A Hole Plate for Measuring Parametric and Volumetric Errors of a Four-Axis Coordinate Measuring Machine

Abstract Recently, a four-axis coordinate measuring machine, which consists of three linear axes and a single rotary axis, has been more widely used than a traditional three-axis coordinate measuring machine. The volumetric error influences the accuracy of the four-axis coordinate measuring machine. 27 parametric errors contribute to the volumetric error. This study proposes a new methodology to analyze the parametric and volumetric error of the four-axis coordinate measuring machine using a hole plate. First, the hole plate setup sequentially in three different planes. We measured the hole plate by using five different styluses. Second, 27 parametric errors were analyzed using the coordinate deviations. The volumetric error was constructed using the homogeneous transform matrixes. The volumetric error ranges were from 0.35 µm to 1.55 µm and from 0.35 µm to 2.83 µm without and with the single rotary axis. Third, three commercial instruments, namely a laser interferometer, an autocollimator, and a polygon-autocollimator, were used to validate the proposed methodology to verify the measured parametric errors. The absolute maximum differences, compared with the laser interferometer for three parametric positioning errors and the autocollimator for six parametric rotational errors for the three linear axes, were 0.56 µm and 0.54", respectively. Moreover, the absolute maximum difference of one parametric positioning error for the single rotary axis, comparing with the polygon-autocollimator, was 0.75". The En-values were 0.27, 0.54, and 0.27, respectively. The results demonstrate the proposed methodology's effectiveness and reliability to the industry's four-axis coordinate measuring machines.