Abstract
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.
Highlights
Gear-loaded tooth contact analysis (LTCA) is important for the design and analysis of gear performance
A two-dimensional (2D) spur gear finite element model (FEM) is built by Wang [16] to calculate the static transmission error, single and combined torsional mesh stiffness, tooth load-sharing ratio, maximum tooth root stress, and surface contact stress against various input torques over a complete mesh cycle
In order to get high-accuracy gear surface, Mao [18] generated the gear tooth profile node coordinates in C++ according to the gear meshing theory, imported the data into the finite element analysis software through Python script to generate the 2D gear geometric model, and extruded the plane model to obtain a 3D helical gear geometry to investigate the gear surface fatigue wear phenomena. e method is only suitable for spur gears or occasions where the accuracy requirement is not very strict
Summary
Gear-loaded tooth contact analysis (LTCA) is important for the design and analysis of gear performance. In order to get high-accuracy gear surface, Mao [18] generated the gear tooth profile node coordinates in C++ according to the gear meshing theory, imported the data into the finite element analysis software through Python script to generate the 2D gear geometric model, and extruded the plane model to obtain a 3D helical gear geometry to investigate the gear surface fatigue wear phenomena. Some progresses have been made in modelling a relatively high-precision 3D helical gear finite model with different methods, most of the models are coarse mesh and none of these studies make further research on the local contact pattern due to the difficulties in hexahedral mesh refinement on the tooth contact surface. An advanced nonlinear tooth contact analysis will be applied to investigate gear contact behaviors based on the helical gear FEM proposed in the article
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