链条套筒与销轴铰链副冲击载荷-往复运动的弹流润滑数值模拟

数值模拟链传动中销轴与套筒之间的定载荷和变载荷弹流润滑接触问题,套筒相对于销轴做纯滑动往复运动。定载荷是假定往复运动过程中载荷恒定不变;变载荷是假定链节在啮入和啮出链轮过程中存在的冲击载荷按正弦函数规律变化。比较在定载荷和变载荷加载条件下线接触往复运动工况的弹性润滑油膜变化情况,分析在动载荷加载条件下不同行程长度对弹性流体动力润滑特性的影响。研究发现,动载荷对油膜的压力、膜厚影响较大:随着动载荷的增加,油膜中压力急剧增大,膜厚减小;但加载方式对摩擦因数的影响不大;在相同的加载方式下,随着行程长度的增加,油膜压力减小,中心膜厚和最小膜厚显著增加。     

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.     

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.     

Minimum and central film thickness formulae for an elastic layer firmly bonded to a rigid cylindrical substrate under entraining motion

Analytical minimum and central film thickness formulae have been derived for elastic layers firmly bonded to rigid cylindrical substrates under entraining motion when the contact width is significantly larger than the layer thickness. The elastic layer has been assumed to be either a compressible or an incompressible material; the corresponding Poisson's ratios are assumed to be 0.4 and 0.5 respectively. Good agreement has been found between the film thicknesses predicted by these film thickness formulae and some numerical solutions for similar conditions. Good agreement has also been found with the general full numerical solution for incompressible elastic layered surfaces.     

表面粗糙度对三叉杆滑球式万向联轴器弹流润滑特性的影响*

为了研究表面粗糙度对三叉杆滑球式万向联轴器滑球与滑道之间弹流润滑特性的影响,基于线接触等温弹流润滑数值计算模型,建立考虑表面粗糙度的线接触等温弹流润滑数值计算模型。采用随机表面粗糙度来代替实际的粗糙表面,计算中采用Newton-Raphson方法对方程进行数值求解,改变表面粗糙度的幅度和间距来研究它们对膜厚和〖JP2〗压力的影响。结果表明：改变表面粗糙度幅度后,膜厚曲线和压力曲线在中心区域产生波动,随着表面粗糙度的增大,两者波动程度逐渐剧烈,产生的压力波动区域的局部压力较大;表面粗糙度间距缩小一倍后,膜厚曲线和压力曲线在波动区域所产生的波动程度更密,随着表面粗糙度的增大,两者波动程度逐渐剧烈,膜厚和压力最大值略微增大。     

椭圆接触纯自旋问题的弹流润滑数值分析

研究了椭圆接触纯自旋问题的等温弹流润滑,用多重网格法求得了完全数值解,研究了速度、载荷、椭圆比和计算区域对压力和膜厚的影响。结果表明,在轻载、高速、大椭圆比条件下,椭圆接触的纯自旋运动可产生润滑膜,油膜的形状和压力分布都和经典弹流润滑截然不同;椭球的自旋速度、载荷、椭圆比以及承载域的大小都对压力和膜厚有很大的影响。     

Numerical Simulations of Groove Topography Effects on Film Thickness and Friction in EHL Regime

The effects of depth and top width of transverse rectangular grooves on film thickness and friction in elastohydrodynamic lubrication (EHL) regime were investigated through numerical simulations. Results were obtained in the form of pressure profiles and Stribeck curves for central and minimum film thickness and for friction coefficient. The results indicate that grooves with narrow top widths reduce the minimum film thickness and that this reduction is greater for deeper grooves. Lubricant shearing inside these grooves was further identified as a dominant factor contributing to friction. Near the groove edges, however, no evidence of micro-EHL effect was observed. Based on the results, a groove volume parameter was proposed to characterise the groove lubrication efficiency. We found that the parameter was linearly related to the average central film thickness and by increasing the groove wavelength the film could be made thicker than that of a smooth contact.     

旋滑条件下弹流润滑数值分析

建立旋滑条件下椭圆接触弹流润滑的数学模型,用多重网格法求得该条件下的完全数值解,研究速度、载荷、偏心距和椭圆比对油膜厚度、形状和压力的影响。结果表明,偏心距较小时,油膜厚度和形状都与普通弹流有明显的不同;速度、载荷和椭圆比增加及偏心距减小,均会导致接触区两侧最小膜厚的差值增大,油膜形状的非对称性增强;速度、椭圆比增加,油膜厚度增加,接触区压力减小,载荷增加或偏心距减小,油膜厚度减小,接触区压力增加。     

Influence of temperature distributions in EHL film on its thickness under high slip ratio conditions

This paper describes the influence of temperature rise of oil film in Hertzian contact area on the film thickness or profile under high slip ratio conditions. Temperatures of both surfaces of a ball and a disk as well as average temperature across the oil film were measured by means of an improved infrared. Two kinds of optical band-pass filters were used to separate the radiations from the ball surface and the oil film through an infrared transparent disk made of sapphire glass. In case of temperature measurement of the disk surface, another sapphire glass disk was coated with 300 nm chromium layer on the contact surface to radiate the infrared from the disk surface and also to intercept the radiation from the ball surface and the oil film. Temperature profiles across the oil film were estimated by assuming a parabolic profile with the measured three kinds of temperatures.For case within 200% in slip ratio, both minimum and central film thickness decreased under constant entrainment velocity as slip ratio increased. Measured film shapes were not flat at central Hertzian contact region under high-slip condition and differed from the results by the conventional EHD theory assuming constant viscosity in the direction of film thickness. The profile of Couette flow varied due to the distribution of oil film temperature in thickness direction. The viscosity wedge action, that is the variation of the profile of Couette flow causes reduction of film thickness or deformation of film profile. For case over 200% in slip ratio, the relation between central film thickness and slip ratio under constant relative slide speed had a great difference from the results calculated from the formula presented by Chittenden et al.     

The Effect of Load (Pressure) for Quantitative EHL Film Thickness

New quantitative numerical simulations of the elastohydrodynamic lubrication (EHL) film thickness using realistic pressure and shear-dependent rheology and realistic compressibility have indicated that the dependence of central film thickness upon Hertz pressure (or load) for the classic Newtonian, slightly compressible solution is merely a lower limit with magnitudes three times as great being possible. Experimental measurements of central film thickness employing Hertz pressures from 1.0 to 2.6 GPa confirm that for a neat mineral oil, the classical pressure dependence is accurate, while for two gear oils the experimental pressure dependence is much larger. Shear-dependent viscosity is a major factor and compressibility plays a lesser role, while there is evidence that mechanical degradation is also important. New experimental evidence of the enhanced scale sensitivity resulting from shear-thinning has also been obtained. These results for the pressure and scale dependence have dire implications for the usual practice of extrapolation of film thickness from experimental measurements at large scale and low pressure using effective pressure–viscosity coefficients. For machines of small scale and high pressure, the extrapolation will sometimes result in substantially overestimated film thicknesses.     

Calculation of Stribeck curves for (water) lubricated journal bearings

This paper describes a mixed elastohydrodynamic lubrication (EHL) model for finite length elastic journal bearings. The finite element method was employed to discretise the coupled system of 2D–3D Reynolds-structure equations and to compute Stribeck curves at constant load. As underrelaxation strategies have been found to be insufficient for an iterative solution of this problem, artificial dynamics have been added to the numerical structure equations in order to solve for stationary solutions of the fluid–structure problem. An ideal plastic asperity contact model together with an effective film thickness formulation according to Chengwei and Linqing was employed in order to compute the contact pressure in mixed lubrication. The method presented in this paper is applied to a typical water lubricated journal bearing problem. Computed Stribeck curves are presented and the numerical performance of the method is evaluated.     

Elastohydrodynamic lubrication of circular contacts at pure squeeze motion with non-Newtonian lubricants

In this study a numerical method for general applications with non-Newtonian fluids is developed to investigate the pure squeeze motion in an isothermal elastohydrodynamic lubricated spherical conjunction under constant load conditions. The coupled transient modified Reynolds, the elasticity deformation, and the load equilibrium equations are solved simultaneously. Computer simulation is carried out to investigate the effects of flow rheology and operations on the relationship between the pressure and film thickness distributions. The simulation results reveal that the larger the flow index (n), the larger the film thickness and the smaller the maximum central pressure. This results in larger time needed to obtain maximum central pressure. In addition, the elastic deformation is more significant for the lower flow index. Therefore, the smaller the flow index becomes, the greater the difference between the hydrodynamic lubrication (HL) solution and elastohydrodynamic lubrication (EHL) solution becomes.     

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.     

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.     

Self-levitating sliding air contact

A linear sliding contact with self-lifting capability due to squeeze film action was theoretically investigated. It was found that this type of contact can operate under a wide range of frequency and load conditions. Calculations for frequency of up to 4000 Hz and the mass of up to 800 g indicate that a air film with thickness of a few microns can be created.It is the unsymmetrical pressure distribution in a time period or positive mean film force that makes squeeze air film contact able of self-levitation. The mean film force is equal to the weight supported. A physical rationale for the load-carrying capacity of a squeeze air film is that because of the viscous resistance around contact boundary, the air is repeatedly compressed and expanded in the central part of the contact, which results in a positive mean film force.     

挤压条件下弹流油膜的摩擦学现象研究

纯挤压条件下弹流油膜的研究已证实了油膜的中央凹陷。研究利用常载荷下的钢球在较小的初始间隙下冲击附有润滑油的玻璃盘,在接触区外围出现了外围凹陷,而不是熟知的中央凹陷。研究结果表明当初始的冲击间隙较大时,油膜的压力分布和厚度以及中心压力-时间曲线中的峰值和接近结束时的中央凹陷都与以前的自由落球问题相似。随着初始的冲击间隙减小,最大压力从接触区中心转换到圆周外围区,相应地,中央凹陷变得越来越不明显而在外围区出现了圆周凹陷,进一步的数值分析,发现当油膜足够厚时在小的初始间隙条件下也出现了外围凹陷。这主要是当初始的冲击间隙变小时,中央油膜厚度比大冲击间隙条件下润滑油被"冰冻"时薄很多,中央凹陷不明显;在外围区域,表面间隙很小,局部挤压效应变强,因此形成了外围凹陷。     

Numerical evaluation of pressure from experimentally measured film thickness in EHL point contact

This paper is concerned with elastohydrodynamic lubrication, especially the determination of lubricant film thickness and contact pressure within a point contact of friction surfaces of machine parts. A new solution technique for numerical determination of contact pressure is introduced. The direct measurement of contact pressure is very difficult. Hence, input data of lubricant film thickness obtained from the experiment based on colorimetric interferometry are used for the calculation of pressure using the inverse elasticity theory. The algorithm is enhanced by convolution in order to increase calculation speed. The approach described in this contribution gives reliable results on smooth contact and in the future, it will be extended to enable the study of contact of friction surfaces with asperities. Copyright © 2007 John Wiley & Sons, Ltd.     

Elastomer-lined bearings: An analysis of a heavily loaded cylinder sliding on a compliant layer

An analytical solution to the elastohydrodynamic lubrication of a rigid cylinder sliding on an elastic layer which is bonded to a rigid substrate is presented. The central film thickness is predicted by assuming that the lubricant film may be divided into a curved inlet region and a central tilted pad region. Expressions for pressure and deformation derived from the dry contact formulae are used to enable compatibility of pressure between the two regions to be established. The computed lubricant pressure distribution is compared with that for indentation in dry contact under the same load. The film thickness results under heavy loads indicate similar trends to those obtained by alternative solutions.     

Film-forming Characteristics of Grease in Point Contact under Swaying Motions

The technique of relative optical interference intensity (ROII) and simple numerical calculations were used to investigate the lubricating behavior of grease lubricant films in the rolling direction under swaying motions (acceleration/deceleration). Experimental results indicate that at a same entrainment velocity of the inlet, the central film thickness under deceleration is larger than that under acceleration. The minimum central film thickness in one swaying cycle does not occur at the moment of zero entrainment, but at the initial period of acceleration. At the moment of zero entrainment, the central film is thicker than its peripheries, and the value of the central film thickness increases with increases in the changing rate of the entrainment velocity. It is thought that the transient behaviors of the grease lubricant film deviate from those in steady state conditions. The profiles of the transient film thickness and the approximate thicknesses of elastohydrodynamic contact in the rolling direction calculated by using a simple numerical method are supported by the experimental results. The numerical method can also be used to explain the behavior of the grease lubricating film under non-steady state conditions. An erratum to this article can be found at     

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.