NC codes optimization for geometric error compensation of five-axis machine tools with one novel mathematical model

Abstract

This paper presents the optimization compensation based on the mathematical expressions of geometric error model for the accuracy enhancement of five-axis machine tools. This method belongs to mathematical optimization. At first, optimal polynomials of basic error components of each axis are established by fitting the measured data of errors. The constant term is set as zero based on the properties of error components. The appropriate degree of polynomials is determined by introducing F value in statistics. Second, the bi-directional transformation between tool poses and NC codes is built with the forward and inverse kinematics of machine tools. More specifically, the postprocessor of SmartCNC500_DRTD five-axis machine tool is proposed for the calculation of NC codes. The obtained NC codes reflect the real movements of all axes relative to their zero positions. Then, one novel geometric error model is established with mathematical expressions. The model contains the ideal tool pose with the input of nominal NC code. It can evaluate the effect of compensation. It lays the foundation for the optimization. Next, the particle swarm optimization (PSO) is used to seek the optimal NC code. Particles are defined as tool poses to accord with the physical meanings of integrated geometric errors. The initial particles are generated around the ideal tool pose. New moving of particles is proposed to avoid the local optimum. The postprocessor is used to transform particles to NC codes to calculate their fitness. Finally, the experiments are conducted on this SmartCNC500_DRTD five-axis machine tool to testify the effectiveness of optimization compensation.