Forming method for milling threads of variable tooth worms

A forming method for milling teeth of variable tooth worms, comprising the following steps:

• on a multi-axis simultaneously-working CNC machine-tool, a first moving coordinate system {σ1(φ1)[O1;
• i1(φ1);
• j1(φ1), k1(φ1)]} is correlated to the worm blank of the VTW worms, wherein the worm blank of the VTW worms rotates around k1(φ1)-axis at angular speed |ω1|;
• a second moving coordinate system {σ2(φ2)[O2;
• i2(φ2);
• j2(φ2), k2(φ2)]} is correlated to the milling cutter, wherein the milling-cutter rotates around k2(φ2)-axis at angular speed |ω2|, |ω1|/|ω2|=i12 and i12 is a constant;
• the feed motion of the milling cutter comprises the radial shift along the i2(O2)-axis and the peripheral shift around the k2(φ2)-axis;
• the equations of each cutting edge of the milling cutter are given as follows:
• x2=u
• y2=rb−v sin β
• z2=v cos β
• where, u, v are the parameters of a generatrix plane Σ of the variable tooth worms tangent to an imaginary cone;
• β is the inclination angle of the generatrix plane Σ relative to the axis of the imaginary cone;
• rb is the radius of the main basic circle of the cutter body;
• x2, y2, z2 are the coordinate values of the cutting edge on the generatrix plane, in which when the center distance between the worm blank and the milling-cutter is from 80 mm to 500 mm, the value of u is from 51 to 378, the value of v is from ±19.4 to ±122, and the value of rb is from 19 mm to 173 mm;
• and βis greater than 0° and less than or equal to 30°;
• and shifting of a cutting edge of the cutter on the inclined generatrix plane in spatial locations about the milling cutter forms a cutter that will form the tooth flank of the variable tooth worms in the worm blank.