An approach to the study of elasto-plastohydrodynamic lubrication in the wire drawing process. Part 2: Theoretical predictions

The generalised Reynolds' equation for Newtonian and non-Newtonian fluids, as applied to the wire-drawing process, together with the plasticity and energy equations have been adopted in solving the elasto-plastohydrodynamic lubrication problem in the wire-drawing process. The equations have been solved numerically using a finite difference technique with Gauss-Siedel iterative scheme to predict hydrodynamic behaviour and to correlate the forming parameters to the lubrication behaviour in an endeavour to find the optimum operating conditions for maximum precision and productivity. The effect of using either Newtonian or non-Newtonian lubricants on the process parameters has been also studied, to predict the most suitable lubricant type. The results indicate that the increase in the flow behaviour index increases the pressure gradient in the work zone, with a consequential reduction in oil film thickness. Also the minimum film thickness is highly influenced by the drawing speed. It can be concluded that the isothermal solution renders lower drawing stress than the adiabatic solution. The maximum shear stress, and hence the power loss, increases with the increase in die convergence angle.     

Frequency-domain analysis of non-Newtonian fluid behavior in head-disk interface lubrication

A lubricant in a head-disk interface is considered as a non-Newtonian fluid. Properties of non-Newtonian lubricants are specified by three nonlinear functions and a modified Reynolds equation is derived for the varied film thickness in the interface. The shear dependent viscosity is the principal factor and it is expressed by a first order transfer function. Its amplitude frequency response describes the process of the viscosity variation and indicates that the shear dependent viscosity is affected not only by the lubricant material parameters, but also by the shear frequency. Based on the modified Reynolds equation, the numerical result of lubrication is given. The load capacity is not always higher or always lower than that of the Newtonian fluid. The effect of the first normal stress difference is enlarged with the slider flying height varies.     

滑动条件下弹流润滑的屈服膜厚与屈服边界

本文讨论了弹流润滑的屈服问题，从润滑剂的极限剪应力可以得到屈服膜厚的表达式。屈服膜厚是弹流润滑膜的下降 ，当利用拟合公式得到的膜厚小于屈服膜厚时，由于润滑已经处在非牛顿区，所拟全公式不再适用。本文还给出了用膜厚形式表示的屈服准则，并详细讨论了最大压力，平均速度和滑滚比对屈服膜厚的影响。     

Hydrodynamic Behavior of Viscoelastic Liquids in a Simulated Journal Bearing

The hydrodynamic effect of viscoelasticity in bearing performance was investigated experimentally by measuring the pressure distribution of viscoelastic liquids and Newtonian liquids in a simulated plain journal bearing. The pressure distribution of the viscoelastic liquids was somewhat different from that of the Newtonian liquids, showing a flattening of the pressure profile and a shift of the circumferential position of the peak pressure. Such a difference contributes to a small recovery of the loss of the load-carrying capacity due to the non-Newtonian viscosity for viscoelastic liquids. It may also contribute to a further reduction of friction beyond the effect of shear thinning. The difference of cavitation on the divergent region of the bearing for these two different kinds of liquid was evident. The viscoelastic liquids showed less extent of cavitation. The experimental conditions conform closely to those used in the classical hydrodynamic lubrication theory. The experimental data indicate that the full fluid film occupies half a bearing starting at 0° and ending at 180°, and the subatmospheric pressure in the divergent region is leveled off at a certain negative pressure. Based on this boundary condition, a computer solution in solving the Reynolds equation for a finite bearing gives very good agreement with experiment.     

A finite element approach of thin film lubrication in circular EHD contacts

So far, most of the numerical studies concerning elastohydrodynamic point contact lubrication have been realized using finite differences. This paper describes a finite element approach for the modelling of both, thick and thin film lubrication in circular contacts under isothermal elastohydrodynamic regime. Multigrid techniques are used to accelerate the convergence and reduce calculation time. The use of the finite element method (FEM) offers two advantages: first, the existence of high level ready-to-use Finite Element commercial software which reduces the time spent in implementing the method and second, the easier adaptability to different and various physical models such as lubricant rheology, starvation effects, thermal effects, non-Newtonian behaviour, etc. The numerical model is presented in detail and an example of its adaptation taking into account non-Newtonian effects is shown. Finally, a comparison is made between Newtonian and non-Newtonian solutions, exhibiting differences obtained when using both models, especially at high shear rates where the film thickness and the friction coefficients are overestimated by a Newtonian approach.     

Hydrodynamic lubrication using co-rotational Jeffreys fluid model

Using the co-rotational Jeffreys fluid model, the performance of a non-Newtonian lubricant in hydrodynamic lubrication is investigated theoretically. Due to the bounded variation of the normal stress components with shear rate in simple shear flow, the normal stress effect has no appreciable influence in hydrodynamic lubrication. In hydrodynamic lubrication applications, the above lubricant model degenerates into an inelastico-viscous lubricant model.     

Calculated journal bearing lubrication of non-Newtonian medium with surface roughness effects

To analyze the effects of non-Newtonian lubricants and surface roughness in journal bearing lubrication, a modified Reynolds equation is derived. In the equation, differential viscosity and the first normal stress function are defined to specify the rheological properties of non-Newtonian medium. Flow factors are used to specify the effect of surface roughness. The modified Reynolds equation is numerically calculated using super over relaxation method. Numerical results of the lubrication show that the differential viscosity is the principal non-Newtonian property affecting the lubrication, it is determined by the material parameters of the lubricant and is affected by the shearing rate. Under its effect, the load capacity of non-Newtonian lubricants is not always higher or lower than that of Newtonian lubricants’. The effect of the first normal stress difference increases under the conditions of dynamic loading. Surface roughness shows an obvious effect on load capacity when it is greater than one-tenth of the film thickness, and the surface with longitudinal pattern affects the load capacity most. However, surface roughness has less effect on lubrication results than lubricants’ non-Newtonian property. __________ Translated from Tribology, 2005, 25(6) (in Chinese)     

EHL squeeze at pin-pulley interface in CVTs: Influence of lubricant rheology

In this paper we analyze the influence of fluid rheology on the strongly non-stationary squeeze process of an oil film sandwiched between the chain-pin and pulley in continuously variable transmission. As recently demonstrated [Carbone G, Scaraggi M, Soria L. The lubrication regime at pin-pulley interface in chain CVT transmissions. ASME Journal of Mechanical Design 2009;131(1)], the spatial pressure distribution is characterized by a non-central annular pressure peak, which first appears in the external region of the contact region and moves toward the center of the pin with rapidly decreasing speed. In this paper we show that the non-Newtonian viscoelastic rheology of the lubricant plays a crucial role in determining the actual value of pressure peaks and leads to a strong reduction of such pressure spikes in comparison to a perfect Newtonian lubricant. Even more, if the threshold value of shear stress τ_l, which characterizes the transition from Newtonian to non-Newtonian behavior of the lubricant, is sufficiently small the annular pressure peak may even disappear. In this case the squeeze process occurs faster, the film thickness distribution is reduced and the lubricant may not be able to avoid direct asperity contact between the two approaching surfaces.     

渐开线直齿圆柱齿轮等温时变非牛顿弹流润滑分析

用多重网格法 ,求得了Ree Eyring流体润滑的渐开线直齿圆柱齿轮瞬时等温弹流润滑完全数值解 ,给出了油膜压力、厚度沿啮合线随时间变化的关系 ,并与相同工况下的牛顿流体润滑的结果进行了比较。     

动载荷下径向轴承的非牛顿介质润滑

为分析动载荷条件下非牛顿介质的流变特性对径向轴承润滑效果的影响，推导了相应的雷诺方程。在方程中用差分粘度和第一正应力差函数表征非牛顿介质的流变特性，用挤压项表示动载荷作用。轴承润滑的数值计算结果表明，差分粘度的变化是影响承载力的主要因素，它取决于非牛顿介质的动态参数和剪切频率范围，使得非牛顿介质润滑的承载力并不总是高于或低于牛顿介质。在动载荷条件下，第一正应力差效应明显增强了油膜压力和承载力，并对轴心轨迹产生影响。     

非牛顿介质中图形化表面对减阻效果的影响

为研究图形化表面在非牛顿介质中对减阻效果的影响,在微摩擦试验机(UMT)上进行了销盘润滑实验。实验中在硅片的表面刻蚀了纵向和横向2种沟槽以形成不同的表面图形。实验表明,与光滑表面相比,当剪切速率处于牛顿流动区时,沟槽具有一定的减阻效果;而当剪切速率处于剪切稀化区时,沟槽表面的阻力上升;并且横向沟槽表面的阻力总是大于纵向沟槽表面的阻力。流体数值计算的结果表明,横向沟槽侧壁的压差阻力和纵向沟槽侧壁的粘性阻力无法完全补偿沟槽底面上的阻力损失,因而产生了减阻效果。     

Comparison of Non-Newtonian Constitutive Laws in Hydrodynamic Lubrication

Present day commercial lubricants incorporate a range of additives of long-chain polymers. Such polymers are called Viscosity Index improvers and were originally introduced to limit the decrease of viscosity with temperature. However, in addition, these polymers cause the oil to exhibit non-Newtonian behavior. The most common, and probably the most important, non-Newtonian effect is the reduction of viscosity with shear rate, so-called shear thinning. In rheological terms this is called generalized Newtonian (purely viscous) behavior. In this study, several ‘true’ non-Newtonian models (as opposed to generalized Newtonian) are compared. There is some experimental evidence that such non-Newtonian effects are favorable to lubrication. The models studied include time-dependent effects—a linear and nonlinear viscoelastic Maxwell model; and they include the effect of particles within the fluid—the Finitely Extensible Nonlinear Elastic (FENE) dumbbell model, and the Stokes couple stress model. The Maxwell and FENE models show a small decrease in load capacity, while the Stokes model shows a significant increase.     

Viscometer using drag force measurements

A robust and precise viscometer using the forces exerted by a laminar flow inside a small duct is presented: the force is measured on a long cylindrical sensor dipped into the flow. Two devices of respective volumes 1.4 and 0.031?ml have been realized, demonstrating that the technique is usable with small fluid volumes. Several Newtonian and non-Newtonian fluids have been tested at shear rates ranging from 0.3 to 10?s(-1) for the first device and from 85 to 2550?s(-1) for the second one. For Newtonian fluids, of viscosities ranging from 10(-3) to 0.1?Pa?s, the linear response of the device has been verified and a 90% agreement with the values provided by commercial rheometers is obtained. For non-Newtonian polymer solutions, the variation of the force with the flow velocity allows one to determine the dependence of the viscosity on the shear rate. Two shear thinning polymer solutions with a power law behavior at intermediate shear rates have been investigated and their rheological parameters have been determined.     

The effect of a non-Newtonian lubricant on piston ring lubrication

The effect of a non-Newtonian oil (shear thinning) on the lubrication of a piston ring is theoretically investigated. A variation of shear strain rate with shear stress that is cubic in form is used to obtain a modified form of the Reynolds equation (dynamic) applicable to a run-in ring profile which is considered to be a double parabola with a central straight portion. Numerical solutions are obtained for the film thickness, pressure and frictional force over a complete stroke for the case of a constant load. Results presented in non-dimensional form show that the effect of pseudo plasticity is to reduce slightly the minimum film thickness, peak pressure ratio and friction coefficient.     

基于Carreau流变模型的圆柱滚子轴承热混合润滑分析*

为了研究圆柱滚子轴承接触区的混合润滑性能,建立基于Carreau非牛顿流体的热混合润滑模型,求解非牛顿流体线接触热混合润滑数值解。研究滑滚比、卷吸速度及载荷对线接触混合润滑特性的影响,并与相同工况下牛顿流体热混合润滑的结果进行对比。结果表明：随着滑滚比、卷吸速度及载荷的增大,油膜温度都会升高,Carreau非牛顿流体的温度要低于牛顿流体的温度;油膜厚度随着滑滚比、载荷的增大而减小,随着卷吸速度的增大而增大,Carreau非牛顿流体与牛顿流体膜厚相差不大;随着滑滚比的增大,2种流体的平均摩擦因数均增大,随着卷吸速度和载荷的增大,2种流体的载荷比均减小。     

Deterministic solutions and thermal analysis for mixed lubrication in point contacts

A deterministic numerical model has been developed for simulation of mixed lubrication in point contacts. The nominal contact area between rough surfaces can be divided into two parts: the regions for hydrodynamic lubrication and asperity contacts (boundary lubrication). In the area where the film thickness approaches zero the Reynolds equation can be modified into a reduced form and the normal pressure in the region of asperity contacts can be thus determined. As a result, a deterministic numerical solution for the mixed lubrication can be obtained through a unite system of equations and the same numerical scheme. In thermal analysis, the solution for a moving point heat source has been integrated numerically to get surface temperature, provided that shear stresses in both regions of hydrodynamic lubrication and asperity contacts have been predetermined. A rheology model based on the limit shear stress of lubricant is proposed while calculating the shear stress, which gives a smooth transition of friction forces between the hydrodynamic and contact regions. The computations prove the model to be a powerful tool to provide deterministic solutions for mixed lubrication over a wide range of film thickness, from full-film to the lubrication with very low lambda ratio, even down to the region where the asperity contact dominates.     

超薄含水油膜Couette流润滑特性的分子动力学模拟

基于分子动力学方法,建立超薄含水柴油膜的全原子分子模型,进行不同含水率下油膜Couette流的润滑特性研究。在相同剪切速度作用下,分析含水油膜的微观结构、速度分布、整体键取向参数、剪切黏度等性质。发现不含水时油膜形成了类固体层,不具有流动性,且在剪切过程中黏度值下降,即表现出剪切时间稀化现象;而含水工况下,油膜出现分层结构,流速符合Couette流的流动特性;且含水率越高,油膜的分层现象越明显,链烃的有序性越强,致使油水混合薄膜的剪切黏度值也越低,呈现出非牛顿流体性质,此时油膜固有的剪切稀化特性被削弱。研究表明,水分子由于具有较强的分子间作用力,能促使油膜中的有机分子重新排布,从而对油膜的润滑性能产生较大改变。     

On the shear stress of elastohydrodynamic lubrication in elliptical contacts

Results of mathematical modelling of elastohydrodynamic lubrication of rolling contacts are presented. Effects of dimensionless parameters such as speed, normal load, elliptical parameters and coefficient of limiting shear stress on shear stress distributions have been studied. Moreover, profiles on hydrodynamic pressure and film thickness in EHD contacts have been studied. It has been found that shear stress profiles on two contact surfaces in entraining direction are similar with each other in some way. Shear stresses of fluid film on contact surfaces vary with many factors, which reveals the mechanism of traction in elastohydrodynamically lubricated contacts.     

冷挤压塑性流体动力润滑分析

应用流体动力润滑理论和塑性成形原理,分析了冷挤压润滑过程。在挤压的起始和终止阶段为非稳态流体动力润滑,而中间阶段可近似为稳态流体动力润滑。考虑冷挤压在高压及大剪切应变率工况下润滑剂的非牛顿特性,运用Ostwald非牛顿体模型,分别建立了冷挤压非稳态和稳态的塑性流体动力润滑（PHD）模型。采用Monte Carlo法得到了冷挤压润滑过程的油膜厚度、油膜压力以及摩擦力的分布规律。     

A lubrication equation including slip velocity for hydrodynamic porous bearings in the lower turbulent regime — a perturbation approach

A first attempt is made to analyse pressure development in the form of a new lubrication equation including slip velocity for finite self-acting hydrodynamic porous metal bearings operating in the turbulent regime (fully developed) with a single phase Newtonian incompressible lubricant. The derivation is based on the analogy of boundary layer theory wherein lubricant motion is treated as a generalized turbulent channel flow in which the impermeable wall is in motion and the porous wall is stationary. The type of flow varies from pure couette flow to shear flow coupled with codirectional and transverse pressure flow. A linearization (or perturbation) technique is used to decouple the two orthogonal flows by assuming that the shear stress in a finite bearing is a small perturbation of the shear stress valid for couette flow. Using Boussinesq's eddy viscosity formulation and the wellestablished power law as a universal law of wall, the governing pressure distribution equation is obtained from considerations of the conservation of momentum and continuity. The surfaces are considered to be hydrodynamically smooth. The whole treatment is approached from the viewpoint of fluid film design rather than from a fundamental fluid mechanics approach. No slip model has been used. The lubrication equation is fully analytical and can be applied to a number of particular bearing problems by using the simplifying restrictive conditions. The lubrication equation derived can be used to predict the bearing performance characteristics even in situations where the permeability of the bearings is anisotropic and the Poiseuille flow in the porous matrix does not obey Darcy's law.