Numerical solution of simultaneous equations based geometric error compensation for CNC machine tools with workpiece model reconstruction

Abstract

This paper presents geometric error compensation of CNC machine tools based on workpiece model modification and the numerical solution of equation set. Firstly, the nominal cutter position is introduced to the geometric error model of machine tool as the compensation goal according to the kinematics of three-axis machine tools. With the polynomials of basic error components, the polynomials of the geometric error model are established, which are the functions about movements of all axes and nominal NC code. The accurate compensation is represented as solution of corresponding simultaneous equations. The high-efficiency numerical calculation can obtain the compensated NC code. Secondly, the polynomial equations about points of workpiece are established based on the simple relationship between workpiece model and NC codes. The compensated points are calculated using numerical solution. STL is chose as the format of reconstructed workpiece model. In order to obtain the precise workpiece model with compensated points, one conversion approach from CAD model to STL model is proposed. The number of points calculated with isoparametric method can control the precision of STL. The reconstructed STL model is inputted to CAM software to generate processing file for machining. The input of the proposed compensation is CAD model of workpiece rather than NC codes and CL data. It makes the compensation convenient and suitable for different three-axis machine tools. Finally, the experiments are carried out on Carver800T CNC machine tool to testify the effectiveness of proposed geometric error compensation.