Mathematical model of forming screw profiles of compressor machines and pumps

The article presents the results of mathematical modeling of screw surfaces shaping for compressor machines and pumps. The study is based on a method of curve movable trihedron. A mathematical model of a flat gearing - the basis for a screw formation - is proposed. The model is based on geometric interpretation of plane curve trihedron motions and known in a geometric theory of plane mechanisms of the Bobillier construction. A geometric scheme of this construction was expanded due to introduction of evolutes simulating instantaneous motions of curves trihedra in a construction scheme. As a result, the mathematical model was obtained, which is more complete in comparison with the known models of flat gearing, which makes it possible to perform synthesis and analysis of profiled screws geometry. It realizes both direct and inverse problems of screws profiling with simultaneous obtaining the curvature of the desired profiles in absent ones. The proposed model can be used as a basis of automated system development for mutually enveloping surfaces screws shaping for compressor machines and pumps.