Abstract: 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.

Key words: 2nd differential surface, ease-off flank, spiral bevel gears, tooth contact analysis