Mathematical Modelling Method of the Compression Process in a Scroll Compressor in Mathcad

摘要

Modelling of processes occurring in crescent-shaped compression chambers in a scroll compressor is a multistage task. The aim of this study was to create a universal method that allows determining the geometric parameters of the scrolls of the designed compressor and conduct its dynamical analysis. Due to the fact that the geometrical compression ratio of such compressors remains constant, but the actual one varies, it is necessary to provide additional compression that occurs in the first space before the discharge pressure. When determining pressures, it is necessary to take into account the pressure drop that occurs immediately after combining the first and second chambers. Also, when designing the geometry of the scrolls, it is necessary to take into account the undercutting of the scrolls at the bottom to ensure the mutual movement of the scrolls relative to each other during the rotation of the shaft. The paper presents a step-by-step method for the dynamic analysis of a scroll compressor. The principles of modelling the compression process in a scroll compressor in the Engineering Math Software Mathcad are described. The case of different geometric and actual degrees of compression is considered. The principle of constructing an indicator diagram of the compressor is described. Methods for determining the forces and moments that arise during the operation of the compressor are proposed, and their diagrams are given. The practical example of modelling shows the advantage of the proposed method.