the surface. Reasonable design parameters can help enhance the attributes of the subsurface. A smaller Sa and a Str greater than 0.5 can achieve ideal subsurface properties on the textured surface.

This paper investigates the influence of surface texture on the friction and subsurface characteristics of EHL interfaces and analyzes the impact of surface texture on interface contact performance while achieving lubrication improvement functional characteristics. The results provide theoretical support for the optimization design and functional regulation of surface texture in EHL interfaces.

The peer review history for this article is https://publons.com/publon/10.1108/ILT-10-2023-0324/

The purpose of this paper is to propose an simple and efficient stiffness model for line contact under elastohydrodynamic lubrication (EHL) and to investigate the gear meshing stiffness by the proposed model.

The method combines the surface contact stiffness and film stiffness as EHL contact stiffness. The EHL contact stiffness can be calculated by the external load and displacement of the load action point. The displacement is the sum of deformation of the film and contact surface and is equal to the distance of the mutual approach of two contact bodies.

The conclusion is drawn that the contact stiffness calculated by the proposed model is smaller than that by the minimum film model and larger than that by the mean film model. It is also concluded that the gear meshing stiffness under EHL is slightly smaller than that under dry contact.

The EHL contact stiffness can be obtained by the increment of external load and mutual approach directly. The calculation of oil film stiffness and surface contact stiffness separately is avoided.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2019-0465

Seeks to study the dependence of the shear strength of a fluid on the fluid pressure and the bulk fluid temperature, respectively, theoretically for given bulk fluid temperatures and fluid pressures in the whole ranges of fluid pressure and bulk fluid temperature.

The analyses are, respectively, carried out with emphasis on the dependence of the shear strength of a fluid in liquid state, i.e. at low pressures on the fluid pressure and the bulk fluid temperature for given bulk fluid temperatures and fluid pressures based on the theory of the compression of the fluid by the pressurization of the fluid.

The fluid shear strength versus fluid pressure curve in the whole range of fluid pressure and the fluid shear strength versus bulk fluid temperature curve in the whole range of bulk fluid temperature, respectively, for a given bulk fluid temperature and a given fluid pressure are obtained. It is shown by this fluid shear strength versus fluid pressure curve that, for a given bulk fluid temperature, when the fluid is in liquid state, i.e. at low pressures, the value of the shear strength of the fluid is insensitive to the variation of the pressure of the fluid and is low: when the fluid is in solidification state, i.e. at medium and high but not extremely high pressures, the value of the shear strength of the fluid is the most sensitive to the variation of the pressure of the fluid and is very approximately linearly increased with the increase of the pressure of the fluid; when the fluid is in high solidification state, i.e. at extremely high pressures, the value of the shear strength of the fluid is insensitive to the variation of the pressure of the fluid and is the highest, i.e. approaches the value of the shear strength of the fluid in solid state.

Extends one's knowledge of the shear strength of a fluid in the while ranges of pressure and temperature.