Page 377 - Automotive Engineering Powertrain Chassis System and Vehicle Body

CHAP TER 1 2. 1 Braking systems

structure, the suspension rates and the rate of de- from which it can be shown that:
celeration. An indication of the extent of this movement
can be seen in Figure 12.1-16. Under severe braking F f zh
conditions, the vertical displacement, dh b , of the vehicle x fv ¼ P þ l (12.1.77)
body centre of gravity equates to approximately 5% of its
original height. A detailed account of the relevant theory and
can be found in Reimpell and Stoll (1996) and from this
the change in height is given by:
F r zh
x rv ¼ (12.1.78)
P l
F F
dh ¼ y f bf þ y r br (12.1.71)
b
F b F b A situation giving rise to the need for a variable braking
ratio might result from a given vehicle design in which
where the maximum deceleration using a fixed braking ratio is
too low. In practice the introduction of a regulating valve
F bf ¼ F þ F af (12.1.72) into the braking system helps to optimize the braking
sf
efficiency over a wide range of operating conditions. Al-
F br ¼ F sr þ F ar (12.1.73) though such devices do not permit a continuously vari-
F ¼ F þ F br (12.1.74) able braking ratio, they do offer a means of improving the
b
bf
overall braking performance. Mathematical models of
deceleration sensitive pressure regulating valves are now
in which F b is the vehicle body weight, F bf , r are the brake
reaction loads applied to the front and rear of the vehicle derived.
body, F af,r are the unsprung weights of the front and rear
axles and F sf , r are the front and rear axle loads. If the 12.1.4.8.1 Deceleration-sensitive pressure
loads due to the unsprung axle masses are ignored then limiting valve
a corresponding expression for the change in the height A typical valve design is shown in Figure 12.1-17.At
of the overall centre of gravity of the vehicle, d h , can be a predetermined deceleration, determined by the mass
found using: of the ball and the angle of installation, the inertial force
acting on the ball causes it to roll up the valve body and
F F sr close the valve thereby isolating the rear brakes. These
d ¼ y f sf þ y r (12.1.75)
h
P P valves are gradient sensitive but do act in a favourable
manner. On a rising slope the valve closes at higher levels
in which P is the total vehicle weight. of deceleration allowing the rear brakes to contribute
more to the total braking effort, whilst on a falling slope
the rear brakes are isolated sooner reflecting the load
12.1.4.8 Braking with a variable transfer to the front of the vehicle caused by the
braking ratio gradient.
The effect on performance brought about by the in-
If a vehicle is to achieve maximum retardation, equal to clusion of a regulating valve in the rear brake line can be
the value of the tyre–ground adhesion coefficient, equa- assessed by deriving equations which define the brake
tion 12.1.22, then the brake system must be designed ratio for all possible values of deceleration. These may
with a continuously variable brake ratio. This must be then be used in the equations for efficiency and adhesion
equal to the ratio of the dynamic load distribution be- utilization, derived earlier, which quantify the brake
tween the front and rear for all values of deceleration. system performance. In the following analysis it is as-
Thus the variable brake ratio, R v , is defined as: sumed the valve isolates the line to the rear brakes when
the vehicle deceleration has reached a certain value of
deceleration, z v . Note that the mechanism through which
x fv
R v ¼ cut-off is achieved depends upon the chosen valve type
x rv and this determines the actual value of z v .
R Figure 12.1-18 shows a typical front to rear brake
¼ f (12.1.76)
R r force characteristic. For all values of deceleration less
F þ Pzh than z v , the brake force is apportioned between the front
f
¼ l and rear axles in the fixed ratio R. Once the deceleration
F r Pzh
l has exceeded z v , the line pressure to the rear brakes is
held constant and so they can no longer generate

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