Geometric Modelling and Analysis of Superelliptic Rotor Profile for Roots Vacuum Pump - Li, Binglin; Luo, Ping; Jiang, Manzhu (Scientific Journal of Technology, 2026)
The rotor profile has a significant influence on the performance of Roots vacuum pump. This paper proposes a novel profile which consists of a superellipse at the top and a conjugate curve at the waist. The mathematical model for the superelliptic rotor profile is established, and the constraint equations of superelliptic parameters are derived to avoid undercutting, carryover, and interference. It is found that the area utilization rate increases with the axis ratio increases when the superelliptic index is constant. In order to evaluate the pumping performance of the superelliptic rotor, three-dimensional numerical simulations are performed to analyze the pressure distribution and flow rate, and the flow fluctuation coefficient and volumetric efficiency are calculated. The results show that as the superelliptic index increases, the flow rate of the Roots pump increases, the flow fluctuation coefficient decreases, and the volumetric efficiency increases up to 88% for constant axis ratio.