Computational approaches for improving machining precision in five-axis flank milling of spiral bevel gears

Abstract

Spiral bevel gears are a critical component in mechanical systems that offers high power transmission efficiency between nonparallel axes. The current gear manufacturing, which normally requires specialized machines and cutting tools specific to one gear type, offers limited production flexibility. An effective alternative is to utilize 5-axis computer numerical control milling on general-purpose machine tools. This paper aims to improve the machining precision in the flank milling of spiral bevel gears, particularly the tooth surfaces, using computational approaches. First, a geometric method was developed to approximate the contact path of a gear pair without solving the complex equations in tooth contact analysis. A quantitative measure was introduced to evaluate the contact path deviation from the center curve of the tooth surface. Second, we proposed an optimization scheme for generating tool paths that induce minimal geometrical errors on the finished surface. It employs a metaheuristics-based search algorithm with the errors as an objective in tool path planning. Test results on real gears verified the effectiveness of the proposed scheme. Three measures of the meshing performance, namely the average sampling error, the contact path deviation, and the transmission error, were cross-compared on different gear pairs to examine whether they consistently distinguish the performance rank. This work provides feasible solutions for controlling machining errors in 5-axis flank milling of complex gears.