Issue34

C. Baron Saiz et alii, Frattura ed Integrità Strutturale, 34 (2015) 608-621; DOI: 10.3221/IGF-ESIS.34.67 613 usually happens [10,19], it has been assumed that the thermal conductivity of the pads material is much smaller than the one of the disc. For this reason, it can be hypothesized that the heat generated during the braking is entirely absorbed by the disc. Basing on these assumptions, the specific heat fluxes on every sector of the disc braking surface have been calculated as follows. During a braking, the variation of the kinetic energy in a single wheel turn can be calculated as:   2 2 1 2 f i E m V V     ; where f V and i V are, respectively, the final and the initial velocity during one wheel rotation. Since the braking is conducted as uniformly decelerated motion, the variation   2 2 f i V V  is constant, and can be expressed as:   2 2 2 2 f i o V V a d a C         constant; where d represents the distance covered in a wheel turn, equal to the tyre rolling circumference C o . Consequently, also E  has a constant value at every single wheel rotation:   2 2 1 2 f i o E m V V m a C         constant. Neglecting both motion resistance and motor braking, the thermal energy, wheel Q , on a single front wheel during a single turn, can be calculated [7,10] as a function of E  : 1 2 wheel Q f E      constant, where f is the dynamic load distribution coefficient on front wheels [20]. In order to simplify the setup of the boundary conditions, without affecting the results, it has been assumed the heat flux constant over a single wheel rotation and equal to: wheel Q q t   ; where t  is the wheel turning time. Considering that the braking is a uniformly decelerated motion, t  increases at every single turn of the wheel and, consequently, q varies accordingly. The routine developed to simulate the relative rotation between pads and disc has required to calculate, from the beginning to the end of the braking, at every wheel turn, the specific heat flux for all the eight sectors in which the braking surface has been subdivided. To do that, knowing q , the specific heat flux in a generic sector of the annular braking surface, equal to S pad , has been calculated as: , 1 1 1 8 8 wheel S pad pad pad Q q q S t S       . The graph of , S pad q vs time, during a complete braking, for one of the eight sectors is shown in Fig. 7.