Algorithm for screws profiling of a conical trilobed compressor - analytical solution

Abstract

Screw compressors, as rotary machinery, are capable of working with high compression ratios for gas compression. They transform the mechanical work done by an electric motor or turbine into the potential energy of a gas, by reducing its volume and increasing the pressure. The essential elements of these compressors are the two helical rotors with lobes, mounted in a housing. Existing rotors in the construction of compressors are working bodies whose composite profiles include circle arcs, line segments and cycloidal curves, while also often including non-analytical curves. Such geometry of profiles gives the gear processes superior characteristics, in the sense of reducing friction and improving sealing conditions. This paper analyses, by analytical approach, the possibility of constructing a multilobated conical screw compressor with a number of lobes Z, Z + 1, of the male and female rotor. The parametric equations of the contained worm and the kinematics of the working process of the conical screw compressor shall be defined. The theory of surface wrapping comprises analytical methods of study, which were developed on the basis of the fundamental theorems on wrapping of known surfaces in differential geometry and the kinematics laws on rotor movements. Thus, this paper proposes an algorithm based on the approach to the problems analyzed under the “virtual focal points theorem” between the complex surfaces of the conical surface lobes, which constitute the active lobes of the male and female rotors. Normal to active surfaces are defined, and also the speed in relative movement, in the “gear” process of the conical screw compressor. Regarding rotors in conical screw compressors, the circular pitch of the teeth is constant. Also, the screw pitch of the conical compressor rotors is a constant value. In these conditions, the rotors of the screw compressors are acknowledged as active surfaces, conical screw surfaces with constant axial screw pitch. The cross section (in the normal plane to the driving rotor axis) determines a plane gear. This defines the specific winding condition, and the shape of the conical screw surface of the female rotor.