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Modelling and assembly of the full vehicle 351
6.9 Modelling of vehicle braking
In Chapter 5 the force and moment generating characteristics of the tyre were
discussed and it was shown how the braking force generated at the tyre contact
patch depends on the slip ratio as the wheel is braked from a free rolling
wheel with a slip ratio of zero to a fully locked wheel where the slip ratio is
unity. In this section we are not so much concerned with the tyre, given that
we would be using a tyre model interfaced with our full vehicle model to
represent this behaviour. Rather we now address the modelling of the mechanisms
used to apply a braking torque acting about the spin axis of the road
wheel that produces the change in slip ratio and subsequent braking force.
Clearly as the vehicle brakes, as shown in Figure 6.26, there is weight
transfer from the rear to the front of the vehicle. Given what we know about
the tyre behaviour the change in the vertical loads acting through the tyres
will influence the braking forces generated. As such the braking model
may need to account for real effects such as proportioning the braking pressures
to the front and rear wheels or the implementation of anti-lock braking
systems (ABS). Before any consideration of this we need to address the
mechanism to model a braking torque acting on a single road wheel.
If we consider a basic arrangement the mechanical formulation of a braking
torque, based on a known brake pressure, acting on the piston can be
derived from Figure 6.27.
The braking torque B T is given by
B T npAR d (6.13)
where
n the number of friction surfaces (pads)
the coefficient of friction between the pads and the disc
p the brake pressure
A the brake piston area
R d the radius to the centre of the pad
Note that depending on the sophistication of the model the coefficient of
friction may be constant or defined as a run-time variable as a function
of brake rotor temperature. Obtaining such data is usually relatively easy,
but the calculation of rotor temperature can be a little more involved.
Weight transfer
Brake torque
Deceleration
x
z
Brake torque
Fxbr
Fxbf
Fig. 6.26
Fzr
Braking of a full vehicle
Fzf