Abstract
Keywords - Coning, Brake, Friction, Judder, FEM
Abstract - The frictional heat generated at the interface of the rotor and pad of an automotive disk brake can result in thermal distortion of the frictional surface. Known as coning, this effect is found to be the main cause of RTV (rotor thickness variation) and judder. It is, therefore, important to predict the temperature rise and thermal deflection in the early design stage.
While axisymmetric finite element analysis can be used for a solid rotor for these purposes, a pie-shaped model is usually used for a ventilated disk that is evidently three dimensional in shape due to its vent holes. It, therefore, requires a tremendous amount of computing time and memory space to do a transient temperature analysis, since a very refined mesh is necessary to avoid the numerical instability in time integration.
In this paper a new analysis technique is proposed for a ventilated disk in which the rotor is represented using an axisymmetric finite element model. To take into consideration the effects due to the cooling passages, a homogenization technique is used to give the equivalent diffusivity and elastic modulus for elements located at the vent holes.
The convective heat transfer coefficient on the vent walls parallel to the friction surface is also transformed to an equivalent one, so that, when it is used as a boundary condition in the axisymmetric analysis, the calculated heat flux at the edge is the same as the total actual heat flux from the corresponding vent walls. Similarly, for the vent walls normal to the friction surface, an equivalent convective coefficient is imposed on the corresponding axisymmetric element face. Lastly, equivalent convective coefficients are used at the element edges at the innermost and outmost radius of the cooling vane.
Numerical tests are carried out using MSC/NASTRAN to find the temperature results by the proposed method closely agree with those from 3-D analysis, although there are some discrepancies due to their inherent geometric differences at the vent holes.
Static analysis from the thermal loading shows also that thermal stress and resulting amount of coning coincide with those from 3-D analysis, indicating that the proposed procedure can be successfully applied in practice, replacing 3-dimensional finite element analysis for optimal shape design to reduce judder in a ventilated disk.