A Modal Approach for the Dynamics of Spur Gears

Spur gear dynamic simulation represents a significant computational challenge with considerable scientific and technological implications. The evaluation of complex and specific design variations in a virtual environment is crucial in reducing the development time and cost. Previous contributions in the field proposed simplified approaches based on lumped modeling of tooth flexibility, model order reduction, and single or multiple degrees of freedom (DoF) systems. Generally, the presented models proved to be accurate and numerically efficient, providing a user-friendly implementation. On the other hand, most of them cannot capture directly the dynamic effects due to manufacturing errors or to tooth profile modifications. Finite element analysis (FEA) can be considered as a possible tool to take into account these sources of error. However, it is computationally impractical in dynamic conditions because of the large number of DoFs involved. In this work, a novel method based on the modal representation of the tooth deformation is presented. According to the proposed approach, the efficiency of the multibody simulation is combined with the tooth flexibility obtained by FEA. The modal analysis leads to a reduction of the system complexity, avoiding the introduction of fictitious visco-elastic components. The proposed model is used to study the meshing of two spur gears, considering different loading conditions. The static transmission errors are evaluated and compared to the results available in the literature. The contact forces during the mesh cycle are also calculated.