Implementation of a finite element model for stress analysis of gear drives based on multi-point constraints

Abstract

Gear researchers are always trying to find a trade-off solution between obtaining accurate results from gear stress analyses and low computational costs. Both factors, accuracy on the one hand, and a low computational cost on the other hand, usually go in opposite directions. In this paper, a finite element model for stress analysis of gear drives is proposed with the ultimate goal of obtaining accurate results regarding contact and bending stresses with lower computational cost than those finite element models where mesh refinement is not applied. The proposed finite element model allows the whole cycle of meshing to be analyzed and is based on the application of multi-point constraints for mesh refinement and the application of elements with a reduced number of integration points. Node coordinates are computationally and automatically determined by application of the gear theory. Several numerical examples are presented for a spur gear drive, although the same ideas can be applied in other types of gear drives. Accurate results of maximum contact pressure along the cycle of meshing with an important reduction of computational cost are achieved, mainly due to the reduction of the number of degrees of freedom that multi-point constrains provide, rather than by the use of reduced-integration elements.