16 2. DYNAMIC MODEL OF VEHICLE ROLLOVER
When only taking the front axle steering into account, the yaw rate gain can be described
as follows:
r
ı
D
u
k
f
k
m
.
a C b
1
/
k
f
k
r
.
a C c
1
/
k
f
k
m
.
a C b
1
/
2
C k
f
k
r
.
a C c
1
/
2
C k
m
k
r
.
c
1
b
1
/
2
mU
2
ak
f
b
1
k
m
c
1
k
r
: (2.39)
Setting
(
l D a C c
1
t D c
1
b
1
:
(2.40)
e yaw rate gain can be simplified as follows:
r
ı
D
U
(
h
k
f
k
m
.
l t
/
2
C k
f
k
r
l
2
C k
m
k
r
t
2
i
=
k
f
k
m
.
l t
/
C k
f
k
r
l
C
U
2
m
ak
f
b
1
k
m
c
1
k
r
=
k
f
k
m
.
l t
/
C k
f
k
r
l
)
: (2.41)
So, the equivalent wheelbase of the triaxle bus can be obtained according to the equiva-
lence of physical meaning as follows:
l
e
D
k
f
k
m
.
l t
/
2
C k
f
k
r
l
2
C k
m
k
r
t
2
k
f
k
m
.
l t
/
C k
f
k
r
l
: (2.42)
en, the equivalent front sprung mass is
m
sf
D
m
s
.l
e
a/
l
e
(2.43)
and the equivalent rear sprung mass is
m
sr
D
m
s
a
l
e
: (2.44)
Also, the equivalent front unsprung mass and the equivalent rear unsprung mass can be
described as
8
ˆ
<
ˆ
:
m
uf
D
m
u
.l
e
a/
l
e
m
ur
D
m
s
a
l
e
:
(2.45)
2.6 MULTI-BODY DYNAMIC MODEL
Experimental testing to improve safety is accurate but it is also expensive and dangerous. ere-
fore, multi-body dynamic model is used by researchers to improve the understanding of rollover
dynamics [16–20]. Typically, Pawel used a complex and highly nonlinear multi-body model
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