# Investigation of Roller-Tape Contact Pair Used in Precision Mechatronic System
## 3 Experimental Research of the Tape-Displacement Measuring System
Table 1 presents the analysis of the results where the standard deviation of the measurements ranges between 0.09% and 0.87%. Errors in the displacement measuring system directly affect the accuracy of raster formation on steel tape. Vertical displacements (see Figure 7) up to 50 um of significant steel tape points (points A and B (also see Figure 4c)) were observed when stretching the tape. The analysis of vertical displacements of point B revealed that they have a periodic shape and vertical displacements of point A have three peaks at 48, 161 and 180 s. Points of support of the tape affect such a change of vertical displacements of the significant points A and B. Figure 8 presents the results of the measurement of the displacement of the tape-angle transducer contact point, which is calculated using the results of the angle sensor. Figure 8a illustrates the time graph and the histogram, Figure 8b presents the spectral density graph and Figure 8c--the spectral graph part expanded to 50 Hz. Figure 6: Block diagram of the test bench of vertical tape displacement (direction Z) and velocity (direction Y). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Measurement Point**} & \multicolumn{4}{c}{**Statistical Parameters, \(\mu\)m**} \\  & **Mean** & **Standard Deviation** & **Minimum** & **Maximum** & **Range (Maximum-Minimum)** \\ \hline \multicolumn{5}{c}{Point A (Figure 7a)} \\ Displacement A1 & 4.127 & 8.753 & \(-\)4.322 & 33.283 & 37.605 \\ Displacement A2 & 3.899 & 8.821 & \(-\)4.505 & 32.904 & 3  
Figure 9 illustrates the results of the measurement of the steel tape velocity (i.e., speed mismatch at 2 mm/s) in the longitudinal direction Y. Figure 9a presents the time graph and the histogram,  
Figure 8: Results of measurements of the displacement (from precision angle transducer) of the tape–angle transducer contact point: (**a**) time graph and histogram, (**b**) spectral density graph, (**c**) spectral graph part expanded to 50 Hz. Figure 9: Results of the measurement of the steel tape velocity (also see Figure 4a): (**a**) time graph and histogram, (**b**) spectral density graph, (**c**) spectral graph part expanded to 50 Hz. Figure 9b--the spectral density graph and Figure 9c--the spectral graph part expanded to 50 Hz. Table 2 presents statistical parameters of the results of the measurement of the displacement of the tape-angle transducer contact point and velocity in the longitudinal direction Y. The assessment of the results of the displacement of the tape-angle transducer contact point (Figure 8 and Table 2) revealed that the value of the displacement of tape-angle transducer contact point varies by about 0.086 \(\upmu\)m. The analysis of the received spectral density results revealed that the the following frequencies appeared in the tape displacement graphs: 1.67; 4.04; 19.9; 32.7; 40; 80.1; 120.9 and 160 Hz. The assessment of the tape velocity results (Figure 9 and Table 2) revealed that the tape velocity value varies by about 0.163 mm/s. The analysis of the obtained spectral density results showed that the following frequencies appeared in the tape displacement graphs: 6.17; 10.04; 17.1 19.9; 32.7; 40; 80.1; 120.9 and 160 Hz. The analysis of the received results showed that frequencies appearing in tape displacement and velocity frequency graphs in Figures 8 and 9 were very close, and the assessment of the tape slip in respect of the angle transducer allows stated that there was no slip in the frequency range from 0 to 200 Hz. The analysis of graphs in Figures 8c and 9c revealed that the displacement and velocity amplitudes at the same frequencies dominated (examining the frequency range up to 50 Hz), which indicated that the band motion patterns were transmitted to the tape-gauge roll assembly and there was no slip between the tape and gauge rolls.