The Research On The Method Of Curve Fitting Of Archimedes Spiral For Variable Cross-section Scroll Profile

Because of its compact structure,energy saving,high efficiency and low noise,scroll compressor has been widely used in refrigeration,turbocharged engine,gas compression and other fieldsa.With the continuous development of industrial technology,the scope of scroll compressor is also expanding.In order to pursue higher performance,scroll plate is the most important part of scroll compressor.With the continuous improvement of compressor performance,its profile has evolved from the original single base involute line to the variable cross-section combined line,and the processing difficulty of the scroll plate is also increasing.At present,there are two fitting methods for the mature NC machining of the scroll type line-the straight line fitting and the arc fitting.For the combined scroll line,which is neither straight nor circular,there is a problem of low machining efficiency or low machining accuracy when fitting the above two ways.Therefore,the machining of a variable cross section combined type scroll plate is a hot and difficult point in the research of vortex machinery in recent years.There are three points in the detailed study:(1)The establishment of mathematical model of variable cross-section scroll plate.According to the meshing theory of the scroll of dynamic and static and the equidistant curve theory of scroll line,we choose the combined line of circular involute,high degree curve and circular involute as the scroll disk bus,and use Solid Works software to establish the three-dimensional model of variable cross-section scroll plate.(2)Fitting method of scroll section with variable cross section based on Archimedes spiral.The basic principle and deduction process of the fitting method are introduced,and the Archimedes spiral is used to approximate the circular involute-high order curve-circular involute combination line,and the theoretical fitting error generated by this method is calculated by using the MATLAB software.Through the comparative study,it is known that the Archimedes spiral approach to the circular involute part of the combined line is better,especially the approximation of the round involute of the outer circle is the best.The proposed Archimedes spiral fitting is compared with the straight line fitting and the single arc fitting.The results show that the fitting method of Archimedes’ s spiral fitting method is less than the line fitting90% less than the line fitting,and 70% less than the arc fitting under the conditionthat the fitting error is less than 0.001 mm.(3)Machining and testing of a variable cross-section scroll plate.Based on the Archimedes spiral fitting method,the variable cross-section scroll plate was machined on the CNC machine tool.The shape tolerances and roughness measurements of the processed scroll plates were made by the three coordinate measuring instrument and the roughness meter.The measurement results show that the vortex disk based on the Archimedes spiral fitting method meets the actual production conditions.In this paper,a method based on Archimedes spiral fitting method is proposed for the machining method of variable cross-section composite line scroll plate,and a complete flow of theoretical analysis,numerical simulation and processing experiment is formed.The test results show that the Archimedes spiral fitting method proposed in this paper provides a theoretical basis for the machining of a combined linear variable cross-section scroll plate,and has certain practical value.