## 4 Case Study  
### Measurement Data Analysis  
In the following part of this article, measurement data and analyses for a selected bearing seat, namely bearing 2, are presented. The correlation between results of CNC measurements and CMM measurements expressed as the Pearson coefficient for this seat is 0.09 and is considered low. It means that the measurement results obtained from the CNC machine do not reflect the measurement results obtained from the CMM. It is thus one of the most difficult cases in the examined subject and stems from the fact that the bearing seat 2 is the farthest seat from base hole B. As a result, when the cover is unclamped after machining, this seat is subject to the greatest displacement with respect to the reference system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Characteristic Number** & **Pearson Correlation Coefficient Value** \\ \hline
1 (base hole A) & 0.13 \\
2 & 0.09 \\
3 & 0.28 \\
4 & 0.02 \\
5 & 0.43 \\
6 & 0.30 \\
7 & 0.18 \\
8 & 0.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Correlation of true positions of bearing seats measured using CNC and CMM. Figure 6: Cover measurement in the measurement laboratory using a CMM. The results of measurements carried out on the CNC machine and on the CMM for 97 covers are presented in Figure 7, whereas instead of coordinate values for hole axes in the reference system, deviations from nominal values are given. Owing to this fact, the differences in the results are more visible. For the data given in diagram 7, measurement errors were calculated on the CNC machine, understood as differences between deviation values:  
\[\text{E}_{2}=|\text{HPD}_{\text{CMM2}}-\text{HPD}_{\text{CNC2}}| \tag{1}\]  
Values of these errors are presented in Figure 8.  
For the considered bearing seat 2, the average value of measurement error is \(\text{E}_{\text{2 AVE}}=0.013\) mm, whereas the maximum value of measurement error is \(\text{E}_{\text{2 MAX}}=0.032\) mm. On the basis of the above analysis, it may be concluded that the measurement results obtained from the CNC machine have low reliability. Error \(\text{E}_{2}\), being the difference between CNC and CMM measurements, takes excessively high values, close to the half of positional tolerance for bearing seat 2. As a result, an approach was suggested dealing with the consideration of system information, in addition to error \(\text{HPD}_{\text{CNC2}}\), that will allow for association of the results of measurements carried out on the CMM and on the CNC machine. In the previous paper of the authors [2], it was demonstrated that the difference between the measurements carried out on the CMM and on the CNC machine is correlated with the cover basing surface  
Figure 8: Error \(\text{E}_{2}\) as an absolute value of the difference of deviations resulting from CMM and CNC measurements for bearing seat 2. Figure 7: Hole position deviations of bearing seat 2 from nominal values determined on the basis of measurements on the CMM (\(\text{HPD}_{\text{CMM2}}\)) and on the CNC machine (\(\text{HPD}_{\text{CNC2}}\)). curvature. In the above paper, curvature was determined on the CMM and constituted one of the ANFIS inputs. Due to the fact that in this paper elimination of CMM measurements is assumed, attention was paid to finding another parameter that would provide ANFIS with information on stress released during machining which, in effect, after unclamping the cover, results in the lack of surface flatness. The specific nature of the cover is such that the machined bearing seats are on free surfaces; i.e., the clamping points of the cover during machining are at a considerable distance from the machined seats, which change their position relative to the other parts of the cover due to the release of stresses. Error \(\text{HPD}_{\text{CNC2}}\) determined with respect to the nominal value contains no information on local cover deformations. Hence, it was suggested that an additional system input was a variable describing the relationship between measurement results of two selected elements.