Effect of EHL Contact Conditions on the Behavior of Traction Fluids

New infinitely variable transmission (IVT) systems are under development for the automotive industry as a means to achieving significant fuel economy benefits. These systems rely on the lubricating fluid to transmit the drive train loads across the interface of the transmission components. This requires the development of new fluids that exhibit high traction properties under elastohydrodynamic lubrication (EHL) conditions. However, it has been reported recently that the traction performance of some fluids can reduce dramatically as temperature is reduced. This may place severe operational limits on IVT systems and suggests that the low-temperature traction properties of fluids for these systems should be studied in order to understand the mechanism for the observed reduction in traction.

The work reported here is an experimental study aimed at identifying whether low temperature traction reduction is related to a fundamental change in rheological behavior specific to the fluids tested or to more generic changes in the EHL contact conditions. A series of model experiments were performed using a mini traction machine (MTM) on three high-viscosity polybutene samples. The results have been mapped against previously reported non-dimensional parameters used to identify different EHL regimes. The results show that dramatic reductions in traction occur when the contact transitions from the rigid piezo-viscous (RP) toward the rigid iso-viscous (RI) region. Similar results were also found for two other high-viscosity fluids of different molecular structure and lower traction properties. The results support the hypothesis that the reduction in traction observed at low temperature is due to a change in EHL contact conditions rather than being solely due to a change in the rheological performance of the test fluids.     

一种简化的点接触热弹流模型及其完全数值解

本文提出了一个简化的点接触热弹流计算模型并进行了完全数值求解。与现有的完全数值模型相比，采用本模型进行求解具有计算量小，精度适中的特点，更适合工程计算的要求。文中对多种工况下点接触热弹流的摩擦牵引性能和表面闪温特性进行了数值分析。     

表面粗糙度对点接触弹流润滑性能的影响

本文应用多重网格法对椭圆接触的部分膜弹流问题进行了完全数值求解，计算中采用了Ｐａｔｉｒ－ｃｈｅｎｇ的平均流量模型及Ｇｅｅｎｗｏｏｄ和Ｔｒｉｐｐ的表面微峰弹性接触模型。在大量数值计算结果的基础上分析了表面粗糙度大小及纹理方向对点弹流的油膜厚度及微峰接触载荷的影响。     

指数率非牛顿流体的等温线接触弹流润滑分析

应用多重网格解法,求得了指数率非牛顿流体在稳态等温线接触条件下的弹流润滑数值解,分析了油膜压力和油膜厚度随指数及滑滚比的变化关系,并与相同工况下牛顿流体弹流润滑的结果进行了比较。     

弹流润滑在摩擦无级变速器疲劳分析中的应用

本文在摩擦传动弹流润滑理论分析与牵引机理试验研究的基础上，进行零件表面牵引力和表层内应力场的研究，而且利用这一方法来分析零件的抗疲劳强度。分析多种设计参数对零件疲劳寿命的影响，研究了壁面附近的滑动对摩擦传动的影响。     

Experimental study of starved EHL contacts based on thickness of oil layer in the contact inlet

Starved lubrication conditions bring the risk of the damage of machine components. The experimental simulation of starved conditions is connected with the need to define the input conditions to joint the amount of the oil entering the contact with the resulting film thickness. This paper describes the experimental approach based on the thickness of the oil layer entering the starved contact. The use of multiple contacts optical test rig based on thin film colorimetric interferometry for film thickness measurement has enabled to simulate starved conditions and to compare the obtained results with theoretical prediction. The first elliptical contact between spherical roller and the glass disc is used to supply the defined oil layer to the second contact formed between the steel ball and the glass disc. Through the comparison with the theoretical prediction it was found that acceptable input conditions for the study of starved contacts can be achieved with such test rig configuration.     

An Experimental Validation of the Recently Discovered Scale Effect in Generalized Newtonian EHL

New quantitative numerical simulations of the elastohydrodynamic lubrication (EHL) film forming ability of generalized Newtonian liquids have elucidated a previously unrecognized property of EHL films. The dependency of the film thickness on the scale of the contact is greater when the viscosity is shear dependent within the inlet. Measurements of film thickness were performed in a ball on disc experiment using balls ranging from 5.5 to 35 mm in diameter. Three liquids were investigated with varying shear dependence in the range of stress important to film forming. The experimental results confirm the previous analytical findings. Numerical simulations using the measured viscosities show that the increased scale sensitivity is substantially the result of shear-thinning. However, the smallest scales produced films thinner than even the shear-dependent prediction, possibly indicating molecular degradation. It is quite likely that some machine components, which were designed using the effective viscous properties derived from a larger scale film thickness measurement, are operating with substantially lower film thickness than the designer had intended.     

粗糙表面等温瞬态点接触弹流润滑问题直接迭代解法比较

在考虑接触表面粗糙度的情况下,采用SOR、Ф变换法、q变换法3种直接迭代解法求解瞬态Reynolds方程。结果表明,SOR法和q变换法收敛速度较快,但在载荷变大或粗糙表面等情形下,较难获得正确的结果,而Ф变换法变换关系式较为复杂,但因采用较精确的Roelands黏压关系式,容易得到理想的结果。因此在数值求解过程中,在轻载或者润滑表面粗糙度影响较小的情况下,可以采用SOR或者q变换法,同时增加网格和采取较低的松弛因子,改善SOR或者q变换法的数值不稳定性,从而较快获得收敛解,在载荷较大或者润滑表面粗糙度影响较大的情况下,应该优先采用Ф变换法。     

EHL line contact central and minimum film thickness equations for lubricants with linear piezoviscous behavior

Full EHL line contact simulations for smooth surfaces are carried out under fully flooded condition to obtain central and minimum film thickness equations pertaining to lubricants with linear piezoviscous response. The present analysis is based upon the assumptions of isothermal condition and Newtonian fluid model. A major drop in the sensitivity of pressure viscosity coefficient (and hence, the material parameter G) is observed. The exponent of the speed parameter U is marginally smaller while that of load parameter is slightly increased. There is close agreement between the simulated and fitted film thickness values.     

On the Numerical Accuracy of Rough Surface EHL Solution

Numerical solution of rough surface elastohydrodynamic lubrication (EHL) is of great importance. In recent years, research efforts have been focused on deterministic modeling, because it is proven to be capable of predicting detailed contact and lubrication characteristics based on measured three-dimensional machined surface topography in a wide range of operating conditions. The accurate calculation of roughness derivatives, ?S/?X and ?S/?T, is found to be crucial for numerically solving EHL problems, especially if machined roughness with high-frequency components is involved. When discretized rough surfaces are employed, one may have to handle three different discretization grids, one for the stationary solution domain of the Reynolds equation and the other two for the moving rough surfaces in contact. Two numerical ways can be employed to fulfill the computation of ?S/?X and ?S/?T. One is to interpolate the topographic heights into the solution domain grid and then conduct the derivation calculations there. The other is to do derivations first in the surface grids and then interpolate the obtained derivatives into the solution mesh. In order to compare these two ways based on an accuracy analysis, a transverse sinusoidal rough surface is exploited and the effects of mesh spacing, differential scheme, interpolation method, and roughness wavelength on numerical errors of ?S/?X and ?S/?T are investigated. It is found that the appropriate way to minimize the errors is to ensure that the surface grids are considerably denser than that of the solution domain and to conduct derivation calculation first on the surface grids. A densified surface mesh may lead to a great reduction in numerical errors without causing any significant increase in the computing time. Densification of the solution domain mesh, on the other hand, is more difficult because it would result in a large increase in computational burden. It is also found that high-order differential schemes and interpolation methods are helpful to improve accuracy. Large roughness wavelengths lead to smaller numerical errors, but roughness amplitude has no influence on numerical accuracy.     

Film thickness in point contacts under generalized Newtonian EHL conditions: Numerical and experimental analysis

The current paper contributes to the understanding of the behaviour of a smooth point EHL contact with a generalized Newtonian lubricant under pure rolling. The film thickness distribution was computed using a numerical simulation with measured rheological lubricant properties. The numerical predictions, obtained solving the generalized Reynolds equation were compared with film thicknesses measured in an optical ball-on-disc device. The numerical results correctly predict the absolute film thickness and the film thickness increase with rolling speed.     

Experimental and numerical investigation on the behavior of transverse limited micro-grooves in EHL point contacts

This study presents experimental and numerical investigations on the effects of transverse limited micro-grooves on the behavior of film thickness and friction in EHL point contacts. The tribological performance has been compared for smooth and textured surfaces in sliding and reciprocating motion and under starvation. The measurements were conducted by using a ball-on-disk tribometer equipped with a high speed camera and torque sensor. The results show that the transverse shallow micro-grooves with a length less than the diameter of the Hertzian contact are efficiently able to enhance the film thickness under different operating conditions. The beneficial effect under starved lubrication requires a mechanism for filling the depleted micro-grooves entering the contact with fresh lubricant. This mechanism can be attributed to the capillary effect in the inlet zone under starvation. The numerical simulation of the transient behavior of transverse limited micro-grooves shows agreement with experimental results. On the other hand, introducing micro-grooves as closed texture cells on one of rubbing surfaces results in a friction reduction in the reciprocating motion. The reduction of friction is substantially attributed to the film thickness enhancement.     

A Rough Shear-Thinning Correction for EHD Film Thickness

A film thickness correction for shear-thinning in elastohydrodynamic contacts has been available that requires parameters obtained from flow curves generated for the specific liquid. For instances for which reduced accuracy is acceptable, a new rough film thickness correction has been formulated for pure rolling and a moderate amount of sliding based on Van Krevelen's graphical technique of estimating shear-thinning from the molecular weight. It has been shown to be useful for high-molecular-weight base oils, when lubricant specific shear-thinning data is absent, although it should most often overestimate the film thinning.     

Calculation of Viscous EHL Traction for Squalane Using Molecular Simulation and Rheometry

Recently, remarkable agreement was reported between nonequilibrium molecular dynamics simulation and high-pressure Couette rheometry on squalane. We have utilized the viscosity-strain rate relationship obtained from this unique combination of experimental and simulation data along with high-pressure viscometer measurements to calculate the viscous traction curve in the elastohydrodynamic lubrication (EHL) regime. A comparison with measured traction at 0.57 and 1.29 GPa shows excellent agreement, confirming the validity of the measurements and simulations. Thus, we present for the first time, a successful calculation of EHL traction from the liquid shear response obtained from both molecular dynamics and rheometry.     

An Approximate Solution Technique for Multilobe Journal Bearings Including Thermal Effects,with Comparison to Experiment

An approximate solution method for multilobe journal bearings that includes thermal effect is presented. The method is based on the assumption of an axial pressure distribution in the form of a polynomial, which allows the solution of Reynolds' equation by a one-dimensional finite element routine with little loss in accuracy from two-dimensional methods. A first order form of the energy equation for an adiabatic film is used to predict temperatures within the bearing, and the viscosity is determined as an exponential function of temperature. Comparison of solutions obtained by the variable viscosity method to effective viscosity solutions after Lund and Thomsen illustrates discrepancies in operating eccentricity and stiffness coefficients between the two approaches. Good correlation was obtained between the variable viscosity solutions and experimental measurements reported by Tonnesen and Hansen of eccentricity, pressures, and temperatures in a two-axial groove bearing.     

多重网格方法在斜齿轮弹流润滑计算中的应用

本文分析了多重网格方法应用于弹性流体动力润滑数值计算快速稳定收敛的原因，给出了压力在粗细网格之间的转换关系式；详细描述了弹流问题的一种多重网格算法，计算了斜齿轮的弹流润滑问题，并与前人的计算结果进行了比较。最后讨论了数值迭代过程中的压力振荡问题。     

点接触全膜弹流最小油膜厚度的模糊评价

本文通过对点接触全膜弹流最小油膜厚度的分析,并引入了现代机械设计方法中的模糊综合评价方法,对影响点接触全膜弹流最小油膜厚度的各个因素进行了综合分析。     

一种适用重载点接触弹流润滑问题的新的直接迭代法

基于快速求解点接触弹流问题的直接迭代算法,通过将压力迭代矩阵由满元矩阵变为带状的稀疏矩阵,提出一个更高效的求解点接触弹流问题的新算法.该算法不仅具有更高的计算效率,而且可适用于重载工况.采用新算法求解了若干重载点接触EHL问题,结果与采用逆解法求得的结果非常接近,表明直接迭代法也适用于重载弹流问题研究.     

用多重网格法准确计算弹流润滑膜厚度的方法

应用多重网格法求解稳态等温线接触弹性流体动力润滑(EHL)问题,得到了不同工况下使用不同的差分格式并采用不同的网格时的数值解。分析了对Reynolds方程的楔形项使用不同的差分格式时,数值解随着网格层数增加的变化趋势。结果表明:各种常见工况下,对楔形项无论是采用两点差分还是三点差分,随着网格层数的增加,得到的最小膜厚、中心膜厚、第二压力峰值及其出现的位置都会趋于稳定。由数值解归纳出了准确计算中心膜厚与最小膜厚的经验公式。网格层数较少时,将对楔形项分别采用两点差分和三点差分而得到的膜厚代入该公式,即可求出与网格层数较多时的结果非常接近的膜厚值。     

弹流润滑点接触问题数值解研究

采用微机对弹性流体动力润滑点接触问题的数值解进行了研究，得出了不同工况下该问题的数值解。经比较所得数值解与公开发表的研究结果一致，且所用方法简明、直观，结果可靠。