## 3 Experimental Study of Squeal Noise
### Characterisation of Squeal Frequencies  
In this section, we are interested in a more precise characterization of the acoustic radiation associated with frequencies \(f_{1}\), \(f_{2}\), \(f_{3}\), \(f_{4}\) and \(f_{5}\) previously identified in Figure 5. The objective is to provide an understanding of squeal noise and its transient evolution over short times associated with the rotation period of the brake system. Due to the fact that the rotation speed of the disc is 200 rpm, the transient evolution over time of each frequency component of the squeal noise is analyzed over two revolutions using nine pictures per revolution, starting at \(t=24\) s. It is verified that this choice of discretization in time is sufficient to properly capture the temporal evolution of the acoustic diagram over a period of rotation, not only in terms of level but also in terms of directivity. In order to conduct this study, a Fourier transform is calculated with a time window \(\Delta t=0.03\) s, which represents a compromise making it possible to isolate and define the local spatial behavior of the acoustic radiation while keeping a good approximation of the frequency estimate, as the sampling frequency of the measurements is 56,250 Hz. Figures 6-10 illustrate the evolution of the squeal noise for all the microphones of the digital antenna and at each frequency of interest (i.e., \(f_{1}\), \(f_{2}\), \(f_{3}\), \(f_{4}\) and \(f_{5}\)). The temporal evolution of the acoustic radiation must be viewed from left to right, in sequence from top to bottom. The pictures are displayed evenly over time by considering two periods of disc revolution. In other words, nine views of the acoustic pattern are taken per time interval corresponding to one revolution of the disc, these views being taken with identical time intervals between each of them (i.e., \(\Delta t=0.33\) s). Figure 5: Spectrogram for one microphone of the digital antenna (dB). Figure 6: Evolution of the acoustic radiation for all the microphones of the digital antenna at \(f_{1}=610\) Hz over two periods of disc revolution (in dB SPL)—to be read from left to right, top to bottom. Figure 7: Evolution of the acoustic radiation for all the microphones of the digital antenna at \(f_{2}=1220\) Hz over two periods of disc revolution (in dB SPL)—to be read from left to right, top to bottom. Figure 8: Evolution of acoustic radiation for all the microphones of the digital antenna at \(f_{3}=1830\) Hz over two periods of disc revolution (in dB SPL)—to be read from left to right, top to bottom. Figure 9: Evolution of acoustic radiation for all the microphones of the digital antenna at \(f_{4}=2440\) Hz over two periods of disc revolution (in dB SPL)—to be read from left to right, top to bottom. At \(f_{1}\) and \(f_{2}\), a variation in terms of both level and directivity that can be linked to the rotating speed of the disc can be observed, although this phenomenon is less pronounced for \(f_{2}\). The maximum level for \(f_{2}\) is lower than that for \(f_{1}\). When comparing the results during the first and the second revolutions (see the nine first pictures compared with the nine last pictures in Figure 6), the temporal evolution of both the pattern and the level are similar. This illustrates good repeatability of the characteristics of the squeal noise  
Figure 10: Evolution of acoustic radiation for all the microphones of the digital antenna at \(f_{5}=3050\) Hz over two periods of disc revolution (in dB SPL)—to be read from left to right, top to bottom. decomposed over these frequencies with a repeatable evolution over a period of revolution of the disc. It can also be noted that the maximum level for \(f_{2}\) remains localized at half \(x>0\) (see Figure 3), although the directivity is not constant on one revolution of the disc. At \(f_{3}\), the acoustic radiation has a relatively homogeneous directivity and level on the two revolutions of the disc.