Numerical analysis of grease thermal elastohydrodynamic lubrication problems using the Herschel-Bulkley model

Grease thermal elastohydrodynamic lubrication (TEHL) problems of line contacts are analysed numerically. The effects of temperature and rheological parameters on grease TEHL are investigated using the Herschel-Bulkley model as a rheological model of greases. The pressure distribution, the shape of grease film, mean film temperature and surface temperature of solid wall in line contacts are obtained. It is found that thermal effects on the minimum film thickness become remarkable at high rolling speeds. The effect of yield stress of the Herschel-Bulkley model on minimum film thickness is negligible, while the flow index and viscosity parameter have significant effects on minimum film thickness.     

Measurement of the Rheology of Lubricant Films Within Elastohydrodynamic Contacts

There is growing need for a reliable model of the rheological response of lubricants in elastohydrodynamic (EHD) contacts, not only to predict behaviour in full-film EHD conditions, but also for use in modelling mixed-film lubrication. One barrier to developing such a model is that measurements of friction actually represent averaged values over the whole, lubricated contact under study. However the fluid film conditions of temperature, pressure and strain rate generally vary over such contacts, which makes it difficult to determine constitutive shear-stress equations from friction measurements. This paper examines the various different techniques used to study the origins of EHD friction and the underlying film rheology. It then describes and applies a technique for obtaining the temperature rise maps of both solid surfaces in a rolling-sliding EHD contacts and thus shear-stress and friction maps. The work shows that the shear stress of the traction fluid studied increases approximately linearly with pressure and decreases approximately linearly with temperature in the high-pressure central region of EHD contacts.     

Non-newtonian thermal analysis of an EHD contact lubricated with MIL-L-23699 oil

A thermal and non-Newtonian fluid model under elastohydrodynamic lubrication conditions is proposed, integrating some particularities, such as the separation between hydrodynamic and dissipative phenomena inside the contact. The concept of apparent viscosity is used to introduce the non-Newtonian behaviour of the lubricant and the thermal behaviour of the contact into the Reynolds equation, acting as a link element between the hydrodynamic and dissipative components of the EHD film, independently of the rheological and thermal models considered. The apparent viscosity enables the application of the rheological model better adapted to each lubricant, without appealing to special formulations of the EHD problem.The Newton–Raphson technique is used to obtain the lubricant film geometry and the pressure distribution inside the EHD contact. The shear stresses developed in the fluid film are evaluated assuming the non-linear Maxwell rheological model. The surfaces and lubricant temperature distributions are determined using the simplified Houpert's method, applied to the inlet contact zone, and the thermal method proposed by Tevaarwerk is applied in the high pressure contact zone.The non-Newtonian thermal EHD model is applied to the analysis of a contact lubricated with MIL-L-23699 oil. Significant results are obtained for the centre and minimum film thickness, for the inlet shear heating and film thickness reduction factor (φ_T), for the temperature rise of the lubricant and of the surfaces and for the friction coefficient inside the contact, considering wide ranges of the operating conditions (maximum Hertzian pressure, inlet oil temperature, rolling speed and slide-to-roll ratio).Finally, the numerical traction curves determined are compared with the corresponding experimental results, showing very good correlation.     

A Generalized Differential Colorimetric Interferometry Method: Extension to the Film Thickness Measurement of Any Point Contact Geometry

Whereas industrial elastohydrodynamic (EHD) contacts are generally noncircular, most experimental observations are made on sphere-on-plane conjunctions. The circular case is indeed a specific elliptical case, and it was widely investigated. The differential colorimetric interferometry (DCI) technique was often used to perform precise film thickness measurements in circular EHD contacts. From a single picture of the dynamic contact, it enables mapping the film thickness of the full conjunction, and postprocessing can be applied afterwards. Moreover, it is possible to record sequences at relatively high-frequency sampling. However, until now, the method could not be directly applied to noncircular conjunctions. In the present article, a generalized DCI method is proposed and assessed by several static and EHD validation cases for elliptical and torus-on-plane contact geometries. This new method no longer necessitates particular requirements on the contact shape while retaining the advantages of the original DCI method. It allows precise film thickness measurements in realistic industrial EHD contacts and opens the way for new experimental observations.     

轴瓦的力学性能对水润滑塑料轴承润滑性能的影响

在线接触热弹流润滑的基础上,对水润滑塑料轴承的热弹流模型进行计算,研究轴瓦的力学性能对水润滑塑料轴承润滑性能的影响,分析不同弹性模量下的压力、膜厚、最高温升曲线和温度分布。结果表明:在载荷等满足要求时,应选择弹性模量小的材料;载荷很大时,应选择弹性模量大的材料;弹性模量很大的材料,材料改性重点是增加自润滑性能和增加热传导系数。     

Comparisons of TEHL Simulations of Newtonian Fluids in Line Contacts between the 3D FEM and the Reynolds Equation–Based Approaches*

Thermoelastohydrodynamic lubrication (TEHL) analysis of line or point contacts is usually done by simultaneously and numerically solving the Reynolds equation, the Boussinesq equation of an elastic semi-infinite body, the energy conservation equation, and the load balance equation. Although a number of publications are available in this field, there is still a lack of general-purpose and widely used TEHL software for engineering applications. On the other hand, commercial software for both the solid structure and fluid flow analyses have become easy design tools. To expand the application of the commercial software to TEHL simulation, coupling of structure and fluid analyses is required. This study gives some demonstrations of the 3D finite element method (FEM) simulations of line contact TEHL problems using ANSYS version 13.0. The equilibrium equations of momentum and continuity and the energy conservation equation of lubricating fluids are solved with CFX. The elastic deformation of solids is calculated with the ANSYS Structure module. Through the fluid–solid coupling interfaces, the fluid pressure, solid deformation, and thermal flow are transferred between the fluid and solid domains. The computational fluid domain is enlarged, enclosing the contact zone, in the 3D model. Further, the 3D model can treat the realistic constraint conditions of solid deformation, whereas conventional TEHL analysis uses the assumption of semi-infinite body. The simulation results for pressure, lubricant film thickness, and temperature distributions are compared with the traditional Reynolds approach, and reasonable agreement for pressure and film thickness distributions has been obtained.     

Thin film lubrication of sliding point contacts of AISI 52100 steel

The mechanism of thin film lubrication of sliding point contacts of AISI 52100 steel has been studied as a function of load, sliding speed, composition and temperature of the lubricant.Below certain critical combinations of Hertzian pressure, speed and temperature the surfaces are kept apart by an elastohydrodynamic lubricant film. The load carrying capacity of this film depends primarily on the effective viscosity of the lubricant in the contact region which decreases with bulk oil temperature and with increasing sliding speed, because of friction induced thermal effects. After breakdown of the EHD film, boundary lubrication may still prevent severe adhesive wear. The transition from the boundary lubricated regime towards the regime of severe adhesive wear is a function of load (normal force), speed and bulk oil temperature and possibly depends on the conjunction temperature. Irrespective of the initial lubrication condition, oxidation of the steel surfaces leads to the (re)establishment of low friction, mild wear conditions.     

Film‐forming properties of castor oil–polyol ester blends in elastohydrodynamic conditions

The viscosity and elastohydrodynamic (EHD) film thickness properties of binary blends of castor oil with polyol esters were determined experimentally. Predicted blend viscosities were calculated from the viscosities of the pure blend components. Measured viscosity values were closer to the values predicted using the Lederer model than the Arrhenius model. EHD film thickness data were mostly in agreement with the predictions of the Hamrock–Dowson model. Observed deviations of EHD film thickness were attributed to boundary film formation and thermal effects. Calculated effective pressure–viscosity coefficients, α, displayed a complex relationship with blend viscosity. At 40°C, the addition of 10% polyol esters resulted in a 12–17% drop in α of castor oil. Higher concentrations of polyol esters resulted in an increase of α. At 70 and 100°C, α displayed an almost linear dependence on blend composition. Copyright © 2011 John Wiley & Sons, Ltd.     

The film-forming properties of polyalkylene glycols

It is now recognised that, for many practical applications, an important property of a lubricant is its ability to generate thick, elastohydrodynamic (EHD) films in concentrated contacts. This paper describes a study of the EHD film- forming properties of polyalkylenie glycol lubricants. A wide range of polyglycol structures have been examined, with different monomer types, initiators, and molecular weights. Film thickness has been measured at several different temperatures using both conventional and ultra-thin film interferometry. From the measured film thicknesses, the effective pressure–viscosity coefficients of the lubricants have been evaluated. This has enabled a systematic investigation of the effect of polyalkylene glycol structure on both pressure–viscosity coefficient and EHD film formation.     

Numerical analysis of TEHL line contact problem under reciprocating motion

This paper presents a full numerical analysis to simulate the thermal elastohydrodynamic lubrication (TEHL) of steel–steel line contact problem under reciprocating motion. The equation system is solved using multigrid techniques. General tribological behaviors of TEHL under reciprocating motion are explained. Comparison between thermal and isothermal results reveals the importance of thermal effect in prediction of the traction coefficient and film thickness. The influences of frequency, stroke length, and applied load on the variations of film thickness, pressure and traction coefficient during one working cycle are discussed. Furthermore, the influence of slide–roll ratio on tribo-characteristics of oil film under same entraining velocity is revealed.     

Computational fluid dynamics and full elasticity model for sliding line thermal elastohydrodynamic contacts

Classically, the EHD problem is solved using the Reynolds assumptions to model the fluid behaviour, and the Boussinesq elastic deformation equation to model the solid response, both being coupled with the load balance equation. The development of an alternative approach is presented here in order to solve at once the Navier-Stokes equations (mass conservation and momentum equilibrium), the full elasticity and energy equations for the line EHD problem in a fluid-structure interaction approach.The Finite Element Method is used to solve the mathematical formulation in a fully coupled way, inspired from Habchi et al. (2008) [1]. After linearisation with the Newton procedure, all the physical quantities (pressure, velocity field, deformations and temperature) are solved together in a unique system. An important benefit of this approach is the possibility to implement in a simple manner the non-Newtonian and thermal effects; in fact all the quantities can vary through the film thickness. The extension to non-Newtonian rheology and the pressure and temperature dependencies for the viscosity and density are taken into account in a direct way to allow an acceptable prediction of the friction coefficient. Gradients across the film thickness and temperature fields in both the fluid and the two solids are naturally computed and analysed. As a case study, we focus first on the pure sliding cylinder-on-plane contact. It is shown that thermal effects due to friction in the central zone of the contact play a role in heating the lubricant at the inlet zone, via heat conduction in the solids. By increasing the Slide-to-Roll Ratio (SRR), the occurrence of dimples and the subsequent effects in different parts of the contact under zero entrainment velocity conditions are then studied.     

On the thermal elastohydrodynamic lubrication of tilting roller pairs

In order to investigate thermal effect of tilting roller pairs, a numerical solution for TEHL of tilting roller pairs has been presented. Variations in the lubricating performance with tilting angle have been investigated. Comparison between thermal and isothermal solutions has been made. Effects of the end profile radius, the velocity, and the maximum Hertzian pressure have been discussed. Profile modification of the roller generatrix has been assumed. Results show that all of the highest temperature, the maximum pressure, and the minimum film thickness occur at the load-carrying end. Larger tilting angle results in more evident thermal effect.     

Multilevel solution for thermal elastohydrodynamic lubrication of rolling/sliding circular contacts

A fast multigrid approach is presented for the analysis of thermal elastohydrodynamic lubrication (EHL) under rolling/sliding circular contacts at high loads and high slip ratios with low computing time on a personal computer. This fast solver combines directiteration, multigrid, Newton-Raphson, Gauss-Seidel iteration, and multilevel multi-integration methods into one working environment that can reduce the computational complexity from O(n³ to O(nlnn) for the thermal EHL problem under rolling/sliding circular contacts. Since the couped Reynolds and energy equations are simultaneously solved by the Newton-Raphson scheme, the iteration for the convergence solution is less than those of the classical approach. Results show that thermal effects on the pressure profile and film thickness are significant for a wide range of loads, speeds and slip ratios. The maximum midfilm and surface temperature rise in the Hertzian contact region increases with increasing slip ratio, dimensionless speed, and load. The minimum film thickness decreases with increasing load and slip ratio, and decreasing dimensionless speed.     

基于动态子结构的主轴承热弹性流体润滑研究

研究基于动态子结构缩聚的轴承热弹性流体动力学(TEHD)基本理论和求解方法;建立某V型8缸内燃机主轴承的TEHD仿真模型,分别计算得到各主轴承在最大载荷工况下的油膜压力、油膜厚度、摩擦功耗、轴心轨迹和油膜温度等润滑特性;针对润滑状况较差的第3主轴承,进行TEHD、EHD(弹性流体动力学)和HD(流体动力学)不同仿真求解方法的对比研究。研究结果表明,该内燃机的第3主轴承最小油膜厚度和最大油膜压力等润滑性能最差,需要进行相应的改进设计;TEHD求解中计及了润滑油和轴瓦热效应的影响,能获得更高的轴承润滑特性计算精度。     

Inverse approach for calculating temperature in EHL of line contacts

This paper proposes a thermal elastohydrodynamic lubrication (TEHL) inverse approach to estimate the pressure, temperature rise, and apparent viscosity distributions in an EHL line contact. Once the film shape is measured, the pressure and estimated film thickness distributions can be calculated from force balance and elastic deformation theories. By using these smoothing pressure and film thickness distributions, the Gauss-Seidel iteration is employed to calculate the temperature rise distribution from energy, surface temperature, and rheology equations. This approach overcomes the problems of pressure and temperature rise fluctuations, and generates accurate results of pressure and temperature rise distribution from a small number of measured points of film thickness, which also saves computing time. Results show that the direct inverse method requires a lot of measured points to establish the amplitude and location of the pressure and temperature rise spikes, whereas the inverse approach can obtain the accuracy results with only 31 measured points. With the error from the resolution in the film thickness measurements, this approach also presents a smooth curve of the pressure and temperature rise distributions with a small error. Furthermore, this approach still provides a good solution in apparent viscosity, whereas the direct method provides a much larger error in apparent viscosity.     

Failure modes of sliding lubricated concentrated contacts

The mechanisms of film failure of lubricated concentrated contacts are discussed in relation to critical failure data of operating variables, calculations of scoring surface temperatures and scanning electron photomicrographs of worn contact zone topographies. Depending on the critical values of operating variables failure modes in the form of local break through of EHD oil film at the outlet end of the contact zone as well as gross thermal desorption effects were found.     

The effect of surface texturing on thin EHD lubrication films

Surface texturing has been successfully used for conformal contacts in many tribological applications in an effort to diminish friction and wear. However, the use of such a surface modifications are still in nascent as far as highly loaded contacts between non-conformal surfaces are concerned. It is mainly caused by the fact that the presence of such micro-features within these contacts can significantly influence the pressure distribution within the contact. Nevertheless, it has been shown in recent studies that the surface texturing can also have beneficial tribological effects if the depth of micro-features is properly designed. This paper is devoted to the experimental study of the effect of the micro-dents of various depths on thin lubrication films to find an experimental evidence of the micro-feature depth threshold for surface texturing applications in highly loaded non-conformal surfaces. The behaviour of an array of micro-dents within thin EHD contacts has been studied by thin film colorimetric interferometry. The influence of surface texturing on lubricant film formation has been observed under sliding/rolling conditions. The significant effect of micro-dents depth on lubricant film thickness is observed for positive slide-to-roll ratio when the disc is moving faster than the micro-textured ball. The presence of deep micro-dents within lubricated contact results in film thickness reduction downstream. As the depth of micro-dents is reduced, this effect diminishes and beneficial effect of micro-dents on film thickness formation has been observed. No significant influence of micro-dents depth on lubricant film shape has been observed in case of negative slide-to-roll conditions when micro-dents do not cause film thickness reduction regardless of their depths.     

Calculation of sliding power loss in spur gear contacts

An engineering-level calculation model for sliding power loss in spur gear contacts is presented. Teeth contact through the line of action is modelled as a constantly changing roller contact whose radius, speed, and load can be calculated from the gear geometry under the given operating conditions. The gear mesh cycle is approximated by a large number of elastohydrodynamic contacts. A constant film thickness and a Hertzian pressure distribution are assumed in each contact. The model includes non-Newtonian lubricant behaviour together with temperature and mixed lubrication effects in contact. The numerical solver is reasonably fast in evaluating effectively the sliding power loss dependence on the essential gear and lubricant parameters. The features and behaviour trends of the calculated sliding power losses have a close similarity with published results obtained from measurements and experiment-based power loss models with mineral oil. The limiting shear stress of the lubricant is observed to have an essential role in the power loss behaviour especially at high loads.     

Analytical model for predicting friction in line contacts

This paper presents the development of an analytical model for the prediction of the friction coefficient in line contacts under thermal elastohydrodynamic lubrication (TEHL). A new theoretical equation is deduced for determining the friction coefficient, taking into account the rheology of common lubricants under TEHL. This approach also considers the heat generated and its penetration into the bulk of the contacting solids. Therefore, the increase in temperature and ensuing variations in the operating conditions are determined. In order to illustrate the use of the new model and verify its accuracy, an experimental stage is performed in a tribological test rig. The predictions of the proposed model are compared with the results obtained in the test rig and other data reported in the literature for diverse lubricants, showing a good agreement in every case. © 2015 The Authors Lubrication Science published by John Wiley & Sons Ltd.     

Influence of the size,geometry, and material of the rollers on EHD traction

The influence of the parameters relating to the rolling elements on traction in EHD contacts is experimentally studied on a two-roller machine, in which experiments with point contacts are conducted for two paraffinic mineral oils, a synthetic naphthene, and a synthetic ester. Firstly, it is shown that the same traction curves are obtained in both internal and external contacts when the effective radius in rolling direction of the rollers is equal. The effect of an increase in the size of the rollers is to increase the film thickness and this results in a gentle decline in the maximum traction coefficient. As the effective radius in transverse direction is increased, so the traction decreases for a paraffinic mineral oil, while that for a synthetic naphthene remains constant independent of the geometry of the rollers. Finally, the effect of the material of the rollers is studied, employing rollers made of steel, ceramics, phosphorus bronze, brass, and aluminium alloy. The traction obtained under an identical normal load can be arranged according to the effective elastic modulus of the rollers for each oil. However, under identical contact pressure the same maximum traction curve is obtained independent of the material, but the decline in traction in the thermal region is slightly steeper with the ceramic than with the steel rollers because of the difference in the temperature rise of the fluid film.