Fillet Shape Optimization for Gear Teeth

Abstract

In this paper, the fillet shape optimization problem is studied using a new shape optimization approach. In order to achieve the optimal performance of gear mechanism, the maximum bending stress is minimized in the fillet region. In the proposed shape optimization approach, there are two new contributions: the application of Boundary Element method (BEM) and B-spline representation of the fillet shape. A Boundary Element model is established for the gear tooth and the bending stress in the fillet region is evaluated by a Boundary Element solver. The use of BEM in the approach instead of the commonly used Finite Element Method (FEM) has significant importance for shape optimization since BEM usually provides more accurate structural responses on the boundary and the remeshing procedure is much easier. For the curve representation of the fillet profile, the uniform cubic B-splines are employed in fillet profile synthesis. The fact that B-spline curves are used to construct the design boundary overcomes limitations resulted from the discrete nodes representation. Therefore, this new approach combines both the BEM solver and the B-spline technique in the shape optimization process. In an example for numerical simulation, a non-involute gear tooth profile is used and the results show that the new shape optimization technique is efficient for optimizing the performance of the gear mechanism. Moreover, the proposed shape optimization approach is able to provide reliable solutions for optimizing a large variety of the non-standard gear tooth profiles.Copyright © 2005 by ASME