Reverse engineering of machine-tool settings with modified roll for spiral bevel pinions

Abstract

Although a great deal of research has been dedicated to the synthesis of spiral bevel gears, little related to reverse engineering can be found. An approach is proposed to reverse the machine-tool settings of the pinion of a spiral bevel gear drive on the basis of the blank and tooth surface data obtained by a coordinate measuring machine(CMM). Real tooth contact analysis(RTCA) is performed to preliminary ascertain the contact pattern, the motion curve, as well as the position of the mean contact point. And then the tangent to the contact path and the motion curve are interpolated in the sense of the least square method to extract the initial values of the bias angle and the higher order coefficients(HOC) in modified roll motion. A trial tooth surface is generated by machine-tool settings derived from the local synthesis relating to the initial meshing performances and modified roll motion. An optimization objective is formed which equals the tooth surface deviation between the real tooth surface and the trial tooth surface. The design variables are the parameters describing the meshing performances at the mean contact point in addition to the HOC. When the objective is optimized within an arbitrarily given convergence tolerance, the machine-tool settings together with the HOC are obtained. The proposed approach is verified by a spiral bevel pinion used in the accessory gear box of an aviation engine. The trial tooth surfaces approach to the real tooth surface on the whole in the example. The results show that the convergent tooth surface deviation for the concave side on the average is less than 0.5 μm, and is less than 1.3 μm for the convex side. The biggest tooth surface deviation is 6.7 μm which is located at the corner of the grid on the convex side. Those nodes with relative bigger tooth surface deviations are all located at the boundary of the grid. An approach is proposed to figure out the machine-tool settings of a spiral bevel pinion by way of reverse engineering without having known the theoretical tooth surfaces and the corresponding machine-tool settings.