This investigation completes a solution, undertaken by K. G. Karlson in his little-known Swedish paper of 1926, for the oil-film thickness between gear teeth. Karlson’s problem is characterized by the use of a parabolic curve for the viscosity-pressure relation. The numerical results here obtained are comparable with those previously published by Gatcombe, who used a more conventional viscosity-pressure formula. It is hoped that the present analysis will help to clarify the assumptions and calculations required in the hydrodynamic theory of gear-tooth lubrication. As an aid to its practical application, the relative film thicknesses found for geometrically similar pairs of gears are here shown by a chart constructed in terms of the appropriate dimensionless variables, and extending from zero to 10 microinches per in. of pitch diameter of the pinion. The limiting case of a lubricant whose viscosity is unaffected by pressure, for which an analytical solution had been given by Karlson, is represented by a straight line on this chart.
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Hersey et al. (1950) studied this question.