Parameterized High-Precision Finite Element Modelling Method of 3D Helical Gears with Contact Zone Refinement

In order to perform a tooth contact analysis of helical gears with satisfactory accuracy and computational time consuming, a parameterized approach to establish a high-precision three-dimension (3D) finite element model (FEM) of involute helical gears is proposed. The enveloping theory and dentiform normal method are applied to deduce the mathematical representations of the root transit curve as well as the tooth profile of the external gear in the transverse plane based on the manufacturing process. A bottom-up modelling method is applied to build the FEM of the helical gear directly without the intervention of CAD software or creating the geometry model in advance. Local refinement methodology of the hexahedral element has been developed to improve the mesh quality and accuracy. A computer program is developed to establish 3D helical gear FEM with contact region well refined with any parameters and mesh density automatically. The comparison of tooth contact analysis between the coarse-mesh model and local refinement model demonstrates that the present method can efficiently improve the simulation accuracy while greatly reduce the computing cost. Using the proposed model, the tooth load sharing ratio, static transmission error, meshing stiffness, root bending stress, and contact stress of the helical gear are obtained based on the quasistatic load tooth contact analysis. This methodology can also be used to create other types of involute gears, such as high contact ratio gear, involute helical gears with crossed axes, or spiral bevel gears.