During a vehicle's braking action, a wheel's kinetic energy is transformed into heat, which doesn't dissipate fast enough into the air stream from the brake to the brake disk. Thus, one of a disk brake's material properties — thermal conductivity — plays a critical role. In addition, thermal judder results from non-uniform contact cycles between the pad and the disk brake rotor, which is primarily an effect of the localized thermoelastic instabilities (TEI) at the disk brake's rotor surface. Localized TEI can generate intermittent hot bands around the rubbing path.

The mechanism of the TEI phenomena has been of interest to many researchers, but this study assumes the thermomechanical phenomenon of each disk is in symmetry about the disk's midplane. It also assumes that the wear taking place during the braking process resulting from the friction between the disk brake and the pad is negligible. This study examines the transient analysis of the thermoelastic contact problem for disk brakes with frictional heat generation using COMSOL Multiphysics finite element analysis (FEA) software. The model simulates the braking action by investigating both the thermal and elastic actions occurring during the friction between the two sliding surfaces (the disk brake and the pad).

Figure 1: 3D Temperature Distribution for a disk brake during a time span of 10 s.

The FEA simulation intended to improve the conceptual design of the disk brakes is divided into two parts: thermal and elastic. During the analysis, the braking parameters are set to certain values based on those in the literature. These parameters include the brake's rotational speed and the cycle of the applied pressure. During the braking process it is assumed that the pressure first increases linearly until it reaches the maximum value within 2.5 s, then the pressure remains constant for another 1.5 s, and finally drops to zero.

Two comparisons were performed using the developed model. The first compared the thermal behavior of several disk materials — gray cast iron (gray iron grade 250, high-carbon grade iron, titanium alloyed gray iron, and compact graphite iron, or CGI), as well as aluminum metal matrix composites (MMCs), namely Al2O3 Al-MMC and SiC Al-MMC (ceramic brakes).

Figure 1 shows a 3D plot of the temperature distribution along the contact surface during and after the braking action (time steps from 1 to 10 s). The temperature produced increases until it reaches its maximum value at the time step 4 s, then it decreases after the applied pressure is released.

Figure 2: Comparison of Temperature Distribution and Heat Flux produced in perforated disks (a & b) and notched disks (c & d).

Both the AMM composites and the ceramic brakes give better temperature distribution than the carbon-carbon composites. In other words, they provide more smoothly distributed temperature; no localized temperature spots can be observed compared to the carbon-carbon brakes. The model results were compared with experimental measurements, and both are in excellent agreement for all of the brake disk materials under study.

A second simulation investigated the mechanical action taking place at the disk's contact surface during the braking process. The deformation obtained from the elastic problem was remarkably small, approximately 200 μm. The model compared two disk designs (the perforated and the notched disks) by determining the temperature distribution and the heat flux developed under the same operating conditions.

Despite the fact that the maximum temperature produced in both were the same, the perforated disks produced better temperature distribution as well as heat flux as compared to notched disks. Figures 2a and 2b show both the temperature distribution and the heat flux at two time steps, 4 and 10 s, produced in the perforated disk brakes. In contrast, Figures 2c and 2d illustrate the same parameters for the notched disk at the same time steps. Both the perforated and the notched disks provide better results as far as the temperature distribution and the heat flux as compared to the standard design, despite the fact that the maximum temperature produced is the same. It can be also concluded that the perforated disks give better temperature distribution and heat flux compared to notched disks.

This work was done by M. Eltoukhy, S. Asfour, and M. Almakky of the Department of Industrial Engineering; and C. Huang of the Department of Biomedical Engineering at the University of Miami using software from COMSOL, Inc. For more information, Click Here