SURFACE ROUGHNESS EFFECTS IN MIXED RHEOLUUICAL YHERN0-ERE ROLLING/SLIDING LINE CONTACTS

Abstract

Elastohydrodynamic lubrication of rolling/sliding line contacts is of great relevance in the successful operation of the mechanical components such as gears, roller element bearings, cams etc. which form a vital part of most of the machines. The success of the lubrication system depends upon the existence of a fluid film which has a thickness of the order of I p.m or even less. Therefore, it is important to be able to predict the fluid film thickness along with the other associated parameters such as pressure distribution, coefficient of friction etc, under the given set of operating conditions at the design stage. In order to meet the growing demand of industry for highly advanced technologies, the operating loads are increasing, the fluid films are becoming thinner and special purpose lubricants are being employed. Moreover, due to increasing competition in the global market, the emphasis is on lower costs and longer lives of the components. In view of these facts, it is necessary to develop a better understanding of EFlL as well as to update and simplify the existing methods for analyzing the problems of elastohydrodynamic lubrication. Due to the aforesaid reasons, the focus of attention has shifted to more realistic and complex situations involving the effects of temperature rise on fluid properties, non- Newtonian behaviour of lubricant, surface roughness and dynamic loading. The analyses based on Newtonian fluid model, in general, fail to explain the experimentally measured traction coefficients for various slide to roll ratios. Therefore, in order to obtain a fundamental understanding of lubrication performance and failure in various triboelements, such as rolling element bearings and gears, it is essential to incorporate the effect of non-Newtonian behaviour of fluid in the numerical scheme. Surface roughness is found to play a significant role for the mechanical components operating under elastohydrodynamic and mixed lubrication conditions. Surface roughness not. only interacts with the hydrodynamics of the fluid film but also induces significant local contact pressures near the asperity tip regions where the fluid film is not thick enough to separate the surfaces completely. This phenomenon in many cases is responsible for initiating premature contact fatigue failure due to micropitting, peeling etc. When mechanical vibrations take place, the EHL films in the contacts have to bear high frequency dynamic loads. Due to the squeeze action produced by the time dependent load, the behaviour of such films can drastically deviate from that of the corresponding steady-state films. This effect in combination with other effects, ie, thermal, non-Newtonian and surface roughness, is responsible for EHL film failure. In this regard, an extensive survey of the literature, presented in Chapter 1, has been conducted. It reveals that a lot of work has been carried out over the Iast few decades in order to replace the conventional elastohydrodynamic lubrication theory based on isothermal Newtonian fluid model by more realistic approach involving the above mentioned physical effects of temperature rise, non-Newtonian fluid behaviour, surface roughness and dynamic load. Despite these efforts, some major aspects of practical EHL behaviour still remain largely unexplored. These include the effects of polymeric fluid additives in smooth as well as rough EHL contacts and combined influence of moving surface roughness and dynamic loading. Hence the objective of the present work is to bridge this gap in literature. A theoretical model is developed for a mixture of Newtonian and non-Newtonian fluid to analyze the individual and/or combined influence of polymeric fluid additives, non-Newtonian fluid behaviour, temperature rise, moving surface roughness and dynamic loading in elastohydrodynamic lubrication of rolling/sliding line contacts. The governing equations for the analysis are presented in Chapter 2. The effect of additives is modelled by assuming the lubricant to be a homogeneous mixture of Newtonian and non-Newtonian (power law) fluids. The shear stress-strain rate relationship of the lubricant mixture has been obtained by rule of mixtures, under the assumption that no chemical reaction takes place and the constituent fluids retain their original mechanical properties after being mixed. The corresponding mixed rheological Reynolds equation is derived by perturbation method. The surface roughness is assumed to be single sided, transverse and sinusoidal. Although sinusoidal roughness model has been used by many workers, but their analyses are mostly restricted to long wavelength surface roughness, whereas, it is well known that the topography of realistic surfaces contain short wavelength components also. Hence, an attempt has been made in the present work to deal with surface roughness of wavelengths as short as 0.12 times the hall-width of Hertzian contact zone. Moreover, in most of the available references the influence coefficients used for the calculation of elastic displacements are derived by assuming parabolic variation of fluid pressure I within a short interval. This assumption may lead to inaccuracies under rough surface conditions due to the presence of high local pressure gradients. Hence the present work employs an FFT (fast fourier transform) based technique recently developed for the evaluation.of these influence coefficients. In this method, the pressure distribution is transformed into frequency domain where the relationship between the pressure and displacement is much simple. The displacement function in the frequency domain is evaluated as the product of pressure function and a transfer function which is much easier than solving the complex convolution integral in space domain. Therefore, the use of FFT simplifies the solution of the elasticity equation to a great extent. The energy equation is reduced to one-dimensional form by using mean temperature formulation. Using the Newton-Raphson technique, the results are obtained and plotted to show the variation of pressure distribution, film shape, minimum film thickness, coefficient of friction and maximum fluid and surface temperatures with the volume fraction, reference viscosity ratio and power law index of the polymeric fluid additive under smooth as well as rough surface conditions. The detailed solution procedure is presented in Chapter 3. Furthermore, from the literature it is seen that attempts have been made to quantify the thermal effect on minimum film thickness in terms of thermal reduction factor. But no attempt has been made to derive similar expressions for correction factor to account for the effect of surface roughness and additives on the minimum film thickness. Therefore, as an attempt to demonstrate the same, an equation for correction factor as a function of volume fraction, viscosity ratio and power law index of the additive and surface roughness amplitude and wavelength along with slide to roll ratio, is derived by regression analysis. This correction factor is intended to be multiplied to the minimum film thickness obtained from isothermal Newtonian fluid analysis for smooth surface in order to account for the above mentioned effects and hence, act as an aid in design by eliminating the cumbersome analysis computations. The main objective is to open a new direction for future research in order to develop simplified and accurate design procedures. The results show that the EHL characteristics of polymer modified oils in rolling/sliding line contacts depend upon the effective viscosity of the lubricant mixture, which is governed by the superposition of shear thinning behaviour and the effect of high reference viscosity ratio (VI?) of the polymeric fluid additive. The effective lubricant viscosity is further modified by thermal effect. The polymeric fluid additives are found to enhance the minimum fluid film thickness which is accompanied with an increase in coefficient of friction. Therefore, judicious selection of additive concentration and properties in order to attain fairly thick fluid films with tolerable levels of friction is recommended. The presence of surface roughness is found to cause significant pressure rippling along with reduction in minimum film thickness and increase in coefficient of friction, which increase with increasing amplitude and decreasing wavelength of surface roughness. These effects are amplified by addition of polymeric fluid additives. The results of transient EHL analysis with Newtonian as well as non-Newtonian (Ree-Eyring) fluids show that the transient fluid flow due to the movement of surface roughness profile leads to a reduction in the flow resistance caused by the presence of surface roughness. The EHL characteristics are found to vary significantly with respect to time due to the movement of surface roughness as well as the squeeze film effect caused by dynamic load. The results corresponding to low and high load conditions are presented in different chapters for the sake of convenience. Chapter 5 presents the results for high speed-low load (HS-LL) and low speed-low load (LS-LL) rolling/sliding EEL line contacts and Chapter 6 deals with the cases of low speed-high load (LS-HL) and high speed- high load (HS-HL). Finally, the conclusions are given in Chapter 7.