The initial selection and determination in error tooth contact analysis(ETCA) of spiral bevel gear were investigated.Based on the geometric equivalent relationship

the point P' which is closer to the initial mesh-point P was calculated.The process of calculating P' wasn't involved with the rotating operation of two tooth surface equations in the installation coordinate system;as compared to the equation of directly solving point P

the new algorithm was simple

then iterative method was used to calculate the initial mesh-point P.The calculation examples show that the new algorithm can reduce the sensitivity of the initial value

and improve the stability and efficiency of ETCA

thus making the algorithm of ETCA more suitable and the selection of initial value more simpler.