Paper: Load sharing and profile modification of spur gear teeth in the general case of any flank geometry.
Author: George K. Nikas
Published in: Proceedings of the International Conference on Gears, 22-24 April 1996, Dresden, Germany, VDI Berichte 1230, pp. 923-935.
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Low-contact-ratio spur gears suffer from abrupt changes of the transmitted load because of the continuous engagement and disengagement of teeth in a meshing cycle. These changes generate noise and vibrations, result in poor lubrication and increased tooth wear, and can even cause tooth breakage!
Gear teeth are neither rigid nor perfectly manufactured. They are compliant, and they often have flank errors, which are inevitable in a production process. Therefore, dynamic loads and reduced performance cannot be avoided, unless the power-to-weight ratio is reduced or the contact ratio is increased. Alternatively, a better solution is to perform an appropriate tooth flank modification that suits each particular gear and even each particular gear tooth.
In a previous work, the author presented a complete and accurate method for the calculation of the optimum profile modification for spur gears. That method omitted tooth flank errors. In the present paper, the previous method has been extended to incorporate in the analysis the general case of flank errors of any form. The method has no constraints of geometrical or operational parameters and can be used with flank geometries other than the standard involute. The application is for dry contacts only. Using this method, spur gears can be modified after their production, in a way that eliminates any static-load abrupt changes and, thus, results in a quieter and longer-lasting gear set.
Some figures from this work
An example of involute gears with smooth linear flank error functions of the form e = c·L, where L is the profile modification perpendicularly to the flank in the case of teeth without errors and c is a constant, was presented in the paper. The value of c used for the pinion was -0.2, whereas that for the gear was 0.6. To demonstrate the generality of the developed method and the accompanying computer program, the gear teeth data were chosen to deviate from common standards. Those data are as follows: pressure angle = 18º, module = 7 mm, rack dedendum = 1.7 times the module, rack addendum = 1.1 times the module, number of teeth of the pinion = 24, number of teeth of the gear = 33, tooth width = 10 mm, transmitted power 80 kW at 10,000 rpm. The computed contact ratio is equal to 1.87. After computing all gear teeth compliances and the static load distribution, the teeth profiles (with the assumed flank errors) are suitably modified to smoothen the load distribution. The static load curves of the ideal teeth (without errors), of the teeth with errors and of the optimised teeth are shown in Fig. 1. The smoothness of the load distribution of the optimised teeth is obvious.
Fig. 1. Static load distribution before and after optimisation.
The necessary flank modifications to achieve the optimised smooth load distribution of Fig. 1 are shown in Fig. 2. On the horizontal axis, Xpoc is the distance from the pitch point along the contact path. The modification perpendicularly to the tooth flank is applied to the tips of the teeth only and is exponential. The whole optimisation process takes a negligible fraction of 1 s of the CPU time of a modern PC using a very high resolution of 1,000 gridpoints on the tooth flanks, i.e., it is practically instantaneous.
Fig. 2. Tooth flank modifications to achieve the smooth load distribution of Fig. 1.
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