The general viscous lubrication of rolling and sliding rigid cylinders is examined. The flow is assumed isothermal and the fluid rheology is assumed completely defined by its compressibility as a function of pressure and by its viscosity as a function of pressure and shear stress. A general problem formulation and a general solution technique are developed. The solution technique is based on the iterative solution of a discrete representation of the problem formulation. These results are specialized for a viscosity function of the form  
Typical solutions are obtained and discussed. A dimensionless survey of design parameters is presented for the above viscosity function with (a) = 0.0. The use of such nonlinear general viscous fluids results in a significant loss of load capacity.
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