The cutter systems of hypoid gear cutting machines contain groups of inside and outside blades. In these cutter systems, the side cutting edges of the blades machine the convex and concave gear teeth while rotating about the cutter rotation axis. The side cutting edges lay on the rake face formed through the blade, rake, and relief angles; hence, the normal cross-section of the cutter swept surface forms hyperboloid gear teeth. Using the accurate geometry of the cutter system, a relationship between the pressure and spiral angles of the gear tooth and the parameters of the cutter system is developed for the FORMAT machining of a hypoid gear. A new parameterization of the gear tooth surfaces is introduced to determine these angles for the accurate gear tooth by the accurate cutter system. A numerical example with different cutter systems and blade parameters is presented, demonstrating the effects of rake and relief angles over the pressure and spiral angles on mean point projections and gear tooth surface. Finally, the change in pressure and spiral angles with respect to the rake and relief angles are plotted, and the results are analyzed. Finally, it is concluded that the pressure and spiral angles are changed up to a few seconds of a degree in the operating area of the tooth with the change in the back and side rake angles. The side relief angle exhibited little or no effect over the geometry of the gear tooth.

准双曲面齿轮切割机的切割器系统包含内部和外部刀片组。在这些刀具系统中，刀片的侧切削刃在绕刀具旋转轴旋转的同时加工凸齿轮和凹齿轮齿。侧面切削刃位于通过刀片，前角和后角形成的前刀面上；因此，刀具后掠表面的正常横截面会形成双曲面齿轮齿。利用铣刀系统的精确几何形状，为准双曲面齿轮的FORMAT加工开发了齿轮齿的压力和螺旋角与铣刀系统参数之间的关系。引入了齿轮齿表面的新参数化，以通过精确的刀具系统为精确的齿轮齿确定这些角度。给出了具有不同刀具系统和刀片参数的数值示例，演示了前角和后角对压力和螺旋角的影响，对平均点投影和齿轮齿表面产生影响。最后，绘制压力和螺旋角相对于前角和后角的变化，并对结果进行分析。最后，得出的结论是，随着后倾角和侧倾角的变化，压力和螺旋角在牙齿的工作区域中的变化幅度达到了几秒钟。侧面后角对齿轮齿的几何形状几乎没有影响。绘制了压力和螺旋角相对于前角和后角的变化，并对结果进行了分析。最后，得出的结论是，随着后倾角和侧倾角的变化，压力和螺旋角在牙齿的工作区域中的变化幅度达到了几秒钟。侧面后角对齿轮齿的几何形状几乎没有影响。绘制了压力和螺旋角相对于前角和后角的变化，并对结果进行了分析。最后，得出的结论是，随着后倾角和侧倾角的变化，压力和螺旋角在牙齿的工作区域中的变化幅度达到了几秒钟。侧面后角对齿轮齿的几何形状几乎没有影响。