针对现有弧齿锥齿轮加工参数计算方法，接触点综合纷繁复杂的问题，提出ease-off曲面综合法。从微分几何学出发，给出二阶密切曲面的定义及其构造方法；在二阶精度范围内，密切曲面与原有曲面具有相同的微分几何属性，从而可以替代原有的曲面分析。通过弧齿锥齿轮加工的产成模型，构造大小轮共轭齿面的ease-off差齿面，利用ease-off差齿面的密切曲面完整地拓扑齿面接触区；利用齿面接触区的可控参数综合确定小轮齿面的接触参数，进而通过数值优化方法求解小轮的加工参数。籍助ease-off密切曲面进行了啮合仿真，完整呈现了齿面接触区大小形状、接触路径方向、抛物线失切量等轮齿啮合信息。所提出的方法适宜于数值方法，基于齿面接触区的完整性，实现了齿面啮合性能较好控制。
In view of the shortages of the point contact synthesis methods being difficulty and complex on the determination of machine-tool generating settings of spiral bevel gears, it is presented a method of ease-off surface synthesis reaching the goal of pre-controlling contact performance based on the integrity of contact pattern. From the view of differential geometry, the definition on the 2nd order osculating surface and the study on its topologic method have been done. Under the precise of 2nd order differential surface, the osculating surface is exactly same as the original curve surface in the differential geometric performance, thus it is able to take place of that geometric analysis of original curve surface. Based on the generating model of spiral bevel gears, the construction of ease-off flank of conjugate surfaces of tooth is carried out. Then the study of topologic method on contact pattern of tooth surface is done by using the osculating surface of the ease-off flank. The determination of contact parameters of the pinion is done by the controllable parameters synthesis of contact pattern. After that the computation of machine-tool generating settings of the pinion is performed by the numerical optimal method. By using the ease-off osculating surface the tooth meshing simulation is carried out，which presents perfectly the behavior of tooth contact such as the size and shape of contact pattern, the orientation of contact path and the parabolic curve of transmission errors of tooth surfaces. This presented method is not only more suitable to the numerical computation, but also able to pro-control the behavior of tooth contact and provide the perfect information of tooth contact.
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