34 3. STABILITY OF UNTRIPPED VEHICLE ROLLOVER
J-turn and Fishhook condition. And at all time, the new rollover index changes more sensitively
than fundamental LTR which is obtained using wheel vertical loads information. So, the validity
of new rollover index can be demonstrated.
In recent years, with the deepening of the research on vehicle rollover, many researchers
have improved the fundamental LTR. For example, Larish proposed a new predictive LTR that
can provide a time-advanced measure of rollover propensity and, therefore, offers significant
benefits for closed-loop rollover prevention [37]. And Li et al. introduced an improved predictive
LTR (IPLTR) as the rollover index based on an 8-DOF nonlinear vehicle model [38].
3.2 ROLLOVER WARNING
e above-mentioned rollover indexes are effective to monitor the process of vehicle. However,
it tends be too slow to actively prevent the rollover, especially for high CG vehicles with slow
brake actuators.
3.2.1 TIME-TO-ROLLOVER
e Time to Rollover (TTR) is one of the most efficient indicators in order to anticipate the
rollover detection. It is defined as the time remaining before wheel lift off will occur, which gives
a clear indication of the beginning of rollover. Chen and Peng used TTR which is computed
from yaw-roll model to prevent rollover for Sports Utility Vehicles [7]. Zhu et al. proposed
a conventional time-to-rollover warning algorithm which was presented based on the 3-DOF
vehicle model and used to investigate integrated chassis control to prevent vehicle rollover [39].
Dahmani et al. computed TTR by assuming that the LTR increases or decreases at its current
rate in the near future, compute the time taken by the LTR to reach 1 or 1, and then compared
the predictive effect of TTR and LTR. Considering that the vertical load of each wheel is difficult
to be measured or estimated in real time, it can be transformed into other expression, as shown
in Section 3.1.3. is is denoted by LTR
d
. e computational formula of TTR is shown as
follows [31, 40]:
TTR D
1 LTR
d
R
LTR
if LTR > 0 (3.10)
TTR D
1 LTR
d
R
LTR
if LTR < 0; (3.11)
with R
LTR
being the LTR rate, which is obtained from a filtered differential signal of the LTR.
In order to test the validity of TTR, two Fishhook tests are conducted with different
steering wheel angles, as shown in Figure 3.13. e input steering angle used in test 2 is defined
such that the wheel liftoff occurs at 2.8 s, whereas in test 1 no wheel liftoff occurs. In this
simulation, the vehicle is driven at a constant speed of 110 km/h in a 6% banked road.
Figure 3.14 shows the comparison of TTR in the two tests. TTR shows good efficiency for
the rollover detection, and the proposed rollover indicator, which is the TTR, bigger anticipation
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