Abstract: In view of the deficiency of the current manufacture technique for the spiral bevel gears, in which the universal motion capability(UMC) of multi-axis simultaneous CNC bevel gear generating machines is unable to be utilized to generate point-meshing tooth surface with predetermined meshing characteristics in whole transmission process, a numerical solution to inverse geometry problem of classical meshing theory is discussed to solve the related motion of the workpiece and the rack-cutter based on the geometrical structure of tooth surface and the rack-cutter: surface-envelopment-approach principle. A new method for generating the meshing characteristic-oriented design of point-meshing tooth surface is presented by application of the five-axis simultaneous CNC cutting machine. Differing from previous studies, the new-process generated tooth surface coincides with the theoretical surface along the path of contact in tangency of second order and satisfies the meshing characteristic-oriented design of point-meshing tooth surface. In regions that differ from the path of contact, the new-process generated tooth surface can approach the theoretical surface with minimum deviation. An example is given to prove the feasibility and accuracy of the proposed method.

Key words: CNC manufacture, Envelopment-approach, Point-meshing tooth surface, Spiral bevel gears