Theoretical Aspects of the Roots Air Motor

Abstract

The following analyses constitute a preliminary attempt to provide a sound theoretical basis for future work to be carried out on Roots motors and blowers, the former only being considered in the present paper. An ideal motor is defined, thereby facilitating the analyses and setting a standard of performance for the conventional motor operating on the non-expansive cycle. The low absolute thermodynamic efficiency of the ideal being a direct consequence of non-expansive working, a standard of performance for expansive working is set by the definition of a perfect motor. It is shown that ideal motor torque is reduced as the number of rotor lobes increases, and that severe alternating torques, which are largely tied up with the motor mean torque, occur in the rotors themselves. In the real motor, deviations from the ideal are due to a number of separate causes. A quasi-analytical solution has been obtained for the adverse torque due to subsonic discharge, whilst a pair of simultaneous differential equations permits an estimate of the adverse torque due to pressure variations between the rotors. The results obtained suggest a number of design changes in the conventional Roots motor.