A General Parameterized High Precision Finite Element Modelling Method of Three-dimensional Helical Gear

Abstract

In order to be able to perform an LTCA with satisfactory accuracy and time consuming, a parameterized approach to establishing a high-precision three-dimension (3D) finite element model (FEM) of involute spur/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 involute tooth profile of the external gear in the transverse plane based on the manufacturing process and an accurate description of the cutter. The bottom-up modelling method is used to build the finite element model of the helical gear directly without create the geometry model in advance. A computer program is developed to establish 3D helical gear finite element model of any parameters and mesh density automatically. Computerized tooth contact analysis of load sharing and con-tact pressure as well as transmission error and mesh stiffness are also simulated and calculated. This methodology can also use to create other types of involute gears, such as involute helical gears with crossed axes or spiral bevel gears.