Meshing characteristics analysis of involute helical gear drive based on the semi-analytical method

This paper employs a semi-analytical approach to conduct a detailed analysis of the meshing process of parallel-axis involute spiral gears. Although such gears are widely used, traditional studies often simplify the meshing process to planar meshing, thereby limiting the understanding of their intrinsic meshing characteristics, especially neglecting the line contact mechanism when there is no direct envelope relationship between the tooth surfaces. To address this, the study treats the gear transmission as a special case of spatial meshing, formulating tooth contact equations and analytically solving their unknowns. A formula for calculating the relative principal curvature across the entire meshing zone is derived. The research reveals that line contact is achieved due to two uncorrelated free unknowns in the contact equations. Numerical examples demonstrate that increasing the helix angle decreases the absolute value of the relative principal curvature, and further reduces the contact stress on the tooth surface. This study lays a solid foundation for the design and optimization of parallel-axis involute helical gears, offering new insights into their meshing geometry.