Geometric analysis and tooth profiling of a three-lobe helical rotor of the Roots blower

This paper proposes a novel three-lobe helical rotor with the cross section as a combination of concave and convex arcs and cycloidal curves for the Roots blower. Based on the geometric analysis, the mathematical model of this new tooth profile is presented, leading to a presentation of a helical tooth profile and a comparative study between the three-lobe helical tooth and a conventional straight tooth. The study reveals the advantage of the new tooth design that creates greater air flow and reduces the peak of the blower pressure. The geometric study leads to the investigation of machining the profile of the new tooth. The cutter trajectory is revealed and the contact characteristics between the cutter and the work piece are identified. By identifying the cutter distance and the cutter mounting angle, the paper characterizes the relationship between these machining parameters that governs the machining of the novel tooth. The simulation and tooth machining are provided in the end of the paper.