Formulation of Parameter Model and Size Optimization of Rotor Profiles with Linear Valley of Roots Vacuum Pump

The rotor profiles with linear valley for roots pump were analytically modeled first with the theoretical profiles for size optimization. Next, the parametric, concise coordinate equation and 3-D model of the realistic profiles and the size optimization equation were derived by mathematical manipulation and approximation with proper assumptions. And finally, the validity of the parameter model and size optimization equation was proved with a specific example. The results show that the valley size can be maximized by minimizing the volume utilization, and only roots pump with a thick shaft requires the maximum valley size. The lobe number strongly affects the pump volume. For example, the volume of roots pump with 3 (4) lobes is 1. 84 (3. 04) times larger than that of the pump with 2 lobes, indicating that 2 lobes are suitable for the rotor profiles with linear valley.