Reverse Engineering for Real Tooth Surfaces of Generated Spiral Bevel Gears

Author(s): Liu Guanglei, Wang Leyun, Li Degeng, Chang Kai

The manufacturing parameters of spiral bevel gear should be reversed first in reverse engineering of spiral bevel gear drives. An approach is proposed to reconstruct the real tooth surfaces of generated spiral bevel gears based on tooth surface grids formed by a coordinate measuring machine (CMM) without knowing the design method of the gear flank and actual manufacturing parameters. The trial tooth surface grid (TTSG), either the concave side or the convex side, represented by the manufacturing parameters of duplex method, are formed by solving a set of non-linear equations based on the CMM tooth surface grid (CTSG) in the projection plane. When the CTSG is rotated until its center node coincided with that the TTSG, the tooth surface deviation is formed. A unified objective for optimization, which consists of the tooth surface deviations of both the concave and the convex sides, is set up. The design variables are the blade pressure angle and the point radius, both for the outer blade and the inner blade in addition to the spiral angle. The constraints are the changing manufacturing parameters and the dedendum angle which are dependent on the design variables. A hybrid strategy for reverse engineering, which consists of the discrete optimization and the continuous optimization, is employed in turn. A pair of spiral bevel gear drives in aviation engine is explored. The results show that: (i) the reversed head cutter diameter is smaller than the one with the least shrinkage ratio of the pinion root slot, indicating that the prototype designer pays more attention on increasing the fatigue strength and decreasing the sensibility of tooth contact pattern due to misalignments; (ii) the pressure angle of the outer blade and the inner blade are almost the same, meaning the pressure angle of the blades are not modified; (iii) the dedendum angle related to tooth taper types is calculated according the addendum or dedendum of the pinion over the whole tooth depth.