3
C H A P T E R 2
Dynamic Model of Vehicle
Rollover
A proper vehicle model is required to study vehicle rollover dynamics. In recent years, to evaluate
the possibility of a vehicle rollover, much efforts have been put on rollover stability. To sum up,
several dynamics models used in literature are reviewed: (1) roll plane model, (2) yaw-roll model,
(3) lateral-yaw-roll model, (4) yaw-roll-vertical model, (5) multi-freedom model, and (6) multi-
body dynamic model.
2.1 ROLL PLANE MODEL
Roll motion is one of the most important causes for vehicle rollover. erefore, a model de-
scribing the roll motion properly is the basis to study vehicle rollover. Many researchers have
analyzed vehicle rollover according to the roll plan model [4]. Yu introduced a suspended roll
plane model to determine the threat of impending rollover [5]. e proposed roll plane model
is shown in Figure 2.1.
Equilibrium for the sprung mass can be derived as follows:
X
F
y
D F
y;RC
cos
B
C F
z;RC
sin
B
m
s
a
y
D 0 (2.1)
X
F
z
D F
y;RC
sin
B
C F
z;RC
cos
B
m
s
g D 0 (2.2)
X
M
RC
D m
s
a
y
d cos
s
C m
s
gd sin
s
k
: (2.3)
According to the geometrical relationships shown in Figure 2.1,
d D
.
H
CG;s
H
RC
/
= cos : (2.4)
Assuming small angles, Equations (2.3) and (2.4) become
k
m
s
a
y
d C m
s
gd
.
B
/
(2.5)
and
d H
CG;s
H
RC
; (2.6)
where a
y
is the lateral acceleration of vehicle; d is the distance from CG of sprung mass to roll
axis; F
y
is the lateral tire force in tire y-axis (of wheel plane); F
z
is the vertical force on tire;
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