A CAE-BASED STUDY OF REDUCTION OF CRASH AGGRESIVITY OF PICKUP TRUCKS

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A CAE-BASED STUDY OF REDUCTION OF CRASH AGGRESIVITY
OF PICKUP TRUCKS
A Thesis by
Vikram Krishnamurthy
B.E., Bangalore University, 2001
Submitted to the Department of Mechanical Engineering
and the faculty of the Graduate School
of Wichita State University in partial fulfillment of
the requirements for the degree of
Master of Science
December 2005
A CAE-BASED STUDY OF REDUCTION OF CRASH AGGRESIVITY
OF PICKUP TRUCKS
I have examined the final copy of this thesis for form and content and recommend that it
be accepted in partial fulfillment of the requirements for the degree of Master of Science
with a major in Mechanical Engineering.
__________________________________
Hamid M. Lanakarani, Committee Chair
We have read this thesis and recommend its acceptance:
___________________________________
Kurt Soschinske, Committee Member
___________________________________
Gamal Weheba, Committee Member
ii
DEDICATION
To my Parents
iii
You say the hill's to steep to climb, climbing
you say you'd like to see me try, climbing
you pick the place and I'll choose the time
and I'll climb the hill in my own way
just wait a while for the right day
and as I rise above the tree-line and the clouds
I look down, hearing the sounds of the things you've said today
……
“Fearless” -- Meddle
Pink Floyd
When someone is seeking
...it happens quite easily that he only sees the thing that he is seeking;
that he is unable to find anything, unable to absorb anything
...because he is obsessed with his goal.
Seeking means: to have a goal;
but finding means: to be free, to be receptive, to have no goal."
Chapter 12, Page 113
Siddhartha
Hermann Hesse
There is a road, no simple highway,
between the dawn and the dark of night,
and if you go,
no one may follow,
that path is for your steps alone.
Jerry Garcia
iv
ACKNOWLEDGEMENTS
I would like to thank Dr. Hamid Lankarani for advising and guiding me through
my graduate education at Wichita State University. Thank you Dr.Lankarani. I would
also like to thank my committee members, Dr. Kurt Soschinske and Dr. Gamal Weheba,
for giving their time in support of this thesis.
I would also like to take this opportunity to extend my deepest gratitude to
Natesan and his loving family for all their support and encouragement.
Finally, I need to thank all my friends who have supported, encouraged, and
inspired me throughout my life.
v
ABSTRACT
During the past few years, the disparity in the structural design of light trucks and
vans (LTVs) and passenger cars and the number of fatalities involved in these vehicles
has become a growing concern among automobile manufacturers. In order to characterize
the problem of compatibility, the National Highway Transport Safety Authority
(NHTSA) has defined an aggresivity metric (AM) as the ratio of driver fatalities in the
collision partner to the number of crashes of the subject vehicle. The aggresivity metric
did prove that the sport utility vehicle (SUV) and LTV class of vehicles were
substantially more aggressive than the rest of the class of vehicles but failed to highlight
the main factor(s) responsible for it. Current research has established that the aggresivity
of vehicles involved in frontal crashes is mainly affected by geometric interaction,
vehicle stiffness, and vehicle mass.
The present study describes a methodology to reduce the aggresivity of pickup
trucks using a Computer—Aided Engineering (CAE) combined with a Design of
Experiments (DOE) approach. Computer—aided crash simulations using finite element
models of an average pickup truck and a small car using LS-DYNA (an explicit finite
element program) and MAthematical DYnamic MOdelling (MADYMO, a multi-body
occupant simulation program) are used to study the vehicle structural deformation and the
occupant’s injury responses.
Categorical responses of small car: intrusion, combined injury index and internal
energy ratio are observed by varying the mass, stiffness, and overlap between the energy
absorbing structures of the vehicles. The variation was modeled to approximately
represent an entire fleet of pickup trucks. Statistical analyses showed that mass is one of
vi
the major factors influencing the overall aggresivity of pickup trucks. Regression
equations showed good correlation to the actual tests and can be used to predict responses
for factor variation within the design space. The overlay plots reveal that reduction in
mass leads to increase in optimum region.
vii
TABLE OF CONTENTS
Chapter
1.
INTRODUCTION ...................................................................................................1
1.1
1.2
1.3
2.
2.5
2.6
2.7
History of Vehicle Safety.............................................................................6
Automotive Structure...................................................................................7
Occupant Safety ...........................................................................................8
Crash Induced Injuries .................................................................................9
2.4.1 Injury Criteria...................................................................................9
2.4.2 Tolerance to Injuries ......................................................................14
Crashworthiness.........................................................................................16
Vehicle Safety Tests ..................................................................................17
2.6.1 FMVSS 208 ..................................................................................18
2.6.2 NCAP............................................................................................19
2.6.3 IIHS Offset Test............................................................................20
2.6.4 Effect of Safety Tests....................................................................20
Compatibility .............................................................................................21
2.7.1 Aggresivity and Aggresivity Metric ..............................................23
SYSTEM SETUP...................................................................................................27
3.1
3.2
3.3
3.4
4.
Motivation....................................................................................................1
Literature Review.........................................................................................2
Objective ......................................................................................................5
BACKGROUND .....................................................................................................6
2.1
2.2
2.3
2.4
3.
Page
Formulation................................................................................................28
3.1.1 Validation......................................................................................31
Selection of Design Variables....................................................................34
3.2.1 Mass ...............................................................................................34
3.2.2 Stiffness..........................................................................................35
3.2.3 Overlap...........................................................................................38
3.2.4 Constant Variables .........................................................................40
3.2.5 Response Variables........................................................................40
Design of Experiment ................................................................................41
3.3.1 Factorial Design .............................................................................42
3.3.2 Optimization Methodology............................................................43
Simulations ................................................................................................44
RESULTS ..............................................................................................................45
4.1
Finite Element Simulations........................................................................45
viii
4.2
4.3
4.4
5.
Response Surface ......................................................................................51
4.2.1 Pair-Wise Comparison ...................................................................51
Regression Analysis...................................................................................57
Optimization ..............................................................................................57
DISCUSSION .......................................................................................................61
5.1
5.2
Conclusions................................................................................................61
Future Research .........................................................................................61
LIST OF REFERENCES...................................................................................................67
ix
LIST OF TABLES
Table
Page
1.
Summary of Recommended Injury Criteria for the Final Rule ................................15
2.
Chevy C1500 and Geo Metro Model Definition ......................................................29
3.
Range of Mass Selected for the Study ......................................................................35
4.
Range of Stiffness Selected for the Study.................................................................37
5.
Selected Response Variables ....................................................................................40
6.
Stat Ease Design Matrix............................................................................................43
7.
Effects List for Dashboard Intrusion.........................................................................52
8.
ANOVA Results for Dashboard Intrusion................................................................52
9.
Effects List for Internal Energy Ratio.......................................................................54
10.
ANOVA Results for Internal Energy Ratio ..............................................................55
11.
Effects List for Combined Injury Index (Pcomb) ........................................................56
12. ANOVA Results for Combined Injury Index (Pcomb) ...............................................57
13.
Comparison of Regression and Actual Results.........................................................58
x
LIST OF FIGURES
Figure
Page
1.
Car occupant fatalities during 2000-03.......................................................................1
2.
Different vehicle structural designs ............................................................................8
3.
Neck injury criteria1 .................................................................................................11
4.
Deaths per 1,000 crash injuries by age and sex ........................................................15
5.
Injuries per 1,000 AIS 2—6 injuries (moderate to maximum).................................15
6.
Different crash configurations ..................................................................................17
7.
Vehicle to barrier tests (reproduced from www.safecarguide.com) .........................18
8.
Front-end profiles of an LTV, a passenger car a small car.......................................22
9.
Mass and stiffness values from NCAP tests .............................................................23
10.
U.S. sales and registrations of LTV and cars............................................................24
11.
Overall aggresivity metric ........................................................................................25
12.
Aggresivity metric frontal-frontal.............................................................................26
13.
Driver fatalities for frontal-frontal in LTV-car crashes ............................................26
14.
Adopted methodology ..............................................................................................27
15.
Finite element models of Chevy C1500 (left) and Geo Metro (right) ......................28
16.
MADYMO interior model of Geo Metro .................................................................30
17.
Inflation of airbag .....................................................................................................30
18.
Head and chest acceleration validation for the MADYMO model ..........................31
19.
NCAP rigid barrier test setup for C1500 ..................................................................32
20.
Placement of accelerometers in C1500.....................................................................32
xi
21.
Acceleration and velocity profiles for C1500 (simulation-blue, actual-red) ............32
22.
Post test view for C1500 (simulation-left, actual-right) ...........................................32
23.
NCAP rigid barrier test setup for Metro ...................................................................33
24.
Placement of accelerometers in Metro......................................................................33
25.
Acceleration and velocity profiles for Metro (simulation-blue, actual-red).............33
26.
Post test view for Metro (simulation-left, actual-right) ............................................33
27.
Mass-stiffness plot for determining the zone of consideration.................................34
28.
Force-deflection of 35 mph NCAP test ....................................................................36
29.
Stiffness calculation at 240 mm of crush..................................................................37
30.
Energy distribution and percentage for Chevy C1500 in NCAP test .......................38
31.
Parts selected for the stiffness variation ...................................................................38
32.
Baseline model and the two levels of overlap ..........................................................39
33.
Parts used to calculate nodal displacements .............................................................41
34.
Model configuration at 0 milliseconds .....................................................................45
35.
Crash simulation representing M, S, and O variable levels......................................46
36.
Intrusion levels..........................................................................................................47
37.
Normalized intrusion levels ......................................................................................48
38.
Percentage energy absorbed......................................................................................49
39.
Normalized IE ratio ..................................................................................................49
40.
Pcomb index ................................................................................................................50
41.
3D plot of the dashboard intrusion at stiffness low (left) and high (right) ...............53
42.
3D plot of the dashboard intrusion at stiffness mass (low) ......................................53
43.
Cube plot of the dashboard intrusion........................................................................53
xii
44.
Pair-wise comparison of internal energy ratio..........................................................55
45.
Factor effects on Pcomb, Pair-wise (left), mass effect (right) .....................................57
46.
Optimal region based on constraints at mass (low) ..................................................59
47.
Optimal region based on constraints at mass (medium-top, high-bottom)...............60
xiii
LIST OF ABBREVIATIONS
AIS
Abbreviated Injury Scale
AM
Aggresivity Metric
ATD
Anthromorphic Test Dummy
CAE
Computer—Aided Engineering
CTI
Combined Thoracic Injury
DOE
Design of Experiments
FARS
Fatal Accident Reporting System
FE
Finite Element
FMVSS
Federal Motor Vehicle Safety Standards
GES
General Estimates System
GSI
Gadd Severity Index
HIC
Head Injury Criteria
IARV
Injury Assessment Reference Values
IE
Internal Energy
IIHS
Insurance Institute of Highway Safety
LS-DYNA
Explicit Finite Element Software developed by LSTC
LTV
Light Truck and Van
MADYMO
MAthematical DYnamic MOdelling
MPH
Miles Per Hour
NASS
National Accident Sampling System
NCAC
National Crash Analysis Center
NCAP
New Car Assessment Program
xiv
NHTSA
National Highway Transport Safety Authority
NPRM
Notice of Proposed Rule Making and Order
SUV
Sport Utility Vehicle
xv
CHAPTER 1
INTRODUCTION
1.1
MOTIVATION
In 2003, Sport Utility Vehicles (SUVs) accounted for 20 percent of registered
passenger vehicles, up from 13 percent. Meanwhile, during the same time, the percentage
of cars dropped to 58 percent from 68 percent, in a decade. This highlights a serious issue
in the present crash environment because the increasing fatalities in collisions between
car and a light pickup truck (LTV) are not only due to the aggressive behavior of LTVs
but also due to the increasing number of stiffer and incompatible structures involved in
collisions. Figure 1 shows car occupant fatalities during 2000-03 [1]. The fatalities in
car-LTVs accounted for nearly 18 percent of fatalities and are the highest in the vehiclevehicle category.
The aggresivity metric (AM) as defined by National Highway
Transport Safety Administration (NHTSA), ranges from 69.27 for large pickups, 30.62
for large SUVs, 14.09 for large cars, and 5.45 for minicars [2]. This vast variation must
be carefully studied to evaluate the possible factors affecting aggresivity. In the case of
vehicle—to—vehicle collisions among different classes of vehicles, a fine balance needs
to be maintained when attempting to effectively alter the aggresivity of vehicles.
42
Single Car
Car-Car
Car-Big Truck
15
16
7
Car-PU
Car-SUV
11
9
Car- 2+
Figure 1. Car occupant fatalities during 2000-03.
1
Reduction
of
aggresivity
may
or
may
not
correspond
to
increased
crashworthiness. The predictive power of computer—aided engineering can be utilized to
form a tool to predict the aggresivity of not only newly introduced vehicles but also
vehicles that are still in the conceptual stage.
1.2
LITERATURE REVIEW
Since the problem of compatibility was first addressed, several institutions,
individual researchers, and automobile manufacturers have explored different facets in
this field. This section, presents some of the research which mainly deals with analytical
and experimental methods used to study the issues of compatibility and aggresivity.
Summers etal. [2] are some of the pioneers who identified the growing concern of
SUV sales in the United States, the increasing fatality rates in car-LTV crashes. They also
introduced the aggresivity metric (AM) and calculated the relative metric for different
classes of vehicles and also sub-divided those into different crash configurations. They
also describe experimental tests conducted using pickups, passenger cars, minivans, and
SUVs. Their results were then correlated into the aggresivity metric.
Brown etal [3] focused on the effectiveness of combining Design of Experiments
(DOE) techniques with conventional Finite Element (FE) analysis and using these
methods to understand the behavior of incompatible structures. They describe principles
that must be followed while designing an experiment. The public domain model of a Ford
Taurus was used in a Taurus-Taurus crash configuration with a 40% offset configuration.
Design variables were selected: mass, front—end stiffness, and available crush length for
each vehicle; and the longitudinal relative height and the vehicle closing speed. Ten
response variables: B post acceleration, footwell intrusion, A pillar intrusion, longitudinal
2
average load and the longitudinal crush for each vehicle were studied. One of the most
significant factors—the time taken to build a model based on the selected combination of
design variables was also considered while deciding upon the DOE matrix. The DOE
model allowed the interrelationships between mass, stiffness, and height to be studied in
detail. It was concluded that closing speed was one of the most influential factors.
Occupant injuries were not considered for this study.
Lee etal [4] used robust parametric studies and structural optimization
methodologies to study the complex design parameters and geometric changes. Study
Wizard, a software tool specifically designed for conducting parametric analytical studies
was used for this study. The main objective of the paper was to identify how vehicle
safety may be improved by structural changes that are designed to interact better during
the crash and by restraint systems that are designed to act properly in the secondary
collision for each. They used oblique offset vehicle to vehicle crash tests to study the
relationship between aggresivity and injuries. Their paper provides an excellent resource
on response surface optimization for crash problems. This DOE study is followed by an
optimization study, the former of which acts as a screening study for the factors
considered using four parameters: engine position, front member inner thickness, sub
frame thickness, and dash lower panel thickness. The results of the DOE show that the
engine position and sub frame have more effect on both deceleration and displacement
responses. The final results of the optimization study were not reported in this paper.
Barbat etal. [5] described a CAE—based optimization methodology for a fullfrontal vehicle-to-vehicle configuration using the finite element models of an average
SUV and an average full-size passenger vehicle. Four variables of the SUV selected for
3
this study included the following: mass, fore rail thickness, fore rail length, and fore rail
height were selected for this study. Latin Hypercube sampling technique was used to
form the simulation matrix. Dash intrusions in the passenger vehicle and the absorbed
collision energy in both the vehicles were response variables. Prediction equations were
developed based on the response surfaces for the selected response variables.
Results indicated that aligning front-end structures has a greater effect on the
responses than mass and stiffness variables. Additionally, the effect of thickness was
observed to be greater than that of mass on maximum dash intrusion. The optimal SUV
configuration showed that the minimum dash intrusion was obtained with the aligned fore
rail, reduced mass, and fore rail thickness, which can be translated to the lightest, least—
stiff and best—aligned SUV. Some important factors like the effect of reduced stiffness
on the SUV’s crashworthiness and occupant responses were not considered in this study.
Kuchar [6] explains a methodology consisting of a parametric three-dimensional
kinematic simulation of crash events. The response was simulated using computational
models that are one—dimensional lumped-parameter systems, with three discrete masses
representing the occupant compartment, engine, and wheels. The models were simulated
and developed using the Structural Impact Simulation And Model Extraction (SISAME)
program. Head and chest injury results for each case were converted to harm vectors in
terms of probabilistic Abbreviated Injury Scale (AIS) distributions based on previously
defined risk analyses.
This methodology was applied to single—and two—vehicle frontal collisions
among passenger cars and light trucks. The model was validated against injury field data
and found to accurately reflect the trends in distribution of injury severity. The model
4
was used for variable sensitivity analyses, wherein changes in LTV/car population mix
and other parameters were evaluated in terms of their effect on occupant harm within the
subset crash environment.
1.3
OBJECTIVE
The solution for developing a compatible fleet is a very tedious process and more
so because the existing safety standards reflect only the crashworthiness of vehicles and
not their compatibility with the rest of the fleet. This study aims to find an optimum
solution for the aggresivity of a pickup truck using CAE based optimization techniques.
5
CHAPTER 2
BACKGROUND
In 1889, New York City recorded the first motor vehicle fatality. This event is
believed to have led to the birth of the field of automotive safety. The past decade has
seen an increase in awareness about vehicle safety from not only consumers but also
manufacturers who started to regard safety as a core design objective. This chapter will
briefly discuss the history of automotive safety and introduce few definitions that were
used throughout this study.
2.1
HISTORY OF VEHICLE SAFETY
Automotive historians have identified three distinct periods in the development of
automotive safety [7]. The first period from the start of the century to early 1935 saw the
development of understanding of the complex process of vehicle collisions. Some of the
basic improvements such as a reduction of tire blowouts, introduction of the self starter,
headlamps for better visibility, laminated glass, and adopting an all-steel body structure
were carried out during this period. The first full-scale crash test was carried out with
car—to—barrier and rollover simulations. The estimated fatality rate in 1935 was
approximately 17 per million.
The second period from 1935 to 1965 was the intermediate safety period.
Collision avoidance systems like turn signals, improved headlamps, and dual windshield
wipers were introduced by manufacturers. Tests simulating the head impacting the
instrument panel were carried out, and GM conducted the first car-to-barrier frontal crash
test. Vehicles were evaluated according to the observed deformation in the vehicle. One
6
of the most significant safety devices introduced during this era were seat belts as an
option in 1956.
The third period started in 1966, with the creation of the NHTSA. Federal Motor
Vehicle Safety Standards (FMVSS) were introduced and dealt with several aspects of the
vehicle development process. Over the past seven decades, vehicle safety improvements
have focused on crash avoidance technology, structural crashworthiness, and occupant
protection devices, which did show a significant decrease in fatality rates. Today, the
automotive industry is focused on not only the above factors but also driver performance,
driver behavior, ergonomics, highway or road construction, and accident avoidance
systems.
Current legislation also has a strong influence on safety. The third period saw
safety become a competitive item for medical, technical scientists, legislators, and more
importantly to automotive engineers. There was an added effect by consumer advocates
such as Ralph Nader, who championed the need for automobile manufacturers being held
responsible for not only faulty designs but also for fatalities that vehicles caused to their
occupants.
The increasing number of consumer information reports, such as
crashworthiness rating reports issued by institutes like Insurance Institute for Highway
Safety (IIHS), Highway Loss Data Institute, has made more information available to the
public about the performance of vehicles. This has led to consumers ranking safety
features as extremely or very important when buying new cars.
2.2
AUTOMOTIVE STRUCTURE
The first patent in the field of vehicle body design relating to safety was published
in 1952 by Bela Bareny. In this patent, he described how structural strength should be
7
greatest in the vehicle compartment and that the front and rear of the vehicle should less
resistant to crushing and capable of absorbing energy during a crash [8]. The evolution of
automotive structure design has been subject to the need to satisfy consumers and many
constraints like materials and energy availability, safety regulations, competition and
manufacturing capabilities. Figure 2 (a), (b), and (c) shows the body-over frame, unitbody design and the ladder frame, respectively. The type of materials used in the
construction has been traditionally steel but current trends have shifted to aluminum and
composites for body panels both of which provide excellent weight reduction.
(c)
(a)
(b)
Figure 2. Different vehicle structural designs.
2.3
OCCUPANT SAFETY
The field of vehicle safety, which focuses on the protection, provided to
passengers a vehicle in a collision, either from the interiors, the restraint system or the
vehicle structure itself, is termed occupant safety. Typical safety systems include
8
collapsible steering systems, safety windshields, belt restraints, and airbags. It is now
common knowledge that belt restraints and airbags have become the two most important
safety devices that reduce the fatality rates considerably.
2.4 CRASH INDUCED INJURIES
This section briefly discusses some common terminology relating to the structure
of the human body and injuries [9]. Anatomy is defined as the study of the body’s
structure, and describing the shape and location of various parts of the body. Usually the
body is referenced according to subdivisions like the head, neck, upper extremities, lower
extremities, and torso. The torso can be further subdivided into upper region, thorax and
lower region, or abdomen.
Vehicle-related injuries may occur to various body regions. Head injuries may be
due to injuries to the skin, bones, or the contents of the skull, or combination. Injuries to
the chest might occur due to a blunt impact (e.g., with the steering wheel), which will
result in compression of the ribcage or even fracture in a severe case. In the lower
extremities, the pelvis might fracture or displace. When a person is seated, bones in the
lower extremities like the femur, tibia, and fibula, may be fractured upon impact with the
vehicle interiors, such as knee bolster.
2.4.1 INJURY CRITERIA
Injury criteria have been developed to address the mechanical responses of crash
test dummies in terms of risk to life or injury to a living human. The different injury
criteria developed for the NHTSA’s FMVSS 208 frontal crash protection program are
presented in this section [10].
9
2.4.1.1
HEAD
Injuries to the head are responsible for 50,000 deaths and nearly one million
hospitalizations per year in the United States. Motor vehicle crashes are responsible for
nearly half of these head injuries. Head injury continues to be a leading cause of death
and disability [10].
A relationship known as the Wayne State Tolerance Curve (WSTC) between the
acceleration level and impulse duration with respect to head injury indicated a decreasing
tolerable level of acceleration as duration increased. WSTC has become the foundation
upon which most currently accepted indexes of head-injury tolerance are based. The
original data only covered a time duration range of 1 to 6 milliseconds but was later
extended to durations above 6 milliseconds.
The WSTC data was plotted by Gadd on log paper and an approximate straight—
line function was developed for the weighted impulse criterion that eventually became
known as the Gadd Severity Index (GSI).
In response to a study of the analysis of the relationship between the WSTC and
the GSI by Versace in 1971, a new parameter, the Head Injury Criterion (HIC), was
defined by NHTSA in 1972. The HIC is currently used to assess head injury potential in
automobile crash test dummies. It is based on the resultant translational acceleration
rather than the frontal axis acceleration of the original WSTC. HIC is computed as
(2.1)
10
where t2 and t1 are any two arbitrary times during the acceleration pulse. HIC is unique
among FMVSS 208 injury criteria in that the HIC limit of 1,000 was not based on tests
where HIC was measured and injuries observed. The HIC has no specific meaning in
terms of injury mechanism.
The NHTSA proposed time interval was reduced to 15 milliseconds from 36
milliseconds but it limited the maximum time interval to 36 milliseconds with
acceleration rising to a limit of 60 g. The analyses of data from the New Car Assessment
Program (NCAP) and FMVSS No.208 showed that almost all the vehicles had a value of
HIC15 ≤ 700, and the average HIC values for the driver was 222.
2.4.1.2
NECK
The concept that a composite neck injury indicator based on a linear combination
of axial tension loads and extension (rearward) bending moments was developed in 1984
by Prasad and Daniel [10] using their results from experimental tests on porcine subjects.
Based on their formulation for a three—year old dummy, the allowable region in the
tension/extension quadrant of the plot becomes the shaded area shown in Figure 3.
Figure 3. Neck injury criteria.
11
Any test falling above the diagonal line in this plot would exceed the tolerance
levels suggested by Prasad and Daniel and was expanded to include the four major
classifications of combined neck—loading modes, namely, tension-extension, tensionflexion, compression-extension, and compression-flexion. Proposed critical intercept
values for tension load, compression load, extension moment, and flexion moment were
established. The resulting criteria are referred to as Nij, where “ij” represents indices for
the four injury mechanisms: namely NTE, NTF, NCE, and NCF. The first index
represents the axial load (tension or compression) and the second index represents the
sagittal plane bending moment (flexion or extension). The intercept values shown are
those proposed for the Hybrid III mid-sized male dummy. The proposed neck injury
criteria can thus be written as the sum of the normalized loads and moments as
(2.2)
where FZ is the axial load, Fint is the corresponding critical intercept value of load used
for normalization, MY is the flexion/extension bending moment computed at the occipital
condyles, and Mint is the corresponding critical intercept value for moment used for
normalization.
2.4.1.3
CHEST
Classic work by Stapp, Mertz and Gadd led to the development of the injury
threshold for chest acceleration of 60 g. The first injury assessment recommendation for
the rib cage and underlying organs using chest deflection was developed by Neathery et
al. [10] for blunt frontal loading. They recommended a chest injury assessment value of
three inches maximum sternal compression for a 50th percentile male in blunt frontal
12
impact. This recommendation represented a 50 percent risk of an AIS 4+ thoracic injury
for a 45— year—old human.
An injury criteria using chest deflection alone may not have predicted the correct
injury level under such circumstances as well as the linear combination of deflection and
acceleration. It is believed that the linear combination model using Dmax and As is the
most appropriate injury criteria for assessing thoracic trauma. However, since only one
deflection measurement is available on most dummies, the central chest deflection will be
used with this formulation. The equation of the 50 percent probability of injury line using
the deflections adjusted for skin thickness is mathematically equivalent to a line that has
intercepts on the vertical and horizontal axes of Dint = 103 mm and Aint = 90 g,
respectively. Thus, the combined thoracic injury criteria, CTI, is defined as
(2.3)
where Amax is the maximum value of 3 ms clip spinal acceleration (As), Dmax is the
maximum value of the dummy deflection (D), and Aint and Dint are the respective
intercepts as defined above. In order to harmonize with the Injury Assessment Reference
Values (IARV) used by Transport Canada, the chest deflection limit for the 50 percent
male was taken to be 63 mm (2.5 inches), and a 3-msec clip value of resultant chest
acceleration limit was taken to be 60 g. Therefore, the recommended performance limits
are Ac = 60 g and Dc = 63 mm for the 50 percent male. The proposed CTI injury criteria
from the Notice of Proposed Rule Making and Order (NPRM) will be used for estimating
the probability of injury.
13
2.4.1.4
FOOT AND LOWER EXTREMITIES
A vast amount of research is currently being conducted to better understand the
complex mechanisms of foot and ankle injuries. The existing IARV for femur load used
in FMVSS 208 is 10 KN for the 50th percentile male. The tibia index was originally
proposed by Mertz [10] as an injury tolerance criterion for the leg which combines the
bending moment and axial compressive loads on the leg, as measured by the Hybrid III
tibia load cell. The modified version of the tibia index (TI) adopted by EEVC is given by
(2.4)
where F is the measured compressive axial force (kN) in the superior-inferior direction
and M is the resultant moment of the medial-lateral and anterior-posterior moments.
2.4.2 TOLERANCE TO INJURIES
It has been observed that the age of the driver has a very strong influence on
tolerance to injuries. Younger drivers tend to get into more severe collisions; older
drivers are more likely to die from their injuries [12]. Evans [13] found that the risk of
fatal injuries increased three times at age 70 than at 20. Drivers from about age 30 to 60
have the lowest involvement rates. As age decreases below 30, rates increase at an
increasing rate but for ages greater than 60, the rates increase much less rapidly. The risk
of crashes is higher among the 16 to19—year—olds than any other age group. In fact, per
mile driven, a 16-year-old driver is seven times more likely to crash than a driver 25 to 29
years old. Drivers 65 and older have higher crash death rates per mile than all others,
except teen drivers [14]. See Figures 4 and 5 [15]. To control for this age effect during
14
the initial analysis, only drivers of ages 26 to 55 were selected for calculating the
aggresivity metric.
Figure 4. Deaths per 1,000 crash
injuries by age and sex.
Figure 5. Injuries per 1000 AIS 2-6 injuries
(Moderate to Maximum).
TABLE 1
Summary of Recommended Injury Criteria for the Final Rule [16]
Large
Sized
Male
MidSized
Male
Small
Sized
Male
Head Injury Criteria: HIC (15msec)
700
700
Neck Criteria: Nij
In position Critical Intercept Values
Tension (N)
Compression (N)
Flexion (N)
Extension (N)
Peak Tension (N)
Peak Compression (N)
1.0
1.0
8216
7440
415
179
5030
4830
N/A
6806
6160
310
135
4170
4000
N/A
4287
3880
155
67
2620
2520
Recommended Criteria
Neck Criteria: Nij
Out-of- Position
Tension (N)
Compression (N)
Flexion (N)
Extension (N)
Peak Tension (N)
Peak Compression (N)
Thoracic Criteria
1. Chest Acceleration (g)
2. Chest Deflection (mm)
Lower Ext. Criteria
Femur Load (KN)
6 YO
Child
3 YO
Child
1 YO
Infant
700
700
700
700
1.0
N/A
N/A
N/A
1.0
1.0
1.0
1.0
3880
3880
155
61
2070
2800
2800
93
37
1490
2120
2120
68
27
1130
1460
1460
43
17
780
2520
1820
1380
960
55
70 (2.8
in)
60
63 (2.5
in)
60
52 (2.0
in)
60
40 (1.6
in)
55
34 (1.4
in)
50
30 (1.2
in)
12.7
10.0
6.8
NA
NA
NA
15
2.5
CRASHWORTHINESS
Crashworthiness is a qualitative measure used to define the ability of the structure
to protect its occupants in collisions. The present automotive structure designs seek to
mitigate two adverse effects of a crash: 1) rapid deceleration of the passenger
compartment, and (2) crush of the passenger compartment survival space, which must be
minimized. The front-end of vehicles are designed to crumple in a controlled manner in a
collision. These progressive crush zones absorb the kinetic energy. But in a severe
collision, the intrusions may extend into the passenger compartment causing injuries.
The goal of all vehicle designers is an optimized structure that can absorb the crash
energy by controlled vehicle deformations while maintaining adequate space so that any
residual crash energy can be managed by the restraint systems.
In the real world vehicles can collide with vehicles of a similar or different size or
mass or they might collide with a stationary structure like a tree or pole, or they may
experience a single or multiple collisions. Almost all collisions can be classified into four
different types, based on the manner in which the collision happens: frontal, side, and
rear as shown in Figure 6.
The constraints that designers and engineers face when designing a new vehicle
are that the structure be crashworthy, be light to improve efficiency and increase mileage,
and be economically mass producible. Another real concern that engineers have is the
safety of the occupant, so that decelerations transmitted to occupants are well within
human tolerance limits. A crash deceleration pulse with an early peak in time and a
gradual decay reduces the potential of injury to restrained occupants.
16
Manufacturers employ a variety of methods to assess the vehicle’s performance
before the vehicle is manufactured. The earliest safety evaluation was started by General
Motors in 1934, where they launched a vehicle into a rigid barrier.
Frontal (Head-On) Collision
Oblique/Angled Collision
Side Collision
Rear-end Collision
Figure 6. Different crash configurations.
2.6
VEHICLE SAFETY TESTS
The two organizations: NHTSA and Insurance Institute for Highway Safety
(IIHS) use crash testing to determine the crashworthiness of vehicles. Beginning in the
1960’s, both the organizations began examining at automobile safety when the public
became more aware of the issue as a result of the book, Unsafe at Any Speed, in which
author Ralph Nader revealed the safety issues associated with the Chevrolet Corvair. In
1967, the first safety regulation, the Federal Motor Vehicle Safety Standards (FMVSS),
No.209 was introduced. The federal standards, now, range from how bright the turn
signal bulbs must be to the crash-testing requirements. NHTSA only started conducting
17
crash tests in 1978, and the IIHS, which is supported by automobile insurance companies,
didn't begin its crash testing for consumers until 1995.
Currently, NHTSA and the IIHS perform both frontal and side crash testing, the
tests however differ from each other. Following is a brief description of the different
frontal crash tests conducted in the U.S.
2.6.1 FMVSS 208
The FMVSS No. 208 defines the requirements for occupant protection in a frontal
crash with the use of restraints and airbags. Testing is conducted with a full-scale vehicle
impacting a rigid barrier from 0 to 30 mph and impact angles from 0 to 30 degrees, as
shown in Figure 7 [17].
Figure 7. Vehicle to barrier tests.
Occupant responses are calculated using an anthropomorphic test dummy (ATD).
This standard originally specified the type of occupant restraints (i.e., seat belts) required.
It was amended to specify performance requirements for ATDs seated in the front
outboard seats of passenger cars and of certain multi—purpose passenger vehicles,
trucks, and buses, including active and passive restraint systems. The purpose of the
standard is to reduce the number of fatalities and the number and severity of injuries to
occupants involved in frontal crashes.
18
2.6.2 NCAP
NCAP was initiated in 1978 with the primary purpose of providing consumers
with a measure of the relative safety potential of vehicles in frontal crashes. Side—crash
rating results were added to the program beginning with model year 1997 vehicles, and
more recently rollover ratings were added beginning with model year 2001 vehicles.
The ultimate goal of NCAP is to improve occupant safety by providing market
incentives for vehicle manufacturers to voluntarily design their vehicles to better protect
occupants in a crash and be less susceptible to rollover, rather than by regulatory
directives [17].
Testing is similar to FMVSS 208, except for the increased impact speed of 35
mph and the use of restraints in addition to airbags. The rigid barrier test is equivalent to
a head-on collision between two similar vehicles, each moving at 35 mph. NHTSA rates
the cars based on how likely the occupants are to be injured during a crash and gives the
vehicle a star rating based on the percent chance of serious injury to the head and chest. A
serious injury is one requiring immediate hospitalization and may be life threatening.
NHTSA's star ratings are as follows:
= 10% or less chance of serious injury
= 11% to 20% chance of serious injury
= 21% to 35% chance of serious injury
= 36% to 45% chance of serious injury
= 46% or greater chance of serious injury
19
2.6.3 IIHS OFFSET TEST
The frontal test that the IIHS conducts is offset, meaning that only one side of the
vehicle's front end is hit. The vehicle being tested strikes a deformable barrier on the
driver side at 40 mph, which means the forces are similar to a frontal offset crash
between two vehicles of the same weight that are each traveling at just under 40 mph.
About 40 percent of the front end of the vehicle is impacted. The IIHS ranks the vehicles
it tests in one of four positions: Good, Acceptable, Marginal, or Poor. Ratings do not
correlate to a chance of injury as in the government's test, because the IIHS is assessing
more than just occupant injury. It is also looking at how well the vehicle structure
performs and the movement of the dummy, such as a partial ejection from the vehicle.
2.6.4 EFFECT OF SAFETY TESTS
Even though the different safety tests have a common goal of increasing the
safety of occupants in a vehicle, the effect of these tests on fatality rates had not been
studied till recently. It was observed [18] that the NCAP scored have improved steadily
since the inception of the program, with the greatest improvement in the early years. By
now, most of the passenger cars meet FMVSS No. 208 criteria in the 35 mph NACP test.
A 20 to 25 percent reduction in the fatality risk for belted drivers in actual head-on
collisions between passenger cars has been observed.
In 1998, an issue was raised by the vehicle manufacturers about the need to
design stiffer LTV structures due to the NCAP tests, which in turn led to increased
aggresivity. A study [19] conducted by NHTSA involving the frontal crash test results of
175 LTVs concluded that the total crush of the LTVs has increased, the peak deceleration
20
has decreased, and the time duration of the crash pulse has increased. This correlates to
the overall reduction in the total stiffness of frontal structures of LTVs.
When considering the NCAP and the IIHS tests, it would seem that they are
measuring basically the same issues, but actually, the tests are conducted very differently,
which means that the results tend to be quite different. Both organizations feel their
respective frontal tests are complements to each other, not competitive. Nathaniel Beuse,
division chief of NHTSA's New Car Assessment Program, says that consumers should
use the results from both tests "together to assess overall frontal crash test safety in terms
of the effectiveness of restraint systems and the integrity of the occupant compartment."
More importantly, both tests can only be used to get an idea of how the vehicle
would perform in a collision with a vehicle of similar size and weight or in a singlevehicle collision, which results in essentially the same forces as a collision with a
similarly sized vehicle. They cannot be used to assess how a vehicle would fare if it
collides with a vehicle that is significantly different in size. Since the rating reflects a
crash between two similar vehicles, vehicles from the same weight class, plus or minus
250 pounds, should be compared when looking at frontal crash star ratings.
2.7
COMPATIBILITY
In general terms, compatibility may be described as the capability of vehicles to
protect occupants in case of collision and at the same time, offer as little aggressiveness
as possible to crash partner vehicles. Figure 8 shows the geometric incompatibility
between different classes of vehicles. The definition can be further specified to state that
regardless of the accident circumstances, both vehicles should have almost the same
probability of injury. The traffic environment includes cars, trucks, pedestrians, and two-
21
C 1500
Ford Taurus
Geo Metro
Figure 8. Front-end profiles of an LTV, a passenger car, and a small car.
wheelers and injuries can occur from to collisions with similar or different vehicles or
even single fixed objects. Naturally, the problem of compatibility is global and requires
careful understanding of the crash mechanism.
The main aspects of the problem of compatibility have been identified as follows:
ƒ
Mass ratio of the colliding vehicles.
ƒ
Ride height or the front end geometry of the vehicles.
ƒ
Force deflection or stiffness of the front end structures of the vehicles.
Other factors that have been observed to effect compatibility are the location, size,
and mass of the powertrain and more importantly the stiffness of the occupant cell itself.
These factors can be broadly classified as mass incompatibility, stiffness incompatibility
and geometrical incompatibility. The issue of vehicle compatibility has been known
since the 1960’s but no organized research had been done until recently by NHTSA and
other agencies worldwide. The trend of increasing mass and stiffness for pickup trucks
is as shown in Figure 9.
22
Mass, Stiffness vs Model Year
2500.00
2000.00
1500.00
1000.00
500.00
Stiffness
Mass
Power (Mass)
Power (Stiffness)
0.00
82
84
86
88
90
Model Year
92
94
96
98
Figure 9. Mass and stiffness values from NCAP tests [20].
The compatibility concerns were condensed into two vehicle categories—SUV
and LTV—not only because of their increasing market share in the past decade but also
because these vehicles are generally designed heavier, stiffer, and with a higher ground
clearance than passenger cars.
2.7.1 AGGRESIVITY AND AGGRESIVITY METRIC
The NHTSA’s vehicle aggresivity and compatibility program was established to
address this serious issue. The initial focus of the program was to identify and
characterize compatible vehicle designs that would result in significant reductions in
crash—related injuries. The group’s major concern was the effect of the structural
modifications that were being done by vehicle manufacturers in response to frontal offset
crash testing. Modifications caused the strengthening of the structures to reduce
intrusions into the passenger compartment, but these in turn caused the vehicle structure
to become stiffer. When the sales trend of the vehicle fleet was studied an interesting
23
pattern emerged. In the United States, the class of light trucks and vans (LTVs) as shown
in Figure 10, account for nearly one-third of the new vehicle purchases.
TRUCK
CAR
Figure 10. U.S sales and registrations of LTV and cars [4].
Aggresivity is a term used to define how fatal a vehicle is to its partner vehicle’s
occupants in a two—or multi-vehicle collision; in other words aggresivity is a relative
measure of the level of incompatibility.
Since 1993 NHTSA conducted studies to investigate the crash compatibility of
passenger cars and LTVs in vehicle—to—vehicle collisions. Crash compatibility is
typically evaluated either by crash testing or analysis of accident data like the Fatality
Analysis Reporting System (FARS) and General Estimates System (GES). These
provided an indisputable record of the safety performance of a vehicle but by nature are
only an historical record and cannot predict the compatibility or aggresivity behavior of
new vehicle models.
In order to characterize the compatibility problem, NHTSA defined an aggresivity
metric based on the FARS and GES crash involvements, defined as:
24
Aggresivity =
Fatalities in Collision Partner
Number of Crashes of the Subject Vehicle
The fatality rates were normalized to include the fatalities in the collision partner
per the number of the crashes in which the subject vehicle was involved, which
accounted for the different vehicle populations and driver demographics. Only two
vehicle crashes where both vehicles were less than 10,000 pounds and had model years
1980 and newer were included because the earlier analyses showed that these vehicles
showed lower aggresivity metrics than the entire model years combined. Only fatalities
of the drivers with ages between 26 and 55 were considered, in order to remove any
injury tolerance shown by younger and older drivers, as discussed in Section 2.4.2.
The vehicle categories studies were LTVs which are a subset of the LTV vehicle
categories provided by FARS and GES and passenger cars which were categorized using
the NCAP vehicle weight ranges. The computed aggresivity metric included all the three
different modes of crashes – front, side and rear. The overall aggresivity metric and
front—front crashes are shown in Figure 11 and 12, respectively. The driver fatalities for
frontal crashes between LTV—car is shown in Figure 13.
Figure 11. Overall aggresivity metric.
25
Figure 12. Aggresivity metric frontal-frontal.
Figure 13. Driver fatalities for frontal-frontal in LTV—car crashes.
About four percent of all two-vehicle crashes were accounted for by frontalfrontal crashes, but 4300 average fatalities were recorded between 1995 and 1999. The
metrics for the frontal-frontal category are much higher than for all two-vehicle crashes,
but the relative rankings of the vehicle categories remain the same.
26
CHAPTER 3
SYSTEM SETUP
The problem of vehicle compatibility and aggresivity led to an attempt to
optimize the aggresivity of a common pickup truck by considering a worst-case scenario
involving a vehicle-vehicle collision involving a common small car. This section will
describe the system formulation and the methodology, as shown in Figure 14, used for
the optimization study.
System Formulation
Model and Configuration Selection
Selection of Parameters
Selection of Experimental Design
Optimization
Design of Experiment Matrix
Intrusions
LS-DYNA Crash Simulations
Acceleration
Internal Energy
MADYMO Occupant Simulations
Combined Injury Index
Injury Criteria - HIC, Chest Acc
Figure 14. Adopted methodology.
27
3.1
FORMULATION
NHTSA and National Crash Analysis Center (NCAC) have developed finite
element models of different vehicles which have been validated against the rigid barrier
NCAP tests and are commonly used for crash studies. The 1994 Chevy Pickup C1500
and the 1997 Geo Metro models for a full—frontal, collinear crash configuration were
selected. Figure 15 shows the two different vehicle models. Table 2 summarizes the
model definitions.
Figure 15. Finite element models of Chevy C1500 pickup (left) and Geo Metro (right).
TABLE 2
Chevy C1500 and Geo Metro Model Definition
Chevy C1500
Geo Metro
Parts
226
211
Nodes
62681
19543
Shell Elements
51324
15374
Solid Elements
3554
522
Beam Elements
171
4
28
The system was setup under the assumption that the Geo Metro represents an
average small passenger car.
A baseline vehicle-vehicle model was constructed by
combining the two vehicle models to represent a full—frontal crash scenario. The closing
velocity was calculated to be 50 mph, which would effectively result in a change of
velocity of 35 mph. This change in velocity represents the 35 mph rigid—barrier NCAP
test. To be able to study the effect of the main parameters on aggresivity, only the three
parameters of the pickup truck were varied, keeping that of the Geo Metro unchanged.
Variation in the parameters, discussed in Section 3.2.1, was used to effectively
encompass the entire fleet of pickup trucks.
The MAthematical DYnamic Model, or MADYMO as it commonly known was
used to simulate the dynamic behavior of mechanical systems. Although originally
developed for studying passive safety, MADYMO is being increasingly used for active
safety and also biomechanics study. Its unique facility of combining finite element (FE)
and multi-body allows it to be used for a multitude of problems.
To study the occupant kinematics and their injury parameters, the occupant
compartment was modeled in MADYMO, as shown in Figure 16. The occupant
compartment of the Geo Metro was modeled using the measurements from the FE model
and actual test data. To simulate occupants, ATDs have been used and in this study a 50th
Hybrid III Dummy was used. The Hybrid III represents an average U.S adult male. The
model of the dummy consists of 69 bodies, with six left and right ribs. The reference joint
is chosen in the lower torso. Accelerometers and load cells are appended in the dummy
database to study the injury parameters. The occupant compartment is modeled using
planes, ellipsoids, and cylinders. Measurements are obtained from the actual rigid barrier
29
test data. The airbag is modeled using the finite element capabilities of MADYMO.
Figure 17 shows inflation of the airbag. The triggering conditions are used to activate the
airbag inflation at a specified time. The dummy is restrained using shoulder and lap seat
restraints. They are modeled using a combination of seat belt segments and finite
elements. Appropriate contact definitions are provided to define contact between the belts
and the dummy parts. Friction between ellipsoids, planes, and finite element nodes are
also taken into account.
Figure 16. MADYMO interior model of Geo Metro.
Figure 17. Inflation of airbag.
30
3.1.1 VALIDATION
The FE models used in this study, developed by NCAC were validated with
respective NCAP tests conducted by NHTSA. Model validation is an integral part of any
study, because the developed models are generic models and the experimenter(s) must
ensure that they correlate to the actual full—scale vehicles.
Figure 18 shows validation graphs for the MADYMO vehicle interior model. The
simulation was based on the NCAP test of the Geo Metro, NHTSA test number 2239.
The head acceleration and chest acceleration are plotted against time and show good
correlation to the actual test (red line) data. The Chevy pickup C1500 model was
validated against test number 1741, conducted by NHTSA under the New Car
Assessment Program (NCAP) [20]. Figure 19 shows the 35 mph rigid—barrier test setup.
The acceleration calculated through the accelerometers placed in the vehicle, as shown in
Figure 20, shows good correlation to the actual test results, shown in Figure 21. The post
—test view shows similar crush patterns as shown in Figure 19. Figures 22 to 26 show
similar results for the Geo Metro [21].
Figure 18. Head and chest acceleration validation for the
MADYMO model.
31
Figure 19. NCAP rigid barrier test setup
for Chevy 1500.
Figure 20. Placement of accelerometers
in Chevy C1500.
Figure 21. Acceleration and velocity profiles for Chevy C1500
(simulation- blue, actual -red).
Figure 22 Post—test view for Chevy C1500 (simulation—left, actual—right).
32
Figure 23 NCAP rigid barrier test setup
for Geo Metro.
Figure 24 Placement of accelerometers
for Geo Metro.
Figure 25 Acceleration and velocity profiles for Geo Metro
(simulation- blue, actual -red).
Figure 26 Post—test view for Geo Metro (simulation—left, actual—right).
33
3.2
SELECTION OF DESIGN VARIABLES
As mentioned earlier, the three main factors affecting the aggresivity of a vehicle,
are the mass, stiffness, and height of the vehicle. A brief description of how the variables
and the levels were introduced into the FE models is presented in the following sections.
3.2.1 MASS
One of the most important variables is the mass of the pickup truck. The stiffness
and the mass values from the NCAP tests were obtained [22] and plotted. Figure 27
shows the zone of consideration for this study.
Stiffness vs Mass (MY 83-97)
3000
Zone of Consideration
Stiffness
2500
2000
1500
1000
500
1350
1550
1750
1950
2150
2350
2550
2750
Mass
Figure 27. Mass-stiffness plot for determining the zone of consideration.
It can be observed from Figure 27 that the mass of pickup trucks typically varies
from 1,400 Kg to approximately 2,500 Kg, and the range selected for the study was 1403
Kg to 2422 Kg, representing the low and the high values. Since a difference in mass was
34
observed between the FE model and the actual NCAP test vehicle, the range was scaled
to account for the discrepancy. Table 3 depicts the selected variables.
TABLE 3
The Range of Mass Selected for the Study
LOW
HIGH
Difference from Original
Model
0.82
1.2
Mass in Kg
1194
2055
In order to vary the mass, the pickup truck mass was varied by changing the
material properties of some of its structural parts, while minimizing the change in the
center of gravity of the model.
3.2.2 STIFFNESS
The stiffness of the pickup truck was modeled using only one parameter - the
thickness of the front—end structural parts. Previous work [3, 5] has modeled the
stiffness change using two parameters: the thickness of the fore rails and length of the
fore rail. Additional members like the bumper system and radiator were translated by
amounts corresponding to the change in fore rail length. This method not only increases
the model preparation time but also increases the number of factors considered, former of
which was not considered to be practical, when considering a design of experiment study.
Therefore, in this study, the method was simplified to include only the variation of
thickness of the structural members.
Figure 28 shows the comparison plot of force—deflection for the simulation and
the actual test of the 35 mph NCAP test. Beuse, N. et al. [23] evaluated the methods of
35
calculating stiffness from the 1982-2001 NCAP crash test data and concluded that the
desirable characteristics were the following:
ƒ Good correlation of linear fit (R2).
ƒ Emphasis on the initial deformation of the vehicle.
ƒ Reflection of the overall slope.
ƒ Allowance for non-zero intercepts.
Figure 28. Force—deflection of 35 mph NCAP test.
It was decided that the correlation should begin within the first 200 mm of
deflection in order to reflect the overall slope; linear stiffness had to correlate for a
minimum distance of 150 mm. The linear fit showed good correlation (R2) at 241 mm of
crush and the stiffness was calculated to be 778.88 KN/m, as shown in Figure 29. To
effectively simulate the entire pickup truck population, stiffness values for the chosen
levels are shown in Table 4.
36
350000
NCAP Test V 1741
300000
250000
200000
Forc e (N)
Test V 1741 Linear Approximation (0-241mm)
y = 1058.5x - 24015
150000
R2 = 0.8659
100000
FE Simualtion
50000
FE Linear Approximation (0-241mm)
y = 778.88x - 15472
R2 = 0.8691
0
0
50
100
241 mm
150
200
25
-50000
Displacement (mm)
Figure 29. Stiffness calculation at 240 mm of crush.
Table 4
The Range of Stiffness Selected for the Study
LOW
HIGH
Difference from Original
Model
0.54
1.89
Stiffness in KN/m
450
1512
Initial simulations with variation of thickness of only the fore rails did not
correspond well to the change in stiffness. To better understand the crash and energy—
absorption characteristics, the frontal structure was analyzed for the 35 mph rigid—
barrier test. Figure 30 shows the percentage of energy that is absorbed by the front end of
37
Chevy pickup and Figure 31 shows the structural parts that were selected. Out of the total
energy absorbed during the NCAP test, approximately 53 percent was absorbed by these
parts.
Bumper, 10.8
Hood, 5.8
Fender, 4.5
Fore Rail, 31.6
Figure 30. Energy distribution and percentage for Chevy C1500 in NCAP test.
Fenders
Hood
Fore
Bumper and Mounting
Figure 16 Energy distribution and percentage Chevy C1500 in a 35 mph NCAP test
Figure 31. Parts selected for the stiffness variation.
38
3.2.3 OVERLAP
The variation of the ride height or overlap of the LTV was modeled by changing
the Z-coordinates of the entire model. Since there were no available databases to
determine the range of the ride height of pickup trucks, the variation was simplified to
overlap the front—end structural members. Similar to mass and stiffness, the height also
was varied in two levels as shown in Figure 32.
Baseline Model
100 % Overlap
No Overlap
Figure 32. Baseline model and the two levels of overlap.
39
3.2.4 CONSTANT VARIABLES
The variables that were kept constant were the closing speed and the processor.
Closing speed is defined as the difference in the initial velocities in a vehicle-vehicle
crash simulation. For this study, the closing speed was determined to be 50 mph. To
remove noise in the simulations arising from different processors and even platforms,
these factors were kept the same for all simulations.
3.2.5 RESPONSE VARIABLES
The responses that were chosen to be studied fall into two categories: (a)
structural intrusions and (b) occupant injury levels, as listed in Table 5.
Table 5
Selected Response Variables
Structural Intrusions
Occupant Injury
Dashboard / Instrument Panel
Combined Injury Index (Pcomb)
Internal Energy Ratio
The structural intrusions were found by calculating the nodal X and Y
displacements of the parts shown in Figure 33. The observed occupant injury: Head
Injury Criteria (HIC) and Chest Acceleration are combined to form a single index,
Combined Injury Index (Pcomb). The HIC and Chest Acceleration are calculated by using
multi-body models of dummy and the vehicle interior. Only the driver-side intrusions
were calculated; intrusions affecting the passenger and the lower extremities injuries are
beyond the scope of this study.
40
Figure 33. Parts used to calculate the nodal displacements.
3.3
DESIGN OF EXPERIMENTS
A Design of Experiments (DOE) is a carefully organized series of trials, based on
sound mathematically theory, where the responses are measured for set combinations of
the variables. This is a highly cost—effective solution for conducting parametric studies
that are then used to develop a statistical model of the system. The model thus created
allows for prediction of various responses by relating them to the variables, either
individually and/or in combination.
The DOE model has the following features:
•
Variables - These are the primary factors of interest that are believed to
affect the responses and in this study, include the mass, stiffness, and height of the
pickup truck.
41
•
Outputs or Responses - These are the responses required from the system
under consideration and in this study, include the intrusions, injury parameters,
and absorbed energy ratio.
Usually the system behaves as a non-linear system, and the variables interact in a
very complex manner, which give rise to the need for good interpretation of these
interactions. Several graphic methods are employed to visualize these interactions.
3.3.1 FACTORIAL DESIGN
Factorial designs are used in experiments involving several factors where it is
necessary to observe the joint effect of the factors on the response [24]. The most
important of these are the k factors, each at two levels. The levels might be qualitative or
quantitative, or the high and low levels of a factor. One of the major assumptions
considered in this type of design is that since there are only levels of factor, the response
varies linearly over their range. This is often desired in factor—screening experiments
which are primarily used to study the process or system. A single replicate 2k design was
selected for this study. The logical explanation behind this is that the replication of a
finite element simulation will not result in variability in the response as long as the other
variables are held constant. Table 6 shows the experimental design developed using
Design-Expert©. The experimental design shows the three factors, each at two levels,
which in turn produce eight runs.
42
Table 6
Stat Ease Design Matrix
Std
A: Mass
B: Stiffness
C: Overlap
Order
Kg
KN/m
1
1194
684.27
0
2
2055
684.27
0
3
1194
2009
0
4
2055
2009
0
5
1194
684.27
1
6
2055
684.27
1
7
1194
2009
1
8
2055
2009
1
3.3.2 OPTIMIZATION METHODOLOGY
The engineering of structural design is a challenge to determine the best one
through an iterative process where a series of structural changes regarded as reasonable
trials show off different responses. Optimization and FE simulation tools can be used to
change the design parameters and obtain the efficient search for the right combination of
design parameters for a certain design. Parametric study and optimization can be usefully
combined to investigate and optimize the behavior of a model. Response surface methods
can handle just a few design variables, since otherwise, the computational effort is too
high. For this study the following procedure was followed:
ƒ Possible numerical errors that affect the responses were excluded.
ƒ Design parameters chosen were proven [4, 9, 10, 11] to be the major factors
influencing the responses.
ƒ The DOE method is used to understand the factorial effects.
43
ƒ A second—order Response surface model is made up with the design
parameters and is used to optimize the system.
3.4
SIMULATIONS
The crash simulations were conducted using LS-DYNA, a general purpose
explicit finite element code used to analyze non-linear dynamic response of structures. Its
fully automated contact analysis capability and error-checking features help solve
complex crash, impact, and forming problems. Each numerical simulation was run on a
WIN32 (PCWIN), OS Level-Windows XP, with single precision (I4R4), 2GB RAM,
using two Xeon processors and LS-Dyna 970. The termination time for each simulation
was 130 milliseconds and they ran for approximately seven hours each.
MADYMO simulations were run using MADYMO 6.2 on a UNIX platform.
Each simulation took approximately ten minutes.
44
CHAPTER 4
RESULTS
The results from the LS-DYNA and MADYMO simulations are presented in this
section. The statistical analysis using Design-Expert, along with optimization solution is
also provided. The prediction equations developed from the statistical data are tested
using original model.
4.1
FINITE ELEMENT SIMULATIONS
The simulation shown in Figure 34 represents the Geo Metro and Chevy C1500 in
a frontal-frontal crash configuration. The response variables calculated from the eight
simulations are shown in Figure 35.
Figure 34. Model configuration at 0 milliseconds.
45
Time: 15 Milliseconds
Time: 30 Milliseconds
Time: 45 Milliseconds
Time: 60 Milliseconds
Time: 75 Milliseconds
Time: 90 Milliseconds
Time: 105 Milliseconds
Time: 120 Milliseconds
Figure 35. Crash simulation representing M, S, and, O variable levels.
46
Figure 36 shows the intrusions that were calculated from the eight runs. It can be
observed that the toe pan intrusions were lower than the baseline model for all runs. The graph
also shows that the intrusion caused variation in the results with the number of runs. This is a
good indication of the fact that the variables considered for this study had a significant effect on
the intrusions and also that there is a possibility of interaction between the variables. The
normalized intrusion which was calculated based upon that of the baseline simulation is shown in
Figure 37. On the average, the toe pan and the B pillar intrusion were reduced, while the footwell,
dashboard, and A pillar showed an increase. Runs 5 and 6 specifically showed a significant
reduction in overall intrusions, while Runs 7 and 8 showed an overall increase. Comparing Runs
7 and 8 shows a reduction in the intrusions in the latter, with the exception of toe pan intrusion.
INTRUSIONS
Toepan
Dashboard
A pillar
Footwell
100
90
80
70
P ercen ta ge
60
50
40
30
20
10
0
Original
Run1
Run2
Run3
Run4
Run5
Figure 36. Intrusion levels.
47
Run6
Run7
Run8
25
20
15
Toepan
B Pillar
10
Footwell
5
Dashboard
0
A pillar
-5
-10
-15
A pillar
Dashboard
-20
Footwell
Run1
Run2
Run3
B Pillar
Run4
Run5
Run6
Toepan
Run7
Run8
Figure 37. Normalized intrusion levels.
A very interesting pattern is observed when the percent of internal energies were plotted
as shown in Figure 38. The internal energies closely relate to the variation in stiffness values as
shown previously in Table 6. Comparing two adjacent runs, Run 1 and 2 for example, the energy
absorbed by the Geo Metro increased marginally by an increase in mass of the Chevy C1500.
From a primary overview, overlap does not seem to affect the energy absorption characteristics of
either vehicle. The normalized percent internal energy (IE) ratio is plotted in Figure 39. The IE
ratio is the ratio between the energy absorbed by the Geo Metro and the Chevy C1500. This graph
also shows a similar pattern, but the difference between Runs 2, 3 and 4, 5 was very large.
48
% C15
% MET
100
90
80
70
60
50
40
30
20
10
0
Run 1
Run 2
Run 3
Run 4
Run 5
Run 6
Run 7
Run 8
C15-ME
Figure 38. Percentage energy absorbed.
Internal Enery Ratio vs Runs
1.00
0.80
0.60
0.40
0.77
0.82
0.58
0.20
0.34
0.00
-0.15
-0.20
-0.38
-0.17
-0.36
-0.40
Figure 39. Normalized IE ratio.
49
Figure 40 shows the combined injury index Pcomb that was used to calculate the
combined effect of the head and chest injury criteria values is observed for the different
runs. As can be seen, there are sharp peaks and corresponding valleys. The initial high
and low points in the curve correlate exactly to the variation in the mass of the pickup
truck. The difference between them is decreased when the stiffness is increased. The
increase in overlap leads to lower probability of injury, the lowest value corresponding to
decreased mass and stiffness and increased overlap. The Pcomb value is equal to the
baseline model when the mass, stiffness, and overlap are increased.
Pcomb
0.24
0.22
0.20
Probability
0.18
0.16
0.14
0.12
0.10
Run 1
Run 2
Run 3
Run 4
Run 5
Run 6
Figure 40. Pcomb index.
50
Run 7
Run 8
Org
4.2
RESPONSE SURFACE
The 2k factorial design can be used to express the responses in terms of a
regression model. These equations show the dependency of the design variables to the
selected responses. The coefficient R2 was used to measure the model’s ability to fit the
response data. The obtained regression was used to generate the response surface plots.
The fitted plots are planar because the regression model is first-order. Design-Expert, a
statistical software package was used for the ANalysis Of VAriance (ANOVA).
4.2.1 PAIR-WISE COMPARISONS
Pair-wise comparisons, as the name suggests, is a means of visualizing the
relative importance of each factor on the responses. This section will discuss the pairwise comparison of the dashboard intrusion, internal energy ratio, HIC, and chest
acceleration.
4.2.1.1
DASHBOARD INTRUSION
Table 7 shows the effects list for dashboard intrusion and Table 8 shows the
ANOVA results. It is clear that all three factors—mass, stiffness, and overlap—had a
significant effect on the dashboard intrusion, overlap being the highest. The two-factor
interactions had a marginal effect on the intrusion. A comparison of mass and overlap,
shown in Figure 41, indicates a strong relationship between intrusion levels and overlap
and stiffness, which were major factors causing intrusion. When overlap and stiffness are
compared, a similar pattern is seen, as shown in Figure 42. The cube plot shows that the
lowest intrusion was observed at low mass, stiffness, and height as shown in Figure 43.
51
TABLE 7
Effects List for Dashboard Intrusion
Term
Effect
SumSqr
% Contribution
Require
Intercept
Model
A
10.25
210.125
16.39
Model
B
9.75
190.125
14.83
Model
C
19.75
780.125
60.86
Error
AB
0.75
1.125
0.09
Model
AC
4.75
45.125
3.52
Model
BC
5.25
55.125
4.30
Error
ABC
0.25
0.125
0.01
TABLE 8
ANOVA Results for Dashboard Intrusion
Response: Dash Intrusion
ANOVA for Selected Factorial Model
Sum of
Squares
DF
Mean
Square
F
Value
Prob > F
Model
1280.6
5
256.125
409.8
0.0024
A
210.13
1
210.125
336.2
0.0030
B
190.13
1
190.125
304.2
0.0033
C
780.13
1
780.125
1248.2
0.0008
AC
45.125
1
45.125
72.2
0.0136
BC
55.125
1
55.125
88.2
0.0111
Residual
1.25
2
0.625
Cor Total
1281.9
7
Source
Std. Dev.
0.791
R-Squared
0.999
Mean
18.625
Adj R-Squared
0.997
C.V.
4.245
Pred R-Squared
0.984
PRESS
20.000
Adeq Precision
58.059
52
significant
DESIGN-EXPERT Plot
DESIGN-EXPERT Plot
Dash Intrusion
X = A: Mass
Y = C: Overlap
Dash Intrusion
X = A: Mass
Y = C: Overlap
Actual Factor
B: Stiffness = 684.27
Actual Factor
B: Stiffness = 2009.00
28.5
43.5
34.6875
22.3125
25.875
Da sh In tru sio n
Dash Intrusion
16.125
17.0625
9.9375
3.75
1.00
1.00
2055.00
0.75
8.25
1839.75
0.50
C: Overlap
2055.00
0.75
1839.75
1624.50
0.25
1409.25
0.50
A: Mass
C: Overlap
0.00 1194.00
1624.50
0.25
1409.25
A: Mass
0.00 1194.00
Figure 41. 3D plot of the dashboard intrusion at stiffness low (left) and high
(right).
DESIGN-EXPERT Plot
DESIGN-EXPERT Plot
Dash Intrusion
X = B: Stif fness
Y = C: Overlap
Dash Intrusion
X = A: Mass
Y = B: Stiff ness
Z = C: Overlap
Actual Factor
A: Mass = 1624.50
Cube Graph
Dash Intrusion
28.5
43.5
36
28.625
B+
8.25
13.75
6.5
B: Stiffness
Dash Intrusion
21.25
13.875
13.5
28.5
1.00
C: Overlap
2009.00
0.75
1677.82
0.50
C: Overlap
B-
1346.64
A-
0.25
1015.45
3.75
9.25
CA+
A: Mass
B: Stiffness
0.00 684.27
Figure 42. 3D plot of the dashboard
intrusion at mass (low).
C+
Figure 43. Cube plot of the dashboard
intrusion.
53
4.2.1.2
INTERNAL ENERGY
The effects list in Table 9 suggests that stiffness is the biggest factor affecting
energy absorption. The effect of the interaction between stiffness and overlap is also
significant but the effect of mass and the other two-factor interaction is very negligible.
An inverse transformation was applied to the model to increase the accuracy. Table 10
shows the ANOVA results for the IE ratio. The response surface plot shown in Figure 44
shows that a decrease in overlap causes an increase in energy absorption by the Geo
Metro, when the stiffness was high. The internal energy ratio decreased as overlap
increased and also the difference between the maximum and minimum values increased
as the overlap increased. The change in IE ratio was reduced when the stiffness was
reduced. The mass effects were negligible at either of the levels. The peak values were
observed when there was no overlap between the engaging structures and stiffness was
highest. Similarly, the lowest ratio was observed when the stiffness was lowest and there
was no overlap.
TABLE 9
Effects list for Internal Energy Ratio
Term
Effect
SumSqr
% Contribution
Require
Intercept
Error
A
-0.048
4.555E-03
0.19
Model
B
-1.00
2.00
84.60
Model
C
-0.21
0.087
3.68
Error
AB
-0.029
1.631E-03
0.069
Error
AC
-3.511E-04
2.466E-07
1.04E-05
Model
BC
0.36
0.26
11.18
Error
ABC
-0.058
6.753E-03
0.29
54
TABLE 10
ANOVA Results for Internal Energy Ratio
Response: I E Ratio
Transform: Inverse
ANOVA for Selected Factorial Model
Sum of
Squares
DF
Mean
Square
F
Value
Model
2.35
3
0.78
242.58
< 0.0001
B
2.00
1
2.00
619.03
< 0.0001
C
0.087
1
0.087
26.91
0.0066
BC
0.26
1
0.26
81.81
000008
Residual
0.013
4
3.235E-03
Cor Total
2.37
7
Source
Prob > F
significant
Std. Dev.
0.057
R-Squared
0.9945
Mean
1.18
Adj R-Squared
0.9904
C.V.
4.84
Pred R-Squared
0.9781
PRESS
0.052
Adeq Precision
33.925
DESIGN-EXPERT Plot
1.0/(I E Ratio)
X = B: Stif f ness
Y = C: Overlap
Actual Factor
A: Mass = 1624.50
1.67463
1.38342
I E Ratio
1.09222
0.80101
0.509804
2009.00
1.00
1677.82
0.75
1346.64
0.50
1015.45
0.25
C: Overlap
B: Stiffness
0.00 684.27
Figure 44. Pair-wise comparison of internal energy ratio.
55
4.2.1.3
Pcomb
The effects of the factors on the combined injury index are shown in Table 11. As
can be observed, mass and overlap were the most significant factors. The effect of the
two-factor interaction between mass and overlap was also significant. Overlap and the
two-factor interaction between stiffness and overlap had a very low effect on Pcomb. To
increase the accuracy of the model, a power transformation was applied. The ANOVA
results are tabulated in Table 12. From the response surface plots shown in Figure 45, it
was observed that the Pcomb value increased when the stiffness was reduced, and there
was no overlap between the engaging structures. The peak values are observed in this
region. The minimum value of Pcomb was observed when each, stiffness was reduced and
overlap were increased. The effect of overlap diminished when stiffness was increased.
Increase in mass caused two percent increase in Pcomb values.
TABLE 11
Effects List for Combined Injury Index (Pcomb)
Term
Effect
SumSqr
% Contribution
Require
Intercept
Model
A
-1.200
2.881
13.222
Model
B
-0.392
0.307
1.410
Model
C
2.262
10.229
46.951
Error
AB
0.290
0.168
0.770
Error
AC
0.392
0.307
1.408
Model
BC
-1.984
7.870
36.121
Error
ABC
-0.114
0.026
0.119
56
TABLE 12
ANOVA Results for Combined Injury Index (Pcomb)
Response: P Comb
Transform: Power Lambda: -1.2, Constant: 0
ANOVA for Selected Factorial Model
Sum of
Squares
DF
Mean
Square
F
Value
Prob > F
Model
21.286
4.000
5.322
31.916
0.0086
A
2.881
1.000
2.881
17.276
0.0253
B
0.307
1.000
0.307
1.842
0.2677
C
10.229
1.000
10.229
61.349
0.0043
BC
7.870
1.000
7.870
47.198
0.0063
Residual
0.500
3.000
0.167
Cor Total
21.786
7.000
Source
significant
Std. Dev.
0.408
R-Squared
0.977
Mean
8.758
Adj R-Squared
0.946
C.V.
4.663
Pred R-Squared
0.837
PRESS
3.557
Adeq Precision
16.868
DESIGN-EXPERT Plot
DESIGN-EXPERT Plot
(P Comb)^-1.2
X = B: Stiffness
Y = C: Overlap
(P Comb)^-1.2
One Factor Plot
0.23
X = A: Mass
0.201651
Actual Factors
B: Stiffness = 1346.64
C: Overlap = 0.50
0.184937
0.205
P Comb
0.168224
0.15151
P Co m b
Actual Factor
A: Mass = 1624.50
0.134796
0.18
0.155
2009.00
1677.82
0.13
0.00
1346.64
0.25
B: Stiffness
0.50
1015.45
1194.00
1409.25
1624.50
1839.75
0.75
684.27 1.00
C: Overlap
A: Mass
Figure 45. Factor effects on Pcomb, pair-wise (left), mass effect (right).
57
2055.00
4.3
REGRESSION ANALYSIS
The regression equations obtained from ANOVA analyses are shown in Table 13.
and R2 values suggest that these equations can be used to predict the responses within the
design space. Mass, stiffness, and overlap were represented as M, S, and O, respectively.
TABLE 13
Comparison of Regression and Actual Values
Regression
Simulation
Dashboard
Intrusion
= -6.20159 + 6.38792E-003 * M + 3.39692E-003 * S
- 8.84784 * O + 0.011034 * M * O
+ 7.92614E-003 * S * O
11.84
17.00
I E Ratio
= 1/ [+2.66629 – 1.02994E-003 * S - 0.94818 * O +
5.49195E-004 * S * O]
0.82
0.88
Pcomb
=[+8.27308 - 1.39385E-003*M + 1.20153E-003 * S
+ 6.29438 * O - 2.99477E-003 * S * O]^1.2
11.67
17
The responses observed in the baseline simulation were compared with the
values obtained from regression equations. Regression values show good correlation to
baseline simulation but also show that values were under—predicted.
4.4
OPTIMIZATION
From the selected responses an overlay plot was created to develop the design
space that would yield the most optimum design. Constraints were based on the obtained
responses and the rigid—barrier tests.
The constraint condition was defined as;
Dash Board Intrusion: 6 -17 cm
Pcomb: ≤ 20
IE Ratio: 0.85 -1.2
58
The upper limit of the dashboard intrusion corresponds to the intrusion level
observed in the rigid—barrier test. The NCAP rates the vehicles according to the
probability of serious injury (AIS 4 +). Therefore, Pcomb was restricted to 20 percent to
account for a four—to five—star NCAP rating. The IE ratio was limited to 0.85 and 1.2
to create a balanced design space, which would not only increase the energy absorbed by
the pickup truck but also that of the Geo Metro. The overlay plot as shown in Figure 46
revealed that reduction in mass led to increase in the optimum region (shaded lighter).
DESIGN-EXPERT Plot
Overlay Plot
1.00
Overlay Plot
Design Points
X = B: Stif f ness
Y = C: Overlap
0.75
Actual Factor
A: Mass = 1194.00
C: Overlap
Dash Intrusion: 17
I E Ratio: 0.85
I E Ratio: 1.2
0.50
0.25
Dash Intrusion: 6
0.00
684.27
1015.45
1346.64
1677.82
2009.00
B: Stiffness
Figure 46. Optimal region based on constraints at mass (low).
Overlap ranged from 0 to 84 percent with reduced stiffness, and 0 to 55 percent
with increased stiffness. Stiffness values for this condition were found to be more than
NCAP values. Thus, considering that increase in stiffness was a constant trend, reduction
in mass of the pickup trucks caused a significant reduction in the aggresivity. However,
the optimum region reduced as mass was increased, as shown in Figure 47. The area
59
reduction was observed to be due to reduction in the overlap or height of optimum area
but the width, or stiffness remained constant.
DESIGN-EXPERT Plot
Overlay Plot
1.00
Overlay Plot
X = B: Stiff ness
Y = C: Overlap
Actual Factor
A: Mass = 1624.50
C: Overlap
0.75
I E Ratio: 1.2
I E Ratio: 0.85
0.50
Dash Intrusion: 17
0.25
0.00
684.27
1346.64
1015.45
1677.82
2009.00
B: Stiffness
DESIGN-EXPERT Plot
Overlay Plot
1.00
Overlay Plot
Design Points
X = B: Stif fness
Y = C: Overlap
0.75
C: Overlap
Actual Factor
A: Mass = 2055.00
I E Ratio: 0.85
I E Ratio: 1.2
0.50
Dash Intrusion: 17
0.25
P Comb: 0.2
0.00
684.27
1015.45
1346.64
1677.82
2009.00
B: Stiffness
Figure 47. Optimal region based on constraints at mass
medium (top) and high (bottom).
60
CHAPTER 5
DISCUSSION
5.1
CONCLUSION
The disturbing trend of increasing number of aggressive vehicles and the
difference between aggresivity of different classes of vehicles is a growing concern
among manufacturers and consumers, alike. This study gave a glimpse into the
mechanisms behind crash—related aggresivity of pickup trucks. Public domain FE
models of Chevy C1500 pickup and Geo Metro were used. LS-DYNA was used to
simulate actual vehicle collisions and MADYMO was used to study the occupant
responses.
The effect of variation of the mass, stiffness, and overlap between the energy—
absorbing structures of the pickup truck was used to observe the intrusion, energy
absorption, and the injury criteria in the Geo Metro. DOE was used to observe the
combined effect of the factors on the responses and Design-Expert was used to develop
the simulation matrix and to analyze the responses.
The statistical analyses showed that intrusion was most affected by change in
overlap and to some extent by change in mass and stiffness. The combined injury index
was largely affected by change in mass and overlap, whereas internal energy ratio was
directly related to stiffness variation. Regression equations obtained from the ANOVA
analyses showed that these equations could be used for prediction but a trend of under—
prediction was also observed. Overlay plots were created by constraining response values
to values observed in NCAP and baseline simulations. They revealed that the region used
61
to form compatible fleets is very narrow. Reduction in mass led to a significant reduction
in response values. When mass was increased, a reduction in the optimum region was
observed which was mainly due to reduction in overlap. This suggested that if mass of
pickup trucks was increased, only a small area corresponding to increased stiffness and
decreased overlap would decrease the aggresivity of pickup trucks. A wider area bounded
by increased stiffness and overlap but with decreased mass meant that manufacturers had
a wider choice for designing compatible fleets.
5.2
FUTURE RESEARCH
The scope of this study was to evaluate a means of reducing the aggresivity of
pickup trucks with respect to small cars. Similar studies can be conducted using different
classes of vehicles.
Recent research has shown that similar optimization studies can be conducted
efficiently, and that a more accurate model can be developed by conducting similar
studies in MADYMO or through the use of lumped-mass systems. The distinct advantage
is that a more diverse group of vehicles can be used. Once these models reveal a general
trend, the FE method can be used to further refine the system parameters. The use of
DOE combined with either of the above—mentioned systems could be developed into a
powerful system that can be used to predict the aggresivity of future vehicle designs.
Further study needs to be conducted to accurately quantify the behavior of the parameters
with respect to responses.
62
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63
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