A mathematical model of a cc-type single-screw compressor

In this paper, a method is proposed for determining a basic profile of a cc-type single-screw compressor including the gate rotor and the screw rotor. The cc-type has a cylindrical screw and two cylindrical gate rotors. Based on this method, a mathematical model of the meshing principles of a cc-type screw rotor meshed with a gate rotor, that has either straight edge teeth or conical teeth, is presented. The inverse envelope concept is used to determine the cutting-edge curve of a gate rotor. Based on this concept, the required cutter for machining a cc-type screw rotor can be obtained by the envelope of a one-parameter family. The obtained screw rotor is an envelope to the family of the gate rotor's surfaces. The obtained envelope becomes the generating surface. The inverse envelope can be used to obtain the envelope to the family of generating surfaces. Then the profile of a gate rotor cutting-edge curve can be easily obtained. The surface analysis including contact lines is shown for the design and manufacture of a screw compressor. As an example, the cc-type single-screw compressor with a compressor ratio of 11:6 was determined with the aid of the proposed mathematical model. Using rapid prototyping (RP) and manufacturing technology, a cc-type single-screw rotor with a gate rotor was designed. The RP primitives provide an actual full-size physical model that can be analysed and used for further development. Results from these mathematical models should have applications in the design of cc-type single-screw compressors.