According to the meshing principle of gear, the analytic equations of the involute and cycloid of screw rotor end profile are derived. Based on the geometric characteristics deduced from involute and cycloid helical surface, a mathematical model for machining screw rotor with spherical milling cutter is established, and the milling cutter center trajectory and feedrate are calculated. The correctness of the mathematical model is verified by numerical control machining simulation and actual numerical control machining experiments. Finally, the accuracy of helical surface of screw rotor is measured and analyzed on the roughness measuring instrument. The results show that the screw rotor machined by the mathematical model proposed in the paper has good surface quality.

screw rotor; helical surface; mathematical model; parametric modeling; normal vector