Micro-geometry optimization has become an important phase of gear design that can remarkably enhance gear performance. For spiral bevel and hypoid gears, micro-geometry 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 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 tested on a face-hobbed hypoid gear set. Three objectives are defined: maximization of 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 ¤Address all correspondence to this author. optimization of any gear type.

Multi-objective ease-off optimization of hypoid gears for their efficiency, noise and durability performances

ARTONI, ALESSIO;GABICCINI, MARCO;GUIGGIANI, MASSIMO;
2011

Abstract

Micro-geometry optimization has become an important phase of gear design that can remarkably enhance gear performance. For spiral bevel and hypoid gears, micro-geometry 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 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 tested on a face-hobbed hypoid gear set. Three objectives are defined: maximization of 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 ¤Address all correspondence to this author. optimization of any gear type.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/203326
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