This study aimed to effectively design, manufacture and simulate a single-screw compressor. In this paper, a mathematical model of a pc-type single-screw compressor was developed. The pc-type single-screw compressor was assembled using two gate rotors, a screw rotor and a frame. First, the mathematical model of a conical tooth was designed and a gate rotor equation was obtained through coordinate transformation. Then, the coordinate systems between the gate rotor and the screw rotor were set up. Using a homogeneous coordinate transformation matrix, the family of gate rotor surfaces was obtained. Based on gear theory, the equations of meshing between the gate rotor and screw rotor were determined. Substituting the equation of meshing into the family of gate rotor surfaces, the gate rotor and the screw rotor were generated and their geometrical model illustrated using a software package. Based on the developed mathematical models, the contact lines and stress analysis between the gate rotor and screw rotor were displayed. An edge contact between the gate and screw rotors was found, indicating the necessity of a plastic or a composite material to encircle the conical surface. A computer-aided manufacturing software package was used to simulate the manufacture of the screw rotor.
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