A family of high-flow Roots blower profiles based on non-circular gears and the coin rotation paradox

Abstract

Roots blowers are positive displacement pumps that trap the air in pockets of counter-rotating rotors. This paper describes and analyzes a new family of high-flow Roots blower profiles. Models and tests show that the new profiles may have flow rates greater than four times the flow rate of those based on epicycloid/hypocycloid arcs. The profiles can be used to build either straight-lobe or helical rotors. For a given airflow requirement, the new profiles allow for reduced RPM, lower acoustic noise, lower power and lower weight. These benefits may open up new applications for Roots blowers in consumer applications. Simplified equations for the profiles of a circle rolling around a noncircular gear are derived using the lessons from the coin rotation paradox. The equations take advantage of previous work in noncircular gear theory but advance that theory to produce an equation that produces a range of identical noncircular gears with any number of lobes. Clearances between the rotors are adjusted by offsetting the profiles. The resulting profiles are more eccentric and have higher flow than traditional Roots profiles. Estimates and measurements of the flow rates show that the small amount of carryover (reverse flow) is more than overcome by the greater flow rates of the new profiles. Multiple variations of the profiles are illustrated by figures showing the meshing of rotors at different angles. Publicly available MATLAB^® code that can be used to graph and analyze different profiles and to export data to mechanical CAD programs for fabricating the rotors.