Equation of hypoid gear face hobbing cutter

According to the cyclo palloid method, the gear is processed with a multi head cutter head. The cutter head adopts a double-layer structure and is composed of an inner cutter head and an outer cutter head. The inner cutter edge on the inner cutter head is used to cut the convex tooth surface of the gear, and the outer cutter edge on the outer cutter head is used to cut the concave tooth surface of the gear. The center point of the outer blade is OA and the center point of the inner blade is OI. The rotation axes of the two cutter heads do not coincide. The coordinate system of the left-hand cutter head is shown in the figure.

During the development process, the inner knife and the outer knife move around their respective rotation axes at the same speed. In practical application, the inner cutter radius r0i is generally taken as the nominal radius of the cutter, and the longitudinal curvature of the concave surface is changed by adjusting the outer cutter radius r0a, so as to obtain the ideal tooth surface contact ellipse. Other tool parameters include tool tooth profile angle α 0. Tool offset angle δ 0. Number of cutter head groups Z0. SM and St are the coordinate systems fixedly connected with the cutting edge and cutter head respectively, and Sn and SP are the auxiliary coordinate systems. The vector equation of any point P on the blade in St coordinate system is:

Of which:


β IK — initial tool angle

U — tool parameters

The subscript k in the transformation matrix represents I and a, and represents the inner knife and outer knife respectively.