Gear researchers and engineers have been seeking systematic approaches to optimize the microgeometry of gear teeth, especially of hypoid gears. Because their tooth surface deviations from their conjugate counterparts (ease-off ) are small (tens to few hundreds of micrometers), their contact properties are quite sensitive to micro-geometry, which has a significant impact on noise, contact pressure distribution, sensitivity to misalignments, and can also affect mechanical efficiency. In gear design, typical objectives are often conflicting in nature. Therefore, ease-off optimization should be formulated and solved as a proper multi-objective optimization problem. Micro-geometry optimization has long been a time-consuming trial-and-error procedure, mostly based on the individual experience of skilled gear practitioners. One of the earliest published contributions to the solution of this problem was given by Litvin [1] with his local synthesis method. Subsequently, methods aimed at improving the contact pattern and the transmission error function through micro-geometry corrections were proposed, e.g. [2, 5, 6]. Nowadays, simulation models for loaded tooth contact analysis (LTCA) enable to accurately predict contact stresses and deformations. In this study, the Hypoid Analysis Program (HAP) developed by Kolivand and Kahraman [9] was used. This work proposes a method for simulation-based multi-objective ease-off optimization. The proposed method was tested on a real face-hobbed hypoid gear set. Three simultaneous objectives were defined: maximization of mechanical efficiency, minimization of loaded transmission errors, and minimization of the maximum contact pressure. Bound constraints on the design variables were imposed as well as a nonlinear constraint aimed at keeping the loaded contact pattern off the tooth edges, 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. Also, the method is general enough to be employed for geometry optimization of any gear type.
Simulation-based multi-objective optimization of hypoid gears
ARTONI, ALESSIO;GABICCINI, MARCO;GUIGGIANI, MASSIMO
2011
Abstract
Gear researchers and engineers have been seeking systematic approaches to optimize the microgeometry of gear teeth, especially of hypoid gears. Because their tooth surface deviations from their conjugate counterparts (ease-off ) are small (tens to few hundreds of micrometers), their contact properties are quite sensitive to micro-geometry, which has a significant impact on noise, contact pressure distribution, sensitivity to misalignments, and can also affect mechanical efficiency. In gear design, typical objectives are often conflicting in nature. Therefore, ease-off optimization should be formulated and solved as a proper multi-objective optimization problem. Micro-geometry optimization has long been a time-consuming trial-and-error procedure, mostly based on the individual experience of skilled gear practitioners. One of the earliest published contributions to the solution of this problem was given by Litvin [1] with his local synthesis method. Subsequently, methods aimed at improving the contact pattern and the transmission error function through micro-geometry corrections were proposed, e.g. [2, 5, 6]. Nowadays, simulation models for loaded tooth contact analysis (LTCA) enable to accurately predict contact stresses and deformations. In this study, the Hypoid Analysis Program (HAP) developed by Kolivand and Kahraman [9] was used. This work proposes a method for simulation-based multi-objective ease-off optimization. The proposed method was tested on a real face-hobbed hypoid gear set. Three simultaneous objectives were defined: maximization of mechanical efficiency, minimization of loaded transmission errors, and minimization of the maximum contact pressure. Bound constraints on the design variables were imposed as well as a nonlinear constraint aimed at keeping the loaded contact pattern off the tooth edges, 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. Also, the method is general enough to be employed for geometry optimization of any gear type.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
