Additives are commonly used to improve the performance of lubricating oils. Correlatively, the lubricant viscosity depends on the rate of shear: the fluid becomes non-Newtonian. Assuming that the nonlinear relationship between the rate of strain tensor and the stress tensor is cubic, the film equations are derived within the approximations of lubrication theory. The governing equation, which generalizes the Reynolds’ equation, is a nonlinear partial differential equation, subject to two nonlinear constraints. The particular case of a finite width journal bearing is considered here; this problem is solved by the finite-element method, using a gradient technique. The numerical results are compared with established results for newtonian lubricants. The influence of the non-Newtonian parameter on the pressure field and on the bearing capacity is predicted.

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