Microgeometry optimization has become an important phase of gear design that can remarkably enhance gear performance. For spiral bevel and hypoid gears, microgeometry is typically represented by ease-off topography. The optimal ease-off shape can be defined as the outcome of a process where generally conflicting objective functions are simultaneously minimized (or maximized), in the presence of constraints. This matter naturally lends itself to be framed as a multi-objective optimization problem. This paper proposes a general algorithmic framework for ease-off multi-objective optimization, with special attention given to computational efficiency. Its implementation is fully detailed. A simulation model for loaded tooth contact analysis is assumed to be available. The proposed method is demonstrated on a face-hobbed hypoid gear set. Three objectives are defined: maximization of gear mesh mechanical efficiency, minimization of loaded transmission error, minimization of maximum contact pressure. Bound constraints on the design variables are imposed, as well as a nonlinear constraint aimed at keeping the loaded contact pattern inside a predefined allowable contact region. The results show that the proposed method can obtain optimal ease-off topographies that significantly improve the basic design performances. It is also evident that the method is general enough to handle geometry optimization of any gear type.
Multi-Objective Ease-Off Optimization of Hypoid Gears for Their Efficiency, Noise, and Durability Performances
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Artoni, A., Gabiccini, M., Guiggiani, M., and Kahraman, A. (December 9, 2011). "Multi-Objective Ease-Off Optimization of Hypoid Gears for Their Efficiency, Noise, and Durability Performances." ASME. J. Mech. Des. December 2011; 133(12): 121007. https://doi.org/10.1115/1.4005234
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