The effects of design parameters on performance of a novel roots profile

The rotor profile is a key factor for improving the performance of Roots pumps. The geometric constraints of a novel Roots profile are derived and discussed in this paper. The available range of four independent design parameters, including lobe number n, ratio R of the center distance to the rotor diameter, base circle coefficient ε₁, and contact ratio ε₂ of the involute segment, were determined according to the design constraints. The area utilization efficiency η_A was defined to evaluate the theoretical working capacity of the Roots pump. From the perspective of geometry, the internal leakages due to the radial and meshing gaps were assessed using the tip concentric arc angle α₁ and the geometric leakage index η_C derived from carryovers between the two intermeshing rotors. The results of the design domain indicated that more lobes produced a larger design domain and reduced the maximum available area utilization efficiency. The variations in the three performance indices within the feasible design domain reflected three optimizing directions: a larger α₁, a higher η_A, and a lower η_C. The goal of area utilization efficiency contradicts that of the geometric leakage index.