Calculation of revolution angle of noncircular gear shaper cutter

When the pitch circle of the gear shaper cutter rolls along the pitch curve of the non-circular gear, it not only rotates around the center of the gear shaper cutter, but also revolves around the rotation center of the non-circular gear. As shown in Figure 1, when the gear shaper cutter moves from the initial position OC to OC1, the meshing point changes from the initial position point P to point P1.

The angle between the point P normal on the pitch curve of non-circular gear and the X axis is α 0, the angle between the normal of point P1 and the X axis is α 1, the angle between two normals θ GZ is the revolution angle of gear shaper cutter.

φ 1- θ GZ1 relation curve φ 2- θ Gz2 relation curve

According to this principle, the revolution angle of gear shaper cutter can be calculated when the driving and driven noncircular gears are machined θ GZ1 and GZ1 θ According to the calculation results, figures 2-3 are obtained; According to the relation curve in the figure, if known φ 1 or φ 2, the interpolation algorithm can be used to solve the problem θ GZ1 or θ gz2.