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.

A load distribution model for hypoid gears using ease-off topography and shell theory

“…The simulations of hypoid efficiency [45], hypoid surface wear and lapping process [46] as well a recent methods to optimize the tooth profiles for desired contact patterns [47] can all be accelerated significantly through use of the proposed model instead of FE-based models. Our current research focuses on application of this model to some of these problems.…”

The numerical methods for determining of the gear contact pattern on the example of the spiral bevel gear

“…Ślady współpracy czy też ślady styku dzieli się na otrzymane bez obciążenia i z obciążeniem, które nazywa się odpowiednio analizą TCA (tooth contact analysis) oraz LTCA (loaded tooth contact analysis) [2][3] [4].…”

Manufacture of Optimized Face-Hobbed Spiral Bevel Gears on Computer Numerical Control Hypoid Generator

“…A new systematic method for identifying the values of the machine tool settings required to obtain flank form modifications in hypoid gears was presented by Artoni et al [15]. The same authors in paper [16] proposed a fully automatic procedure to optimize the loaded tooth contact pattem in hypoid gears. correction methodology derived directly from the six-axis Cartesian-type CNC hypoid generator is proposed in Ref.…”