润滑理论中的广义雷诺方程和不等变分问题
Generalized Reynolds Equation and Variational Inequality in Lubrication Theory
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摘要: 本文运用张量分析工具和S-坐标系,推导了润滑理论中的广义雷诺方程及相应的不等变分问题,它计及了润滑流动中的弯曲效应,轴和轴瓦曲面内蕴性质对流动的影响.Abstract: This paper has derived generalized Reynolds equation in lubrication theory in terms of tensor analysis and S-coordinate system, and has provided corresponding varia-tional inequality. The curved effect of flow of lubricant fluid is considered, and the influence of intrinsic properties of surfaces of axis and axle sleeve on flow are counted.
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[1] Capriz G,variational techniques for the analysis of a lubrication problem,"Mathematical Aspects of Finite Element Methods".Rome,(1975). [2] Wannier,G.H.A contribution to the hydrodynamics of lubrication,Quant.Appl.Math.8(1950).1-32. [3] Elrod H.G.A derivation of the basic equation for hydrodynamic lubrication with a fluid having constant properties.Quant.Appl.Math.17(1960).349-359. [4] Murthy,M.K.V.and Stampacchia,G,A variational inequality with boundary conditions.Israel.J Math.13(1972).188-224. [5] Mosco U.Error estimates for some variational inequalities,"Mathematical Aspects of Finite Element Methods,Rome.(1975). [6] Browder F.E.Existence theorems for nonlinear partial differential equations,"Proc.Sym.Math".,V,16.(1970).
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