Derivation of Rotor Profiles of Roots Vacuum Pumps

The "single" profile and "double" profiles of the rotor of Roots vacuum pump were mathematically derived. The single profiles consist of a short outer profile and its conjugated profile for the driving/driven rotors, respectively; whereas the double profiles comprise the conjugated outer and inner profiles of the valley and peak of the rotor, respectively, which are the same for the driving and driven rotors. The realistic and analytical single profile and double profiles were evaluated and the validity of the derivation was proven. The results show that the maximum shape coefficients can be listed in a descending order:the involute and/or arc profiles > double profiles > single profile. We suggest that the single profile may work for the internal rotor only, simply because when it comes to the external rotor, the profiles of the driving and driven rotors are completely different.