A New Algorithm for the Identification of CNC Geometric Errors

Abstract

This paper proposes a geometric error model for the three-axis machine tool using the homogeneous transformation matrix. An error-prediction model for the three-axis CNC machine tools is presented. This model takes the geometric errors into consideration, using the homogeneous coordinate transformation matrix(HTM) to analyze the geometric error model, which can change the tool's complex position and orientation changes in space into matrix calculations to make the model simpler and more intuitive. A simple method using the cubic polynomial functions to fit the geometric error components is proposed. Using this method, the high-order, non-linear spatial geometric problem can be transformed into algebraic equation. To large extent, the difficulty of calculation is reduced. The QC20 ball-bar is used to measure, analyze and separate all the geometric error components. A new kind of particle swarm algorithm based on the genetic algorithm is developed to solve the algebra equation.