# Calibration of a Hybrid Machine Tool from the Point of View of Positioning Accuracy
## 3 Test Results
### Measurement Uncertainty of Positioning Accuracy Measurement
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Measurement Parameters** & **X Axis** & **Z Axis** & **Y Axis** & **Units** \\ \hline n—number of cycles & 5 & 5 & 5 & - \\ U(R+, R\(-\)) & \(1.15\) & \(1.15\) & \(1.15\) & \(\upmu\)m \\ U(B) & 4.12 & 4.12 & 4.12 & \(\upmu\)m \\ U(R) & 4.27 & 4.27 & 4.27 & \(\upmu\)m \\ U(E, E+, E\(-\)) & 2.88 & 4.64 & 2.99 & \(\upmu\)m \\ U(M) (n = 10) & 2.87 & 4.63 & 2.98 & \(\upmu\)m \\ U(A) & 3.33 & 3.59 & 3.35 & \(\upmu\)m \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Uncertainty values of the measurement parameters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Device—u\({}_{\text{D}}\)** & **X Axis** & **Z Axis** & **Y Axis** & **Units** \\ \hline
**Temperature—u\({}_{\text{T}}\)** & & & & \\ \hline Standard uncertainty of sensor & 0.7 & 0.7 & 0.7 & \({}^{\circ}\)C \\ u(\(\Theta\))\({}_{\text{calculated}}\) & 0.2021 & 0.2021 & 0.2021 & \({}^{\circ}\)C \\ u\({}_{\text{M}}\)\({}_{\text{Machine tool}}\) & 0.4850 & 0.1697 & 0.6547 & \(\upmu\)m \\ u\({}_{\text{M}}\)\({}_{\text{Device}}\) & 0 & 0 & 0 & \(\upmu\)m \\ T\({}_{\text{M}}\)—Machine temperature & 24 & 24 & 24 & \({}^{\circ}\)C \\ \(\Delta\)T & 4 & 4 & 4 & \({}^{\circ}\)C \\ u(\(\alpha\)) & 0.0006 & 0.0006 & 0.0006 & \(\upmu\)m/mm\({}^{\circ}\)C \\ u\({}_{\text{E}}\)\({}_{\text{Machine tool}}\) & 0.4619 & 0.1617 & 0.6235 & \(\upmu\)m \\ u\({}_{\text{E}}\)\({}_{\text{Device}}\) & 0 & 0 & 0 & \(\upmu\)m \\ u\({}_{\text{T}}\) & 0.6697 & 0.2344 & 0.9041 & \(\upmu\)m \\ \hline \hline
**Environmental Variation—u\({}_{\text{EVE}}\)** & & & & \\ \hline E\({}_{\text{VE}}\)—drift & 1 & 1 & 1 & \(\upmu\)m \\ u\({}_{\text{EVE}}\) & 0.2887 & 0.2887 & 0.2887 & \(\upmu\)m \\ \hline
**Repeability of the Setup—u\({}_{\text{S}}\)** & & & & \\ \hline O\({}_{\text{ABBE}}\) & 50 & 50 & 50 & \(\upmu\)m \\ D\({}_{\text{angle}}\) & 50 & 50 & 50 & \(\upmu\)m/m \\ \(\Delta\)L\({}_{\text{S}}\) & 3.5355 & 3.5355 & 3.5355 & \(\upmu\)m \\ u\({}_{\text{S}}\) & 1.0206 & 1.0206 & 1.0206 & \(\upmu\)m \\ \hline
**At the Measuring Length—u\({}_{\text{P}}\)** & & & & \\ \hline u\({}_{\text{P}}\) & 1.4610 & 2.3319 & 1.5169 & \(\upmu\)m \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._As in the case of serial mechanisms, the test indicates the necessity of calibrating machine tools with non-linear kinematics. This is indicated by the reduction values of the two-way system error along the axis (E) and the two-way positioning error along the axis (A). The results are shown in Table 5.  
The obtained results indicate the efficiency of the process of calibrating machine tools as well as the possibilities realized by the application of unidirectional and bidirectional calibration for all examined axes. Calibrating machine tools with non-linear kinematics implies the process of defining compensation values, which includes the conversion of external coordinates into internal coordinates, as well as calculating the contribution of the internal axis to the error that occurs at the top of the tool during movement. This process includes the application of expressions determined by the inverse kinematics of the mechanism and the modification of the calibration procedure following the specifics of the specific type of mechanism. In all calibration stages, measurements of current positioning accuracy values according to ISO 230 were performed three times. Control measurements showed that only two measurements (before and after the introduction of compensations) were needed to achieve the full effects of the process. This confirms the hypothesis that the calibration process of machine tools with non-linear kinematics can be realized with the same efficiency level as for machines with a linear kinematic structure. During positioning accuracy measurements, as per ISO 230-2, the platform's speed was constant. Since the measurements were made on a machine tool with non-linear kinematics, the slide speeds were not linearly related to the platform speed, resulting in variable slide speeds during the measurement.