F test-based automatic modeling of single geometric error component for error compensation of five-axis machine tools

Abstract

This paper presents one automatic modeling method of position-dependent geometric error components based on F test in statistics and one error compensation method of five-axis machine tools to ensure textures of the workpiece. At first, according to the definition of error components, the polynomials with zero constant term are chosen as the expressions. The calculation of corresponding coefficients is presented in details. Then, F test is introduced to evaluate the overall significance of polynomials. The automatic modeling of position-dependent geometric error components is expressed as seeking the polynomial with the best overall significance among a series of the polynomials with different orders. It is automatic and programmatic to improve the efficiency and precision of modeling. It can overcome the difficulty in determining the order of the polynomials. Next, geometric error compensation by limiting ideal tool positions of tool poses is proposed to ensure machining requirements of textures of the workpiece. The rotation angles of two rotary axes are optimized by particle swarm optimization (PSO) with the mathematical expressions of integrated geometric errors of five-axis machine tools. The movements of linear axes are calculated with inverse kinematics of the machine tool by inputting ideal tool positions and optimized rotation angles. Finally, the experiments are carried out on one SmartCNC500_DRTD five-axis machine center to testify the precision of the automatic modeling and the effectiveness of the error compensation.