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Brake discs are essential components of an automobile. They are subjected to intermittent or fatigue loading during vehicle operations. This will not only lead to mechanical stresses but also thermal. In this work a finite element (FE) model of a periodically symmetric brake disc is developed. The heat transfer coefficients (HTCs), that are incorporated into this model, are estimated from computational fluid dynamic (CFD) simulations which are out of scope of this publication. The radiation effects are implemented into this model using emissivity values that are estimated using mathematical extrapolation techniques. Dyno test of the brake disc is considered as a reference to calibrate the performance of the numerical model. The rotational velocities, the associated acceleration and decelerations and the applied brake pressures are referred from the brake dyno tests. The numerical simulation is performed using the Eulerian technique. At first, thermal simulations are performed followed by the mechanical. Here, the geometry of the mesh is stationary, but the mass encompassed inside this mesh is non-stationary and is modelled to rotate with the velocity of the brake disc (this velocity is as per the rotational speed of the disc in the dyno test). This is achieved using a FORTRAN subroutine. From this simulation, the thermal distribution is determined over nodes which act as a boundary condition for the mechanical simulation. In the mechanical simulation, a steady state transport technique is used to model a rotating disc with rotational speeds corresponding to dyno tests. Cyclic brake pad pressure is applied on brake-pad contact patch to simulate the conning behaviour of the disc. The final behaviour of the FE model is thus a cumulative behaviour of thermal and mechanical loading. From the results, it was observed that the estimation of emissivity and the implementation of the same in the simulation model reduced the temperature of the disc. The estimated thermal behaviour was accurate to that of the temperatures measured on the dyno test. Additionally, the coning behaviour displayed a good match with that of the test. Most importantly, not only were the prediction of results accurate but also the methodology reduced the overall computational time to 2-3 days. To conclude, the methodology of estimation and implementation of emissivity in the Eulerian brake disc model emerged to be congruent with tests and hence successful. This model can be a used to simulate the brake disc behaviour for faster estimation of results compared to the conventional Lagrangian model.



Ing. Fabio Squadrani, Senior Manager, Applus IDIADA; Mr. Narcis Molina Montasell, Project Manager, Applus IDIADA; Dr. Eng. Bharath Anantharamaiah, Project Engineer, Applus IDIADA; Mrs. Ines Lama Borrajo, Head of Body Performance, Applus IDIADA; Mr. Ersen Cerit, Chassis Systems, TOGG | Türkiye’nin Otomobili Girişim Grubu Sanayi ve Ticaret A.Ş.

Implementation of radiation effects in thermo-mechanical coning model of a brake disc

EB2023-MSL-015 • Full • EuroBrake 2023 • Rotor based fundamentals

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