CHAPTER THREE
METHODOLOGY
3.1 INTRODUCTION
There are two main stages in this research area. The first one is computational simulation
stage and the second is actual manufacturing process implementation. First stage consists of
simulations collected from the researchers that had done. They were using the Computational
Fluid Dynamics (CFD) software to develop their model. To have a better understanding of
this research, the data given were used to act as a guideline for the completion of Final Year
Project 1.
3.2 DESIGN PARAMETERS
The loading corresponds to the heat flux on the disc surface. The dimensions and the
parameters used in the thermal calculation are recapitulated in Table 3.1
The material of brake disc is grey cast iron (GF) with high carbon content, with good
thermophysical characteristics, thermoelastic characteristics of which adopted in this
simulation of the rotor and the pads are recapitulated in Table 3.2
Description Value
Inner disc diameter, mm 66
Outer disc diameter, mm 262
Disc thickness (TH), mm 29
Disc height (H), mm 51
Vehicle mass m, kg 1385
Initial speed 0 , m/s 28
2 tstop
Deceleration A, m/s 8
Effective rotor radius Rrotor, mm 100.5
Rate distribution of the braking forces , % 20
Tire radius RTIRE, mm 380
Surface of the pad Ac [mm2] 5246
Factor of charge distribution of the disc p 0.5
2
Surface disc swept by the pad Ad, mm 35993
Table 3.1: Input parameters
Properties Disc Pad
Thermal conductivity, k (W/mC) 57 5
Specific heat, c (J/kg C) 460 1000
Thermal expansion, (106/C) 10.85 10
Young modulus, E (GPa) 138 1
Poissons ratio, v 0.3 0.25
Density, (kg/m3) 7250 1400
Coefficient of friction, 0.2 0.2
Angular velocity, (rad/s) 157.89 -
Hydraulic pressure, P (MPa) 1 -
Table 3.2: Mechanical properties of the disc and pad
3.3 MODELLING IN ANSYS CFX
3.3.1 Geometry
Considering symmetry in the disc, one took only the quarter of the geometry of the fluid field
in Figure 3.1 using software ANSYS ICEM CFD.
This stage consists in preparing the mesh of the fluid field. In our case, one used a linear
tetrahedral element with 30,717 nodes and 179,798 elements in Figure 3.2
Figure 3.1: Definition of surfaces of the fluid field
Figure 3.2: Mesh of the fluid field
3.3.2 Meshing
The goal of meshing in Workbench is to provide robust, easy to use meshing tools that will
simplify the mesh generation process. The model using must be divided into a number of small
pieces known as FEs. Since the model is divided into a number of discrete parts, to carry out a
FE analysis. A FE mesh model generated is shown in Figure 3.3. The mesh results are as shown
in Table 3.3. The elements used for the mesh of the model are tetrahedral three-dimensional
elements.
Model Number of elements Number of nodes
Full disc 114421 172103
Ventilated disc 94117 154679
Table 3.3: Details of mesh model.
Figure 3.3: FEA model mesh model for solid disc and ventilated disc.
3.3.3 Thermal boundary conditions
The boundary conditions are introduced into module ANSYS Workbench [Multiphysics], by
choosing the mode of first simulation of the all (permanent or transitory), and by defining the
physical properties of materials. These conditions constitute the initial conditions of our
simulation. After having fixed these parameters, one introduces a boundary condition
associated with each surface.
(1) Total time of simulation = 45 s.
(2) Increment of initial time = 0.25 s.
(3) Increment of minimal initial time = 0.125 s.
(4) Increment of maximal initial time = 0.5 s.
(5) Initial temperature of the disc = 20 C.
(6) Materials: grey cast iron FG 15.
(7) Convection: one introduces the values of the heat transfer coefficient (h) obtained for
each surface in the shape of a curve.
3.3.4 FE model and simulation
In this work, a three-dimensional CAD and FE model consists of a ventilated disc and two
pads with single slot in the middle as illustrated in Figures 3.4 and 3.5 respectively. The
materials of the disc and the pads are homogeneous and their properties are invariable with
the temperature.
A commercial FE software, namely ANSYS 11 (3D) is fully utilized to simulate structural
deformation and contact pressure distributions of the disc brake during single braking stop
application. Boundary conditions are imposed on the models (disc pad) as shown in Figure
3.6(a) for applied pressure on one side of the pad and Figure 3.6(b) for applied pressure on
both sides of the pad. The disc is rigidly constrained at the bolt holes in all directions except
in its rotational direction. Meanwhile, the pad is fixed at the abutment in all degrees of
freedom except in the normal direction to allow the pads move up and down and in con-tact
with the disc surface. In this study, it is assumed that 60% of the braking forces are supported
by the front brakes (two rotors) as cited in (Mackin et al. 2002). Using vehicle data as given
in Table 1 and Equations (1)(3), braking force on the disc, rotational speed and brake
pressure on the pad can be calculated, respectively.
1
(30%) 0 2
2
= 1
= 1047.36 Eq. 3.2
2 [0 ( 0 ) 2 ]
2
The rotational speed of the disc is calculated as follows:
0
= = 157.89 Eq. 3.3
The external pressure between the disc and the pads is calculated by the force applied to the
disc; for a flat track, the hydraulic pressure is, as referred to Oder et al. (2009):
= = 1 Eq. 3.4
.
Where Ac is the surface of the pad in contact with the disc and is the coefficient of friction.
Figure 3.4: CAD model of the disc and pads
Figure 3.5: FE model of the disc and pads
Figure 3.6: Boundary conditions and loading imposed on the disc pads
3.3.5 Coupled thermomechanical analysis
The purpose of the analysis is to predict the temperatures and corresponding thermal
stresses in the brake disc when the vehicle is subjected to sudden high speed stops as can
occur under autobahn driving conditions [3]. A commercial front disc brake system consists
of a rotor that rotates about the axis of a wheel, a calliperpiston assembly where the piston
slides inside the calliper, which is mounted to the vehicle suspension system, and a pair of
brake pads. When hydraulic pressure is applied, the piston is pushed forward to press the
inner pad against the disc and simultaneously the outer pad is pressed by the calliper against
the disc. Figure 3.6(a) shows the FE model and boundary conditions embedded
configurations of the model composed of a disc and two pads. The initial temperature of the
disc and the pads is 20 C, and the surface convection condition is applied to all surfaces of
the disc and the convection coefficient (h) of 5 W/m2 C is applied to the surface of the two
pads. The FE mesh is generated using 3D tetrahedral element with 10 nodes (solid 187) for
the disc and pads. Overall, 185,901 nodes and 113,367 elements used in Figure 3.5.
In this study, a transient thermal analysis will be carried out to investigate the temperature
variation across the disc using Ansys software.
