基于奥利康制准双曲面齿轮切齿原理和加工方法，分析了三面刀刀头的结构和安装位置，提出了基于刀具NS（neutral surface）平面法向基准下刀盘数学模型的建立方法。在此基础上，推导了奥利康制准双曲面齿轮的加工机床坐标系，建立了成形法大轮和展成法小轮的齿面数学模型，整理了一套基于三面刀盘奥利康制准双曲面齿轮精确化建模流程。通过齿面模型得到的数学齿面与通过KIMOS软件得到的45点齿面进行对比和实际接触印痕与理论接触印痕对比两种方法进行齿面验证。结果表明：大小轮推导齿面与实际齿面齿线和几何形貌基本一致，小大轮齿面基本重合；小轮凹面最大误差位于小端偏齿顶处，其值为0.007 5 mm，大轮凸面最大为0.002 3 mm；KIMOS计算的理论轮齿接触分析（TCA）、轮齿承载接触分析（LTCA）印痕与有限元计算印痕的位置方向基本一致，验证了齿面的正确性。
Based on the tooth cutting principle and manufacturing method of Oerlikon's hypoid gear, the structure and assembly location of three-faced blade is analyzed and the method to establish the mathematical model of three-face cutter head and plate (SPIRON) by the normal benchmark of the NS plane of tool is proposed. According to the manufacturing coordinate systems through HFT methods, the mathematical models of pinion with generating method and gear with shaping method is established on the basis of the NS benchmark. Furthermore, the technological process of Oerlikon's hypoid gear modeling based on the three-face cutter is proposed. The two compare methods were made between the mathematical tooth flank by tooth surface mathematical model and 45 point tooth surface by the KIMOS of both pinion and gear and the contact pattern with actual and theory. Results reveal that the geometry and tooth line of theoretical tooth surface of gear and pinion corresponds well with the actual tooth surface, the maximum the concave error of pinion was 0.007 5 mm,the maximum convex error of gear about 0.002 3 mm. The contact pattern is consistent between the contact patterns of tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) by KIMOS and calculated by the initial element method, it verified the precision of the mathematical model.