Based on the theory of tooth surface up and including third order contact

this paper presents a new methodology for transmission performance design of spiral bevel gears and hypoid gears with low-noise and low misalignment error sensibility. The relation between 2 rd ?3 rd contact characteristics and the transmission function is found by investigating the transmission function. Characteristics concerning errors sensibility are selected from 3 rd contact characteristics simultaneously

and the assignment criterion of these parameters as 3 rd optimization objective is provided. Finally

a numerical example for verifying the proposed theory is provided.