## 6 Working Principle of Volumetric Verification  
Besides studying the adequacy of volumetric verification to improve the accuracy of long-range MTs, tests were conducted with the aim of studying and comparing the equipment and techniques that currently exist. For this purpose, the linear axis of a Zayer TB5000 machine center was tested with all of them, providing relevant information to management and metrology departments as well as researchers interested in the use of LT and multilateration techniques. Verification of Machine Tool Using API Motorized Retroreflector with and without Previous Compensation  
The use of a motorized retroreflector as an active target allows us to increase the MT workspace to be verified. This is especially relevant when the part to be machined is above the axes of movement, because the LT must replace the part to show the same errors as the part (Figure 7), and the incidence angles of the SMR and cat's eye reflectors are limited. However, the motorized retroreflector can only be used by the API LT in ADM mode. Using an MT workspace with 0 mm \(\leqslant\) X \(\leqslant\) 5050 mm, 0 mm \(\leqslant\)\(Y\)\(\leqslant\) 2050 mm, 0 mm \(\leqslant\)\(Z\)\(\leqslant\) 750 mm, \(C\) = 0\({}^{\circ}\), and \(B\) = 0\({}^{\circ}\), the system can verify a workspace of 0 mm \(\leqslant\)\(X\)\(\leqslant\) 5000 mm, 0 mm \(\leqslant\)\(Y\)\(\leqslant\) 2000 mm, 0 mm \(\leqslant\)\(Z\)\(\leqslant\) 750 mm, \(C\) = 0\({}^{\circ}\), and \(B\) = 0\({}^{\circ}\) using as intervals 500 mm to the \(X\)-axis, 500 mm to the \(Y\)-axis, and 250 mm to the \(Z\)-axis. It provides a verification mesh with 219 points (Figure 7). Based on information of reference [27] the preheating of the MT is carried out using specific NC cycles. It is formed with the eight points that define the large workspace of the machine and its diagonals. This vacuum cycle prior to capturing points is repeated for 45 min until all MT components are hot. Figure 6: Procedure for the identification of errors. Among the non-geometric errors of the MT such as repeatability, deformations, and so on, one of the most relevant is the backlash error of the axis of movement. It is not introduced in the kinematic model of the machine. However, to reduce its influence, verification points are measured twice; in the first measurement the effect of backlash has a certain direction while in the second one it has the opposite direction. In this case, the coordinates of the measured point are the average of the coordinates obtained in the backward and forward measurements. In the same way, temperature variations should be controlled during verification, preventing the occurrence of thermal gradients due to light sources, air currents, and so on. This source of error changes the machine structure and affects the measured points. Therefore, it is necessary to monitor the temperature variations during and between tests. Firstly, the current status of the machine and the suitability and performance of its compensation were analyzed. For this purpose, the accuracy of the MT was obtained using verification points with and without compensation. The variations in the temperature of the environment during measurement and validation are presented in Figure 8. The variation is approximately 1 \({}^{\circ}\)C in both cases. Variation between measurements is also reduced because both points are measured twice. Consequently, temperature variations are not depreciable but assumable. However, temperature influence is deeply studied in order to reduce it [29; 30]. This one is not considered in the verification process proposed but it is minimized. Calibration times are divided in three steps with three different times, preparation, acquisition, and identification:  
Figure 8: Evolution of environmental temperature: data acquisition (**a**) and validation results (**b**). Figure 7: MT volumetric verification using Active Target. Preparation is the step which requires more time.