# Influence of Material-Dependent Damping on Brake Squeal in a Specific Disc Brake System
## 3 Pad-on-Disc System Description
### Analyses of Brake Squeal on Simplified Experimental Brake Model  
For the analyses of the modal content of the given system, frequency response function (FRF) measurement was performed on free and mounted and loaded discs. The measurements revealed possible modes as candidates for mode coupling leading to squeal. The measurements were recorded by an accelerometer sensor placed on the disc structure and the modal hammer (Figure 4) equipped with a hammer tip with a steel insert (hard), permitting the energy content of the force impulse to excite the structure of the disc within the range of the desired frequencies. The maximum sampling time interval for FRF measurements was 5 s and the acceleration frequency range of interest was 1-10 kHz. The sampling frequency was 102.4 kS/s.  
Performing fast Fourier transform (FFT) on multiple measured signals, multiple FRFs were obtained from the time signals and their averaged value for the free disc is shown in Figure 5a. The numbers in brackets (d,c) represent the number of nodal diameters and the number of nodal circles of a given mode. Nodal diameter (d), also called cyclic symmetry mode number, is the number of waves, or the number of diameters in the structure, along which the displacements are zero. Nodal circles number (c) is the number of circles in the structure along which the displacements are zero. Three bending modes of three, four, and five nodal diameters were identified using experimental modal analysis (EMA).  
Figure 5b shows details of the FRF for the attached and loaded disc around a couple of (4,0) modes, which are considered the most prone to coupling. Comparing Figure 5a,b, the natural frequency of the (4,0) disc-bending mode increases when the disc is attached to the hub. This effect is due to the stiffening by the disc to the hub attachment. A couple of natural frequencies also slightly move away from each other due to the lack of an ideal axisymmetry  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\phi D_{D}\) (mm) & \(t_{D}\) (mm) & \(l\) (mm) & \(w\) (mm) & \(h\) (mm) & \(\phi D_{H}\) (mm) & \(t_{t}\) (mm) \\ \hline
215 & 14 & 40 & 20 & 8 & 108 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Basic dimensions of pad-on-disc system components: \(\phi D_{D}\)—disc diameter, \(t_{D}\)—disc thickness, \(l\)—yellow friction material (FM) length, \(w\)—FM width, \(h\)—FM height, \(\phi D_{H}\)—hub diameter, \(t_{t}\)—thin plate thickness.  
Figure 4: Schematics of frequency response function (FRF) measurement on the (**a**) free and (**b**) attached discs.  
of the disc-hub attachment. The frequency shifting is visible when the pad comes into contact with the disc. The pad having higher damping brings additional damping to the system. We concluded from the widening of the FRF, that the tips correspond to natural frequencies of the system. Different damping of neighboring modes due to pad contact was identified at this point.  
The characteristic squeal frequency of the studied system occurred in the region of 5800 Hz-6000 Hz, depending on physical conditions like temperature, contact pressure distribution between the FM and the disc, as well as fiction intensity. A typical measurement of squeal frequency, captured using two accelerometer sensors (Figure 6a) placed on a slowly rotating disc structure, is shown in Figure 6b.