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C. Baron Saiz et alii, Frattura ed Integrità Strutturale, 34 (2015) 608-621; DOI: 10.3221/IGF-ESIS.34.67 620 However, from data in Tab. 4, it can be observed that the thermo-mechanical strains reach very low values, so demonstrating a very good behaviour of the analysed discs throughout the brake fading test. Disc type Min (mm/mm) Max (mm/mm) Straight -0.00043581 0.0003498 Pillar -0.0005097 0.00035072 Curved -0.00050126 0.00032796 Table 4 : Minimum and maximum radial strain values. C ONCLUSIONS ehaviour of different types of disc brake rotors has been investigated by means of coupled thermo-mechanical numerical analyses. Very hard working conditions have been imposed to the discs in order to evaluate and to compare their performances when subjected to fourteen repeated hard braking. Three ventilated discs (respectively with straight, curved and pillar-shaped vanes) and a full one have been studied. This last has shown a poor behaviour, reaching an out-of-use condition after the sixth braking. All the analysed vented rotors, instead, have shown very good performances in terms of heat transfer, so allowing their safe use in extreme braking conditions. By comparing the temperature distribution maps, it can be stated that the best disc is the one with curved vanes, whereas the worst one is the straight-vanes disc. This last one reaches a maximum temperature of about 890 °C, which is appreciably higher than the temperature reached by the curved-vanes disc (840 °C). In terms of stresses, instead, previous results are completely reversed. The best disc, in fact, is the straight vanes one, which reaches a maximum value of Von Mises stress of about 38 N/mm 2 , whereas the curved-vanes disc has a maximum value of 43 N/mm 2 . However, these values are much lower than the material yield strength so, under the imposed working conditions, the discs are not much stressed. Also with regard to the deformations, all the analysed discs have shown very good performances, reaching very low value of strains. For these reasons, considering that the maximum stress and strain values over the discs are quite low, the discriminating and most important factor in the choice of the best solution should be related to the thermal results. High values of temperature, in fact, can affect the rotor material properties and, consequently, the right functionality of the whole braking system. Then, basing on the obtained results, it could be stated that, among the analysed rotors, the best solution for very hard repeated braking is the curved-vanes disc. The methodology implemented in this work could be effectively used also during the design phase in order to evaluate, in a preliminary stage, the best shape of the brake rotor depending on the planned working conditions. Thanks to the developed parametric CAD models of the discs, in fact, it is possible interfacing the FEM numerical models and an optimization software with the aim to identify the optimal solutions in terms of shape and number of the vanes, rotor thicknesses, etc. R EFERENCES [1] Milenković, P. D., Jovanović, S. J., Janković, A. S., Milovanović, M. D., Vitošević, N. D., Đorđević, M. V., Raičević, M. M., The Influence of Brake Pads Thermal Conductivity on Passenger Car Brake System Efficiency, Thermal Science, 14 (2010) S221-S230 [2] Belghazi, H., Analytical Solution of Unsteady Heat Conduction in a Two-Layered Material in Imperfect Contact Subjected to a Moving Heat Source, Ph. D. thesis, University of Limoges, Limoges, France, (2010). [3] Mackin, T. J., Noe, S. C., Ball, K. J., Bedell, B. C., Bim-Merle, D. P., Bingaman, M. C., Zimmerman, R. S., Thermal cracking in disc brakes, Engineering Failure Analysis, 9(1) (2002) 63-76. [4] Nakatsuji, T., Okubo, K., Fujii, T., Sasada, M., Noguchi, Y., Study on Crack Initiation at Small Holes of One-piece Brake Discs (No. 2002-01-0926), SAE Technical Paper (2002). [5] Gao, C. H., Lin, X. Z., Transient temperature field analysis of a brake in a non-axisymmetric three-dimensional model, Journal of Materials Processing Technology, 129(1) (2002) 513-517. B