2.4. YAW-ROLL-VERTICAL MODEL 9
2.4 YAW-ROLL-VERTICAL MODEL
e above-mentioned 3-DOF model only applies to untripped rollover. However, most of the
rollover accidents in real life are tripped rollover, and at present, there is little research on tripped
rollover. So, some researchers proposed yaw-roll-vertical model which takes vertical road exci-
tation [14]. A new rollover index was proposed based on this model to evaluate the possibility of
vehicle rollover under both untripped and special tripped situations. Jin et al. established vehicle
model which consists of the lateral and yaw motions, and the roll and vertical motions of sprung
and two unsprung masses [15], as shown in Figure 2.7.
ϕ
z
s1
z
c
k
s1
k
s2
c
s1
c
s2
k
t1
m
1
m
s
a
y
m
2
k
t2
z
s2
z
u1
z
u2
z
r1
z
r2
T
w
I
x
ß
r
ß
f
¥
F
r
F
f
u
r
b
a
y
x
o
o
⤶
Figure 2.7: 6-DOF model of vehicle.
In order to simplify the rollover stability model, some assumptions are made as follows.
e pitch dynamics can be ignored, and the front and the rear steering angles are small. Also,
the properties of tire are regarded as symmetric with respect to x-axis. Furthermore, the effects
of the lateral wind, the longitudinal motion, and the roll motion of unsprung mass are neglected
since they are of the secondary importance.
From D’Alembert’s principle, the equations of the above model are as follows.
Lateral motion:
ma
y
m
s
h
R
D 2F
f
C 2F
r
: (2.17)
Yaw motion:
I
z
Pr D 2aF
f
2bF
r
C M
B
: (2.18)
Roll motion:
I
x
R
D
.
F
s2
F
s1
/
T
w
2
C m
s
ha
y
C m
s
hg: (2.19)
Vertical motion of sprung mass:
m
s
Rz
c
D F
s1
C F
s2
: (2.20)
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