Abstract: A half-modified roll(HMR) method for the optimization of transmission error function of spiral bevel gears was proposed.Based on local synthesis,the pinion machine-tool settings were firstly obtained,then tooth contact analysis(TCA) was carried out and a contrast was made between the predesigned transmission error function with that of TCA.In order to narrow the differences between these two transmission error functions,the cutting ratio and the third-order modified-roll coefficient were slightly adjusted.By applying HMR to optimize the transmission error function of a pair of spiral bevel gears in aviation,the researches find that the cutting ratio of the pinion has some influence on the magnitude of transmission error function,and the third-order modified-roll coefficient has influences on the whole deflection of transmission error function.The optimized transmission error function agrees very well with the predesigned curve,and the contact pattern meets the design requirement,so the validity of HMR is proved.