Influence of combined assembly error and bearing elasticity on spur gear tooth contact load distribution

A numerical method to analyse the influence of assembly error on spur gear tooth contact load distribution considering bearing elasticity is formulated. In the proposed approach, a set of transformation matrices are used to define the deviation in tooth geometry orientation from the ideal position due to the bearing elasticity and assembly error. To calculate the gear tooth deflection, the theory of contact mechanics is applied to determine the micro deformation field at the surface layer of the contact region, while the finite element model is used to represent the bulk deformation in the rest of the gear structure. An efficient search strategy for obtaining the true contact points of the deformed tooth is employed. In this strategy, the tooth contact load distribution is determined based on the smallest distance between each pair of candidate contact points within a cross-section of the mating teeth, and as well as the corresponding force and moment balance conditions. Finally, the proposed model is applied to analyse the effect of assembly errors defined at eight circumferential positions on the tooth deformation in a geared rotor system comprising of four elastic bearings.