Paper: Minimization of spur gear dynamic loading through the Generalized Theory of Gearing.
Authors: Costopoulos, Th., Nikas, G. K.
Published in: Proceedings of the International Congress - Gear Transmissions 95, 26-28 September 1995, Sofia, Bulgaria, vol. 1, pp. 52-56.
Download a copy of this paper (Microsoft WORD document; 2.1 MB)
Abstract
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 effects of tooth profile modification on the load response of spur gears with involute external teeth were studied, for contact ratio below 2. Such gears suffer from abrupt changes of the transmitted load due to the successive engagement and disengagement of gear teeth and because teeth are compliant. As a result, dynamic loads can cause severe disruption of lubricant films, increased wear, noise and vibrations.
The GTG is used to determine gear dimensioning. Tooth stressing results from the static-load analysis. An optimised profile modification is found to eliminate the abrupt load changes and minimize the dynamic loading. This is achieved by calculating all teeth compliances and the resulting static load distribution during rotation of the gears, then imposing appropriate tooth flank modifications that result in a perfectly smooth static-load distribution.
Some figures from this work
Spur gears suffer abrupt changes of the tooth transmitted load because of the continuous engagement and disengagement of teeth during a mesh cycle. This paper presents a method to completely eliminate the abrupt changes of the tooth static load by a suitable modification of the teeth flanks. Figure 1 shows a modified tooth profile. The modification takes place at the tip area of the tooth.
Fig. 1. Modification of a tooth profile.
Figure 2 below shows a typical modification of the teeth contact path (a linear and a parabolic modification shown) used widely in practice. Starting from this modification, the contact path is related to the actual tooth flank through the Generalized Theory of Gearing (GTG).
Fig. 2. Original and modified gear contact path.
Figure 3 below shows the result of an exponential-type contact path modification on the static load distribution. The original ("initial") unmodified distribution can be clearly seen with the abrupt load changes. Then the modified smooth distribution is seen for various values of a parameter "z", which is the exponent of the aforementioned exponential-type function of the modified contact path. It is obvious that the smoothest load distribution is achieved for z = 2. The results refer to ideal teeth without any flank errors.
Fig. 3. Effect of teeth profile modification on static load distribution.
See also a follow-up and more general paper of the author.