Correlation assessment and modeling of intra-axis errors of prismatic axes for CNC machine tools

This paper presents an experimental study conducted to assess the correlation between the intra-axis errors of prismatic axes for CNC machine tools. The validity and reliability of parametric models for the modeling of intra-axis errors (IAEs) of CNC machine tools in the context of indirect calibration are also assessed in this work. Three CNC machine tools with various controllers and guidance technologies were tested using two different measuring instruments. Two predictive models, namely Bézier and B-spline curves, are described and compared for the first time in this work. Both models are experimentally evaluated for accuracy and predictive efficiency using four evaluation criteria and new data sets from the three tested CNC machine tools. Results show a strong correlation between the positioning errors and the pitch and yaw errors for all the tested machines. The results also show that both proposed models are appropriate for the modeling of intra-axis errors, with the B-spline curves coming slightly on top in terms of performance. Moreover, with the same number of control points ( n = 5), the two models provide residuals that are lower than the repeatability of the machine for most intra-axis errors tested. This experimental study thus confirms that a Bézier model of degree four and a B-spline model of degree two, both with five control points, are sufficient to represent the intra-axis errors for the tested CNC machine tools.