Brake Disc Thermal and Heat Analysis
During braking, the kinetic energy of the moving vehicle is converted into thermal energy through friction at the disc and pad interface. Frictional heat is generated at the rubbing surface due to the interactions between the pad and disc. The disc absorbs up to 90% of the generated heat energy by means of conduction away from the friction interface between disc and pad (Limpert, 1975). The energy is quickly dissipated to the surrounding air. Radiation also helps to dissipate the heat energy stored within the rotor when the temperature is high.
Prediction of the surface temperature of a disc brake as well as that of the pad is complicated (Thuresson, 2000). This difficulty is due to the complex interactions between the thermal and mechanical behavior of the brake components (Ouyang et al., 2005). The finite element method (FEM) is the most popular and widely used tool to simulate the influence of temperature in brake system design and performance. Bolt (1989) defined several numerical procedures for thermal analysis using the FE method to investigate disc brake performance. He revealed that FEA is the fastest and most accurate way to study the influence of temperature at the early design stage of a brake system. There are three main categories of FE thermal modeling discussed in the following subsections: heat transfer analysis, thermal stress analysis and coupled thermo-mechanical analysis.
heat transfer analysis
The non-uniform heat flux input to the disc brake is calculated from the non-uniform pressure distribution, friction coefficient and sliding velocity along the disc-pad interface. The amount of heat flux that flow into each component depends on the disc and pad material (Thuresson, 2004). The value of calculated heat flux is applied to the FE model to examine the resulting temperature distributions (Koetniyom, 2000).
Limpert (1975) studied the thermal performance of a solid disc brake during braking. The heat flux for the disc was derived from the coefficient of friction and heat proportioning between the rotor and pad under uniform pressure loading. Experimental work was carried out to support the results obtained from the theoretical calculations. During a series of brake applications, the results obtained from the experimental work and the theoretical calculations were well correlated.
Sheridan et al. (1988) studied different techniques for the thermal modeling of a disc brake ranging from a simple axis symmetric FE model to a complex 3-dimensional FE model. The paper also reviewed methods to calculate the thermal boundary conditions of the model. The effect of energy input and output as well as the material properties, such as thermal conductivity and specific heat, had a significant influence on the temperature response. Their findings suggested that 90% of the heat generated during braking is transferred by convection to the ambient air.
Huang and Chen (2006) constructed a 3-dimensional FE model of a disc brake to investigate its cooling performance in terms of the design parameters and boundary conditions. Each surface of the rotor was subjected to different values of convection heat transfer coefficient obtained from theoretical calculations. The neck fillet radius, which connects the rubbing plate to the top hat, was modified to study its influence on the cooling process during braking. The simulation shows that the highest temperature appeared at the mean radius location of the rubbing surface for both outboard and inboard side and this magnitude significantly depended on the fillet radius of the neckSun (2006) developed a thermal model of disc brake system using ABAQUS by combining this with computational fluid dynamics (CFD) and a FORTRAN user subroutine to study the brake equilibrium temperature rise. The thermal model was correlated to physical test data during braking under mountain test schedules to study the effect of rotor, dust shield, wheel, wheel cover and air deflector on the brake performance. The simulation indicated that the modifications made to the rotor, dust shield and wheel geometry greatly improved the brake cooling performance when the brake temperature rise was between 370oC to 480oC. The results also showed that the number of vanes and the air deflector design also influenced the brake equilibrium temperature rise.