An optimized algorithm and the verification methods for improving the volumetric error modeling accuracy of precision machine tools

摘要

Referring to the error modeling technology used in precision machine tools, it is difficult for machine tool builders to understand the effects of the theoretical modeling accuracy on the precision machining in the designing stages, where error components are represented by parameters. Therefore, this study is proposed to overcome certain theoretical calculation errors for a parametric form of volumetric error modeling and to examine verification method for judging the modeling precision. Based on the mathematical theory, a novel optimized algorithm is presented, as well as its verification methods. With the two new methods, it is effective to identify theoretical calculation errors and verify the accuracy of error modeling. Meanwhile, the proposed algorithm, with a form grinding machine tool being as an illustration example, is tested and validated by means of numerical simulations in the Matlab. The results reveal that the modeling accuracy of the error characteristic matrix is improved and enhanced by the algorithm, and the two verification methods can check the veracity of parametric modeling precision in different ways. Especially, the second method can check and isolate quantitatively the theoretical calculation errors. At the same time, it is a theoretical guidance for choosing a suitable treatment to meet the accuracy of an error model represented by parametric variables during iterations of the characteristic matrices. These two prediction veracity and uncertainty of the modeling precision can be evaluated. Furthermore, the algorithm and checking methods can be extended to ultra-precision multi-axis machine tools.