# Passive Multi-Layer Composite Damper of Flat Belt Tensioner Idler
## 3 Results  
The three types of passive damper were sequentially mounted in the test bench structure, and the dynamic signals were recorded at continuously changing rotational speeds from 70,000 to 135,000 rpm. The significant differences in vibration amplitude damping for passive dampers of type 1 to 3 were measured (Table 2). During operation without a damper, the maximum amplitude was 50 g Peak, reducing to a maximum of 30, 27, and 26 g Peak for dampers 1, 2, and 3, respectively. The original undamped root mean square (RMS) amplitude value was 33.1 g PtP. The root mean square (RMS) of amplitudes at resonance speed were 25.1, 23.6, and 23.5 g peak to peak (PtP) for dampers 1, 2, and 3, respectively. The most significant reduction was for damper 3, which consisted of flexible rubber foam and solid layers. Table 2 provides the percentage reduction in maximum amplitude and RMS amplitude at resonance for each damper type. A change in amplitude and frequency modulation is visible when the passive damper is used (Figure 5), comparing the time records of 0.1 s at a resonant speed in Figure 5, up, and (fast Fourier transformation (FFT) spectrum in Figure 5 (below). The frequency 2.15 kHz in Figure 5,b is for the rotational speed of the rotor bearing. The original sidebands were suppressed by the passive damper. The amplitudes at frequencies of 7, 9, 13, 17, 22, and 24 kHz were also reduced. The overall operation is \"calmer\", and the pressure of the flat belt on the bearing pin is more stable. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Undamped** & **Type 1** & **Type 2** & **Type 3** \\ \hline RMS amplitude at resonance (g PTP) & 33.1 & 25.1 & 23.6 & 23.5 \\ Reduction in RMS amplitude at resonance & - & 24.2\% & 28.7\% & 29.0\% \\ Maximum amplitude (g Peak) & 50 & 30 & 27 & 26 \\ Maximum amplitude reduction & - & 40\% & 46\% & 48\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dynamic parameters at resonant rotational speed. Figure 5: Time record (up) and fast Fourier transformation (FFT) spectrum (below) for a structure with no damper (**a**) and a structure with passive damper type 2 (**b**). The shape of the resonant peak was also considered as a dynamic parameter. For operation without a damper, the resonant peak is sharp, as it is when damper 3 is used. By contrast, dampers 1 and 2 have preferred rounded resonant peaks (Figure 6). The performance of a passive control system to mitigate a structural vibration depends on its mass and damping status [18]. All of the tested passive dampers have a certain proportion of mass and damping contribution (Figures 6 and 7). The considerable reduction in the RMS amplitude at resonances of 24.2%, 28.7%, and 29.0% was achieved by increasing the mass of the original steel plate by the mass of passive dampers and by using the material damping of layer dampers made of polymers and cork with solid, foam, and honeycomb structure. However, the mass of each passive damper was different: Damper 3 had the greatest additional mass (36.3 g), and damper 2 had the lowest additional mass (16.0 g), which was 44% of additional mass of damper 3 (Table 3). Their respective results in terms of amplitude decrease were similar, although one might have expected an advantage for damper 3 due to its greater mass. Although almost the same resulting effect was achieved for both, an additional mass of damper 2 was 56% lower. Figure 6: Comparison of resonance peaks for structures without a damper or with dampers type 1, 2, and 3. Figure 7: Comparison of root mean square (RMS) amplitude. In addition, the stiffness of non-damped and damped steel plate is not the same. [PERSON]'s modulus E of each damper layer material is much lower than [PERSON]'s modulus of steel. The homogenized Young's modulus of passive dampers \(E_{\text{pd}}\) was determined by its deflection \(w_{\text{pd}}\), which was calculated using the computational finite element method (FEM) software.