# State of the Art of Tactile Micro Coordinate Metrology
## 4 System Calibration and Performance Verification
### Performance Tests  
Performance tests of micro CMMs can be made in the same way as for conventional machines following the procedure of the acceptance and reverification test ISO 10360-2 [38] using specially designed small artefacts. Since the target uncertainties are in the nanometer range, the stability of these artefacts is a particular challenge. The quantity to be determined in the above cited ISO test is \(E_{0}\), the error of indication of a calibrated test length.  
Ball bars of different lengths ranging from 20 mm to 100 mm were manufactured using Zerodur bars and ruby spheres (Figure 7). The results shown in Figure 7 assess the \(E_{0}\) value of the machine in the whole volume to be 27 nm + 0.2 \(\times\) 10\({}^{-6}\)\(\times\)\(L\)[35]. Since the test requires the ball bar to be measured along the diagonals of the volume, one can compute the squareness between the three machine axes. It is an accurate method since the longest diagonal length can be measured.  
Ball plates are another suitable artefact to test the performance of a CMM. The calibration method requires measurements in 4 positions (two from each side of the plate) in order to be able to separate the errors of the CMM from the deviations of the ball plate nominal positions. The ball plate used  
Figure 7: **(left)** Micro ball bars used for performance verification; **(right)** Length deviations measured with 5 different ball bars each oriented in different axial and diagonal directions. Red squares denote the symmetric 95% confidence intervals, red lines the fitted 95% confidence length measurement error \(E_{0}\) = 27 nm + 0.2 \(\times\) 10\({}^{-6}\)\(\times\)\(L\).  
in the test hereafter was manufactured using 25 ruby spheres, \(\mathcal{O}\) 3 mm, pressed into the holes of an 85 mm \(\times\) 85 mm invar frame (Figure 8).  
Apart from the squareness error between the axes, as it is also obtained from ball bar measurements described above, the method also provides information about other error contributions, such as axes straightness or angular distortions. As shown in Figure 8 the measurement results on the METAS micro CMM exhibit a residual squareness error of (0.17 \(\pm\) 0.05)\". The contributions from other error sources, which are smaller than 40 nm, are largely dominated by temperature drifts. Evaluating the 300 relative distances between all measured ball center positions in a similar way as in Figure 7 (right) leads to a 95% confidence length measurement error of \(E_{0}\) = 26 nm + 0.23 \(\times\) 10\({}^{-6}\)\(\times\)\(L\), a value very close to the one obtained using the ball bars.  
PTB and METAS carried out a bilateral comparison on a 90 mm \(\times\) 90 mm Zerodur plate with hemispheres [39]. The average difference of the hemisphere \(x\)- and \(y\)-coordinates was 12 nm and 7 nm respectively, with a maximum value of 28 nm. It must be noted that, since an error separation calibration procedure was applied, these measurements do not represent the deviations of the machine, but only the capability and comparability of calibrating a ball plate standard.