Hypoid gears are widely used in the transmission systems of automobiles, ships and helicopters because of their high load carrying capacity, high degree of overlap and smooth transmission (Sheveleva et al., 2007). As an important part of hypoid gear design and manufacturing, the type of cutting edge curve affects the performance of the gear pair directly and the design of cutter section is a significant direction to improve the performance of gear. The cutter cross-section with an additional transition section between the major cutting edge and the fillet segment is equivalent to the root modification of gear teeth, which can effectively avoid tooth root edge contact, but the influence laws on tooth root bending stress, transmission error and meshing stiffness are not clear. Thus, it is necessary to study the influence law of tool parameters on meshing performance for this type of cutter cross-section.In recent years, a large number of scholars have researched the theory of tooth surface forming and tooth surface modeling methods for hypoid gears. Litvin (Litvin et al., 1991) established a gear surface modeling method based on tool geometry based on the kinematics of face-hobbed hypoid gears. Shih (Shih et al., 2007) investigated the mathematical modeling method of generalized tooth surface based on gear transmission theory and differential geometry theory. Based on grinding mechanism and machine-tool settings of the Gleason modified roll hypoid grinder, a mathematical model for the tooth geometry of spiral bevel and hypoid gears is developed by Lin (Lin et al., 1997). By using theory of gearing, the mathematical representation of gear tooth surfaces was derived, Vimercati (Vimercati, 2007) proposed a mathematical model able to represent tooth surfaces of a complex gear drive for hypoid gears cut by face-hobbing method. Peng (Peng et al., 2020) established the mathematical tooth flank model by simulating the actual generation process. Then, a novel collaborative machine tool settings compensation considering both the tooth flank geometric and physical performances was proposed. Focusing on comprehensive effect of both macro and micro geometries, accurate flank geometric