Tooth profile of a Roots rotor with a variable trochoid ratio

Vacuum pump plays an important role in vacuum applications. The rotor profile is one of the key factors for improving pump performance. In this paper, a new tooth-profile design method is proposed based on the most commonly used rotor, namely, the Roots rotor. The proposed method introduces an extended cycloid curve with variable trochoid ratio in rotor design. Variable trochoid ratio designs based on third-, fifth-, and seventh-order polynomials and sinusoids are used to illustrate the effectiveness of the new method. In particular, higher area efficiencies are obtained compared to the traditional constant trochoid ratio design. Furthermore, constraint equations predicting maximally allowable variations in trochoid ratio of the proposed method without incurring undercutting and carryover are also derived.