A fast compound direct iterative algorithm for solving transient line contact elastohydrodynamic lubrication problems

A fast compound direct iterative algorithm for solving transient line contact elastohydrodynamic lubrication (EHL) problems is presented. First, by introducing a special matrix splitting iteration method into the traditional compound direct iterative method, the full matrices for the linear systems of equations are transformed into sparse banded ones with any half-bandwidth; then, an extended Thomas method which can solve banded linear systems with any half-bandwidth is derived to accelerate the computing speed. Through the above two steps, the computational complexity of each iteration is reduced approximately from O(N ³/3) to O(β ² _N), where _N is the total number of nodes, and β is the half-bandwidth. Two kinds of numerical results of transient EHL line contact problems under sinusoidal excitation or pure normal approach process are obtained. The results demonstrate that the new algorithm increases computing speed several times more than the traditional compound direct iterative method with the same numerical precision. Also the results show that the new algorithm can get the best computing speed and robustness when the ratio, half-bandwidth to total number of nodes, is about 7.5%–10.0% in moderate load cases.     

Effect of real longitudinal surface roughness on lubrication film formation within line elastohydrodynamic contact

In many applications (e.g. roller, barrel or needle bearings) surface features exhibit longitudinal alignment to the direction of motion. These features are produced by surface finishing techniques in the circumferential direction and are associated with line or very wide elliptical contact geometries. In such a case, the contact length in the direction of motion is considerably shorter comparing its width and the effect of a longitudinal roughness could significantly influence the lubrication film formation. Recent experimental studies have indicated less severe effect of a longitudinal roughness on lubrication film formation in the comparisons with that observed with transversely orientated roughness caused by the inlet perturbation. Nevertheless, these experimental studies have been focused on the behaviour of artificially produced asperities within a circular contact. The quantitative experimental study of longitudinal real surface roughness within a line contact has not been realized yet. That is why, in this study, the line contact formed between a steel tapered roller and glass disc is observed within an optical test rig and the effects of real surface roughness on lubrication film formation are studied. Experiments carried out under pure rolling conditions have shown that the depth is the key parameter that influences the effect on the film thickness. If the roughness features are shallow, the lubrication film shape within the contact follows the shape of the surface closely. However, the groove having only about 800 nm in depth divided the line contact into two parts that behave as two separate line contacts. Such an effect can increase the risk of the wear of rubbing surfaces as the lubrication film thickness between the real machine components can be significantly lower than expected.     

Effects of surface coating on elastohydrodynamic lubrication of line contacts

A numerical solution to the elastohydrodynamic lubrication (EHL) problem of two coated elastic bodies in line contact is introduced. The non‐Newtonian behavior of the lubricant is incorporated into EHL analysis using Eyring's nonlinear viscous model. The surface elastic deformations are computed from full elasticity analysis of layered elastic half‐space. The iterative Newton–Raphson technique is used in the numerical solution. Subsurface stresses are calculated using two different techniques, the numerical integral scheme based on Fourier transformation and the finite element method. The effects of surface coating (material and thickness) on the pressure profile and subsurface stresses are presented and discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

A theoretical simulation of thermal elastohydrodynamic lubrication for a Newtonian fluid in impact motion

In this work, the thermal elastohydrodynamic lubrication (TEHL) in an impact motion is explored using multigrid (MG) method and column by column scanning techniques. A steel ball impacts onto an infinite steel plane lubricated with a thin layer of oil. The study starts from a smooth contact problem and the results are compared with the corresponding isothermal ones. Then surface waviness is imposed on the steel ball surface to check the fluctuation in the oil film.     

Numerical analysis of non-Newtonian TEHL line contact problem based on real-coded genetic algorithm

This paper presents a new simple numerical method to solve the non-Newtonian thermal elastohydrodynamic lubrication (TEHL) line contact problem based on real-coded genetic algorithm (RGA). To solve the line contact TEHL problem by means of RGA, the initial population producing method is deeply investigated, an appropriate grid partition method is proposed and an appropriate evolutional computation technology is determined. Finally, the fitness evaluation function and the iterative stop qualifications are put forward. The algorithm is examined by some examples, and the results are compared with empirical solutions. The study shows that the application of RGA in the numerical analysis of the TEHL line contact problem is feasible, reliable and sufficiently accurate.     

Numerical analysis of grease thermal elastohydrodynamic lubrication problems using the Herschel-Bulkley model

Grease thermal elastohydrodynamic lubrication (TEHL) problems of line contacts are analysed numerically. The effects of temperature and rheological parameters on grease TEHL are investigated using the Herschel-Bulkley model as a rheological model of greases. The pressure distribution, the shape of grease film, mean film temperature and surface temperature of solid wall in line contacts are obtained. It is found that thermal effects on the minimum film thickness become remarkable at high rolling speeds. The effect of yield stress of the Herschel-Bulkley model on minimum film thickness is negligible, while the flow index and viscosity parameter have significant effects on minimum film thickness.     

Parametric elastohydrodynamic study of a linear contact applied to SiC lubricated with a low‐viscosity fluid

Ceramic materials are often used in tribological applications because of their good mechanical properties. Silicon carbide (SiC) has a low density, high Young's modulus, high corrosion resistance, and very low friction in water. It is a very good candidate for replacing waterproof oil‐lubricated bearings in water pumps and for applications when water is used as a lubricant. In such applications the SiC dissolves very slowly in water to form silicilic acid. After running in, journal and bearing surfaces look like mirrors with very low roughness and very small friction coefficient. This paper reports on a parametric study to model the cylinder—plane configuration, which is then utilised in the specific case of SiC in water. The study was carried out in order to reduce the number of parameters and to ensure good precision of the results. The numerical model is applied to an SiC contact with a very low‐viscosity lubricant (water) using elastohydrodynamic (EHD) conditions. Multigrid techniques for the Reynolds equation and multilevel, multi‐integration methods for the elasticity equations are used to solve the EHD problem. These results are given in non‐dimensional form using the Moes parameters M and L for several velocities and loads. Comparison is made between the two‐ and three‐dimensional cases in order to assess the effects for the cylinder ends.     

A study on the effect of starvation in mixed elastohydrodynamic lubrication

The effect of starvation in mixed elastohydrodynamic lubrication (EHL) regime is studied. Numerical simulations are conducted for both line and point (elliptical) contacts with the consideration of the surface roughness. The degree of starvation is linked directly to the reduction in the lubricant mass flow rate. Results are presented to gain insight on the influence of starvation on the film thickness as well as the interaction between the surface asperities. Extensive sets of simulation results are used to quantify the effect of starvation in the EHL of rough surfaces. Expressions are developed to predict the percentage of the load carried by the surface asperities (asperity load ratio) as well as the reduction of the central and minimum film thickness in the starved mixed EHL.     

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。     

Analysis of the thermal elastohydrodynamic lubrication of a finite line contact

A complete numerical solution for the thermal elastohydrodynamic lubrication (EHL) problem of a finite line contact between an infinite plane and an axially profiled cylindrical roller is obtained. The pressure profile and the film shape in the middle part of the roller are very different from those at the ends. However, the finite line contact results in the middle part of the roller are nearly the same as those of the corresponding infinite line contact. It is revealed that, in a finite line contact, the maximum pressure, the highest film temperature and the minimum film thickness all occur at the end regions of the roller. A comparison is made between isothermal and thermal solutions of a finite line contact. In addition, variations in the minimum film thickness, the maximum pressure and the highest temperature with the dimensionless velocity parameter, the slide/roll ratio and the radius of the end profiles of the roller are discussed.