Reconstruction of real tooth surfaces of spiral bevel pinions with modified offset

Abstract

Reverse engineering has been successfully applied in many fields; however, it is not the case for spiral bevel gears. In order to reconstruct the real tooth surfaces of spiral bevel pinions based on the original tooth surface grids (OTSG) provided by coordinate measuring machine, meshing performances were achieved by tooth surface scanning method. Three meshing conditions necessary for local synthesis, i.e. the directional angle, the magnitude of major axis of contact ellipse and the second derivative of transmission errors at the mean contact point, were filtered from the meshing performances obtained by discrete tooth contact analysis. Computational tooth surface grids (CTSG), corresponding to OTSG node to node, were expressed by manufacturing parameters derived by local synthesis. Tooth surface grid difference was formed by making the centre node of CTSG through rotation operation coincided with that of OTSG. Optimization objective was built up by summing up the deviations of all nodes on either OTSG or CTSG. The three meshing conditions, the mean contact point position and the higher order coefficients of blank offset correction were taken as the design variables. The internal function fminsearch of MATLAB was chosen to minimize the tooth surface grid difference. After the manufacturing parameters were achieved, the pinion tooth surfaces were reconstructed based on the reversed CTSG. A zerol spiral bevel pinion in an aviation engine accessory gear box was employed to demonstrate the proposed methodology. The results show that OTSG is unable to give perfect meshing performance. The convergent results of reversing show that many of the field of distance between the reversed CTSG and OTSG is less than 1 μm. This demonstrates the feasibility of the proposed reversing techniques.