30 3. STABILITY OF UNTRIPPED VEHICLE ROLLOVER
14.7
14.6
14.5
14.4
14.3
14.2
14.1
14.0
13.9
13.8
0.0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
e Steering Coefficient Induced by Roll at the Rear Axle
Critical Forward Speed (m/s)
stable
Figure 3.10: Stability region on (c
r
, U
c
) plane.
LTR D 1 and the left wheel just lifts off the ground. Also, if F
z2
D 0, then LTR D 1 and the
right wheel just lifts off the ground.
Figure 3.11 shows the rollover stability at different conditions ( J-turn, Fishhook, and
Double Lane Change maneuvers) and different vehicle speed (60 km/h, 80 km/h, and 100 km/h)
based on the LTR. It is observed that LTR can effectively predict the vehicle rollover. It also
shows that the higher the speed, and the more likely it is to be rollover.
LTR is considered as a very useful index to study the dynamics and simulation of vehicle
rollover, while the vertical load of each wheel of the vehicle is difficult to be measured or esti-
mated in real time. So, the LTR cannot be used to predict the risk of vehicle rollover directly,
especially in the case of emergency. Many researchers derived new rollover indexes based on the
vehicle rollover dynamics model and the definition of the LTR [15, 29–36]. For example, ignore
the vertical motion of the vehicle, so
(
F
z1
F
z2
D F
s2
F
s1
F
z1
C F
z2
D mg:
(3.5)
F
s1
and F
s2
are the left and right supporting force of suspension. According to moment
equilibrium equations, the difference value between the left and right suspension force can be
described as follows:
T
w
2
.
F
s2
F
s1
/
D k
.
s
u
/
c
P
s
P
u
; (3.6)