GEOMETRIC MODELING OF WORKING PROFILES AND VOLUME OF ROTARY-PLANETARY MACHINES

Abstract

A method for calculating a rotary planetary machine of the Wankel system is presented. A feature of the Wankel machine is that the movement of the rotor in relation to the body is carried out using a planetary mechanism, which is based on an internal gear.

The proposed method makes it possible to take into account the connection between the parameters of the geometric shape of two pairs of mutually conjugate curves characteristic of the Wankel machine. The first pair of curves are the working profiles of the casing and the rotor. The second pair is formed by the tooth profiles of the internal gears. Accounting for this connection made it possible to find a description of the function of the change in time of working volumes limited by the profiles of the body and rotor (i.e., to determine the productivity of the machine). As a result of the research, it was found that the performance of the Wankel machine can be found by taking into account three features of this machine. The shaping of the conjugated working profiles of the rotor and stator is carried out using a planetary mechanism, for the calculation of which the functions of complex variables are used. The performance function of the machine is determined by the change in time of the volumes of space limited by the working profiles of the rotor and housing. An approximate description of the functions of changing the working volumes of the machine with time was carried out using specially developed graphic constructions. To match the geometrical parameters of the Wankel with the parameters of the tooth profiles of the gear train of the internal clutch, a method of graphic running has been developed. The results obtained are useful because the scheme of the considered Wankel machine is embedded in the design of the internal combustion engine of the same name, as well as in the design of various hydraulic machines, pumps, compressors, etc.

Key words: geometric modeling, rotary planetary mechanism, Wankel machine, functions of a complex variable, internal gearing.