Profiling Rotors for Limaçon-to-Limaçon Compression-Expansion Machines

Limaçon-to-limaçon compression-expansion machines have housings and rotors whose profiles are manufactured of limaçon curves. For these machines to perform satisfactorily, extreme care should be given to the geometric particulars of their rotor profile. The main characteristics that govern the quality of the rotor profile are the volumetric efficiency and the prevention of interference. In this work, the interference problem is handled from two different mathematical standpoints: the slope of tangents to both the rotor and housing curves at the apices; and the value of the minimum radial clearance that separates the two limaçon curves. In the first case, mathematical expressions, relating the radii of the limaçon base circles is presented to ensure that interference would not take place during normal operations of the limaçon-to-limaçon machine. The second mode of analysis produces a set of nonlinear equations that can be solved to obtain a value of the radial clearance. This value has to be machined off the rotor profile to prevent interference. A numerical example is given at the end of the paper to prove the validity of the models proposed and graphs are produced to support the claims presented.