Journal Article

Research on Curvature Interference Characteristics of Conical Surface Enveloping Cylindrical Worm–Face Worm Gear Drive

Qu, Sheng, Sun, Xingwei, Yang, Heran, Liu, Yin, Zhao, Yaping, Dong, Zhixu, Mu, Shibo, Zhao, Hongxun, Zhang, Weifeng

2025

Overview

This study proposes the use of Physics-Informed Neural Networks (PINNs) to further advance the curvature interference analysis method. The nonlinear equation system encountered in determining the curvature interference limit line is embedded into the PINN loss function, thereby enabling the solution of high-dimensional, nonlinear equations. Computational results demonstrate that the PINN model achieves a solution accuracy on the order of 10−13 when solving multidimensional nonlinear systems, which is comparable to the classical Fsolve algorithm. The curvature interference analysis reveals the presence of two curvature interference boundary lines, although they rarely extend to the worm gear tooth surface. A study on the influence of design parameters on the interference boundaries indicates that the axial installation distance has the greatest impact. Inadequate axial spacing causes the interference limit line to shift toward the inner end of the worm gear, significantly increasing the risk of interference in that region. The proposed curvature interference analysis method based on PINNs can be extended to other types of gear drives. It also lays the foundation for future work on establishing both forward and inverse mappings between design parameters and curvature interference using PINNs.

• Publisher: MDPI AG
• Subject: curvature interference / Design optimization / face worm gear / Fluid dynamics / gear drive / meshing theory / Neural networks / Nonlinear equations / Parameter estimation / Partial differential equations / physics-informed neural networks / undercutting / Velocity