Mathematical model and manufacture programming of loxodromic-type normal circular-arc spiral bevel gear

In this paper, loxodromic-type normal circular-arc spiral bevel gear is proposed as a novel application of the circular-arc tooth profile at the gear transmission with intersecting axes. Based on the principle of molding-surface conjugation, the study develops a mathematical model for the tooth alignment curve and the computational flow at the design stage to enable the generation of the tooth surface. Machining of the tooth surface is then carried out to determine the interference-free tool path of the numerical control (NC). Moreover, a pair of loxodromic-type normal circular-arc spiral bevel gears is manufactured on computer numerical control (CNC) machine tools. The proposed theory and method are experimentally investigated, and the obtained results primarily reflect the superior performance of the proposed novel gear.