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Concern for the problems on the global environment and the depletion of petroleum resources has led to that internal combustion engines should have lower exhaust emissions and greater fuel economy. Reducing mechanical power losses in the engine is vital to improving fuel economy. Most of the mechanical losses are attributed to the friction of the piston assembly, bearings in the crank system, and the valve train system. It is recognized that the frictional contribution of piston assembly, especially the piston ring pack, to the total power losses is significant [1,2]. Several measures have been taken to reduce the friction loss. Making the profile of ring sliding surface optimum is one of the important measures. The method of finishing the cylinder liner is an essential measure since the surface topography of cylinder liner produced by the process of boring and horning greatly influences the friction, wear and scuffing. Regarding the piston rings, a highly curved ring decreases the friction loss since it develops a large hydrodynamic pressure by wedge action. However, less pressure due to the squeeze action would generate by a highly curved surface. The thin film in the neighborhood of dead centers results in an increase in boundary friction and causes the wear and the occurrence of scuffing Rohde [3] carried out the mixed lubrication analysis of piston rings by using the average flow model of Patir and Cheng (PC) [4,5] and the asperity contact model of Greenwood and Tripp (GT) [6]. Since then, a number of mixed lubrication analyses have been reported [1,2,7-11]. The former model used the stochastic process theory to determine effects of surface roughness on the mixed hydrodynamic lubrication. The model can be utilized to analyze any general three dimensional roughness structure, isotropic or nonisotropic surface roughness, and to calculate the average pressure in the EHD contacts. However, the latter cannot be applied to nonisotropic surface roughness since the surface orientation is assumed to be isotropic in the model. Hu [12] pointed out that the formula of GT underestimates the asperity contacts pressure. Lee and Ren (LR) investigated the effects of the surface topography, material hardness and load on the deformation behaviour of rough surfaces [13]. They formulated the average gap and the real contact area as functions of material hardness and statistical roughness properties, which are composed of the surface pattern parameter, rms roughness and autocorrelation length. In the present study, a theoretical analysis on the mixed lubrication of piston rigs in a 4-stroke cycle diesel engine is presented. The analysis uses the average Reynolds equation, which governs the mean hydrodynamic pressure generated between two partially lubricated surfaces. The asperity contact pressure and the real contact area are estimated by using the formulas of LR. Mixed lubrication calculations are performed for a piston ring pack in a diesel engine with the bore of 135 mm and the stroke of 140 mm. The piston has two compression rings and a two-land type oil control ring. Effects of statistical roughness parameters, surface pattern parameter, the ratio of material hardness to equivalent Young's modulus and the ratio of autocorrelation length to rms roughness, on the film thickness and friction characteristics are investigated. The frictional characteristic values obtained by the LR model are compared with those of the GT model. As to the ring with nonisotropic surface roughness, the effects of barrel height on the characteristic **Oita University, Department of Mechanical Engineering,

An Analytical Study on the Mixed Lubrication of Piston Rings in a 4-Stroke Cycle Diesel Engine