On the Generation of Analytical Noncircular Multilobe Internal Pitch Curves

Abstract

A method for the design of general analytical noncircular multilobe internal pitch curves is presented. The method is based on a reshaping algorithm. A selected monotonic function can be assigned as the initial profile for the outer rotor of the designed pitch curve. This initial function will be reshaped to satisfy the wholeness of the number of lobes. This final pitch curve function can then be obtained analytically. To archive smooth profile design, the C1 continuous conditions on pitch rotors are established. A dimensionless parameter geometrically interpreted as the noncircularity of pitch rotor is introduced for the systematic design of pitch curves. Results from this research have applications to the design of compressors, gerotor pumps, and rotary engines.