Optimization of the Loaded Contact Pattern in Hypoid Gears by Automatic Topography Modification

Abstract

Systematic optimization of the tooth contact pattern under load is an open problem in the design of spiral bevel and hypoid gears. In order to enhance its shape and position, gear engineers have been assisted by numerical tools based on trial-and-error approaches, and/or they have been relying on the expertise of skilled operators. The present paper proposes a fully automatic procedure to optimize the loaded tooth contact pattern, with the advantage of eventually reducing design time and cost. The main problem was split into two identification subproblems: first, to identify the ease-off topography capable of optimizing the contact pattern; second, to identify the machine-tool setting variations required to obtain such ease-off modifications. Both of them were formulated and solved as unconstrained nonlinear optimization problems. In addition, an original strategy to quickly approximate the tooth contact pattern under load was conceived. The results obtained were very satisfactory in terms of accuracy, robustness, and computational speed. They also suggest that the time required to optimize the contact pattern can be significantly reduced compared with typical time frames. A sound mathematical framework ensures results independent of the practitioner’s subjective decision-making process. By defining a proper objective function, the proposed method can also be applied to affect other contact properties, such as to improve the motion graph or to decrease the sensitivity of the transmission to assembly errors. Furthermore, it can be easily adapted to any gear drive by virtue of its systematic and versatile nature.