# Comparison of Current Five-Point Cylindicity Error Separation Techniques
## 3 Applicative and Comparative Analysis for In Situ Measurement of Cylindricity
### Experimental Verification and Analysis of Parallel Scan EST  
An experimental system based on the parallel scan EST was setup as shown in Figure 6. The headstock and tailstock supported the cylinder. The carriage had three parallel sections separated by a distance \(d=40\) mm. Five inductive displacement probes (TESA GTL 21 DC) were mounted onto the carriage, in which Probes 1-3 were mounted in the left section according to the three-point roundness EST, and Probes 4 and 5 were located in the middle and right sections. An angular encoder (RENISHAW RESM 52, 8192 lines, zero line, 5 subdivisions) was mounted on the rotor in the headstock to control the course of data acquisition so as to obtain uniform sampling on the circumference. The total number of sampling points per revolution \(N\) was 1024. In order to avoid the non-first harmonic suppression [3; 4; 5; 8; 14] and achieve the large error transfer function \(\mathbf{\Omega}(p)(p=0,2,\cdots,15)\), the angular positions of the Probes 1-3 were set respectively \(\alpha=77.03^{\circ},\ \beta=86.84^{\circ}\) as shown in Figure 7. The rotational speed of the cylinder was 1 rpm. It can be seen from Figure 3 and Equation (6) that the parallel scan EST is to simultaneously execute the three-point roundness and sequential three-point straightness ESTs [5,8] for the detection of the radius deviation, out-of-roundness, and LSC of each cross-section of the cylinder, respectively. A novelty of the EST is to accurately detect the spatial curved median line of the cylinder and to measure and reconstruct cylindrical profile consistent to the standard ISO 12180 [6]. The key to verifying the validity of the EST is to evaluate the accuracy of the measured curved median line profile of the cylinder. Currently, there is not a mature method to calibrate the curved median line profile, and it is difficult to investigate the error motions of the cylinder. Therefore, we will compare the repeatability of the curved median line profiles to prove the accuracy. In engineering practices, the high repeatability of measurement results will indicate high-precision of the measurements, and also high accuracy to some extent. Six measurement experiments were conducted on the experimental system for same cylinder shown in Figure 6, the number of the cross-section divided in the cylinder was \(M=25\). A set of software was developed to sequentially control the course of measurements and data collections of Probes 1-5. By calculating Equation (6) with iterative, the LSC vector \(2\mathbf{R}\left(z_{j},N-1\right)/2\) of the \(J\text{th}(J=1,2,\cdots,M)\) cross-sectional profile of the cylinder was extracted, with which the curved median line profile was fitted in each experiment, as shown in Figure 8. Although the profiles of the curved median line were quite consistent among in the six experiments, the variations of the extracted LSC vector of each cross-sectional profile were significant, being approximately within the range \(\pm 2.5\pm 2.5\text{i}\upmu\)m, which cannot be a convincing proof of the accuracy of the parallel scan EST for measuring cylindrical profile. Figure 6: Photograph of the parallel scan EST experimental system. Figure 7: Angular positions of Probes 1–5. Theoretically, this EST can eliminate the radial and tilt error motions of the cylinder as well as the carriage straightness error motions. Actually, similarly to the sequential three-point straightness EST, the double integration calculations [15] as Equation (6) are executed for detecting the LSC vectors of each cross-sectional profile of the cylinder, which reduces the anti-interference capacity of the EST. Influences of various interferences on detecting the LSC vectors of each cross-section are amplified, which conduct the large variations in the measured median line profiles.