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Dynamic Stability and Control of Tripped and Untripped Vehicle Rollover
Zhilin Jin, Bin Li, and Jingxuan Li
www.morganclaypool.com
ISBN: 9781681735603 paperback
ISBN: 9781681735610 ebook
ISBN: 9781681735627 hardcover
DOI 10.2200/S00916ED1V01Y201904AAT006
A Publication in the Morgan & Claypool Publishers series
SYNTHESIS LECTURES ON ADVANCES IN AUTOMOTIVE TECHNOLOGY
Lecture #6
Series Editor: Amir Khajepour, University of Waterloo
Series ISSN
Print 2576-8107 Electronic 2576-8131
Dynamic Stability and Control
of Tripped and Untripped
Vehicle Rollover
Zhilin Jin
Nanjing University of Aeronautics & Astronautics
Bin Li
Aptiv PLC
Jingxuan Li
Nanjing University of Aeronautics & Astronautics
SYNTHESIS LECTURES ON ADVANCES IN AUTOMOTIVE TECHNOLOGY
#6
C
M
&
cLaypoolMo
r
gan publishers
&
ABSTRACT
Vehicle rollover accidents have been a serious safety problem for the last three decades. Although
rollovers are a small percentage of all traffic accidents, they do account for a large proportion of
severe and fatal injuries. Specifically, some large passenger vehicles, such as large vans, pickup
trucks, and sport utility vehicles, are more prone to rollover accidents with a high center of gravity
(CG) and narrow track width. Vehicle rollover accidents may be grouped into two categories:
tripped and untripped rollovers. A tripped rollover commonly occurs when a vehicle skids and
digs its tires into soft soil or hits a tripping mechanism such as a curb with a sufficiently large
lateral velocity. On the other hand, the untripped rollover is induced by extreme maneuvers
during critical driving situations, such as excessive speed during cornering, obstacle avoidance,
and severe lane change maneuver. In these situations, the forces at the tire-road contact point
are large enough to cause the vehicle to roll over. Furthermore, vehicle rollover may occur due
to external disturbances such as side-wind and steering excitation. erefore, it is necessary to
investigate the dynamic stability and control of tripped and untripped vehicle rollover so as to
avoid vehicle rollover accidents.
In this book, different dynamic models are used to describe the vehicle rollover under both
untripped and special tripped situations. From the vehicle dynamics theory, rollover indices are
deduced, and the dynamic stabilities of vehicle rollover are analyzed. In addition, some active
control strategies are discussed to improve the anti-rollover performance of the vehicle.
KEYWORDS
vehicle rollover, dynamic stability, tripped rollover, rollover index, rollover warning,
anti-roll control, active safety of vehicle
vii
Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 What Is Vehicle Rollover? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Risk of Vehicle Rollover Accidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Factors Affecting Vehicle Rollover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2
Dynamic Model of Vehicle Rollover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Roll Plane Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Yaw-Roll Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Lateral-Yaw-Roll Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Yaw-Roll-Vertical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Multi-Freedom Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.6 Multi-Body Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3
Stability of Untripped Vehicle Rollover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 Roll Index of Untripped Vehicle Rollover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 Static Stability Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.2 Dynamics Stability Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.3 Lateral Load Transfer Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Rollover Warning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Time-to-Rollover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.2 Prediction Rollover Warning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4
Stability of Tripped Vehicle Rollover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1 Roll Index of Tripped Vehicle Rollover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.1 Rollover Index on Uneven Roads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.2 Rollover Index on Banked Roads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Energy Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
viii
5
Active Control for Vehicle Rollover Avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.1 Anti-Roll Bar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Active Suspension System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.3 Active Steering System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.3.1 Active Front Steering Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3.2 Pulse Active Rear Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3.3 Four-Wheel Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.4 Active Braking System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.5 Integrated Chassis System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6
Rollover Control Strategies and Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.1 Proportional-Integral-Derivative Control Method . . . . . . . . . . . . . . . . . . . . . . 61
6.2 H-infinity Control Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.3 Model Prediction Control Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.4 Linear Quadratic Regulator Control Method . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.5 Sliding Mode Control Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
A
Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Authors’ Biographies
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
111
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