## 2 Measurement System
### Configuration of the Experimental Modal Test  
This analysis applies the modal analysis system, which is produced by the Bruel & Kjaer (B&K) company. The system contains four parts: a modal hammer, an accelerometer, acquisition hardware, and PULSE software (Figure 1). The modal hammer is used to exert an impact to excite the structure. An 8208 hammer is used in the experiment, which is designed for excitation on a medium to a very large structure. It has a mass of 1.36 kg, and the maximum measuring range can reach up to 22,200 N. Four types of impact tips are offered: a hard tip, a tough tip, a medium tip and a soft tip. The accelerometer is attached onto the end effector of the robot, which is a three-directional B&K 4524 transducer (Table 1). The transducer and modal hammer are connected to the four input channels of the acquisition hardware, which is a type 3050-A-040 from B&K [18]. The data are then transmitted by this acquisition hardware to the computer for vibration analysis with PULSE software (Type 7770) [19]. Figure 1: Modal analysis system configuration. ### Configuration of the Experimental Modal Test  
The configurations of the forced vibration experiment setup are illustrated in Figures 2 and 3. The setup contains six components: the IRB 4400 industrial robot, the PONTOS metrology system, the PULSE vibration measuring system, the stimulator, the force sensor and the accelerometer. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Device** & **Type** & **Dynamic Characteristics** & **Unites** & **Value** \\ \hline \multirow{6}{*}{Accelerometer} & & Measuring Range & m/s\({}^{2}\) & \(\pm\)500 \\ \cline{3-5}  & & Amplitude Response \(\pm\)10\% & Hz & X: 0.2 to 5500 \\  & B\&K 4524 & Amplitude Response \(\pm\)10\% & Hz & Y: 0.25 to 3000 \\  & & & Z: 0.25 to 3000 \\ \cline{2-5}  & transducer & Residual Noise (1 to 6000 Hz) & mg & X: \(<\)0.4 Y: \(<\)0.2 \\  & & Broadband & mg & Z: \(<\)0.2 \\ \cline{2-5}  & & Transverse Sensitivity & \% & \(<\)5 \\ \hline \multirow{3}{*}{Modal hammer} & & Sensitivity & mV/N & 0.225 \\ \cline{2-5}  & B\&K impact & Full Scale Force Range Compression & kN & 22.2 \\ \cline{1-1} \cline{2-5}  & hammer 8208 & Linear Error at Full Scale & \% & \(<\)\(\pm\)2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of the accelerometer and the modal hammer [(20; 21)]. Figure 3: Stimulator and sensors. Figure 2: Configuration of vibration experiment setup. The IRB 4400 robot is designed for robotic machining. The main applications are cutting, deburring, grinding and polishing. The maximum reach of its arm is 1.96 m, and the payload can reach up to 60 kg. Its position repeatability can reach 0.19 mm. The high-speed camera measuring system used in this work, named PONTOS, is developed by the Gesellschaft fuer optische Messtechnik (GOM). The maximum camera resolution can reach 2048 \(\times\) 2048, and the corresponding frame rate can reach 1080 Hz. Based on the triangulation principle, its accuracy can reach 0.001 mm depending on the measuring area. The static position is measured with this metrology system for 7 s to obtain the actual accuracy. The results show that the absolute position accuracy values of the measuring system are X = 0.0016 mm, Y = 0.0019 mm and Z = 0.0051 mm [22]. The Z direction has the lowest accuracy because it is in the direction of the focal depth axis. The metrology system tracks the robot's motion by identifying a special marker. As shown in Figure 3, markers are attached on the robot flange to track its motion. A measuring frequency (frame rate) of 500 Hz is set to track the vibration displacements. Specified parameters are stated in the table below (Table 2). To measure the vibration, a stimulator and variant sensors are installed on the robot. From right to left in Figure 3, the force sensor is installed on the flange of the robot's sixth axis. The stimulator is mounted on the force sensor, while the accelerometer is fixed on the spindle flange. These objects installed on the robot flange have a total weight of 4.7 kg.