The effect of surface roughness on tlie performance of hydrodynanric slider bearings is studied. A generalized form of surface rorrghness characterized by a stochastic random variable with tron-zero mean, variance and skewness is assrtnred to define the bearing srtrface topograplry. Various film shapes srtch as: plane slider; esponential, secant and hyperbolic are considered. The results are obtoitred for the general lubricant film shape in inregral form which are nrmlerically computed for the shapes under consideration. The results are presented both graphically as well as in tabular form. The performance of a rorrgh bearing can be considered in terms of an identical snzootl~ bearing with an equivaletrt film thickness. It is observed, for the lubricant filnr shapes rmder consirleration, that the increasing positive values of a, a and E decrease the load carrying capacity, frictional force and Final manuscript approved January 12, 1999 Review led by Marc Carpino temperature rise while it increases tlie coeflcient of friction. Increasing positive values of a and E sliifr the center of press~tre towards the outlet edge. For negative valrres of a, the increasing value reverses tire trend of the effect on petfortnrrnce choructeristics which is in conformity with the physical aspects of the problem. A sinrilar trend is observed in case of the effect of negative valrtes of E. Thus, a negatively skewed surface rortghness nrodijies the performance of the slider bearings whereas the petfornlance of a bearing suffers on account of positively skewed srrrface ro~rghness. Moreover, it is noticed that in the case of e.vpotienria1 and hyperbolic slider bearings the effect of increasing vairres of a is more pronoutrced ~jher-eas in case of platre slider and secant shaped slider this effect is marginal. KEY WORDS Hydrodynamic Slider Bearings; Surface Roughness NOMENCLATURE d = variance E = expected value h(s)= film thickness P = viscosity of the lubricant h(x) = film thickness measured between the nominal mean levels /'I = inlet film thickness of the bearing surfaces h0 = outlet film thickness /IS = stochastic film thickness measured from the nominal mean = h, -h, level of the bearing surface F = dimensionless frictional force P = lubricant pressure f = dimensionless friction co-efficient P = expected value of the lubricant pressure x = dimensionless center of pressure P = dimensionless pressure AT = dimensionless temperature rise W = load carrying capacity = gravitational acceleration W = dimensionless load carrying capacity J =Joule's mechanical equivalent of heat a = mean of the stochastic film thickness c = specific heat of the lubricant o = standard deviation of the stochastic film thickness P = density of the lubricant E = measure of symmetry of the stochastic random variable h 29 1

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This article aims to discuss the combined effect of roughness and slip velocity on the performance of a ferrofluid based rough porous secant shape slider bearing. The slip model of Beavers and Joseph has been deployed to study the effect of velocity slip while the stochastic model of Christensen and Tonder has been used to calculate the effect of surface roughness. The concerned statistically averaged Reynolds' type equation is solved with suitable boundary conditions to obtain the pressure distribution leading to the calculation of load carrying capacity. Further, the expression for friction and the position of center of pressure are obtained. It is observed that the bearing suffers due to surface roughness. However, this adverse effect can be reduced considerably by the ferrofluid lubrication taking the slip parameter at minimum. In this type of bearing system, the combination of slip velocity and skewness may play a crucial role in augmenting the bearing performance. Besides, the friction is found to be mostly decreasing or nominally increasing.

The effect of longitudinal surface roughness on the behaviour of slider bearing with squeeze film formed by a magnetic fluid has been analysed. The roughness of the bearing surface is modelled by stochastic random variable with non-zero mean, variance and skewness. The concerned Reynolds' equation is stochastically averaged with respect to the random roughness parameter. Results for bearing performance characteristics such as load carrying capacity of the bearing, centre of pressure, frictional force and coefficient of friction for different values of a (mean), s (standard deviation) and 1 (measure of symmetry) are numerically computed. In order to investigate the quantitative effect of roughness on the performance characteristics, four shapes namely; plane slider, exponential slider, hyperbolic slider and secant slider for the lubricant film are considered. The results are presented in tabular form as well as graphically. It is observed that the bearing performance is significantly affected by all the three parameters characterizing the surface roughness.