Investigation of Gears Using an Elastic Multibody Model with Contact

Abstract

The classical approach to simulate contacts between gears is to use rigid body models coupled with a parallel spring damper combination. However, these models had been developed for properly meshing gears with smooth contacts and cannot cover wave propagation caused by hard contacts or impacts. Moreover, as they are based on the assumption of rigidness, often light weight designs, resulting in very compliable gear bodies, cannot be considered appropriately. To evaluate how appropriate these rigid body models are to simulate impact forces, a very detailed finite element model is used to simulate several impacts and the results are compared to simulations with a rigid body model. The results reveal that for compliable gear bodies, there exist dynamic effects that considerably affect contact forces and motion and that these effects cannot be covered by rigid body models at all. Hence, a flexible model is imperative to precisely simulate impact forces. To reduce integration time, we present a modally reduced elastic multibody model including contact that allows very precise simulations in reasonable time. For the contact calculations a node-to-segment penalty formulation is introduced and is integrated using central differences. Even though the elastic model is a reduced model, it is still of huge size, as any node on any flank is a potential contact node. Also, the transformation data between modal and nodal coordinates must be accessible during integration. To reduce the required amount of memory a coarse collision detection is introduced that allows to dynamically reload only the transformation required in the current integration step. This approach allows very precise simulations of contacts between gears with integration times about 400 times faster than for associated finite element simulations. At the same time the model is robust and fast enough to allow the simulation of many contacts and many revolutions. To validate this approach basic experimental investigations with simple impact bodies have been carried out. The results from these experiments and related simulations agree very well.