4569846498

Modelling and assembly of the full vehicle 355
10000
3000
Axle load (N)
8000
6000
4000
2000
Front axle load
Rear axle load
0
0 0.2 0.4 0.6 0.8 1
Ideal rear axle brake force (N)
Ideal
2000
Typical
1000
0
0 2000 4000 6000 8000 10000
Deceleration (g)
Front axle brake force (N)
Fig. 6.30
Force distribution for ideal and typical braking events
the vehicle, such as drive or transmission clutches. Typical values of the
convection constant hAc are around 150 W K 1 for a front disc brake installation,
around 80 W K 1 for a rear brake installation and as low as 20 W K 1
for a rear drum brake.
A further key factor in modelling brake performance is the distribution of
brake torques around the vehicle. While decelerating, the vertical loads on
the axles change as described in section 4.8.1 due to the fact that the mass
centre of the vehicle is above the ground.
It may be presumed that for ideal braking, the longitudinal forces should be
distributed according to the vertical forces. Using the above expressions,
the graphs in Figure 6.30 can be calculated for vertical axle load versus
deceleration. Knowing the total force necessary to decelerate the vehicle it
is possible to calculate the horizontal forces for ‘ideal’ (i.e. matched to vertical
load distribution) deceleration. Plotting rear force against front force
leads to the characteristic curve shown in Figure 6.30. However, in general
it is not possible to arrange for such a distribution of force and so the typical
installed force distribution is something like that shown by the dashed
line in the figure. Note that the ideal distribution of braking force varies
with loading condition and so many vehicles have a brake force distribution
that varies with vehicle loading condition. For more detailed information
on brake system performance and design, Limpert (1999) gives
a detailed breakdown of performance characteristics and behaviour, all
of which may be incorporated within a multibody system model of the
vehicle using an approach similar to that shown in Table 6.1 if desired.
Described in some detail in Limpert’s work is the function of a vehicle
ABS system. The key ingredient of such a system is the ability to control
brake pressure in one of three modes, often described as ‘hold, dump
and pump’. Hold is fairly self-explanatory, the wheel cylinder pressure is
maintained regardless of further demanded increases in pressure from the
driver’s pedal. ‘Dump’ is a controlled reduction in pressure, usually
at a predetermined rate and ‘pump’ is a controlled increase in pressure,
again usually at a predetermined rate.
The main variable is the brake pressure p. In the work by Ozdalyan (1998) a
slip control model was initially developed as a precursor to the implementation
of an ABS model. This is illustrated in Figure 6.31 where it can be seen
that on initial application of the brakes the brake force rises approximately