Universal Solution to Conjugated Profiles of Roots-Pump Rotor: A Theoretical Study

The conjugated profiles of driven rotors, including but not limited to the circular arc, parabola, involute, theoretical and realistic driving-rotors of Roots vacuum-pump with given shape-profiles, were empirically approximated, mathematically modeled, analytically described in fully parameterized equations and derived with universal solution in shape-angle and pitch-angle methods.The newly-developed universal solution was exemplified with a circular arc rotor.The calculated results show that the when it comes to conjugated profiles of all kinds of driving rotor with known shape-profile, the universal solution scheme works pretty well.To be specific, in shape-angle method, the two corresponding conjugated points were calculated indirectly in terms of the known shape-angle variable;and in pitch-angle method, the conjugated point was directly calculated in terms of the given pitch-angle variable.We suggest that the pitch-angle method may outperform the shape-angle method in calculation of the conjugated profile.