Law governing the change in the thickness of a variable cross-section scroll tooth based on Frenet frame

Abstract

A variable cross-section scroll tooth formed by circular involutes with different base circle radii was constructed by using the Frenet frame to investigate the trends shown by the change in the tooth thickness of a variable cross-section scroll compressor quantitatively. A mathematical model for calculating the thickness of a variable cross-section scroll tooth was constructed in accordance with the geometric model. The profile parameters (radius of base circle, radius of rotation, and connection points) that influence tooth thickness were analyzed systematically. The relationship between tooth thickness and profile parameters were established precisely. The relationship between the variations in profile parameters and in scroll tooth thickness was summarized by solving the mathematical model. Results show that the proposed mathematical model can accurately describe the law governing the change in the thickness of the variable cross-section scroll tooth. Moreover, scroll teeth can be flexibly designed given that tooth thickness and the initial tooth thickness can be quantitatively adjusted in accordance with design requirements. The mathematical model can also be applied to calculate tooth thickness in other combination profiles.