# Calibration of a Hybrid Machine Tool from the Point of View of Positioning Accuracy
## 3 Test Results
### Measurement Uncertainty of Positioning Accuracy Measurement  
Following the ISO 230 standard, analysis of the test conditions and used measuring equipment was performed for the conducted tests, and in accordance with the ISO 230-9:2005 [26] standard, the measurement uncertainty was presented. Measuring equipment is set to meet all manufacturer's regulations and minimize unwanted sources of errors such as misalignment error, Brayan error (generalized Abbe error), dead path error, etc. During the measurement, the laboratory temperature was in the range of 23 \({}^{\circ}\)C \(\pm\) 1 \({}^{\circ}\)C. The measurement time did not last longer than 15 min for an individual axis. The instruments were not previously calibrated, so the uncertainty values provided by the equipment manufacturer were used. The instrument was aligned within 1 mm of the axis under test by aligning the return beam of the laser beam. The repeatability of the setting was in increments of 50 mm, and the deflection gradients were a maximum of 50 \(\upmu\)m/m. The environmental variation error was taken from recommendations [27]. The laser interferometer was positioned so that the path error could be minimized. Table 1 shows the obtained uncertainty values for the farthest measurement point for all axes. The laser measurement system used includes automatic compensation of the environment and the coefficient of expansion. \(\upmu_{\text{M,Device}}\) and \(\upmu_{\text{E,Device}}\) were considered zero. For steel, a thermal expansion coefficient of \(\alpha\) = 0.012 \(\upmu\)m/mm \({}^{\circ}\)C was used, and the uncertainty range was set to \(\Delta\alpha\) = 0.002 \(\upmu\)m/mm \({}^{\circ}\)C, following ISO recommendations. For testing, a helium-neon laser interferometer with automatic Zeeman-split two-frequency output, model number HP 5500C, was used. Table 3 presents the influential parameters of measurement uncertainty for the equipment used. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Axis** & **Stage of Analyzing** & **B [mm]** & **R [mm]** & **E [mm]** & **M [mm]** & **A [mm]** \\ \hline \multirow{3}{*}{X} & Initial state & 0.01658 & 0.05487 & 0.245 & 0.23984 & 0.265148 \\  & Unidirectional calibration & 0.0116 & 0.04464 & 0.1059 & 0.08746 & 0.11996 \\  & Bidirectional calibration & 0.01014 & 0.02226 & 0.06842 & 0.06131 & 0.07114 \\ \hline \multirow{3}{*}{Y} & Initial state & 0.02371 & 0.389342 & 0.87764 & 0.6703 & 0.93336 \\  & Unidirectional calibration & 0.010784 & 0.37486 & 0.81262 & 0.54364 & 0.85545 \\  & Bidirectional calibration & 0.00492 & 0.32972 & 0.58622 & 0.41036 & 0.63381 \\ \hline \multirow{3}{*}{Z} & Initial state & \(-\)0.01384 & 0.03363 & 0.08956 & 0.08302 & 0.09754 \\  & Unidirectional calibration & \(-\)0.00588 & 0.03306 & 0.0656 & 0.0489 & 0.0681 \\ \cline{1-1}  & Bidirectional calibration & \(-\)0.0039 & 0.02768 & 0.04806 & 0.04025 & 0.05266 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the calibration process of the O-X glide mechanism. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Device–uD** & **X Axis** & **Z Axis** & **Y Axis** & **Units** \\ \hline L—measurement length & 200 & 70 & 270 & mm \\ a—accuracy & 3.4 & 3.4 & 3.4 & ppm \\ u\({}_{\text{accured}}\) & 0.1963 & 0.0687 & 0.2650 & \(\upmu\)m \\ Wavelength stability & 0.04 & 0.04 & 0.04 & ppm \\ u\({}_{\text{wavelength}}\) & 0.0023 & 0.0008 & 0.0031 & \(\upmu\)m \\ u\({}_{\text{device-estimate}}\) & 0.1986 & 0.0695 & 0.2681 & \(\upmu\)m \\ r—resolution & 0.1 & 0.1 & 0.1 & \(\upmu\)m \\ u\({}_{\text{resolution}}\) & 0.0289 & 0.0289 & 0.0289 & \(\upmu\)m \\ u\({}_{\text{D}}\) & 0.2007 & 0.0753 & 0.2697 & \(\upmu\)m \\ \hline \multicolumn{3}{c}{**Misalignment–uM**} \\ \hline Misalignment & 1 & 1 & 1 & mm \\ \(\upgamma\)—angle & 0.2865 & 0.8185 & 0.2122 & \({}^{\circ}\) \\ \(\Delta\text{L}_{\text{m}}\)—misalignment & 2.5000 & 7.1432 & 1.8519 & \(\upmu\)m \\ u\({}_{\text{M}}\) & 0.7217 & 2.0621 & 0.5346 & \(\upmu\)m \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Table of influential parameters of measurement uncertainty.