Page 294 - Understanding Automotive Electronics

2735 | CH 8 Page 281 Tuesday, March 10, 1998 1:19 PM

VEHICLE MOTION CONTROL 8

operation of this ABS is based on estimating the torque T applied to the wheel
w
at the road surface by the braking force F :
b
T = RF b
w
In opposition to this torque is the braking torque T applied to the disk by the
b
calipers in response to brake pressure P:
T = k P
b
b
where k is a constant for the given brakes.
b
The difference between these two torques acts to decelerate the wheel. In
accordance with basic Newtonian mechanics, the wheel torque T is related to
w
braking torque and wheel deceleration by the following equation:
˙
T = T + I W
w b w
where
I is the wheel moment of inertia
w
˙
W is the wheel deceleration (dw/dt, that is, the rate of change of wheel
speed)
During heavy braking under marginal conditions, sufficient braking
force is applied to cause wheel lock-up (in the absence of ABS control). We
assume such heavy braking for the following discussion of the ABS. As brake
pressure is applied, T increases and w decreases, causing slip to increase. The
b
wheel torque is proportional to µ , which reaches a peak at slip S .
o
b
Consequently, the wheel torque reaches a maximum value (assuming
sufficient brake force is applied) at this level of slip.
Figure 8.15 is a sketch of wheel torque versus slip illustrating the peak T .
w
After the peak wheel torque is sensed electronically, the electronic control
system commands that brake pressure be reduced (via the brake pressure
modulator). This point is indicated in Figure 8.15 as the limit point of slip for
the ABS. As the brake pressure is reduced, slip is reduced and the wheel torque
again passes through a maximum.
The wheel torque reaches a value below the peak on the low slip side and
at this point brake pressure is again increased. The system will continue to
cycle, maintaining slip near the optimal value as long as the brakes are applied
and the braking conditions are poor.
The mechanism for modulating brake pressure is illustrated in Figure
8.16. The numbers in Figure 8.16a refer to the following:
1. Applied master cylinder pressure
2. Bypass brake fluid
3. Normally open solenoid valve
4. EMB braking action
5. DC motor pack

UNDERSTANDING AUTOMOTIVE ELECTRONICS 281