The lubrication of a conventional, finite width plane bearing, using a power-law, non-Newtonian lubricant, is studied. The basic assumptions in this analysis are: thin fluid-film, no thermal effects, and a modified Reynolds’ equation for small bearing aspect ratios. Results from this study include bearing pressure, load, and friction formulas. Similar results for the not-so-small bearing aspect ratios are found via an Euler-Lagrange equation. This Euler-Lagrange equation is derived from the optimization integral for the modified Reynolds’ equation. Approximate solutions to the modified Reynolds’ equation and to the Euler-Lagrange equation are contrasted with numerical solutions for the modified Reynolds equation. Bearing aspect ratios in the range 0.1 to 0.6, clearance ratios in the range 1.2 to 4.0, and non-Newtonian power-law index in the range 0.4 to 1.0 are considered.

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