When the small wheel is machined by the variable method, the tooth profile angle of the small wheel cutter head can be selected according to the standard. When the pressure angle is 20 °, the tooth profile angle of the inner cutter is 18 °and that of the outer cutter is-22 °.
When machining the small wheel by the variable method, if the point M0 is required to be calculated on the tooth surface, it must be machined with a cutter head with a tooth profile angle of af1. When machining the small wheel with the cutter head with tooth angle A01 ≠ af1, the small wheel must be turned around the axis and developed at a certain position in the space. Let the calculation point at this time be M, and the wheel calculates the normal vector of point M:
When machining the pressure angle of the pitch cone, the actual tooth profile angle of the cutter head is A01, and if the helix angle of the pitch cone of the small wheel is β f, the actual normal vector is:
The rotation angle λ can be calculated:
The meshing node between the pinion and the production wheel is the distance between the wheel and the production wheel:
The node radius of the gear cutter pitch cone is r’a1.
The distance from point M to the plane of the machine tool is:
The distance from the node M’ to the machine tool plane hR can be obtained:
The theoretical value of the tip radius is:
Let the angle between the length direction of the bevel tooth of the gear cutter and the length direction of the cone tooth of the technological pitch be Δ:
The normal curvature and short-range torsion along the cutting pitch cone direction are:
The forming radius of the modified cutter head at the node M’ is rnM,rnM, which can be calculated from the following formula.