## 3 Results  
### Experimental Setup  
The test bench used for the experimentation is presented in Figure 5. It consists of a steel rotor with a mass \(M\) = 0.819 kg, mounted on a flexible shaft with diameter \(d\) = 19 mm, and supported symmetrically between two bearings separated by 700 mm. An electric DC motor drives the shaft through a flexible coupling. The disk has M5 x 1 mm pitch threaded holes for unbalanced masses at a \(\phi\) = 65 mm concentric circle and 16 equally  
Figure 4: Schematic representation of a dry friction rotor.  
Figure 3: Graph of angular speed \(\omega\) (rpm) versus shaft deflection \(y\) (mm).  
-spaced positions. The test mass is a constant weight of 12 g and it is located symmetrically in a single hole. The unidirectional accelerometer is in the horizontal position at the base of bearing A. The friction plate has a unitary width of 38 mm for contact with the disc surface and a flexible arrangement. According to the design of the bench, the friction force increases with imbalance degree and speed.  
The data acquisition system consists of a cBio-9074 CompactRIO embedded controller (8 slots, 400 MHz CPU, 128 MB RAM, 256 MB storage, 2M FPGA Gateways) from National Instruments. It contains an NI9234 4-channel module for dynamic data acquisition, an NI9205 analog input channel, and another NI9403 32-channel digital module. The data were acquired and processed using a program developed in LabVIEW.  
The acceleration was measured by an ADXL103 uniaxial accelerometer with a measurement range of \(\pm\)1.7 g, a sensitivity of 1000 mV/g, and a bandwidth from 0.5 Hz to 2.5 kHz. The accelerometer was placed horizontally on the transverse axis under bearing A, as shown in Figure 5. The friction load was registered with a Rhino load cell model RH1242. The validation of the proposed integration method was performed with a single-point vibrometer model PV-100 from Polytec.  
The sampling frequency was 3 kHz, and each measurement time series vector had 1042 data. According to Table 2, two cases were studied: (a) Case 1 consisted in taking a measurement of the rotor with a constant unbalanced test mass of 12 gr; (b) in Case 2, in addition to the first case conditions, a dry friction contact was applied on the outer diameter of the disk. Both cases were calculated at 700 and 1800 rpm.  
Initially, it is important to know the critical speed of the system to avoid working close to its value. The critical velocity of the system was \(\omega_{n}\) = 4775.7 rpm, from Equation (16), given a disk mass \(M\) = 0.819 kg, \(a\) = 350 mm, \(b\) = 350 mm, \(L\) = 700 mm, \(E\) = 210 GPa, \(I\) = 6397.1 mm\({}^{4}\), and assuming that the shaft and the disk are manufactured with AISI 4140 steel. The velocity test range is less than 40% of the critical speed, thus \(\omega_{n}\) will not affect the results.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Case** & **Test Conditions** & **Instrument** & **Test Velocities (rpm)** \\ \hline
1 & Unbalanced disk & Accelerometer & 700, 1800 \\ \hline
2 & Unbalanced disk + Friction & Accelerometer & 700, 1800 \\ \hline \end{tabular}
\end{table}
Table 2: Test conditions for the experiment.  
Figure 5: Schematic test bench.