Measuring Parametric and Volumetric Errors in a Four-Axis CMM Using a Hole Plate

Recently, a four-axis coordinate measuring machine (four-axis CMM), which consists of three linear axes and a single rotary axis, has been more widely used than a traditional three-axis CMM. The volumetric error influences the accuracy of the four-axis CMM. There are 27 parametric errors that contribute to the volumetric error. This study utilized a touch probe to measure the hole plate. This methodology can evaluate errors more accurately and reflect the operational conditions of the machines. The main procedures are as follows: (1) The hole plate was sequentially set up in three different planes. The touch probe was used to measure the hole plate using five different styluses. (2) The 27 parametric errors were analyzed using the coordinate deviations. The volumetric error was constructed using homogeneous transformation matrices. The volumetric error ranged from 0.35 to 1.55 μm without the single rotary axis and from 0.35 to 2.83 μm with the single rotary axis. (3) Three metrology instruments, namely a laser interferometer, an autocollimator, and a polygon-autocollimator, were used to validate the proposed methodology and verify the measured parametric errors. The absolute maximum differences compared to 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. Additionally, the absolute maximum difference of one parametric positioning error for the single rotary axis, compared with the polygon-autocollimator, was 0.75″. The E n-values were 0.27, 0.54, and 0.27, respectively. These results demonstrate the effectiveness and reliability of the proposed methodology for the industry’s four-axis CMMs.