# Laser R-Test for Angular Positioning Calibration and Compensation of the Five-Axis Machine Tools
## 5 Experiment and Results
### Angular Positioning Verification with Milling Workpiece  
The process is executed on one CNC machine tool but with two compensation data from the XR20-W and Laser R-test. The experimental process is shown in Figure 25 excluding the translational axis compensation process done in advance. The workpieces after the process are put in an inspection by using the coordinate measuring machine (CMM) ABLE-686-CNC (Jingsh Meng Technology Co. Ltd., Taichung City, Taiwan) [22]. There are two workpieces prepared, one for XR20-W and the other for the Laser R-test. They are cut by the following method, as shown in Figure 26, with milling specifications as shown in Table 1.  
Figure 24: Residual error of Laser R-test.  
Figure 25: Experimental process.  
The captured result from CMM ABLE-686-CNC is archived by absolute measuring of the angles that the P1 path and every other path form, as shown in Figure 27. The error result from Figure 27 is re-expressed in Figure 28, which shows the comparison of the two systems. Through these results, the performances of the XR-20 and Laser R-test (LRT) are very close.  
Another measuring method on CMM ABLE-686-CNC is executed by relative measuring of the angles that the current path and next path form (P1 path and P2 path form, P2 path and P3 path form,...). In this method, the formed angles are equal to 150\({}^{\circ}\) theoretically. Figure 29 shows the results of this method, and the following error shown in Figure 30 shows two systems are equivalent.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Machine Tool Model** & **QUASER MF400U** \\ \hline Controller & Siemens 840D sl \\ \hline Cutting tool & \(\mathcal{O}\)16 end mill \\ \hline Cutting speed & 4000 rpm \\ \hline Feed rate & 620 mm/min \\ \hline Tool path & straight line \\ \hline Axial depth of cut & 30 mm \\ \hline Radial cutting width & 0.2 mm \\ \hline Cutting material & Aluminum 6061 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Technical milling specification.  
Figure 26: Cutting method.  
Figure 27: The measured result from CMM ABLE-686-CNC: **(a)** results from the workpiece using XR-20W and **(b)** results from the workpiece using Laser R-test.  
Figure 28: Comparison of the error result between two systems.  
Through these results with actual milling, we could demonstrate that our system is feasible in the real case.  
After all the results, we have a picture of these experiments, including the system configurations (radius and measurement pitch) and the repeatability from the verification shown in Table 2. This lists basic specifications of the Laser R-test yielded in this study,  
Figure 30: Comparison of the error result between two systems.  
Figure 29: The measured result from CMM ABLE-686-CNC: (**a**) results from the workpiece using XR-20W; and(**b**) results from the workpiece using Laser R-test.  
including comparison and deviation with XR-20 instrument. The radius and the measurement are two parameters that affect the performance of the system. Thus, these two parameters could be set to meet the requirement in different cases.