Geometric study and simulation of an elliptical rotor profile for Roots vacuum pumps

The rotor profile is one of the key factors for improving the performance of the Roots vacuum pump. A novel elliptical rotor profile consisting of the elliptical arc and its conjugate curve is proposed in this paper. The mathematical model of the elliptical rotor profile is established, and profile equations without incurring undercutting and carryover are derived. The elliptical rotor profile is tested using six Roots rotors, including five new elliptical rotors and one conventional circular arc rotor. Additionally, to assess the performance of the elliptical rotor profile, three-dimensional numerical simulations of the above six Roots rotors are conducted, and then the working process of the Roots vacuum pump is analyzed. The results indicate that all the new designs produce higher flow rate than the traditional circular rotor under the same conditions. As the elliptical axial ratio decreases, the area efficiency of the elliptical rotor increases.