# Cutting path equation of equal height spiral bevel gear

The tooth surface hobbing method is adopted for the processing of equal height spiral bevel gear, that is, while the cutter head rotates to process the gear, the cutter head rotates around the axis of the forming wheel to complete the processing of the extended epicycloid.

The figure is the schematic diagram of cutting path of equal height spiral bevel gear. I-J in the figure is the plane of the machine tool, which passes through the center of the cutter head and is perpendicular to the axis of the shovel wheel. When the tool inclination is 0, the tool tip M0 is in the plane of the machine tool; IOJ coordinate system is the coordinate system of the machine tool, and O is the coordinate origin, that is, the center of the machine tool; S is the radial tool position, which is the distance between the center O of the contour spiral bevel gear cutting machine tool and the center OC of the cutter head. The included angle Q between OOC and the horizontal plane of the machine tool is the angular tool position. Taking the center OC of the cutting cutter head of equal height spiral bevel gear as the coordinate origin as the cutter head coordinate system, so that the included angle between x-axis and OCM is the cutter tooth direction angle ν。 Point m is any point on the tooth surface and also any point on the cutting surface of the cutting cutter head of equal height spiral bevel gear, θ Is the phase angle of point M.

In the figure, RC is the nominal cutting radius of the cutter head, R0 is the radius from the top of the tool tip to the center of the cutting cutter head of equal height spiral bevel gear, and the R0 values of the inner and outer cutter bars are different. The calculation formula is:

In the formula, R0 is calculated as the radius from the apex position of the inner cutter tip to the center of the cutter head when cutting the spiral bevel gear with equal height teeth, and the “+” sign is taken when calculating the outer cutter.

The equation RM0 of M0 point at the tool tip of contour tooth spiral bevel gear cutting machine tool is:

The unit normal vector of any point m on the tooth surface of contour spiral bevel gear is n, and the unit vector along the cutting edge direction of contour spiral bevel gear is t. it can be seen from Fig. 1 that the equations of N and t can be expressed as:

If the distance between points m and M0 on the cutting edge is s, the equation of cutting surface of equal height spiral bevel gear is:

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