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.     

Measuring contact pressure distributions under elastohydrodynamic point contacts

Circular point contact EHD pressure distributions were investigated under various operating conditions using a thin film piezo-resistive pressure transducer. A series of controlled experiments, in which the active element of the transducer is positioned at various contact cross-sections, was carried out. The results are analysed and presented in the form of isobars. The pressure distribution closely describes the Hertzian pressure profile with a secondary pressure peak appearing prior to and near the exit constriction.     

Analysis of internal cracks in railway wheels under experimentally determined pressure distributions

In recent years much effort has been devoted to the definition of design approaches of railway systems based on the analysis of the system itself and on accurate knowledge of its effective working conditions. In this paper, the attention is focused on railway wheels. This latter component is subjected to different types of damage: sub-surface crack propagation is considered. The prediction of the evolution of this process depends on the knowledge of the stress intensity factors concerning modes I, II and III, which are dependant both on the total load acting on the wheel and on how the load is transmitted through the wheel/rail interface. However, until now the solutions commonly used consider a theoretical (Hertzian) pressure distribution, even if, due to wear or to the dynamic phenomena, the actual contact patch can be strongly different for most of the lifespan of the wheel. An approach is developed with the aim to solve the case of an internally cracked wheel subjected to an arbitrary contact patch and pressure distribution. It is based on Boussinesq's formulae and utilises a three-dimensional finite element model of the part of the wheel close to the crack to calculate the stress intensity factors along a curvilinear crack front. Pressure distributions experimentally determined by means of a technique based on the reflection of high-frequency ultrasonic waves from the wheel–rail interface were applied to internal cracks in wheels: the results were critically compared with the those obtained by considering Hertzian pressure distributions, the aim being the assessment of the influence of the contact conditions in respect of damage cause by internal crack propagation.     

一个表面带单粗糙峰的线接触时变微弹流润滑数值分析

通过数值求解研究了一个固体表面的单粗糙峰对两固体形成的线接触时变弹流润滑区压力、膜厚分布曲线的影响。结果表明：粗糙峰的出现，使其对应位置上的压力、膜厚发生急剧变化；粗糙峰的移动，对压力和膜厚的变化、固体表面的凹陷现象以及Hertz接触区的出口颈缩均有不同的影响；另外，压力峰和油膜形状随着粗糙峰幅值和半波长的变化而变化。结果亦表明：准稳态解比时变解过高地估计粗糙峰对压力和膜厚的影响。     

Effect of coatings on thermal conditions of EHL

The thermal EHD model of rectangular contact has been applied to analysing the effect of coatings on thermal conditions in EHL. The model takes into account variation of oil viscosity along and across the oil film according to the Barus formula. The solution has been obtained by means of the Newton-Raphson method. The effect of the coating has been examined by comparison of the temperature distributions in the oil film and on the surfaces of rollers for the cases with and without coating. In addition, the oil film shapes and minimum values, the pressure distributions and traction coefficients, have also been compared.     

The contact pressure distribution during plastic compression of lead spheres

Pressure-sensitive film has been used to examine the form of the contact pressure distribution for lead spheres plastically compressed between hard steel platens. The mean contact pressure attained a maximum value of 0.6–0.7 times the Vickers hardness of the undeformed sphere when the sphere had been deformed to , where a is the contact radius and R is the radius of the undeformed sphere. The form of the pressure distribution changed markedly as the contact area increased in size, with an increasingly larger proportion of the load being supported towards the contact perimeter. The results are compared with theoretical pressure distributions proposed by Matthews [Acta Metall.28, 311–318 (1980)] for contact between spheres. Fair agreement is obtained if the sphere is assumed to deform by power-law creep, which is thought to reflect the observed time-dependent plastic deformation of the lead.     

Coupled effects of surface roughness and flow rheology on elastohydrodynamic lubrication

The coupled effects of surface roughness and flow rheology on elastohydrodynamic lubrication (EHL) circular contact problems are analyzed and discussed. The averaged type Reynolds equation utilizing the average flow model on the interactions between couple stress fluids and surface roughness, the elastic deformation equation, the viscosity–pressure and density–pressure relations equations, and the force balance equation are solved numerically by the multilevel multi-integration (MLMI) algorithm to calculate the pressure distributions and film thickness shapes. The results show that the transverse type roughness and standard deviation of composite roughness enhance the pressure and film thickness in the central contact region. Moreover, the longer the characteristic length of the couple stress fluids is, the smaller the pressure distribution is in the central contact region and the greater the film thickness is in all regions.     

Temperature rise due to sliding in rolling/sliding elastohydrodynamic lubrication line contacts: an efficient numerical analysis for contact zone temperatures

An efficient numerical method based on Lobatto quadrature analysis is adopted for a rigorous analysis of temperature in elastohydrodynamic lubrication (EHL) line contacts. Temperature distributions are calculated for maximum Hertzian pressures and rolling speeds varying between 0.5 to 2.0 GPa and 1 to 30 m/s, respectively. Significant mid-film temperature and surface temperature increases have been observed at higher rolling speeds with an increase in loads and slip ratios. Results have been compared with the results of Manton, S. M., O'Donoghue, J. P. and Cameron, A., Temperatures at lubricated rolling/sliding contacts. Proceedings of the Institution of Mechanical Engineers, 1967–68, 182(417), 813–824. An empirical equation is presented for the prediction of non-dimensional maximum mid-film temperature in the contact zone in terms of the dimensionless thermal loading parameter Q, dimensionless load W and slip S, as:

     

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.     

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.     

A non-Newtonian model based on limiting shear stress and slip planes—parametric studies

Parametric studies and corresponding results are presented using a rheological model based on the limiting shear stress and possible occurrence of slip planes. The model is applied to elastohydrodynamically lubricated line contacts with smooth surfaces and isothermal conditions. A few investigations are carried out where different parameters are varied. The first study investigates the influence on the film thickness distribution due to a variation of the maximum Hertzian pressure when the slide-to-roll ratio is constant. The second study investigates how far the non-Newtonian region propagates at low slide-to-roll ratios for a few different values of the Hertzian pressure. The results show that it is a remarkably small slide-to-roll ratio necessary to cause slip planes in a large part of the Hertzian contact zone. A third study regards the influence of the entrainment velocity on the film thickness generation at different slide-to-roll ratios. Finally some rheological parameters are varied. First, only the limiting shear stress at atmospheric pressure (τ₀) is varied, and second, a few different lubricants are studied, each with their own set of rheological parameters.     

On the thermal elastohydrodynamic lubrication in opposite sliding circular contacts

Cases of elastohydrodynamic lubrication (EHL) point contacts running under opposite sliding conditions have been studied with consideration of the thermal effect for various loads and entrainment velocities. A thermal EHL solver has been developed and proven to be able to deal even with extreme cases under an infinite slide–roll ratio. Results show that film profiles featuring a dimple can be formed in the contact zone when the slide–roll ratio exceeds a certain level. Moreover, the present study provides theoretical evidence for the lubricating film build up in the case where the two bounding surfaces run with equal but opposite velocities. An effective lubricating film under zero entrainment speeds was experimentally proven by Dyson and Wilson [1] (Proc Instn Mech Engrs, 1968–1969 183(3P) 81) in the 1960's, which, however, cannot be explained by the isothermal EHL theory.     

Squeeze films between a rigid cylinder and an elastic layer bonded to a rigid foundation

A numerical solution to the elastohydrodynamic lubrication problem of a rigid cylinder and an elastic layer firmly bonded to a rigid substrate in normal approach and separated by a fluid of constant viscosity is presented. The rate of change of the deformation with time was neglected in the present investigation. The governing equations were solved via an iterative method in order to compute the pressure distribution and the corresponding film profile.Influences of the layer thickness, the layer compressibility and the central squeeze-film velocity on the results were investigated. In the case of the Hertzian contact, the present method was validated against the results reported in Herrebrugh [Elastohydrodynamic squeeze films between two cylinders in normal approach, Trans ASME, J Lubric Technol Ser F 1970; 92:292–302] where the results showed a very good agreement.     

Transient EHL analysis of an elastomeric hydraulic seal

Recent steady-state numerical analyses of reciprocating hydraulic rod seals have revealed many important details about the operation of such seals, including the fact that they generally operate with mixed lubrication in the sealing interface. However, these seals frequently operate under transient conditions, with the rod speed and sealed pressure undergoing cyclic variations with time. In the present study, a transient numerical model has been developed to take account of the varying rod speed. The model consists of a fluid mechanics analysis of the lubricating film of hydraulic fluid, a contact mechanics analysis of the contacting asperities on the seal lip and a structural analysis of the seal deformations. The fluid mechanics analysis consists of a finite volume solution of the Reynolds equation using a mass-conserving algorithm, which accounts for possible cavitation. The contact mechanics analysis utilizes the Greenwood–Williamson model. The structural analysis consists of a finite element analysis. Typical results are presented for an injection molding application. Of greatest importance is the net leakage per cycle. Also presented are the cyclic histories of such performance characteristics as the lubricating film thickness, contact pressure and fluid pressure distributions, the friction force on the rod and the instantaneous flow rate.     

Thermal elastohydrodynamic lubrication of starved elliptical contacts

For the starved thermal elastohydrodynamic lubrication in elliptical contacts, a numerical solver based on the multi-grid technique was developed and numerical solutions were achieved. The influences of the thickness of oil-supply layer, elliptical ratio, entrainment velocity, slide-roll ratio, and the maximum Hertzian pressure on the lubrication behaviour were investigated. The thermal solutions were compared with isothermal solutions. The numerical results show that, for an oil-starved contact, the central and minimum film thicknesses predicted by both thermal and isothermal solutions change at the same trend as the thickness of the oil-supply layer increases. That is, as the thickness of the oil-supply layer increases, in the beginning both the central and minimum film thicknesses increase rapidly, however, their increasing rates become smaller gradually, at last, when the thickness of the oil-supply layer reaches a certain value, both the central and minimum film thicknesses almost stop increasing. Such situation was called a quasi-fully flooded state in this study. It has been found that the amount of the supplied oil for the quasi-fully flooded state differs with the elliptical ratio, and the maximum amount of the supplied oil is required by a circular contact.     

Analysis of viscosity interaction on the misaligned conical–cylindrical bearing

Viscosity is an essential property in hydrodynamic lubrication. In general, the lubricant is not considered to have uniform viscosity within a given bearing. The viscosity of the lubricant is affected by both pressure and temperature. The viscosity of the lubricant increases with pressure and for most lubricants, this effect is much larger than that of temperature or shear when the pressure is significantly above than the atmospheric pressure. This study analyzes the thermal effect of conical–cylindrical bearing performance parameters via the viscosity–pressure–temperature relationships of lubricants. The results reveal that pressure increases both the film viscosity and temperature as well.     

点接触弹流润滑供油条件退化的乏油分析

在点接触弹流润滑中,如果不能及时补充新油,则接触区的供油条件会随着润滑次数而退化。分析了供油油膜厚度、中心膜厚、最小膜厚和润滑油膜压力区形成位置与润滑次数的关系。结果表明:润滑开始时,由于供油油膜厚度较大,系统处于充分供油状态;随着润滑次数的增加,有一部分油从两侧泄漏,系统逐渐转到乏油状态,供油油膜厚度、中心膜厚和最小膜厚均逐渐变小,压力区形成位置则逐渐向Hertz接触区靠近;最终供油油膜厚度、中心膜厚和最小膜厚趋于定值,压力区趋于Hertz接触区,从而达到一种稳定乏油状态。     

卷吸速度为任意方向的椭圆接触弹流润滑分析

以往的点接触弹流润滑研究往往局限于分析卷吸速度方向与接触椭圆短轴相重合的工况。但在实际工程问题中,有时卷吸速率方向与接触椭圆长轴相重合,有时卷吸速度方向与接触椭圆的对称轴成一夹角,针对这一问题,本文提出了一种独特的解决方法,压力和膜厚分析分别采用多重网格和多重网格积分法,无论卷吸速度的方向如何,总让Ｘ轴与速度方向一致,而Ｙ方向速度永远等于０。这样任意卷吸速度方向的工况和卷吸速度与接触椭圆短轴相重合     

Influence of a ring flat zone in the point contact surface on thermal elastohydrodynamic lubrication

This paper describes a geometrical profile, an elastohydrodynamically lubricated point contact surface with a ring flat zone, aimed at building up local line contact elastohydrodynamic lubrication (EHL) in point contact conjunctions to reduce the influence of side-leakage on the central film thickness. Effects of the ring flat zone on the thermal EHL characteristics are studied. A dimensionless coefficient, r_W, is defined to represent the relative half width of the ring flat zone in a point contact EHL surface. Thermal EHL numerical simulations have been performed to investigate the influence of r_W on the film thickness as well as pressure, temperature and friction coefficients under different operating conditions. In the range of 0≤r_W≤1.0 results show that the minimum film thickness decreases with increasing r_W and the central film thickness increases with increasing r_W, and the influence of r_W on the film thickness is more pronounced than those on the maximum pressure, the maximum temperature and the friction coefficients. It is revealed that the proposed ring flat zone with appropriate width is beneficial to the thermal lubrication.