Shapes different from the traditional ones have been proposed for face worm gears and for conical and cylindrical worms that mesh with them. The proposed shapes are based on the concept of generating a face worm gear surface by use of a tilted head cutter instead of by the traditional use of a hob. (As used here, "head cutter" is also meant to signify, alternatively, a head grinding tool.)The gear-surface-generation equipment would be similar to that used for generation of spiral bevel and hypoid gears. In comparison with the corresponding traditional hob, a tilted head cutter according to the proposal would be larger, could be fabricated with greater precision, and would enable the generation of gear surfaces with greater precision and greater productivity.
A face worm gear would be generated (see figure) by use of a tilted head cutter, the blades or grinding surfaces of which would have straight-line profiles. The tilt of the head cutter would prevent interference with teeth adjacent to the groove being cut or ground.
A worm to mesh with the face worm gear would be generated by use of a tilted head cutter mounted on the cradle of a generating machine. The blades or grinding surfaces of the head cutter would have a parabolic profile and would deviate from the straight-line profiles of the head cutter for the face worm gear. The shortest distance between the worm and the cradle would follow a parabolic function during the cycle of meshing in the generating process to provide a parabolic function of transmission errors to the gear drive.
The small mismatch between the profiles of the face-worm-gear and worm head cutters would make it possible to localize the bearing contact in the worm gear drive. The parabolic function of transmission errors could absorb discontinuous linear functions of transmission errors caused by errors of alignment; this could afford a significant benefit, in that such errors are main sources of noise and vibration in gear drives.
The main advantage of using tilted head cutters is that cutting speeds are independent of the shape-generation processes, making it possible to choose cutting speeds that are optimum with respect to requirements to minimize temperatures and deformations during fabrication and improve the quality of finished parts.
The profile of the cutting or grinding surface and the machine-tool settings for the position and orientation of a head cutter would be derived from the theoretical shape generated by a hob. The derivation would be effected by use of an algorithm that takes account of the tilted-head-cutter geometry and enforces the requirements for meshing and non-interference.
A tooth-contact-analysis computer program has been developed for simulation of meshing and contact of the proposed worms and face worm gears. In a test case, the program showed that, as desired, the function of transmission errors would be a parabolic function of low magnitude, the contact would be localized, and the path of contact would be longitudinal in the sense that it would lie along the gear-tooth surfaces. The program also showed that the bearing contact region would be free of areas of severe contact stresses and that the contact ratio would be larger than 3 (signifying that at any given instant, there would be at least 3 pairs of teeth in contact).
This work was done by Faydor L. Litvin, Alessandro Nava, Qi Fan, and Alfonso Fuentes of the University of Illinois for Glenn Research Center. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com/tsp under the Mechanics category.
Inquiries concerning rights for the commercial use of this invention should be addressed to NASA Glenn Research Center, Innovative Partnerships Office, Attn: Steve Fedor, Mail Stop 4–8, 21000 Brookpark Road, Cleveland, Ohio 44135. Refer to LEW-17596-1.