Most machine elements, such as gears and bearings, are operated in the mixed lubrication region. To evaluate lubrication performance for these tribological components, a contact model in mixed elastohydrodynamic lubrication is presented. This model deals with the EHL problem in the very thin film region where the film is not thick enough to separate the asperity contact of rough surface. The macro contact area is then divided into the lubricated area and the micro asperity contact areas by the contacted rough surfaces. In the case when asperity to asperity contact is present, Reynolds equation is only valid in the lubricated areas. Asperity contact pressure is determined by the interaction of two mating surfaces. The applied load is carried out by the lubricant film and the contacted asperities. FFT techniques are utilized to calculate the surface displacement (forward problem) by convolution and the asperity contact pressure (inverse problem) by deconvolution for non-periodic surfaces. With the successful implementation of FFT and multigrid methods, the lubricated contact problem can be solved within hours on a PC for the grids as large as one million nodes. This capability enables us to simulate random rough surfaces in a dense mesh. The load ratio, contact area ratio and average gap are introduced to characterize the performance of mixed lubrication with asperity contacts. Discussions are given regarding the asperity orientation as well as the effect of rolling-sliding condition. Numerical results of real rough topography are illustrated with effects of velocity parameter on load ratio, contact ratio, and average gap.

This paper presents a numerical solution for the elastohydrodynamic lubrication in point contacts, using optically measured three-dimensional rough surface profiles as input data. The multi-grid computer program originally developed by Ai and Cheng (1993, 1994) is modified, so that both contacting surfaces can be three-dimensional measured rough surfaces moving at different velocities. Many different engineering surfaces are measured and analyzed in the present study, demonstrating that the numerical analysis is practical for real surfaces of bearings, cams, gears and other components, as long as a significant EHL film still exists. In addition, discussions are given in this paper for the effects of three-dimensional rough surface topography, which is related to machining process. It appears that, for the circular contact cases analyzed, surface roughness texture and orientation do not have a significant effect on the average film thickness, but they do affect the maximum pressure peak height and asperity deformation in the contact zone considerably.

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A transient analysis for a dent passing through the conjunction of a point EHL contact was developed and solved numerically by w i n g the multigrid method. Results show that the presence of sliding produces a noticeable pressure ridge and t h w , a surface indentation at either leading side of the dent if the dent moves slower than the opposite surface, or at the trailing side if the dent moves faster than the opposite sutface. The pressure ridge and surface indentation extend their lengths fonoard or backward from the dent i n the sliding direction at a rate approximately half the sliding speed. The pressure jluctuution associated with the dent increases with increusing slideto-roll ratio a d dent depth, and decreases with increasing dent w d t h i n both x-andy-directions. The agreement between numerical simulation and experimental results obtained by Wedeven and Cusano ( 1 ) is r,emarkably close. a = Hertzian contact half width in x-direction b = Hertzian contact half width in y-direction co,cb = pressure-density coefficients U~X Ca,Cb = C, = c.Ph, Cb = cbPh non-dimensional parameters in density-pressure relationship E' = effective Youngs modulus G I = a l E 1 , Dowson material parameter GI = a2E1 Dowson material parameter G f = a1Ph GB = a2Ph h = film thickness H = Ma, non-dimensional film thickness ha = dent depth h, = central film thickness H, = h,1(2a), non-dimensional dent depth K, = bla, contact ellipticity ratio 1, = dent width in x-direction C, = dent width in y-direction L, = lxla & = hlb p = pressure P = PIPI, non-dimensional pressure pl = break pressure PI = p,/Ph non-dimensional break pressure Ph = nominal Hertzian pressure X. Y X Y a1 a2 rl 'lo = effective contact radius in x-z plane = effective contact radius in y-z plane 2(u1 -. U P ) ----, slide-to-roll ratio U I + UP = time = aLlu = ( U I + u2)12 = surface speeds = ( U P -u1)/2, sliding velocity of Surface 2 with respect to the dented surface 1 -l l o u --, 1)owson speed parameter E'R, = non-dimensional load at time instant i = load W ---13owson load parameter E'R:' = coordinates = xla, non-dimensional coordinate = ylb, non-dimensional coordinate = pressure-viscosity index = pressu1:e-viscosity index = lubricant viscosity = lubricant viscosity at inlet rl = -non-dimensional lubricant viscosity rlo = lubricant density = lubricant density at inlet P = -non-dimensional lubricant density PO

The plastic zone developed during elastoplastic contact may be effectively modeled as an inclusion in an isotropic half space. This paper proposes a simple but efficient computational method to analyze the stresses caused by near surface inclusions of arbitrary shape. The solution starts by solving a corresponding full space inclusion problem and proceeds to annul the stresses acting normal and tangential to the surface, where the numerical computations are processed by taking advantage of the fast Fourier transform techniques with a parallel computing strategy. The extreme case of a cuboidal inclusion with one facet on the surface of the half space is chosen to validate the method. When the surface truncation domain is extended sufficiently and the grids are dense enough, the results based on the new approach are in good agreement with the exact solutions. When solving a typical elastoplastic contact problem, the present analysis is roughly two times faster than the image inclusion approach and six times faster than the direct method. In addition, the present work demonstrates that a significant enhancement in the computational efficiency can be achieved through the introduction of parallel computation.