AGMA 06FTM15-2006 pdf download.Optimal Tooth Modifications in Spiral Bevel Gears Introduced by Machine Tool Setting Variation by: V. Simon, Budapest University of Technology and Economics.
Papers [13-19] deal with loaded tooth contact analysis and stress analysis in spiral bevel gears. Wilcox 113 in his paper outlines the general theory for calculating stresses in bevel and hypoid gears using flexibility matrix method in combination with the finite element method. The loaded tooth contact analysis predicting the motion error of spiral bevel gear sets, by applying influence matrices, is presented by Gosselin et al (14]. Handschuh and Bibel [15] analytically and experimentally rolled through mesh a spiral bevel gearset to investigate the tooth bending stress by finite element method. Paper published by Falah et al. [16] summarizes the experimental and numerical results of the meshing of spiral bevel gears under load, from which the actual contact ratio is evaluated. Linke et al. [171 calculate the load distribution based on a method for using influence coefficients and also calculate the correspending tooth root and contact stresses. By Fuentes et al. [18] the FEM was used for stress analysis in spiral bevel gears. Fang and Wei [19] consider the edge contact in loaded tooth contact analysis.
Conjugated spiral bevel gears are theoretically in line contact. In order to decrease the sensitivity of the gear pair to errors in tooth surfaces and to the mutual position of the mating members, carefully chosen modifications are usually introduced into the teeth of one or both members. As a resuft of these modifications, the spiral bevel gear pair becomes mismatched,” and a point contact of the meshed teeth surfaces appears instead of line contact. In practice these modifications are usually introduced by applying the appropriate machine tool setting for pinion and gear manufacture. It is usually assumed that the theoretical point contact under load spreads over an elliptical area. In this paper a new approach for the computerized simulation of load distribution in mismatched spiral bevel gears wfth point contact is presented. The main feature of this method is that the tooth deflections of the pinion and the gear are calculated by FEM. and the tooth contact is treated in a special way instead of using the usually applied theory of elliptical contact area. The main idea is: As the tooth surface modifications are relatively small and the conjugation of the mating surfaces is relatively good, thus the point contact under load spreads over a surface along the whole or part of the potentiar contact line, which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces along the tooth face width are minimal. The load distribution calculations made for hypoid [20] and worm gears [21J have shown that this approach gives a more realistic contact pattern arid contact pressure than the elliptical one.
The method is implemented by a computer program. By using this program the influence of machine tool settings for pinion tooth manufacture on load distribution, stresses and transmission errors is investigated. On the basis of the obtained results the optimal machine tool settings are determined introducing the optimal tooth modifications.
Theoretical Background
A Gleason type spiral bevel gear pair with the generated pinion arid gear is treated. The pinion is the driving member. The convex side of the gear tooth and the mating concave side of the pinion tooth are the drive sides. The modifications are introduced into the pinion teeth, therefore, only the generation of the pinion tooth surface will be presented in this paper. The processing of gear teeth is described in Ref. (22J.
Generation of the Pinion Tooth Surface
The machine tool setting used for the generation of pinion teeth is given in Fig. 1.AGMA 06FTM15 pdf download.