Article by: Juan Jesús García, PhD, Product Manager, Braking Systems in Applus IDIADA

This article on Innovative Visualization of Drum Brake Shoe Squeal Dynamics presents an experimental methodology aimed at interpreting the movement of a primary shoe under squeal conditions. In the first part, the problem has been introduced; in the second part, the fundamental theory of the so-called movement decomposition method has been explained. It is the third in a series of four articles. The first two can be found by clicking on the appropriate phrase: Article 1 or Article 2.

Data Analysis

As an example of the type of results obtained with the movement decomposition method, figure 5 shows the two dimensional representation of the time history of the displacement (combination of tangential and radial displacement) of points 7 and 8 on the lower shoe during the squeal occurrence (see the 1st article, figure 1, for the identification of the points). The total displacement is depicted in cyan color and the part of the movement that can be associated to a rigid-body motion is depicted in red color.

As expected, the part of the displacement that can be explained as a rigid solid movement is smaller than the total displacement. This is particularly true for point 8. However, for point 7, both, the total and the rigid-body component of the displacement are quite similar. This suggests that the mobility of point 7 is almost independent of the flexibility of the shoe. The horizontal and vertical axes refer to tangential and radial displacements in mm respectively.

Figure 5: Left: The 2D representation of the movements of points 7 and 8 in the lower brake shoe. Red: total movement; Cian: rigid solid movement. Note that the axes refer to radial and tangential displacement during squeal.

Figure 6 depicts an overall view integrating the results of the rigid body movement and the total displacement of points 5 to 8 on the lower shoe brake. Similar results can be reported for the upper shoe brake. We observe that this type of representation offers a good understanding of the overall vibration pattern, level and orientation of the movements of the various points of the shoes and can be used efficiently to clarify movement attributes that can affect brake shoe stability during squeal.

Figure 6: Two dimensional representation of the measured displacement of the points on the lower shoe during squeal. The figure depicts de 2-D plots of the movements measured for points 5, 6, 7 and 8

As an example, figure 7 depicts polar representations of the total displacements of points 7 and 8, using local polar coordinates (tangential and radial). The green dot depicts the time history of the displacement before squeal and the red locus corresponds to the time history during squeal. These results show that the displacement of the points on the brake exhibit an elongated shape with a well-defined relationship between maximum tangential and radial amplitudes. We observe that, during squeal, the acceleration level increases by a factor around one or two orders of magnitude. This conclusion can be generalized for the magnitude of all the measured points in both the upper and lower shoes.

Figure 7: Change in the displacement of points 7 and point 8, before (green) and after (red) squeal. (system of reference X-Y). The axes denote tangential and radial components

It is interesting to compare the relative size and orientation of the two trajectories shown in figure 7. The results in this figure suggest that point 8 (leading edge of the lower brake shoe in figure 1) has a higher radial displacement compared with the one exhibited by point 7. Also, in this case, for example, the level of radial penetration of point 8 is about ±0.6 µm and ±0.4 µm for point 7. This suggests that the local radial force between the drum and point 8 is about 50% greater than the radial force produced at point 7.

As an example, figure 7 shows a short interval of 2ms of the time history of the displacement at point 8 on the lower brake shoe. From these results, it is clear that, during squeal, the form of the movement of the shoe can be expressed as

where, At and Ar, are the amplitude of the tangential and radial displacements respectively, f is the frequency of the squeal and – is the relative phase between the tangential and radial movements. In our case, the movement shown in figure 8 occurs at about 7.7 kHz, which is the squeal frequency of the brake shoe. One observes that this interpretation of the local movements of the brake shoe can be generalized to any other point.

Figure 8: Example of the trajectory and velocity field of point 8 on the brake shoe during squeal. Duration of trajectory: 2 ms. (Frequency of oscillation: 7.7 kHz). The figure also depicts the relative movement of the shoe and the drum.

The main interest of figure 8 is that, for each point analyzed, it contains information from four time histories: the tangential and radial displacement and velocity vector respectively. In our case, the order of magnitude of the tangential speed of the drum is about 0.5m/s. We note that during squeal, drum tangential speed is about one order of magnitude greater than the tangential speed of the training edge of the shoe. For each point of interest we can generate figures like the one shown in figure 8. These will allow the holistic interpretation of the movement, velocity and relative movement with respect to the drum.

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