Geometry and Leakage Aspects of Involute Rotors for the Roots Blower

For maximum operating efficiency of Roots type blowers, the leakage of compressed air through clearance must be reduced to a minimum. At the same time it is desirable to keep the design as compact as possible. The following analysis endeavours to show, for involute rotors, the effect of the geometrical design variables, pressure angle, rotor tip radius, and base circle radius, on leakage and compactness. Firstly limits of permissible values of the geometrical design variables, to allow correct mating between rotors, are established. Within these limits, relative blower compactness and carry-over of compressed air back to the inlet tract is obtained for the ideal blower with no clearance between relative rotating parts. The analysis and results are expressed in dimensionless form independent of blower size, and results are compared with cycloid rotors. Leakage through blower clearances, in terms of the geometrical design variables, is then determined for a range of pressure ratios, and the dependence on blower size is examined. It is concluded that optimum design values cannot be obtained. A compromise solution between minimum total leakage and maximum compactness is necessary, depending on the operating requirements for a particular Roots blower.