4 2. DYNAMIC MODEL OF VEHICLE ROLLOVER
CG
m
s
a
y
m
s
a
y
m
s
g
m
s
g
t
w
H
CG,s
H
RC
K
ϕ
j
F
z,RC
F
y,RC
d
CG
RC
RC
ϕ
ϕ
B
ϕ
B
ϕ
S
Z
Y
Figure 2.1: Schematic representation of suspended roll plane model.
g is the acceleration of gravity; H
CG;s
is the CG height of sprung mass respect to grand; H
RC
is the height of roll axis respect to grand; K
is the roll stiffness of suspension; M
RC
is the roll
moment, measured about roll center; m
s
is the sprung mass; is the total roll angle of vehicle;
and
B
is the road bank angle.
By the roll plane model, a threshold used to determine the degree of rollover can be de-
rived. is model can also be used to design the rollover control strategy.
2.2 YAW-ROLL MODEL
ere are many factors that cause the vehicle to roll over. Since it only considers the influence
of roll motion on the rollover, the roll model has some limitations. Some researchers consider
the yaw motion on the basis of the roll plane model. Yu established a yaw-roll model for heavy-
duty vehicle and designed a prototype active roll control system [6]. Chen also used simplified
yaw-roll model to compute a Time-To-Rollover index and then corrected it using an Artificial
Neural Network [7]. As can be seen from Figure 2.2, the proposed yaw-roll model is separated
into a yaw and a roll part. is serial arrangement may have less accurate results compared with
an integrated yaw-roll model. However, this simplified structure was found to be superior in
two aspects: (1) ease of model construction and (2) faster computations.