Measurement and analysis of machine tool errors under quasi-static and loaded conditions

Abstract

Machine tool testing and accuracy analysis has become increasingly important over the years as it offers machine tool manufacturers and end-users updated information on a machine’s capability. A machine tool’s capability may be determined by mapping the distribution of deformations and their variation range, in the machine tool workspace, under the cumulative effect of thermal and mechanical loads. This paper proposes a novel procedure for the prediction of machine tool errors under quasi-static and loaded conditions. Geometric errors and spatial variation of static stiffness in the work volume of machines are captured and described through the synthesis of bottom-up and top-down model building approaches. The bottom-up approach, determining individual axis errors using direct measurements, is applied to estimate the geometric errors in unloaded condition utilizing homogeneous transformation matrix theory. The top-down approach, capturing aggregated quasi-static deviations using indirect measurements, estimates through an analytical procedure the resultant deviations under loaded conditions. The study introduces a characterization of the position and direction dependent static stiffness and presents the identification how the quasi-static behavior of the machine tool affects the part accuracy. The methodology was implemented in a case study, identifying a variation of up to 27% in the stiffness response of the machine tool. The prediction results were experimentally validated through cutting tests and the uncertainty of the measurements and the applied methodology was investigated to determine the reliability of the predicted errors.