The increasingly demanding service conditions for aviation spiral bevel gears necessitate higher machining accuracy of the tooth surfaces. The conventional constant roll ratio, a critical parameter governing the relative motion between the cradle and the workpiece during machining, proves inadequate in accommodating kinematic variations. This limitation leads to inaccurate tooth surface generation and degraded meshing performance. To address this challenge, the higher-order roll ratio modification coefficients are introduced to enhance motion adjustability, optimizing tooth surface topography and improving meshing behavior. To elucidate the mechanism of higher-order roll ratio modification coefficient on meshing behavior of aviation spiral bevel gear, this paper establishes a mathematical tooth surface model incorporating higher-order roll ratio polynomials based on gear meshing theory and homogeneous coordinate transformation. A finite element-based loaded tooth contact analysis (LTCA) model is developed to systematically investigate the effect of variations in both roll ratio modification coefficients and higher-order roll ratio polynomial orders on meshing performance. The results demonstrate that: Negative variations in second-order roll ratio modification coefficient significantly influence root bending stress and the peak-to-peak transmission error, while positive variations predominantly affect tooth contact stress. Negative variations in third-order roll ratio modification coefficient significantly affect both tooth contact stress and the peak-to-peak transmission error, while positive variations predominantly influence root bending stress. The second-order roll ratio modification coefficient demonstrate more significant impacts on gear meshing behavior than third-order counterparts. The zero-order roll ratio modification yields the poorest meshing performance, whereas higher-order roll ratio modification improves meshing behavior, with second-order demonstrating optimal comprehensive performance. The research provides a theoretical foundation for design and precision manufacturing of spiral bevel gears, with significant engineering value for enhancing load capacity and reliability of transmission systems.
YANG et al. (Thu,) studied this question.