Abstract This paper proposes a novel approach to analyze the inverse problems of elastohydrodynamic lubrication (EHL). First, a finite-difference method is employed to discretize the elastic deformation and the force balance equations. The discretizing equations can be rearranged into a matrix form. The pressure distribution can be expressed in an appropriate function and then substituting it into the matrix form. The least-squares error method is adopted to find the undetermined coefficients, which generates a smooth pressure distribution based upon a small number of measuring points on the film thickness map and overcomes the problems of pressure fluctuations obtained from the traditional methods. The apparent viscosity can be solved from the Reynolds equations by using the least-squares method to predict the optimum value of the pressure-viscosity index ( ). The proposed method is applied to analyze four kinds of the inverse problems, namely, EHL of line contacts, EHL of point contacts, pure squeeze EHL motion of circular contacts, and elastohydrodynamic thin film lubrication (EHTFL). This paper discusses the effects of the implemented errors on the predicted value of apparent viscosity. The errors are implemented at the film thickness, the load, the effective elastic modulus, the viscosity at ambient pressure, and the mean velocity. Results show that the implemented errors in load and effective elastic modulus have a significant influence on the accuracy of the results, but the errors in average velocity and in the viscosity at ambient pressure do not have a significant effect. In these implemented errors, the resolution of the film thickness measurement plays the most important role in determining the accuracy of the apparent viscosity. Even when errors in the film thickness measurements are deliberately introduced, the inverse approach still provides a satisfactory value of the pressure-viscosity index. The resulting apparent viscosity errors are much smaller than those generated when using the traditional inverse method. The inverse approach can allow higher measurement error than traditional inverse method, and the allowable resolution range can be increased to about 3-10 times. Base on the viscous adsorption theory, the modified Reynolds equation is derived for EHTFL. In this theory, the film thickness between lubricated surfaces is simplified as three fixed layers across the film, and the viscosity and the density of lubricant vary with pressure in each layer. The difference between classical EHL and EHTFL is investigated to find the important parameters of EHTFL. Results show that the proposed model can reasonably calculate the film thickness and the viscosity under EHTFL. Adsorbent layer thickness and viscosity significantly influence the lubrication characteristics of the contact conjunction. The inverse approach is developed to evaluate the pressure of contact region, pressure-viscosity index ( ) of oil film, and the film thickness and viscosity of adsorbent layer under EHTFL. This paper also uses a self-development EHL tester with the optical interferometry equipment to observe the EHL film thickness map of circular contacts under the steady state and the pure squeeze motion. The inverse approach can be used to estimate the pressure distribution on a film thickness map obtained from optical EHL tester. By using this pressure distribution, the estimated pressure-viscosity index can be obtained. Result shows that the inverse approach predicts a larger value of the pressure-viscosity index than the actual value. The error between the actual and the estimated values of is less than 7 percent. When the minimum film thickness is less than 30 nm, the inverse approach based on EHTFL theory can reduce the error between the actual and the estimated values of .

Abstract Since emulsions combine good lubricating and cooling capabilities, they have been widely used in metal rolling and cutting. This study first uses AR2000 rheometer to measure viscosity of emulsions under atmospheric pressure. The results of the test show that the viscosity of emulsions is approximately the highest in the 80% oil volume fraction. Meanwhile, the viscosity drops along with increasing the shear rate, it proves that emulsions are a pseudoplastic fluid. This study uses an EHL squeeze tester to explore the effects of squeeze velocity, load and volume fraction concentration of oil phase of emulsions on the dimple film thickness in the contact conjunction of squeezing lubrication. Results show that the dimple becomes deeper with increasing squeeze velocity. When the load increases, the dimple can keep longer due to higher hertz pressure. Furthermore, emulsions which have the higher oil volume fraction, have the higher maximum dimple depth under the same load and squeeze velocity. The results are different that the viscosity of 80% emulsions is higher than crude oil under atmospheric pressure. It is because that the significantly effect of pressure on the viscosity of oil phase, and the surface viscosity between oil and water phases can be ignored. Keywords: emulsions, EHL, dimple

The prime function of lubricating additives are to strength or improve the effect of lubrication and the unti¡Vwear capability of lubricating base oil. This research use the self-development EHL tester to explore the effects of ellipticity parameter of ring , load, speed, concentration and particle of lubricating additives and slip ratio on the film thickness.. During pure rolling, the film thickness increases with increasing speed, but decreases with increasing load, and the effect of speed on the film thickness is more obvious than the effect of load. The film thickness of lubricating additives varies insiginificant when the concentration of lubricanting additives are 1% and 3%, but it increases evidently at 7%. The effect of concentration developes good function of lubricant just under the condition of high speed and low load. Smaller particle of MoS2 has better lubricant effect than that it bigger. The number of particle of MoS2 distributed over lubricant contact zone increase with increasing concentration . The film thickness is getting thick when the ellipticity parameter increases. The minimum film thickness and central film thickness will decrease when slip ratio increase. That means , slip ratio and film thickness have a inversive relationship. Furthermore, when slip ratio increases, the central film thickness will decrease rapidly, but the minimum film thickness will just have a gentle decrease. It still has lubricant effect under the roll-slip state when the particles are smaller. During pure slipping, the bigger the particles, the easier it piles up on the entering area, and it makes lubricating oil can not enter the contact area easily.

Abstract With the advent of new technology, various machine structures and elements appear delicate and diminutive so that the nanotribological studies are needed in the modern mechanical technological development. Thin film lubrication will be indispensable as the basis of key-technology in high-technological devices and ultra-precision machines. Therefore, the research of thin film lubrication in the nanometer order is very important. In this research uses a self-development optical elastohydrodynamic lubrication (EHL) tester to simulate the oil film characteristics in the contact region between steel ball and sapphire under the pure rolling condition. First, the variation of oil film thickness on the contact region is observed by using the optical interference principle. An inverse approach of EHL is employed to investigate the pressure distribution on the contact region of lubricant. Final, the oil thickness and pressure distribution are substituted into Reynolds equation to predict the pressure-viscosity index of lubricant. Results show that the oil film thickness increases with increasing rolling speed, and curvature radius of steel ball, but decreases with increasing load. Moreover, when the oil thickness of ester lubricant is less than 17nm, the film thickness is obviously deviated that predicted by the classical EHL theory, and the pressure-viscosity index increases from 0.8195 to 0.9093. This result indicates that the ratio of the adsorbent layer to the oil film increases and causes the increase of the lubricant viscosity.

Elastohydrodynamic lubrication (EHL) allows transfer of power and forces in gears and rolling bearings without surface-to-surface contact and is the basis for a continuously variable transmission studied in this report. Previous research constructed models and derived solution methods, but often lacked full explanations of the approach and was usually applied to limited and specific cases. This report precisely develops the numerical solution of EHL contact and includes the more general cases of elliptical contacts and side-slip. The model and numerical method are validated on known benchmark cases and test results. Side-slip is investigated and the results shown in this report. Finally, the model is used to determine the film thickness and pressure of a contact patch under identical conditions to that in a physical drive developed by Fallbrook Technologies in Austin, TX. A minimum film thickness of 0.8978 [mu]m is found, setting a benchmark for the maximum allowable surface roughness values to prevent surface-to-surface contact. Additionally, under normal drive conditions the film thickness to surface roughness ratio is in the range of ideal values for maximum life. / text

This study focuses on a secondary school in an Indian-African suburb of Merewent in KwaZulu-Natal, an example of a suburban school where English as a Home Language (EHL) is taught to a majority of non-native English learners from township schools. The EHL classrooms were investigated for ‘communicativeness’ and then compared to English as a Second Language (ESL) classrooms. It might be expected that EHL classrooms would exhibit an affinity with ESL classrooms. However, although non-native EHL has many aspects in common with ESL, there were significant differences between the two. The most important difference from the standpoint of Communicative Language Teaching (CLT) was in the learning content selection, with the EHL settings using more literary works, and so focusing less on the direct teaching of grammatical forms. However, a disturbing pattern was the inability of the learners in both sets of settings to take full advantage of CLT, which suggested that the learners might not be at the appropriate level of language development.

The reduction or elimination of leakage of hydraulic fluid from fluid power systems is considered a fundamental prerequisite for the expanded use of fluid power. There is also a need to reduce seal friction to both reduce energy dissipation and eliminate control problems. These seals are developed through empirical means at the present time, since the fundamental physics of seal operation has been unclear. This research develops numerical models for analyzing reciprocating hydraulic rod seals with various rod surfaces. These models consist of coupled fluid mechanics, contact mechanics and deformation analyses. Both flooded and starved lubrication boundary conditions are applied. For seals with a smooth rod and a plunge-ground rod, the model combines a 1-D finite volume Reynolds equation solver with a 2-D axisymmetric finite element deformation and static contact mechanics analyses, and a Greenwood-Williamson contact mechanics analysis with rod motion. Leakage and friction, along with sealing zone details with the plunge-ground rod are compared with those with the smooth rod. The influence of rod surface finish on seal performance is investigated and explained, under both flooded and starved conditions For seals with a micro-patterned rod, the model consists of finite volume Reynolds equation solver, finite element deformation and static contact mechanics analyses and a Greenwood-Williamson dynamic contact mechanics analysis. This model is able to handle rod surface pattern with 3-dimensional geometrics. Simulations with different micro-pattern geometries are performed to analyze the fundamental mechanism of surface pattern effects on seal operation. Again, both flooded and starved conditions are applied and the results for both cases are compared and analyzed.

<p>Rolling contact fatigue (RCF) is the primary mode of failure in tribological contacts like rolling-element bearings (REBs), gears, and cam-follower systems. RCF processes have a crack initiation phase followed by a propagation and coalescence phase, resulting in spalls that lead to catastrophic failure. Crack initiation is a highly localized process that is strongly influenced by the inhomogeneity of the material microstructure. Therefore, a microstructure-sensitive model is required to simulate the damage evolution and failure due to RCF loading. This document presents the development of a microstructure-based finite element (FE) framework for RCF, which accounts for the inhomogeneity of bearing steel microstructure by using an explicit definition of polycrystal topology and material anisotropy. The granular topology of the bearing steel microstructure is described using randomly generated Voronoi tessellations. A cubic elastic material definition with a random spatial orientation is specified for each Voronoi grain to simulate the material anisotropy. The Voronoi grains generated using this approach were used to model the critically stressed microstructural volume in RCF loading. A domain size study was conducted to estimate the minimum number of grains that need to be contained by the critically stressed volume such that the macroscopic material response of the polycrystalline aggregate matches the linear elastic material properties of bearing steel. The estimated critically stressed volume was then embedded into a semi-infinite domain for the FE simulation of RCF line contact loading. The RCF domains developed were then subjected to a moving Hertzian pressure over the surface to simulate a bearing load cycle. A boundary averaging scheme was used to estimate the effective stresses along the grain boundaries of the Voronoi cells. Due to the anisotropy of the polycrystalline material, local stress concentrations occur at the grain boundaries as compared to isotropic models. The resolved grain boundary stresses were used to predict critical locations for RCF crack initiation, which closely match observations from RCF bench test data. Since RCF failures typically exhibit subsurface locations for the first crack initiation, the model uses the critical resolved shear stress (RSS) reversal along the grain boundaries and the corresponding subsurface location of the maxima as the driving parameters for RCF fatigue failures. The parameters from the model were fit into a Weibull distribution to estimate the stochasticity in initiation life. The Weibull predictions corroborate well with experimentally measured RCF life scatter. The framework was then extended using a coupled damage mechanics - cohesive element method (DM-CEM) to individually model the crack initiation and propagation phases in RCF. An explicit definition of the grain boundaries was incorporated using cohesive elements. Damage is initiated at the grain boundaries by degradation of the cohesive elements and the rate of damage/degradation is used to characterize the evolution of fatigue life. The rate of damage was calculated at each grain boundary using a fatigue damage law based on the RSS reversal parameter. The model is able to simulate the crack initiation and the propagation/ coalescence phases in RCF, with distinct life estimates for each phase. This model framework is further extended to investigate the effects of lubrication conditions in RCF by integrating an elastohydrodynamic lubrication (EHL) model to simulate the pressure load with the DM-CEM model. Further improvements to the fatigue life predictions using the DM-CEM model are made by coupling it with a crystal plasticity (CP) based submodel approach to predict the crack initiation life in RCF. CP-based metrics are used to correlate the microplasticity developed under RCF loading with the formation of fatigue micro-cracks and the corresponding initiation life estimations. The resulting final spall patterns and RCF life estimates were found to match well with experimental data available in the open literature.</p> <p><br></p>

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