Compensation of errors of alignment caused by shaft deflections in face-gear drives generated by shaper cutters

Abstract

A numerical-analytical approach for the determination of relative errors of alignment based on the finite element analysis of face-gears drives and their supporting shafts is proposed. The face-gear member of the gear set is generated based on the errors of alignment to be compensated by adjusting the position of the shaper cutter to replicate the relative position of the pinion in misaligned condition. The results obtained show that the face-gear drive with compensated geometry has better contact conditions and develops lower contact and bending stresses that the respective face-gear drive with no deflections compensated under a nominal transmitted torque. For the purpose of machining convenience, an alternative and simplified method of compensation of errors of alignment is proposed based only on the compensation of an equivalent error of shortest distance between axes. Finally, the application of a longitudinal crowning to the face-gear tooth surfaces by using a shaper with a larger number of teeth than the mating pinion is compared with the above compensation methods in terms of contact patterns and contact and bending stresses obtained.