A uniform expression model for volumetric errors of machine tools

This paper proposes a new method, a Self-adaptive Mathematical Expression Model (SMEM), to describe volumetric errors of machine tools based on Non-Uniform Rational B-Spline (NURBS). The NURBS parameters of expression model were optimized by an improved Genetic Algorithm (GA). Simulation method was adopted to verify the effectiveness of the parameter optimization method of the SMEM, and the measurement experiment and machining experiment with error compensation based on the SMEM were conducted on a five-axis machining center with a titling rotary table. It was found that the SMEM can be used to uniformly express the position-dependant error parameters. Compared with the traditional methods, which adopt largely discrete database tables or polynomial method, the presented method is more concise, accurate and robust. In addition, volumetric errors of any position among the workspace of the machine tools can be quickly obtained by searching the SMEM of error parameters. And volumetric error of tool paths and the actual surface of the machining parts also can be expressed by the SMEM. The accuracy of the linear measured paths can have a great improvement of 70.63% with error compensation based on the SMEM. The accuracy of the part's predicted machining precision using the SMEM was 76.34%, and the surface profile error of the part can be improved significantly, up to 61.29%, when the SMEM was used for error compensation. Therefore, the expression model established in this study is feasible and robust, and could be used to express error parameters and volumetric errors. Moreover, it could be used to predict machining precision of part before machining and provide the basis for error compensation.