Rolling-Element Bearing Internal Temperatures

The internal temperature distribution within tapered rolling-element bearings was investigated. A simple experimental procedure using thermocouples for the stationary outer race and a temperature-sensitive medium on the moving components was used to determine bearing operating component temperatures. Circulating oil was used to lubricate the bearings. Temperatures for two different loads and three taper conditions (simulating bearing misalignment) are given. Corresponding contact pressure distributions and the calculated EHL films are shown. The correlation between temperatures and changes in pressure distributions, as well as their calculated effects on the lubricant film, can be easily seen.     

Analysis on Isothermal Elastohydrodynamic Lubrication of Orthogonal Face Gear

Face-gear drives have been applied in aviation transmissions, in particular, helicopter transmissions, and the lubrication characteristics are an important indicator for estimating the load-carrying capacity of face-gear teeth. In order to analyze the lubrication performance of the face gear under load, equations for the contact path of the face gear loaded tooth contact analysis (LTCA) were established on the basis of the load equivalent error of alignment (LEEA) and the load distribution among the teeth was calculated. Then a method for calculating the contact area and tooth surface velocity of face-gear drives was studied. Face-gear isothermal elastohydrodynamic lubrication (EHL) dimensionless equations are presented. A multigrid algorithm was used to complete the solution of the minimum film thickness and film pressure of face-gear drives. The lubricant film thickness and film pressure variation in the mesh cycle are expressed using example calculations that provide a theoretical basis for face-gear lubrication design.     

渐开线直齿轮瞬态微观热弹流润滑分析

考虑了瞬态效应、轮齿表面油膜温度场和轮齿表面纵向粗糙度等因素,对渐开线直齿圆柱齿轮的弹流润滑问题进行研究。载荷由双齿或单齿承担,根据实际载荷谱简化的轮齿载荷曲线,利用压力求解的多重网格法和弹性变形求解的多重网格积分法以及温度求解的逐列扫描技术,得到渐开线直齿轮瞬态微观热弹流润滑问题的完全数值解,讨论了轮齿间油膜的厚度、压力、温度沿啮合线的变化规律。数值计算结果表明,齿轮表面纵向粗糙度对轮齿间油膜的压力、膜厚、温升都有较大影响。考虑轮齿表面粗糙度后,油膜压力和温升明显增大,并随压力的增加而影响越来越显著,粗糙峰使油膜压力分布和温度分布产生振荡,轮齿表面的粗糙峰对摩擦因数影响较小,摩擦因数和最高温升在节点两侧最大。     

Elastohydrodynamic Lubrication of Rough Surfaces under Oscillatory Line Contact with Non-Newtonian Lubricant

This paper presents the results of a transient analysis of elastohydrodynamic lubrication (EHL) of two parallel cylinders in line contact with a non-Newtonian lubricant under oscillatory motion. Effects of the transverse harmonic surface roughness are also investigated in the numerical simulation. The time-dependent Reynolds equation uses a power law model for viscosity. The simultaneous system of modified Reynolds equation and elasticity equation with initial conditions was solved using the multigrid, multilevel method with full approximation technique. The film thickness and the pressure profiles were determined for smooth and rough surfaces in the oscillatory EHL conjunctions, and the film thickness predictions were verified experimentally.

For an increase in the applied load on the cylinders or a decrease in the lubricant viscosity, there is a reduction in the minimum film thickness, as expected. The predicted film thickness for smooth surfaces is slightly higher than the film thickness obtained experimentally, owing primarily to cavitation that occurred in the experiments. The lubricant film under oscillatory motion becomes very thin near the ends of the contact when the velocity goes to zero as the motion direction changes, but a squeeze film effect keeps the fluid film thickness from decreasing to zero. This is especially true for surfaces of low elastic modulus. Harmonic surface roughness and the viscosity and power law index of the non-Newtonian lubricant all have significant effects on the film thickness and pressure profile between the cylinders under oscillatory motion.     

A Theoretical Analysis of Mixed Lubrication by Macro Micro Approach: Part I—Results in a Gear Surface Contact

Mixed lubrication is a key to bring the performance analysis to the failure analysis in most tribological components. A macro-micro approach to mixed lubrication has been developed in the present model. The relation between the average contact pressure and the average gap for a typical rough contact patch is first determined numerically in micro scale. Using this relation, the average gap, average oil-film pressure, and average contact pressure in a mixed-lubricated elastohydrodynamic contact can be solved simultaneously in macro scale by treating the contact to be smooth. The total pressure is assumed a superposition of average asperity contact pressure and lubricant pressure. The new approach is simple, efficient and robust, and covers entire range of the load ratio, from unity (dry contact) to zero (full-film EHL). In addition, it can be used for a wide range of operating conditions and on a much larger contact area with a much less computing time than deterministic simulation of mixed lubrication. Implementation of the Fast Fourier Transform (FFT) allows for a rapid calculation of the elastic deformation and asperity con/act pressure. As a demonstration to this new approach, a parametric study of dimensionless speed, load and contact shape on the load ratio and gap ratio was conducted for a gear rough surface of the load ratio, from unity (dry contact) to zero (full-film EHL). In addition, it can be used for a wide range of operating conditions and on a much larger contact area with a much less computing time than deterministic simulation of mixed lubrication. Impletmentation of the Fast Fourier Transform (FFT) allows for a rapid calculation of the elastic deformation and asperity contact pressure. As a demonstration to this new approach, a parametric study of dimensionless speed, load and contact shape on the load ratio and gap ratio was conducted for a gear rough surface     

Wavelength Dependence of Micro-EHL Pressure Rippling with Random Surface-Roughness Profiles

This paper studies line-contact elastohydrodynamic lubrication (EHL) between two rough surfaces of random roughness profiles. A transient micro-EHL model is used to simulate the problems. Numerical results are obtained for a range of practical operating conditions and for relatively small specific film thicknesses (i.e., the A-values). The study reveals the wavelength dependence of micro-EHL pressure rippling. For the same A-value, the size of the pressure rippling is shown to be significantly smaller than those predicted earlier using more idealized system models. Furthermore, the pressure distribution is essentially unaffected by the short-wavelength components in the random surface-roughness profiles, except under near rolling conditions. It is shown that lubricant non-Newtonian shear-thinning is the mechanism that suppresses the short-wavelength pressure ripples. With a Newtonian lubricant, sharp pressure rippling is generated by the small-scale surface roughness textures. Since EHL lubricants exhibit significant shear-thinning and since the surfaces possess random roughness profiles, the results reported in this paper reflect a main feature that may prevail in realistic EHL conjunctions. Future work will establish a theoretical basis for the numerical analysis conducted in this research.     

In Situ Raman Microspectrometry of Lubricated Tribologic Contacts. Part Two: Simultaneous Measurements of Pressure,Lubricant Film Thickness and Temperature Distributions in a Running EHD Contact

Raman micro-spectrometry is used to acquire point spectra in a running EHL contact. The quantitative method developed in part one of this study, measuring the lubricant film thickness, is complemented by a data treatment yielding quantitative values of the pressure and temperature in the lubricant. The comparison between experimentally measured pressure and film thickness distributions and numerical calculations shows an excellent quantitative agreement. The simultaneous quantitative measurement of pressure, film thickness and temperature distribution carried under pure rolling afforded a direct and quantitative correlation between the three parameters.     

Transient thermo‐elastohydrodynamic lubrication of gear teeth

During a gear mesh cycle, load, rolling and sliding velocities, curvature, and temperature change rapidly. In this paper, a transient, thermo‐elastohydrodynamic lubrication model is presented that has been used to study the lubrication parameters at 250 contact points along the path of a contact. The working flanks were assumed to be smooth. The line load was calculated at every contact point, using the finite‐element method. Dynamic loading was not considered. The steady‐state temperature field of the working flanks was used to obtain the surface temperature at the inlet of each contact point, determined by an experimental‐analytical method presented previously. In this model, the lubricant is considered to follow the Ree‐Eyring constitutive equation. The influences of both pressure and temperature on density, thermal conductivity, and specific heat of the lubricant are also taken into account. Results are presented for an FZG type A gear pair lubricated with an FVA No. 4 reference oil; these include film shape, pressure and temperature distributions, as well as friction coefficient.     

On Reciprocating Elastomeric Seals: Calculation of Film Thicknesses Using the Inverse Hydrodynamic Lubrication Theory

The elastohydrodynamic lubrication (EHL) problem of an axi-symmetric, elastomeric, reciprocating seal may be considered as one of a heavily loaded line contact with only small piezo-viscous effects. A method is presented to calculate the overall film thickness for the stationary, isothermal situation with sufficient lubricant supply and negligible surface roughness effects. It applies the inverse theory to the frictionless dry contact pressure distribution, considering the influence of the boosting action in the entry zone of the film. Its validity is shown for the isoviscous EHL of the Hertzian contact. The finite element method (FEM) may be used to calculate the contact situation of mounted and pressurized seals. Important aspects of such calculations are discussed. To calculate film thicknesses using such FEM results, a computer program PROGRES was written. Good correspondence between the predictions of PROGRES and experimental outstroke film thicknesses are obtained for a rectangular rod seal with rounded edges.     

The Prediction of Contact Pressure–Induced Film Thickness Decay in Starved Lubricated Rolling Bearings

Under starved conditions the thickness and distribution of the lubricant film in an elastohydrodynamically lubricated (EHL) contact is directly related to the distribution of lubricant on the track in the inlet to the contact. In starved lubricated rolling bearings this lubricant distribution is determined by many effects. The authors have developed a model to predict the oil lost from the track induced by EHL pressure with no replenishment. A complete bearing is modeled with multiple rolling element EHL contacts and with the applied load to the rolling elements varying along the circumference of the bearing. Results of the oil layer thickness on the track are presented for a ball bearing and a spherical roller bearing for different bearing loads and rotational speeds. The predicted layer thickness decay rate for a ball bearing is significantly larger than for a spherical roller bearing and the predicted effect of the bearing load on the decay rate is small compared to the effect of the rotational speed. The predicted decay periods due to the contact pressure effect are small compared to the observed (grease) life of bearings. The results show that a bearing cannot sustain an adequate layer of oil on the running track unless significant replenishment takes place.     

线接触热弹流润滑的数值分析

基于Ree—Eyring流变模型，建立线接触热弹流润滑方程，通过数值计算得出了载荷参数、速度参数、材料参数和滑滚比对于二次压力峰、最小油膜厚度和最大油膜温度的重要影响。     

齿轮传动的瞬态弹性流体动力润滑

本文考虑了流体可压缩性，衙合度对轮齿荷的影响以及变曲率，变速度的瞬态效应，给出了齿轮传动瞬态弹流润滑方程及其求解方法，在引入齿轮传动的实际工况参数后进行完全数值解，得到了两齿轮在啮合线任意上的油膜压力分布和油膜形状以及最小油膜厚度沿啮合线的变化曲线。     

急停问题的椭圆接触弹流润滑分析

将机械急停时滚动轴承、齿轮等的弹流润滑油膜的渐变过程简化为从稳恒状态突然转化为恒载荷纯挤压状态,然后随时间的推移挤压效应逐渐消失的过程,建立了椭圆接触瞬态弹流润滑模型。假设润滑油为牛顿流体,在等温条件下用多重网格技术进行了动态数值求解,讨论了急停前卷吸速度分别沿椭圆接触区的长轴和短轴方向时,不同参数条件下的残留弹流润滑膜的压力和膜厚随时间的变化规律。数值计算结果表明,急停后润滑油会逐渐被挤出接触区,因此残留油膜只能保持很短的时间;较高的Hertz接触压力会通过增加润滑油粘度而延长残余油膜的维持时间,但不能根本上改变上述变化趋势,卷吸速度的方向也不能改变上述变化趋势。     

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.     

Transient EHL analysis on spur gear teeth with consideration of gear kinematics

Transient 3-dimensional elasto-hydrodynamic lubrication (EHL) analysis is performed on the contacting teeth surfaces of involute spur gears. Kinematics of the gear and the pinion are taken into account to get accurate geometric clearance around the EHL region of the contacting teeth. The surface pressure and film thickness distribution for the whole contact faces in a lubricated condition at several time steps are obtained through the analysis. Besides the pressure spike at the outlet region, a representative phenomenon in EHL regime, the pressure at the inlet region is slightly higher than that of the center region. The film thickness of transient condition is thicker than that of steady condition.     

EHL Performance of the Lubricant With Shear Strength: Part I — Boundary Slippage and Film Failure

This paper analytically investigates the isothermal line contact elastohydrodynamic lubrication of three lubricants with much different shear strengths under the nondimensional operating parameters of w = 2.15e-4 and U = 2.53e-10 applying the lubricant ideal viscoplastic rheological model. The boundary slippage of the low-shear-strength lubricant occurring in the EHL inlet zone was found and results in a much thinner film compared to the classical EHL theory prediction. The film boundary slippage and its growth with the slide/roll ratio variation of tile low-shear\- strength lubricant exhibit special phenomena, which are much different from those of the high-shear-strength lubricant. The easy occurrence of film failure in concentrated contact in the case of high sliding speed, heavy load, large slide/roll ratio, and low-shear-strength lubricant was concluded due to the severe friction heating on the surface conjunction and the lubricant thermal desorption on tile lubricant/surface boundary. The EHL film failure mechanism was further recognized.     

Investigation into the Normal Contact Stiffness of Rough Surface in Line Contact Mixed Elastohydrodynamic Lubrication

In this work, the statistical asperity microcontact models in combination with the acoustic spring model and the load sharing concept are utilized to study the interfacial normal contact stiffness for a rough surface in line contact elastohydrodynamic lubrication (EHL). Two different statistical microcontact models of Greenwood and Williamson (GW) and Kogut and Etsion (KE) are employed to derive the normal contact stiffness expressions for a dry rough line contact considering the purely elastic contact and the multiple regimes elastic–elastoplastic–fully plastic contact, respectively. The liquid film stiffness is calculated based on the relationship between film thickness and bulk modulus of the lubricant. The lubricant film thickness equations are employed in conjunction with the load sharing concept and the empirical formulas for the maximum contact pressure in a dry rough contact are fitted for the GW model and the KE model, to evaluate the relationship between film thickness and motion velocity for the purely elastic GW microcontact model and the multiregime KE microcontact model, respectively. The comparison with experimental results shows that the KE model predicts closer total contact stiffness results than the GW model. The stiffness contributions from the solid asperity contact and lubricant film are obtained and effects of surface roughness, applied load, motion velocity, and type of lubricant on the normal contact stiffness are analyzed.     

固液两相流体弹流润滑研究

应用微极流体理论,考虑流体的可压缩性,建立线接触微极流体动力润滑的基本方程,进行固液两相流体稳态流动弹流润滑数值分析,获得了润滑油膜压力、形状以及摩擦力分布,分析了微极参数对润滑性能的影响,并与不可压缩流体结果进行比较。结果表明,固液两相润滑流体较单相牛顿流体,在增加膜厚、提高承载力方面有显著的作用,而接触表面的摩擦因数有所降低,流体的可压缩性降低了油膜压力与油膜厚度。     

Thermo-elastohydrodynamic lubrication of an involute gear

This paper analyses the thermo-elastohydrodynamic lubrication on an involute spur gear tooth surface and the influence of the inlet temperature of the lubricant. The oil film temperature distribution shows a minimum near the point where the pressure distribution is a maximum and the energy loss a minimum. Then the temperature increases slightly in the outlet region. Calculated results show a decrease of a few percent in the maximum pressure distribution compared with an oil film on a rigid surface. Based on oil film thickness and gear tooth deflection, the load sharing coefficient and the relative transmitting errors are calculated. The behaviour of the oil film due to the variation of the normal tooth load at the transition point of the meshing is investigated also     

固液两相流体热弹流润滑

应用Ｅｒｉｎｇｅｎ的热微极流体理论，对含有固体微粒添加剂的润滑流体进行线接触热弹流润滑理论分析，借助于牛顿一拉夫逊方法，获得了热弹流润滑的完全数值解，得到了油膜内温度，剪应力分布及润滑表面上的摩擦力。