SIMULATION OF ROOTS VACUUM PUMP ROTOR GEOMETRY

Abstract

Mathematical model for designing the surface geometry of the Roots pump rotor based on the Cassini oval principle was derived. The polar coordinate system was used, and the radius vector, the direction of which was set by the φ angle, characterizes the location of the point on the surface of the rotor. The distance of this point from the axis of rotor rotation was set by the calculated value of the ρ_R polar radius vector. The γ angle of rotors rotation characterizes their mutual orientation in the plane of rotation. Peculiarities of the choice of the a and b parameters that satisfy the shape of the rotor surface geometry are considered. An example of rotor geometry is given for rotor radius R = 50 mm, rotor rounding radius r = 20 mm, parameters a = 33.166 and b = 28. Rotor geometry depends on normalized parameters of a and b, which are constant for a given shape of the surface and constructive dimensions. A mathematical model of the usable cross-sectional area of the pump has been developed. The usable cross-sectional area of the pump was simulated by the geometry of the rotors. The area of the rotor was determined by the geometry of the surface, which was described by an elliptic integral of the 2nd kind. The usable cross-sectional area for the given parameters is modelled. The results of simulation in the form of graphical dependences are given. Parameters a and b must meet the condition of √2⁄2<b⁄a<1. Under such conditions, the geometry of the rotor surface will be a Cassini oval. The rotation of the two rotors against each other will be by rolling one surface over another.