Novel Geometrical Model of Scroll Compressors for the Analytical Description of the Chamber Volumes

Most scroll compressor models are based on a geometrical description of the scroll wraps. Since geometry is one of the main factors affecting the efficiency of the compressor, a complete description of the geometry of scroll wraps has to be known in order to establish an accurate thermodynamic model. Most authors do not yield an analytical expression of the discharge chamber, also because their assumptions are questionable. This paper gives a novel description of the geometry based on the parametric equations for the circle involutes in a novel reference system, in order to exploit the symmetry of the compressor. This approach simplifies the scroll model and yields an exact analytical expression of the compression and discharge chamber volumes, together with all the geometrical parameters and constraints, thus allowing the compressor to be optimized geometrically. The existence conditions of the conjugacy points, as well as the manufacturing constraints are also considered.