Paper: Generalized theory of gearing and elastohydrodynamic lubrication of spur gears.
Authors: Nikas, G. K., and Costopoulos, Th.
Where: Proceedings of the International Congress - Gear Transmissions 95, 26-28 September 1995, Sofia, Bulgaria, vol. 1, pp. 118-123.
Download a copy of this paper (Microsoft document (docx extension); 2.7 MB)
The Generalized Theory of Gearing (GTG - developed by Th. Costopoulos) is a method that relates the geometrical characteristics of production spur gears with the geometry of the rack that "produced" them. From the geometry of the rack, one can calculate all geometrical parameters of the end spur gears and can, thus, evaluate various aspects of their performance before the gears are physically produced.
In this paper, the GTG is used to examine the elastohydrodynamic lubrication of spur gears with involute external teeth, used in power transmissions and gear pumps. A forward iterative numerical method is used to solve the steady-state, smooth, Newtonian and isothermal EHL problem of two engaged spur-gear teeth. The equivalent radii of curvature of the teeth as well as their surface tangential velocities, which are needed in the solution of the EHL problem, are calculated through the GTG. In this way, the effectiveness of the lubrication is directly related to the geometrical characteristics of the rack and can be checked against different geometries and even flank errors of the rack.
A figure from this work
The following figure shows an example of the distribution of the maximum elastohydrodynamic pressure and corresponding minimum film thickness at 20 points on the teeth flanks of involute-type gears, using a steady-state, isothermal and Newtonian elastohydrodynamic analysis. Parameter Y1 is the distance from the pitch point on the line of contact. Notice that the maximum "maximum pressure" and corresponding minimum "minimum film thickness" appear close to but not on the pitch point (point Y1 = 0). This might correlate with experimental observations of pitting damage appearing slightly offset to the pitch point.
Maximum elastohydrodynamic pressure and minimum film thickness at 20 points on the teeth flanks of involute-type gears.
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