# Separation Method for Installation Eccentricity Error of Workpiece
## 5 Experimental Study
### Experimental Results and Discussions
#### 5.2.3 The Influence of Different Workpieces  
In this section, the influence of different workpieces on workpiece installation eccentricity separation results at the same spindle speed is studied. This experiment collected displacement data obtained by measuring three different workpieces at fixed positions using four displacement sensors at a spindle speed of 300 r/min with an axial distance of 80 mm and calculated the installation eccentricity error. The radial runout error of the spindle before the separation of different workpieces is shown in Figure 15. Each figure consists of two parts: experimental measurement values and their first harmonic components. The separation result of workpiece 1 is given in the previous section. The first harmonic component of the spindle radial runout error measured during the installation of different workpieces was substituted into the proposed separation method, and the separation results of workpiece installation eccentricity error at three different axial distances were obtained. Figure 14: Measured values and simulated signals at different axial distances. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Axial Distances** & **Along the \(x\) Direction** & **Along the \(y\) Direction** \\ \hline
80 mm & 0.9816 & 0.9714 \\
90 mm & 0.9861 & 0.9691 \\
100 mm & 0.9984 & 0.9823 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The \(R^{2}\) between measured values and simulated signals at different axial distances. Table 10 shows the results of both amplitude \(R_{1}\) and phase \(\lambda\) of the installation eccentricity error separated from the first harmonic component of the radial runout error at different axial distances, and the amplitudes \(a\), \(b\) and phases \(\phi_{1}\), \(\phi_{2}\) of the spindle radial runout error. The calculation error of installation eccentricity error for different workpieces is less than 0.6%, indicating that the surface morphology of different workpieces will not affect the calculation and separation of installation eccentricity error. Meanwhile, this also indicates that the installation eccentricity error is not introduced during the workpiece clamping process but stems from the misalignment between the chuck rotation center and the spindle geometric center. Subsequently, the separated parameters were used to construct simulation signals, which were compared and analyzed with experimental measurements to verify the accuracy of the separation results. Figure 16 compares experimental measurements and simulated signals at different axial distances. It can be clearly observed that the simulated values have a high degree of coincidence with the measured values. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Workpiece 1** & **Workpiece 2** & **Workpiece 3** \\ \hline \(R_{1}\) (\(\mu\)m) & 14.75 & 14.66 & 14.82 \\ \(a\) (\(\mu\)m) & 23.17 & 23.13 & 23.18 \\ \(b\) (\(\mu\)m) & 30.90 & 31.02 & 31.33 \\ \(\lambda\) (rad) & 1.43 & 1.42 & 1.40 \\ \(\phi_{1}\) (rad) & 0.83 & 0.81 & 0.83 \\ \(\phi_{2}\) (rad) & 0.31 & 0.31 & 0.31 \\ \hline \end{tabular}
\end{table} 
Table 10: Calculation results of parameters of different workpieces. Figure 15: The radial runout error of the spindle of different workpieces. Table 11 shows the \(R^{2}\) between the experimental measurement values and simulated signals at different axial distances. The results showed that the \(R^{2}\) was close to 1, indicating that curve similarity exceeds 97%, further displaying the high accuracy and reliability of the installation eccentricity error separation method proposed in this investigation. The results in Table 11 further confirm that the method maintains high consistency (\(R^{2}>0.97\)) across different workpiece geometries, with the calculation errors of installation eccentricity error varying by less than 0.6%. This insensitivity to the shape of the workpiece, coupled with the negligible influence of spindle speed (variation < 0.3%, Table 6) and axial distance (variation <0.5%, Table 8), collectively demonstrates the method's generalizability.