41
C H A P T E R 4
Stability of Tripped Vehicle
Rollover
At present, most studies on the stability of rollover focus on untripped rollover. However, tripped
rollover accounts for a large proportion of rollover accidents. It is necessary to analyze the tripped
rollover deeply. Some scholars have put forward the roll index for tripped rollover on uneven
roads, slopped roads and banked roads and so on. And the energy methods for the stability of
tripped rollover is also analyzed.
4.1 ROLL INDEX OF TRIPPED VEHICLE ROLLOVER
4.1.1 ROLLOVER INDEX ON UNEVEN ROADS
According to the definition of the LTR and yaw-roll-vertical model mentioned in Section 2.4,
an improved definition of the lateral load transfer ratio is proposed to describe the tripped vehicle
rollover on uneven roads by Jin et al. [15]. From the dynamics of the wheel vertical motion, the
total vertical load is consisted of the dynamic vertical force and the static vertical force of the
tire. So, the total vertical loads of the left and right wheels can be described as follows:
F
z1
D k
t1
.
z
u1
z
r1
/
C mg=2 (4.1)
F
z2
D k
t2
.
z
u2
z
r2
/
C mg=2: (4.2)
Substituting Equations (4.1) and (4.2) in Equations (2.21) and (2.22), respectively, the
total vertical loads will be rewritten as
F
z1
D m
1
Rz
u1
C F
s1
C mg=2 (4.3)
F
z2
D m
2
Rz
u2
C F
s2
C mg=2: (4.4)
From Equations (3.4), (4.3), and (4.4), a new index can be defined as follows to evaluate
the danger of vehicle rollover for both tripped and untripped:
RI D
m
1
Rz
u1
m
2
Rz
u2
C F
s1
F
s2
m
1
Rz
u1
C m
2
Rz
u2
C F
s1
C F
s2
C mg
: (4.5)
As the suspension forces are difficult to obtain in real time, the rollover index in Equa-
tion (4.5) also cannot predict the risk of vehicle rollover directly. Fortunately, the difference
42 4. STABILITY OF TRIPPED VEHICLE ROLLOVER
between the left suspension force and the right suspension force can be obtained from Equa-
tion (2.19), and the sum of the left suspension force and the right suspension force can be
obtained from Equation (2.20). at is,
F
s2
F
s1
D
2
T
w
I
x
R
m
s
ha
y
m
s
hg
(4.6)
F
s1
C F
s2
D m
s
Rz
c
: (4.7)
Substituting Equations (4.6) and (4.7) in Equation (4.5), the rollover index for both un-
tripped and special tripped situations can be rewritten as
RI D
T
w
.
m
1
Rz
u1
m
2
Rz
u2
/
2
I
x
R
m
s
ha
y
m
s
hg
T
w
.
m
1
Rz
u1
C m
2
Rz
u2
C m
s
Rz
c
C mg
/
: (4.8)
e new rollover index can be obtained in real time with some unknown parameters which
can be measured and estimated, such as vertical accelerations of the sprung mass and unsprung
mass, lateral acceleration and roll angle.
To verify the new rollover index, the dynamic performance of a vehicle rollover is sim-
ulated in CarSim, an industry-standard vehicle dynamic simulation software. e model of a
large passenger vehicle is used, and the lateral load transfer ratio and new rollover index are
obtained in three different cases below.
Case I
In an untripped rollover situation, the vehicle roll is induced by driver’s maneuver, such as the
step steering at 1.0 s. e final value of the steering angle of the front wheel is ı D 2
ı
, and the
vehicle speed is 100 km/h. en, the untripped rollover indices of the vehicle can be obtained.
As shown in Figure 4.1a, the new rollover index agrees with the fundamental definition
of the LTR very well when the vehicle rolls with all wheels keeping on road due to step steering.
Case II
In a tripped rollover situation, the vehicle rollover happens due to external road input, such as
an unpredictable road bump under the right wheel when vehicle moves on a straight lane. In
this case, the maximum height of the road bump is 0.15 m, and the vehicle speed is 100 km/h.
e tripped rollover indices of the vehicle are plotted in Figure 4.1b.
e improved rollover index also fits the fundamental definition of the lateral load transfer
ratio very well in a tripped rollover situation, except that the right wheels lift off a few seconds.
So, the new rollover index can be used to detect the danger of tripped rollover if its value is
outside the range from 1 to 1.
4.1. ROLL INDEX OF TRIPPED VEHICLE ROLLOVER 43
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
LTR
New RI
6420 8 10
Time (s)
(a) Under an untripped rollover situation
Rollover Index
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
LTR
New RI
6420 8 10
Time (s)
(b) Under a special tripped rollover situation
Rollover Index
Figure 4.1: Rollover indices under different situations. (Continues.)
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