Volute type twisted-blade roots rotor, compressor and expansion machine

The invention discloses a volute type twisted-blade Roots rotor, a compressor and an expansion machine, the rotor comprises a female rotor and a male rotor which have the same molded line structure, and one rotor molded line single-tooth tooth profile is formed by sequentially connecting a volute line envelope line section A1B1, a volute line section B1C1, a volute line section C1D1 and a volute line envelope line section D1E1; the two rotors can be continuously and correctly meshed in the process of rotating in different directions; the complete rotor profile rotates around the original point of the rotor profile from the single-tooth profile and then is connected with the single-tooth profile end to end, the operation is repeated for z times, and z represents the number of teeth of the rotor. The molded line structure of the rotor has a plurality of adjustable molded line parameters, single-tooth symmetric and asymmetric molded lines can be obtained according to different values of orders of a single-tooth