Development of an Occupant and Vehicle Interaction Simulation
Except where reference is made to the work of others, the work described in this thesis is
my own or was done in collaboration with my advisory committee. This thesis does not
include proprietary or classified information.
Marc Jarmulowicz
Certificate of Approval:
Peter D. Jones
Associate Professor
Mechanical Engineering
Winfred A. Foster Jr., Chair
Professor
Aerospace Engineering
Nels H. Madsen
Associate Dean for Assessment & Special
Programs
Mechanical Engineering
George T. Flowers
Interim Dean, Graduate School
Development of an Occupant and Vehicle Interaction Simulation
Marc Jarmulowicz
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Master of Science
Auburn, Alabama
December 17, 2007
Development of an Occupant and Vehicle Interaction Simulation
Marc Jarmulowicz
Permission is granted to Auburn University to make copies of this thesis at its
discretion, upon the request of individuals or institutions and at
their expense. The author reserves all publication rights.
Signature of Author
Date of Graduation
iii
Vita
Marc Daniel Jarmulowicz, son of Wesley and Mary Ann Jarmulowicz was born October
20, 1983 in Long Beach, California. In 2001, he graduated from Beaufort Academy, in
Beaufort, SC. He attended Auburn University in 2001 and graduated with a Bachelors of
Science degree in Aerospace Engineering in 2005. In 2005 he began graduate school in
the Aerospace Engineering Department at Auburn University and received his Masters of
Science in 2007.
iv
Thesis Abstract
Development of an Occupant and Vehicle Interaction Simulation
Marc Jarmulowicz
Master of Science, December 17, 2007
(B.S., Auburn University, 2005)
118 Typed Pages
Directed by Winfred A. Foster Jr.
The focus of this thesis was on performing a non-linear, transient occupant and struc-
ture interaction simulation. A finite element model was created of the Auburn University
2005 Baja SAE vehicle in combination with an occupant model. The objective of this work
was to develop and verify this model for structural interaction with occupant kinematics.
The work consisted of obtaining experimental data from tests and comparing them with a
computer simulation. The results of the simulation showed that the model gave an adequate
reproduction of low speed impacts, and was useful in simulating the effects of transferring
externally applied loads to the vehicle and in turn, to the occupant.
v
Acknowledgments
I would like to acknowledge Dr. Winfred Foster for allowing me the flexibility to do
my own research in Finite Element Analysis, it has made all the difference in keeping my
motivation and enjoyment in this project. To Dr. Peter Jones, who since my earliest years
on the Auburn Baja Team has provided me with both opportunity and challenge. Without
his guidance, I would not be the engineer that I am today. To Dr. Nels Madsen, for his
time and commitment in being on my thesis, and for his enthusiasm in the value of my
research. To my family, for their support thought the difficult times. Finally to Darrell and
Taylor, without whom I might never have stayed in engineering.
vi
Style manual or journal used Journal of Approximation Theory (together with the style
known as ?aums?). Bibliography follows van Leunen?s A Handbook for Scholars.
Computer software used The document preparation package TEX (specifically LATEX)
together with the departmental style-file aums.sty.
vii
Table of Contents
List of Figures x
List of Tables xiv
1 Introduction 1
2 Background 4
2.1 The Value of An Occupant and Vehicle Interaction Simulation . . . . . . . 8
3 Review of earlier dynamic simulations 10
4 Development of an Occupant and Vehicle Interaction Simulation 26
4.1 Construction of a Finite Element vehicle . . . . . . . . . . . . . . . . . . . . 27
4.2 Tuning the properties of the vehicle . . . . . . . . . . . . . . . . . . . . . . 28
5 Validation 33
5.1 Modal Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.1.1 Constrained Modal Solution . . . . . . . . . . . . . . . . . . . . . . . 34
5.1.2 Determining Natural Frequencies . . . . . . . . . . . . . . . . . . . . 36
5.1.3 Determining Mode shapes . . . . . . . . . . . . . . . . . . . . . . . . 40
5.2 Dynamic Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2.3 Belt testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2.4 Cases Run and their Application to the Simulation . . . . . . . . . . 54
6 Results 56
6.1 Modal results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.1.1 Natrual Frequencies of the Experimental Frame . . . . . . . . . . . . 56
6.1.2 Modal Analysis of the Simulated Frame . . . . . . . . . . . . . . . . 62
6.2 Dynamic results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2.1 Low-Friction Belt Experiment and Simulation . . . . . . . . . . . . . 69
6.2.2 Low Tension Belt Experiment and Simulation . . . . . . . . . . . . . 72
6.2.3 High tension belt experiment and simulation . . . . . . . . . . . . . 77
6.2.4 Effect of friction coefficient on seat . . . . . . . . . . . . . . . . . . . 77
6.2.5 Head acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.2.6 Chest accelerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.2.7 Motion of the vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
viii
6.2.8 Gross Body Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7 Conclusions 96
8 Future Work 97
Bibliography 98
Appendices 100
.1 Contact Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
.2 MATLAB Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . 101
.3 Modal solution with Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
.4 Effects of seat belt friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
ix
List of Figures
2.1 2005 Auburn Baja SAE Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Early Baja SAE experimentation, obstacle (a), theoretical model (b), vehicle
(c), and experiment (d) - Source: [16]. . . . . . . . . . . . . . . . . . . . . . 11
3.2 Results from MATLAB simulation, vehicle accelerations (a) and loads (b) -
Source: [16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Static displacement test experiment (a), and simulation (b) - Source: [13]. . 13
3.4 Modal testing, experiment (a), comparison table (b), FFT of position 1 (c),
FFT of position 2 (d) - Source: [13]. . . . . . . . . . . . . . . . . . . . . . . 14
3.5 Rollover image history, ATB vs. Experiment 1988 minivan - Source: [18] . . 15
3.6 Rollover image history, ATB vs. Experiment 1989 minivan - Source: [18] . . 17
3.7 Developmental simulation head accel. (a), chest accel. (c), validation simu-
lation head accel. (b), chest accel. (d) - Source: [18] . . . . . . . . . . . . . 18
3.8 Witness reports of accident (a), simulation results (b). . . . . . . . . . . . . 20
3.9 Sequence images of rollover in experiment and simulation. . . . . . . . . . . 21
3.10 Passenger head acceleration results - Source: [6] . . . . . . . . . . . . . . . . 22
3.11 Driver seatbelt load history - Source: [6] . . . . . . . . . . . . . . . . . . . . 22
3.12 Experiment drop test - Source: [1] . . . . . . . . . . . . . . . . . . . . . . . 23
3.13 FEM illustrations - Source: [1] . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.14 Fuselage accelerometer results (a), Hybrid II dummy results (b) - Source: [1] 25
5.1 2005 Baja SAE Frame under modal evaluation . . . . . . . . . . . . . . . . 37
5.2 Physical constraints for the modal evaluation . . . . . . . . . . . . . . . . . 37
x
5.3 Accelerometer and associated mounting bracket . . . . . . . . . . . . . . . . 39
5.4 2005 Auburn Baja SAE car . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.5 Integration of Load cells into Belts . . . . . . . . . . . . . . . . . . . . . . . 42
5.6 Detail of Shoulder Load Cell (a), Lap Load Cell (b) . . . . . . . . . . . . . 43
5.7 Helmet Accelerometer (a), and Chest Accelerometer (b). . . . . . . . . . . . 44
5.8 Detail of Method used to find Center of Gravity . . . . . . . . . . . . . . . . 45
5.9 Detail of Frame Load cell and attachment . . . . . . . . . . . . . . . . . . . 45
5.10 Detail of Experimental System . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.11 Plot of Typical Load vs. Time . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.12 Calibration Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.13 Calibration Rig Detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.14 Plot of Load cell Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.15 Plot of Volts vs. Newtons for Calibration . . . . . . . . . . . . . . . . . . . 50
5.16 INSTRON - 4500 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.17 Detail of Belt Mounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.1 Position of the accelerometers in relation to the experiments. . . . . . . . . 57
6.2 FFT of data from position 1 (a), and position 2 (b). . . . . . . . . . . . . . 58
6.3 FFT of data from position 3 (a), and position 4 (b). . . . . . . . . . . . . . 59
6.4 FFT of data from position 5 (a), and position 6 (b). . . . . . . . . . . . . . 60
6.5 FFT of data from position 7 (a), and position 8 (b). . . . . . . . . . . . . . 61
6.6 FFT of Position 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.7 Finite Element Modal Solution Fixed at Rear . . . . . . . . . . . . . . . . . 64
xi
6.8 Typical load history of the frame load cell (a), and a detailed view (b);
TABLED1 load (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.9 The FEM element position . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.10 Load cell physical location . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.11 Detail of wax paper to provide low friction surface . . . . . . . . . . . . . . 71
6.12 The zero-friction, shoulder belt results for the Experiment (a), with detail
(b), and the Simulation (c), with detail (d). . . . . . . . . . . . . . . . . . . 73
6.13 The zero-friction, lap belt results for the Experiment (a), with detail (b), and
the Simulation (c), with detail (d). . . . . . . . . . . . . . . . . . . . . . . . 74
6.14 The low tension, shoulder belt results for the Experiment (a), with detail
(b), and the Simulation (c), with detail (d). . . . . . . . . . . . . . . . . . . 75
6.15 The low tension, lap belt results for the Experiment (a), with detail (b), and
the Simulation (c), with detail (d). . . . . . . . . . . . . . . . . . . . . . . . 76
6.16 The high tension, lap belt results for the Experiment (a), with detail (b),
and the Simulation (c), with detail (d). . . . . . . . . . . . . . . . . . . . . . 78
6.17 The high tension, lap belt results for the Experiment (a), with detail (b),
and the Simulation (c), with detail (d). . . . . . . . . . . . . . . . . . . . . . 79
6.18 The effect of seat friction on lap belt loads (a), and shoulder belt loads (b). 80
6.19 The zero-friction, head X-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d). . . . . . . . . . . . . . . 82
6.20 The zero-friction, head Z-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d). . . . . . . . . . . . . . . 83
6.21 The low tension, head X-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d). . . . . . . . . . . . . . . 84
6.22 The low tension, head Z-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d). . . . . . . . . . . . . . . 85
6.23 The high tension, head X-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d). . . . . . . . . . . . . . . 86
xii
6.24 The high tension, head Z-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d). . . . . . . . . . . . . . . 87
6.25 Typical chest X-acceleration results for the Experiment (a), with detail (b),
and the Simulation (c), with detail (d). . . . . . . . . . . . . . . . . . . . . . 89
6.26 Typical chest Z-acceleration results for the Experiment (a), with detail (b),
and the Simulation (c), with detail (d). . . . . . . . . . . . . . . . . . . . . . 90
6.27 Plot of acceleration vs. time from accelerometer (a), with detail (b). . . . . 91
6.28 Plot of acceleration vs. time for point on vehicle frame. . . . . . . . . . . . 91
6.29 Plot of velocity vs. time for point on vehicle frame. . . . . . . . . . . . . . . 92
6.30 Plot of position vs. time for point on vehicle frame. . . . . . . . . . . . . . . 92
6.31 Occupant response Simulation (a) and Experiment (b) . . . . . . . . . . . . 95
1 Finite Element Modal Solution Including Table . . . . . . . . . . . . . . . . 102
2 Belt forces: lower belts .20 (a), upper belts .20 (b), lower belts .50 (c), upper
belts .50 (d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
xiii
List of Tables
5.1 Plot of Data with Load cell at Rest . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Plot of Experimental Results of Load vs. Elongation . . . . . . . . . . . . . 53
6.1 Table of experimental frequency changes . . . . . . . . . . . . . . . . . . . . 65
6.2 Table of simulated bracketed runs . . . . . . . . . . . . . . . . . . . . . . . . 66
6.3 Table of Lumped Frequencies vs. Coupled Frequencies . . . . . . . . . . . . 67
6.4 Table of Experimental Frequencies vs. Nastran Frequencies . . . . . . . . . 67
1 Contact card in MSC.Dytran . . . . . . . . . . . . . . . . . . . . . . . . . . 100
2 Frequencies of Modal analysis with table included in boundary condition . . 104
xiv
Chapter 1
Introduction
The design of an off-road race vehicle is unique among motor sports vehicles. The de-
sign of such a vehicle is often viewed to be less sophisticated in comparison to a Formula one
race car, when in reality the simplicity of construction makes the vehicle more robust. Very
often drivers in off-road race cars will damage their vehicles, proceed to fix the damage, and
continue on. As such, the vehicle as a whole must be damage-tolerant under a wide range
of conditions, including roll-overs. Roll-overs is a term used to describe a vehicle rotating
end over end or on its side, and in this type of accident the loads are unknown, and diffi-
cult to obtain with data acquisition equipment. This example is juxtaposed to a Formula
One vehicle accident, where the design loads are often in the plane of travel, or with no
roll-overs. Furthermore, the design of the off-road vehicle lends itself to be easily simulated
on the computer. Due to the need for a robust and damage tolerant structure, the frames
of these vehicles are space-frames where tubes of steel alloys make up a webbing through
which all the loads on the vehicle are transfered. The space-frame is ideal to model in a
finite element solution with beam elements, and provides a convenient method to attach all
of the vehicle substructures, including occupants.
Very little work has been done to incorporate occupant simulations into off-road vehi-
cle simulations, but the simplicity of the vehicle allows a single simulation to do occupant
dynamics, vehicle dynamics, frame stress and loads analysis. Coupling the explicit tran-
sient solution capabilities in MSC.Dytran [12], with the kinematics solver of the Articulated
1
Total Body (ATB) [7] simulation, and with the human database of the Generator of Body
Data (GEBOD) [14] computer program, provides the ability to do just such a simulation.
MSC.Dytran is used to build the finite element vehicle frame, and solves the stiffness ma-
trices as well as the contact between arbitrary surfaces and the frame. This simulation also
calculates seatbelt motion and forces. The ATB program calculates the motion of ellipsoids
with mass and volume in relation to joints of many types. These joints may represent pin
joints in one direction or Euler joints with motion in all directions. The mass for all of
the ellipsoids and the joint stiffness data all come from the GEBOD program, which inter-
polates human body data from Air Force research. The goal of the work presented is to
apply a known force to a Baja SAE vehicle and compare the response of the experimental
occupant to that of the simulated occupant, specifically though the load in the seat belts.
The ability to apply a known force allows for stress analysis in what would normally be a
rigid body dynamics analysis. It is possible to simulate the stress distribution in a frame
of a vehicle as it encounters an obstacle, with known suspension loads for that obstacle.
Since the simulation is a free body in space, this presents an opportunity to analyze overall
vehicle dynamics. Due to the simplicity that off-road vehicles inherently have in their tube
structure, single simulations can be run to obtain data that would normally come from
different programs.
Background into the development of off-road vehicle finite element analysis is presented
in chapter 2. A review of applicable literature to accident dynamics is presented in chapter
3. Detail of the development of the computer simulation is explained in chapter 4. The
methodology and theory for verifying the simulation presented matches the experimental
2
results is described in chapter 5. The results of the simulation compared to the experiment
along with an explanation of those results are presented in chapter 6, and the conclusions
developed from the overall work are presented in chapter 7.
3
Chapter 2
Background
This research is based on the usage of a particular vehicle, known as a Baja SAE vehi-
cle, shown in Figure 2.1. The Baja SAE vehicle is used in the collegiate racing series offered
by the Society of Automotive Engineers. In this racing series, college students design and
build vehicles to compete against each other in specific tasks. Examples of these tasks are
events to compare the top speed, the maneuverability, or the robustness of the design. The
general layout of a Baja SAE car is a steel alloy tube space frame vehicle, whose driver sits
in front of an engine and drive-train, with a bulkhead called a firewall in between. The
maximum speed of such a vehicle is around 35 mph.
Figure 2.1: 2005 Auburn Baja SAE Vehicle
The competition?s most demanding task is an endurance race, where the vehicles race
wheel to wheel over an off-road track that under normal conditions is impassable to all ve-
hicles except to All-Terrain Vehicles or ATVs. It is common for the vehicles in this race to
4
overturn on their side and impact the ground in ways that the suspension cannot dissipate
any energy from such an impact. The resulting loads from this type of impact are unknown.
Without this load history, the frame of the vehicle is designed to assumed maximum loads
since actual values are not typically available. The assumed loads are large in magnitude
so that a factor of safety is built into the design, but how large a safety factor is unknown.
Simulating the response of the Baja SAE vehicle to different load cases is accomplished
by several methods. In considering the methods in which a finite element model can be
used, there are two types of analysis, static and dynamic, that can be used to determine the
stress in the frame. In a static analysis the forces are applied to a node of the model and
these forces are reacted at points which are constrained. The points which are constrained
make up a part of a set known as the boundary conditions, this set can incorporate many
different effects depending on the type of linear simulation. In general, the static analysis is
defined by Equation 2.1, where f represents a column of applied forces, K is a matrix with
stiffness terms of all degrees of freedom, and d is a column vector which represents enforced
displacements to the model.
{f} = [K]{d} (2.1)
In finite element terms, boundary conditions are locations of prescribed movement, and are
represented by removing columns or rows corresponding to specific degrees of freedom out
of the f and d vectors and the [K] matrix [17]. In a static solution, if a force is applied, a
boundary condition must be applied as well. Thus the problem in representing a vehicle
event like jumping becomes a choice of boundary conditions to represent a dynamic event
5
with a static solution. The vehicle frames are often designed to repeatedly withstand a so-
called single wheel jumping load, which represents a worst case scenario in which twice the
total weight of the vehicle is applied at one shock absorber attachment point. A common
boundary condition for this scenario is to constrain the motion of the firewall. If another
boundary condition was chosen, like constraining the motion of the seat (the location where
the occupants mass has a great dynamic effect), the applied loads would have to be symmet-
ric across all the shock points. If the applied loads are not symmetric, unrealistic stresses
and deformations will result from the seat being loaded in bending, which with an occupant
is not a way that it can be physically loaded. With these inherent problems, the dynamic
solution becomes the next step in a more accurate solution.
A dynamic solution, also called a transient solution since it is time-dependent, involves
solving the equations of motion for a structure to determine the motion of the structure in
spaces as well as the resulting stresses in such a structure. The general form of the equation
of motion is shown in Equation 2.2.
[M] d
2
dx2 {x}+[C]
d
dx {x}+[K]{x} = {f} (2.2)
In Equation 2.2, [M] represents the mass for the model, [C] represents the dampening ma-
trix, and [K] represents the stiffness matrix. For each of these terms, there is an {x},
d
dx {x}, or
d2
dx2 {x} vector which resolves into a force. Mass times acceleration, damping
times velocity, and spring stiffness times position all resolve into forces. The mass matrix
can be represented as lumped or coupled, the differences being that a lumped mass matrix
places all the mass of an element at its nodes, while a coupled mass matrix assumes that
6
there is coupling between the translational degrees of freedom and the rotational ones. As
such, a lumped mass matrix is diagonal and easier to compute, where a coupled mass ma-
trix is full and more difficult to compute since its equations are not linearly independent [15].
The dynamic solution comes in many types, two of which are linear and non-linear. A
linear solution is computationally easier since the geometry of the model is unchanged due
to the load applied. A non-linear solution changes the stiffness and mass matrices, which
allow for the geometry to move in the direction of the loading and also allows for non-linear
material effects like plastic deformation. Plastic deformation is permanent deformation of
a structure due to an applied load. In modeling a dynamic event, boundary conditions
can be applied to constrain the motion of the model, but are not a requirement. Unlike a
static model which may have unrealistic boundary conditions, a dynamic model can be very
realistic assuming the mass is properly represented and the force is applied in a reasonable
fashion. For vehicles like the Baja SAE vehicle, a major problem still remains in modeling
the effects of the human body. The total weight for the Baja SAE vehicle and occupant
used in this work was 288 kg (635 lbs); the occupant?s weight made up 113 kg (250 lbs) of
the total weight. Thus the occupant represents roughly one third of the total mass, and so
it is not negligible. The mass of the occupant can be represented in a number of different
ways, one of them with the body idealized into a point mass and another with the body
represented as segments free to move in space. Representing the occupant as a point mass
cannot represent the dynamic behavior of the human body, and has an inherent problem of
attaching the mass to the vehicle. Even though it is possible to connect a point mass to the
larger structure using only the translational degrees of freedom, the geometry of the model
7
will still create bending moments where there should be none. An example of this problem
can be visualized if a point mass is connected to a seat model; due to the seat being two
dimensional, the length and width of the seat create moment arms in attaching the point
mass. However, in reality the seat can transmit no rotation to the body, only normal forces.
Using the Articulated Total Body simulation allows the mass and dynamic properties of
the human body to interact with a finite element structure in a free dynamic environment,
using computational contacts between objects in a model. These contacts allow for normal
and in-plane forces to be developed in the seat, but do not transfer rotations directly.
2.1 The Value of An Occupant and Vehicle Interaction Simulation
The advantages to the proposed model are that the geometry and physics can be cap-
tured with high fidelity, and the occupant response can be determined. Since the vehicle
represented in this simulation is relatively simple, the finite element model can have high
fidelity with relatively few elements. This high fidelity allows for the occupant model to
interact with the vehicle model in a way that gives a good approximation of reality. The
occupant is constrained to the vehicle through the seat and the seat belts, which apply
normal forces like pressures and tangential forces like friction. These are the only two types
of forces that are applied to the occupant, and other modeling techniques may introduce
bending moments where there should be none. This simulation is also more accurate due
to the ability to model non-linear structural dynamics such as changes in geometry. The
human body response allows for determination of body accelerations and HIC loads [7].
Potential problems with this simulation stem from modeling the occupant and the
8
contact between the occupant and the vehicle. The occupant is modeled in a way that as-
sumes that the joints are torsional springs, and that there is no active control of the body.
Both of these assumptions have a significant effect on the dynamic response of the occupant.
The contact routines between the occupant and the vehicle use assumed friction coefficients
and contact parameters such as penetration depth. The MSC.Dytran solver updates the
geometry of the stiffness matrix in response to loads, as in a non-linear analysis. In this
way the seat belt elements are allowed to conform to the occupant so that the simulation
determines the geometry of the belts and how they contact the body. The frame geometry
is also updated as the solution progresses, but the loads used in the validation of this model
do not create plastic deformations in the structure of the frame.
The practical value of this simulation is the application of known load data that allows
for detailed structural analysis. This analysis can lead to results such as a reduction in
weight of the space frame, while maintaining reliability. In the case of structural failure, a
simulation could be developed to analyze the effect of the vehicle impacting a tree. This
simulation environment allows for the flexibility to give initial conditions about the tree
and the vehicle and allow the computer to determine the applied loads. This ability is very
useful for a majority of problems where the type of contact the initial conditions may be
known, but the actual forces are not known. In this way, the model proposed in this work
allows for a level of analysis previously not performed in the Baja SAE racing community.
9
Chapter 3
Review of earlier dynamic simulations
Much of the past work done in off road vehicle simulation has been documented in
engineering journals like those from the Society of Automotive Engineers. The first docu-
mented dynamic simulation of a Baja SAE car was from da Silva et al. [16]. Their work
focused on verifying a two degree of freedom simulation in a MATLAB environment. The
theory of their two degree of freedom model is shown in Figure 3.1 (b). Their experiment
consisted of driving a Baja SAE vehicle over an instrumented object as seen in Figure 3.1
(d). In this experiment both the obstacle and the vehicle were instrumented with load cells
as shown in Figures 3.1 (a) and (c). Due to the sinusoidal shape of the obstacle and the
theoretical requirement that the tires never loose contact with the obstacle, the speed of
the vehicle was limited to less than 2.0 m/s (4.5 mph). They determined that for low speed
conditions, a two degree of freedom model adequately matched the available data as seen in
Figure 3.2. They proposed that their model could be used to study the suspension system
performance and to modify it for pilot comfort [16].
Investigation into computer simulations to reproduce dynamic simulations was contin-
ued in the work by Owens et al. [13]. In this work a dynamic simulation of a Baja SAE
vehicle was made after verifying the frame finite element model with both a static and a
modal analysis. All simulations were run in the ABAQUS finite element environment. The
static analysis of the Baja SAE frame involved applying a known torque to the frame with
known constraints as shown in Figure 3.3. The static simulation produced good results,
10
(a) (b)
(c) (d)
Figure 3.1: Early Baja SAE experimentation, obstacle (a), theoretical model (b), vehicle
(c), and experiment (d) - Source: [16].
11
(a) (b)
Figure 3.2: Results from MATLAB simulation, vehicle accelerations (a) and loads (b) -
Source: [16].
and the torsional rigidity of the frame was found to be within 8% of the simulation [13].
Torsional rigidity is the spring rate of the frame if one end is twisted and the other is con-
strained. For the modal analysis, the frame was constrained to a rigid table and impacted.
A full spectrum of frequencies from two accelerometer locations were recorded. The modal
experimentation procedure presented in [13] was the basis for the procedure used to verify
occupant and vehicle simulation.
The dynamic model that was constructed in [13] is based on the model that they val-
idated in their static and modal analyses. This model had a high fidelity frame model,
and incorporated a point mass occupant representation. The point mass was connected
to several nodes on the frame that represented the seat attachment locations and harness
attachment locations. To represent the inertia of the vehicle as a whole, correction masses
and inertias were added to the frame model. They concluded that the simulated stresses
12
(a) (b)
Figure 3.3: Static displacement test experiment (a), and simulation (b) - Source: [13].
were high in magnitude for an applied loading in a place that did not see fatigue failure.
The Articulated Total Body simulation has many documented verification tests to
prove its capability. In the one of these tests, Smith et al. [18] simulated two different
rollover events for the same type of minivan. Called a developmental test, the first rollover
was of a 1988 Dodge Caravan. The rollover was initiated by a rollover test device, which
gave the minivan an initial velocity of 48.3 kph (30 mph) before flipping it. In this case, the
minivan landed on its left side and slid on its left side. Video from inside the vehicle was
compared with results from the gross body motion of the simulation, and seemed to agree
well. The plots of the acceleration are shown as well, and seem to exhibit good trends, but
have unknown asymptotic peaks.
13
(a) (b)
(c) (d)
Figure 3.4: Modal testing, experiment (a), comparison table (b), FFT of position 1 (c),
FFT of position 2 (d) - Source: [13].
14
Figure 3.5: Rollover image history, ATB vs. Experiment 1988 minivan - Source: [18]
15
The second rollover test was called a validation test, and this rollover was simulated
with data collected from a rollover of a 1989 Dodge caravan. In this rollover, the minivan
completed two full rolls and came to rest on its tires. The video sequence of the rollover and
its complement in the ATB simulation are shown in Figure 3.6. When they simulated the
rollover in the ATB environment, two components had to be added to make the simulation
match well. These components were roof crush and seat belt slack. The roof crush was cre-
ated in the simulation by hyper-ellipsoid planes that moved into the cockpit in a predefined
manner. The seat belt slack was added to the simulation so that the body could move up
into position such that it could impact the roof. The results, shown in Figure 3.7, show
that the simulation over-predicts the acceleration load. This effect may be due in part to
the impact of the dummy with a rigid vehicle. This simulation was described as accurate,
however the validity of the simulation was based on knowing the correct values beforehand.
There is a limitation to the utility of an ATB analysis where not all the conditions are known.
More work with the ATB program was done by Huanining et al. [5], who simu-
lated a complex vehicle roll over. In this case, they knew the very little information about
the accident, but had data on the length of tire marks, total distance traveled after the
collision, and number of times that the vehicle rolled. The goal of the work was to create a
model that could reasonably re-create the accident. The model of the Toyota pickup in the
accident had the exterior modeled as hyper ellipsoid planes and the core of the model was
represented as mass and inertia. Although this was a simple model, it was able to represent
when the rollover occurred and how it occurred very well. Figure 3.8 shows the drawing of
the accident, and the simulated motion of the vehicle. The results of this simulation:
16
Figure 3.6: Rollover image history, ATB vs. Experiment 1989 minivan - Source: [18]
17
(a) (b)
(c) (b)
Figure 3.7: Developmental simulation head accel. (a), chest accel. (c), validation simulation
head accel. (b), chest accel. (d) - Source: [18]
18
?In the simulation, the vehicle completed three rolls and stopped 85.1 m from
the collision point. The Figure 1 (Figure omitted) measurement is 84.7 m for
this distance. Stating from the same yaw angle measured from Figure 1, at the
collision point, the simulated vehicle stopped at a yaw angle of -159. degrees,
very close to the actual vehicle?s orientation angle of -146. degrees in Figure 1.
Furthermore, the maximum deflection of the roof created by the roof/ground
contact, which is one of the most important numbers, is 0.15 m according to
the simulation results. This value is very close to the NASS (National Accident
Sampling System) value of 0.16 m, according to the Interior Vehicle Form as
illustrated in Figure 2. The simulation also generated a very similar skidding
motion in the first part of the accident. The trajectory of this skidding is
nearly identical to that shown in the accident diagram, with a simulated forward
skidding distance of 15.54 m compared to the actual measured value of 14.33 m
in the NASS report [5].?
Huanining et al. continued their work in the same accident, applying the data from
the simulated rollover to occupant response [6]. The roll-over of the Toyota truck resulted
in a passenger being ejected out the window, and their goal was to show that the simulated
occupant was also ejected out of the vehicle. The data for the vehicle rollover was obtained
in [5], and was subsequently used in this model. Instead of the vehicle being shown as an
external assembly of hyper-ellipsoid planes, it is now a vehicle interior. The driver and
passenger were run separately, but in a specific fashion. Since the contact between the
passenger and driver could affect the passenger?s body motion, the driver was represented
in the passenger simulation as an extra set of contact planes. The motion of the driver is
19
(a)
(b)
Figure 3.8: Witness reports of accident (a), simulation results (b).
20
shown in Figure, 3.9 (a) and the motion of the passenger is shown in Figure, 3.9 (b). Few
results for the passenger are given, but more are given for the driver. The driver, being
harnessed by a seatbelt, was injured with cuts and bruises and as such the simulation did
not show magnitudes so high as to cause greater injury.
(a) (b)
Figure 3.9: Sequence images of rollover in experiment and simulation.
One of the few documented simulations with MSC.Dytran and the ATB program is
covered by Fasanella et al. [1], who summarized the results of dynamic work with a crash
worthy aircraft body. This simulation was run in the MSC.Dytran/ATB environment so
that the interaction of an aircraft structure, seats, and human models could be analyzed.
An experimental drop test was done on a prototype composite fuselage with a crushable
bottom structure, Jungle Aviation And Radio Service (JAARS) energy absorbing seats,
21
Figure 3.10: Passenger head acceleration results - Source: [6]
Figure 3.11: Driver seatbelt load history - Source: [6]
22
and 50th percentile Hybrid II dummies. The experiment is shown in Figure 3.12 and the
MSC.Dytran model is shown in Figure 3.13.
Figure 3.12: Experiment drop test - Source: [1]
This model included many non-linear effects, including plastic deformation of the sub-
floor?s crushable foam, the seat frame and seat cushion?s ability to absorb energy. The
results compare the acceleration histories from accelerometers mounted on the floor of the
substructure as well as pelvic accelerations from the dummy. The results find that there is
good agreement with the magnitude and duration of the acceleration pulses.
The previous work done shows the limitations of the using the ATB program alone
and the advantage of using it in combination with MSC.Dytran. A kinematic solver like
the ATB program cannot solve for finite element stresses and geometric changes, and a
23
Figure 3.13: FEM illustrations - Source: [1]
24
(a) (b)
Figure 3.14: Fuselage accelerometer results (a), Hybrid II dummy results (b) - Source: [1]
non-linear transient solver like MSC.Dytran cannot solve for occupant kinematics. The two
programs running concurrently allow for occupant and structure interaction, which is im-
portant when the dynamic response of the occupant has a significant effect on the response
of the vehicle system. The design of the Baja SAE vehicle allows for the entire structure
to be analyzed with high fidelity. With the entire Baja SAE vehicle in the simulation, the
response of the occupant can drive design changes in the entire vehicle, not just a subsection
as was done in [1]. The development of this simulation was unique in that the entire vehicle
was modeled.
25
Chapter 4
Development of an Occupant and Vehicle Interaction Simulation
The goal of the occupant and vehicle interaction simulation was to develop a computer
model where a simulated occupant would interact with a simulated vehicle, through the
seat and seat belts. A force or combination of forces can be applied to the vehicle, and the
vehicle can interact with the occupant. By applying the load to the vehicle, the occupant
and vehicle interaction model can simulate a much wider variety of load cases, especially
those where the inertia of the system as a whole is important. The final model developed
has approximately 11,000 degrees of freedom.
The occupant and vehicle interaction simulation uses both the MSC.Dytran and the
ATB programs running concurrently. Each of the programs requires their own input file; an
.AIN file is for use in the ATB program, and a .DAT file is read into the MSC.Dytran solver.
Each of the programs were developed to run independently and so there are many redundant
inputs between the two. The .DAT file contains the input data for MSC.Dytran, including
the control statements for the simulation, output requests, the finite element model, and
parameters for contact. The .AIN file contains the input data for the ATB program, and
contains information about the occupant model. Since the ATB program is an independent
program, it requires position data for the occupant in the file. The example files included
with the release of MSC.Dytran [12] had the characteristics that the ATB input file pro-
vided: the seat, occupant mass and joint properties, and the contact functions between the
seat and body; while the MSC.Dytran input provided the human body position, seatbelt
26
mesh, seatbelt properties, and the interface between the MSC.Dytran and ATB programs.
This was not adequate since a finite element seat, developed in MSC.Dytran, was required.
4.1 Construction of a Finite Element vehicle
The simulated vehicle was comprised of four parts: the frame, seat, seat belts, and
point masses. The frame is a mesh of beam elements with approximately 4674 degrees of
freedom. It has adequate fidelity for the seat, seat belts, and point masses to all integrate
with it. To integrate the occupant model into the vehicle, it was essential that the vehicle
be in the occupant coordinate system, which was with the positive Z direction point into the
ground [7]. The seat is a mesh of quadrilateral shell elements that support bending. It has
two components, the firewall and the seat bottom, that for the purposes of the simulation
are tied together. The complexity of the seat bottom was too high to be practical to model.
The seat component has approximately 5448 degrees of freedom. The element mesh density
of the seat is higher than that of the mesh on the dummy. This is important because the
slave surfaces, which in this case are the seat surfaces, must be finer than that of the master
surface, which in this case is the occupant model, as noted in the MSC.Dytran users guide
[12]. The seat connects to the frame through 59 grid points. For the firewall part of the
seat, these grid points are positioned in approximately the same location of the clamps that
mount the experimental firewall to the frame. For the seat bottom, a surface was created
on the seat mounting structure to represent the bottom of the seat, and for the seat back
a surface was created from the bottom of the seat up to the firewall, as shown in Figure,
6.9. The seat belts connect to the frame in the same locations as the experimental belts.
The shoulder belts loop around a tube and back onto themselves to provide an attachment.
27
This effect was not practical to reproduce, so the simulated belts connect directly to this
tube. The belts are rod elements that support a special MSC.Dytran specific belt routine,
and they represent 1500 degrees of freedom. All the belt nodes are used as slave surfaces in
contacting the occupant model?s master surfaces. The point masses represent components
of the vehicle whose mass has an effect on the simulation, but whose stiffness does not have
a large influence on the results. The point masses represent the suspension, engine, and
transmission of the vehicle. These points represent a mass of 141.45 kg (311.84 lbs), and
are positioned in the approximate positions of the centers of gravity of the corresponding
experimental parts. The total mass of the vehicle without occupant was 174.63 kg (384.99
lb).
4.2 Tuning the properties of the vehicle
The mass of the simulated vehicle needed to match the experimental vehicle for the
validation. Getting the mass correct was important so that the same applied force between
both the simulation and experiment, produces the same gross accelerations. Tuning the
mass of the vehicle was a two step process. The first step involved only the Baja SAE
vehicle?s frame. Since the frame was the component used to determine modal frequency
response, its mass had to match between the simulation and experiment. The finite element
frame was built with sufficient detail to provide all major mounting points for the point
masses referred to in the previous section. To match the mass of the simulated frame to
the experimental one, the density was adjusted to 8846.23 kg/m3 (0.68086 lbs/in3). This
resulted in a final frame weight of 34.33 kg (75.69 lbs), which matched the mass of the
experimental frame. The moment of inertia and the center of gravity of the vehicle were
28
not adjusted. The dynamic validation constrains the motion of the vehicle in the Y and
Z directions, only allowing it to move in the X direction, so the position of the center of
gravity will not affect the acceleration in the X direction. Note that the constraints in the
Y direction were applied at the suspension interface points, and in the Z direction they were
applied at the shock absorber interface points.
The simulated occupant mass had to match the experimental occupant as well. A
95th percentile Hybrid III dummy was used to represent the occupant in the simulation.
A 95th percentile occupant has a body height and weight for a person that is statistically
within the top 5 percent of the tallest person in the study group. In this case this group
was 2420 male subjects in an Air Force research study [14]. In this study, the height of a
100th percentile subject would be 1.96 m (77.0 in), which is the height of the experimental
occupant. As such, the simulated dummy should be shorter by about 5% or 0.01905 m
(0.75 in). The height was able to be adjusted, however this is not a trivial matter and
was out of the scope of this validation. The mass of the simulated occupant needed to be
adjusted, and it was assumed that for a change in weight of 13.60 kg (30.00 lb), all the
appendages of the body would change by the same percentage. For large changes in body
size, it is assumed that the appendages of the body may change at different rates. The
final mass of the occupant was 113.40 kg (250.0 lbs). This produced a total system mass of
292.57 kg (645.00 lbs). The simulated occupant did not exactly match the position of the
experimental occupant. The simulated dummy did not have their forearms resting on their
upper legs, and there was no constraint of the hands like the experimental occupant had
with the steering wheel. The differences betwen the two are shown in the results section
29
under gross body motion.
Contact routines were used in this model to apply similar loads to the occupant be-
tween the simulation and the experiment. These contact routines allow the occupant to
move in all degrees of freedom. The occupant?s motion is restricted only by the interaction
between the seat and the seat belts, which are similar to the conditions of the experiment.
The simulation solves the first .0001 seconds without contact routines in order to allow the
integration routine to stabilize. Since the body is well restrained inside the vehicle, contact
is limited to specific areas. The contact of the head of the occupant with the seat is an
example of a contact that will occur in a specific area. Reducing the size of the contact
areas reduced the total number of contacts that had to be computed, which lead to a drastic
decrease in computation time. The initial conditions for contact are different between the
ATB program and the MSC.Dytran program. In the ATB manual [7], it is suggested that
the body be initially positioned so as to penetrate the seat an adequate amount to balance
the forces and come close to making the occupant static. This initial position is based on
the balance of the contact planes with the occupant, and is possible due to the formulation
of the contact routines in the ATB program. In MSC.Dytran the contacts will fail and
the occupant will fall through the seat if the occupant has penetrated the contact surface
initially. In this way the occupant model must be allowed to fall into a static position.
Many parameters were required to correctly model the contact in this fashion. Due to the
complexity of the contact input, an example input from this simulation is provided in Ap-
pendix 1. Specific values on the contact input had a major effect on the solution outcome.
These values include the friction coefficients, and node penetration distance.
30
The friction coefficients were assumed since there was no data to support their val-
ues. The experimental results include several cases where the friction was significant and
unknown. However a specific experimental case was run in order to approximate a low
friction condition that could be matched in the simulation. The equation used to simu-
late friction in MSC.Dytran is shown in equation, 4.1 and is from the MSC.Dytran quick
reference guide [12].
? = ?k +(?s ??k)e??? (4.1)
In Equation 4.1, ? represents the friction in the simulation, ?s is the static coefficient of
friction, ?k is the kinetic coefficient of friction, ? is the exponential decay coefficient, and
? is the relative sliding velocity. Determining the effects of each of these variables was
outside the scope of this research, especially since the experimental friction values were not
known. The friction values used in developing this model assume that the static and kinetic
coefficient of friction are the same and the coefficient of exponential decay is one. In the
work by Fasanella et al. [3], a friction coefficient of .62 was applied, however in this work
the coefficient of friction was .12. This value was decided upon after doing a series of cases
where the coefficient of friction was modified for the seat belts. The results, in Appendix 2,
show that when the coefficient of friction was increased from .20 to .50, the seat belts locked
themselves at a artificially high force. In the low friction case, the simulated coefficient of
friction was zero. When the simulated coefficient of friction is zero, the seat belt routine
has difficultly converging, which lead to high frequency noise as shown in the low friction
results section.
31
The penetration check and penetration distance inputs were essential to obtaining
a well behaved solution. In an early case, the acceleration history of the head and chest
had numerous asymptotic spikes of acceleration that could not be explained, and made
the data unreadable. One explanation for this was a lack of fidelity in the seat, and that
more elements were needed to match the nodes between the seat and the body. However,
the spikes in the data were reduced from hundreds to one or two by allowing the body
to penetrate the seat and remove some of the grid points from the contact solution. The
penetration check provides a method to deactivate some of the slave nodes of the body
when they have penetrated a set distance, which is the penetration distance value, through
the contact surface. By making this change, grid points that penetrated too far, and thus
would have had the most reaction force on them, were eliminated. It is assumed that these
handfuls of points with high normal forces, would have had equally high frictional forces,
and due to the points moving across the elements in the contact there were discontinuities
in the results. Thus it is assumed that the effect of distributing the contact forces evenly
among many grid points greatly reduces the amount of acceleration spikes.
Building the finite element model for the vehicle in this simulation was not a triv-
ial matter. There were numerous specific data inputs that were essential to getting well
behaved contact routines. The final model uses a completely flexible finite element struc-
ture interfacing with the rigid shells of the occupant. In validating the performance of this
model, a series of tests had to be developed which could be applied to both the simulation
and the experiment.
32
Chapter 5
Validation
To validate that the simulation produced accurate and reproducible results, two vali-
dations were done, a modal validation and a dynamic validation. A static validation for the
vehicle was determined to be time prohibitive since the validation required significant con-
struction of test apparatus and validation work had already been done by Owens et al. with
adequate results [13]. The modal validation used the finite element solver MSC.Nastran and
consisted of determining the natural frequencies for the vehicle under specific set of circum-
stances, and then determining how well the simulation matched the experiment. Due to the
complexities of the entire vehicle and possible non-linear effects from the tires and suspen-
sion system, only the frame of the vehicle was chosen to do the modal validation. The Baja
SAE vehicle frame interconnects all components of the vehicle and provides a load path for
applied forces, making it an ideal component to study. The modal response of the vehicle
frame must agree with results from the simulated frame in order for the dynamic response
to be in agreement. The dynamic validation, which was done in the MSC.Dytran environ-
ment, compared the simulated vehicle and occupant versus the experimental vehicle and
occupant in terms of the seatbelt loads, accelerometer output, and gross occupant motion.
This validation took into account the vehicle as a complete system, including point masses
for the tires and suspension components as well as the engine and drive-train. The effect of
certain variables like friction coefficients and pretension in the seat belts on the simulation
had to be determined through running several different cases. In order to determine these
effects, cases with low contact friction, low belt pretension, and high belt pretension were
33
run. With the modal response of the frame, and time history output from seat belt loads
and occupant accelerations, the performance of this model was validated.
5.1 Modal Validation
A modal validation of the finite element model seeks to prove that a finite element
model depicts a real structure by comparing natural frequencies and mode shapes. In the
work by Silva et al. [16] a random vibratory load was input by shaking equipment into
their frame so that they could determine the frequency response function of the frame
via accelerometers. Since shaking and high-bandwidth data acquisition equipment were
cost prohibitive, the method chosen to determine frequency response was to input a near
instantaneous force into the frame and record the acceleration output from a single point
on the frame as it resonated. Moving the accelerometer to different points on the frame
allowed for the determination of natural frequencies with respect to specific mode shapes. In
order to accurately compare natural frequencies between the two models, similar boundary
conditions had to be applied in the form of constraints.
5.1.1 Constrained Modal Solution
A constrained modal solution was run since it was not possible to replicate a true free-
free boundary condition in which the vehicle has no interaction with external structures.
An overall example of the modal validation system is shown in Figure 5.1. In other modal
validations, it is common to suspend the structure in question by a bungee or similar re-
straint to replicate the free-free condition [16]. This has the effect of creating a system by
which the structure that is being analyzed has much higher stiffness than the suspension
34
mechanism, and so the frequency output is dominated by the response of the structure.
Since it was unknown how a suspension mechanism would interact with the experimental
structure, this method was discarded. The specific concern was the possible interaction of
rigid body motion with natural frequencies due to the impulse load. The method chosen was
to constrain the experimental structure with rigid boundary conditions, which can be repli-
cated in the model. A detail of the experimental structural constraint is shown in Figure 5.2.
A rigid boundary condition is not actually possible to replicate due to finite modu-
lus of elasticity and inertia in the constraining structure. It is assumed that the stiffness of
the constraining structure is much higher than that of the experimental structure, and so the
frequency response of the experiment is not influenced by the response of the constraints.
In order to apply these constraints in the simulation, single point constraints were utilized,
which apply an enforced displacement to the model. In a constrained case, the displacement
is zero and has the affect of removing rows and columns of specific degrees of freedom out
of the stiffness and mass matrices. As will be seen in the results chapter, the frequencies of
the first three modal solutions in the simulation had significant error. In order to determine
if the error could potentially be from incorrect assumptions about the boundary conditions,
another model was developed with different boundary conditions. This model added a part
of the constraint structure, the table top, to the model. This table top was a rectangular
mesh of quadrilateral elements that supported shear and bending loads. A thickness for the
tabletop, which determines the cross-sectional moment of inertia, was assumed since this
value was unable to be determined experimentally. The tabletop structure was supported
by a steel framework that was assumed to be very stiff in comparison to the tabletop and
35
the frame. The supporting steel framework was modeled as pinned nodes at the table top
interface points. The results of this solution are shown in Appendix 1, and suggest that
the stiffness of the tabletop could potentially be low enough to interact with the first three
modes of the experimental structure. This potential effect cannot be made certain without
more experimental modal solutions using a variety of boundary conditions.
5.1.2 Determining Natural Frequencies
The natural frequencies of the experimental structure and the simulated structure had
to be determined in order to compare them. To determine the natural frequencies of the
experimental structure, the Baja SAE frame was excited by an impulse load and this exci-
tation was recorded by accelerometers. The natural frequencies of the vehicle frame were
also determined using the eigenvalue solver in MSC.Nastran.
The natural frequencies of the experimental structure were found by applying an im-
pulse load to the frame and allowing it to resonate. The applied load was an impact by the
palm of the hand to the frame, which from previous work was known to produce cleaner
response than impacting the frame with a hammer or mallet. Reproducing the same mag-
nitude of the force applied to the frame was not essential since the frequency response was
used. It was not possible to obtain accelerometer data from many points along the frame si-
multaneously, otherwise the magnitude of the applied force would have to have been known
in order to get the frequency response function. Using the finite element modal solution
as a guide, positions were found that represented the location of highest deflection for a
particular mode. This allowed for nine positions to be identified. These positions resonate
36
Figure 5.1: 2005 Baja SAE Frame under modal evaluation
Figure 5.2: Physical constraints for the modal evaluation
37
at higher magnitudes for some modes and not others, allowing for frequencies to be matched
with mode shapes. The Analog Devices ADL302 accelerometer can detect frequencies up to
100 hz before the on-board capacitors begin to low pass filter the data. Frequencies up to
112 hz are recorded, and through the use of Fast Fourier Transforms (FFT), the response
can be separated into frequencies. The FFT solver used in this work was derived from an
example program off of the MATHWORKS website [10]. Note that the FFT is a special
implementation of the Discrete Fourier Transform or DFT, and accepts a time-varying func-
tion as input and computes the frequency spectrum of this signal [2].
The stiffness and mass matrices of a Finite Element model have distinct eigenvalues
and eigenvectors. The eigenvalues represent the frequency of a mode, and the eigenvectors
represent the shape of the mode. The Lanczos method in MSC.Nastran was used to de-
termine the eigenvalues and eigenvectors. The Lanczos method uses Krylov subspaces to
reduce the original matrix to a sequence of matrix problems [19].
The formulation of the mass matrix can have an effect on the results. A lumped
mass matrix formulates the matrix such that all the mass along a beam or a shell is placed
at the nodes, with no dynamic coupling between the element displacements [15]. This makes
the mass matrix diagonal and sparse which makes it faster to compute. However using the
lumped mass method also produces results that can be lower in frequency than the actual
model. A second way to build the mass matrix is called the coupled mass method. This
method builds elements with distributed mass and off-diagonal terms which couple trans-
lational and rotational inertia. The coupled mass method can be more accurate than the
38
lumped mass method [17].
Since adding mass to a system with a constant spring rate will lower the original
frequency, adding the accelerometer mounting bracket would lower the frequency of the
natural modes. How much this effect changed the solution was an unknown. Thus the
lumped mass model was run several times with an additional point mass which represented
the accelerometer and bracket. Each time the point mass was moved to a different location
in order to analyze the effect that this mass had on the frequency. The accelerometer and
bracket had a total mass of 0.61 kg (1.35 lb), and was made of an aluminum center with
steel end caps. The mounting block for the accelerometer is detailed in Figure 5.3. Since
this bracket was positioned in different places on the experimental frame, it is reasonable
to assume that the experimental frequencies may have changed as well.
Figure 5.3: Accelerometer and associated mounting bracket
39
5.1.3 Determining Mode shapes
Specific points on the frame have a much larger response for a given frequency and
less response for other frequencies. For instance, the center of the firewall will move in
response to an excitation of the first mode which is a pitching motion. However the center
of the firewall has no motion when the third mode of the frame is excited. In this way,
an accelerometer placed on the center of the firewall should show some response for mode
one and very little for mode three. Using the Fast Fourier Transform to translate the
accelerometer response data from the time domain to the frequency domain, the frequencies
of the body can be found. In addition, the location of the accelerometer and the general
magnitude of the response of some frequencies relative to others can indicate which mode
shapes are resonating. Using the individual frequencies and their associated magnitudes,
an experimental mode and frequency pair can be associated together. This applies to
a unique problem in this research whereupon the experimental frequency for the second
mode matched the finite element?s frequency for the first mode. If experimental frequencies
were not matched to specific mode shapes, it would have been incorrectly assumed that
the frequencies matched very well, when in fact they are different by approximately 1.5
hz. The first three natural frequencies for the simulated constrained model are 9.36 hertz,
12.62 hertz, and 16.81 hertz. The first three experimental frequencies are 7.97 hertz, 9.85
hertz, and 14.75 hertz. If the original boundary condition is assumed valid, then the first
experimental frequency could be viewed as an anomaly, and the other two frequencies valid.
However positioning the accelerometer in places of peak response, and analyzing the relative
response of some frequencies compared to others validated that 7.97 hertz was indeed the
frequency of the first mode of the experimental system.
40
5.2 Dynamic Model Validation
The dynamic model validation of the occupant and vehicle simulation was done to
reproduce the experimental conditions and return similar results. The experimental condi-
tions included the forces applied as well as the belt and seat properties. The experiment
was a type of sled test that involved quickly decelerating the vehicle which was moving at
a constant speed. For safety reasons, the magnitude of acceleration was kept below 10G?s
for any part of the body.
5.2.1 Experimental Setup
The experimental vehicle was a 2005 era Baja SAE car, depicted in Figure 5.4. In
order to compare the same loads between the simulation and the experiment, three load
cells and an accelerometer were placed in specific locations. Two load cells were built into
the seat belts to provided restraint data. They were placed on the driver side shoulder belt
and the passenger side lap belt as shown in Figure 5.5.
Figure 5.4: 2005 Auburn Baja SAE car
Equipment had to be fabricated to integrate the load cells into the seat belts. It
41
was critical that none of the load cells receive damaging bending moments, and due to the
flexibility in the belt, a large range of motion was needed. Ball and socket joints were used
to achieve the desired range of motion. To integrate the shoulder seat belt to the load cell,
the belt was redesigned to transition from the fabric of the belt to a ball joint fastener which
was fastened to the load cell as shown in Figure, 5.5. On the other side of the load cell,
another ball joint was fastened to an adapter which locks into the latching mechanism. To
adapt the lower belt, a similar adapter from the belt fabric to the load cell was used, and
the frame side of the load cell was fastened to a ball joint which was in turn bolted to tabs,
welded to the frame. These parts are detailed in Figure, 5.6.
Figure 5.5: Integration of Load cells into Belts
42
(a) (b)
Figure 5.6: Detail of Shoulder Load Cell (a), Lap Load Cell (b)
To determine the acceleration history of the vehicle and the occupant, accelerome-
ters were placed at various locations on the system. The occupant had accelerometers
placed in two locations, one on the helmet to resolve head accelerations, and one on the
chest to determine chest accelerations. The ATB program outputs acceleration history for
the body segments in their local coordinate system [7], so the accelerometers for the head
were fixed to the helmet such that they rotated with the head, as can be seen in Figure 5.7
(a). The chest accelerometers were taped to the chest in a loose fashion, as shown in Figure
5.7 (b). However the acceleration of the chest in the simulation is strongly influenced by
the contact routines. There are many unknowns that limit this analysis to the comparison
of rough order of magnitude results and response shape trends.
The applied load to the vehicle had to be known in order to properly load the sim-
ulation in the same way. So that there would be no unknown loads transmitted through
the suspension, the applied load had to be collinear with the center of gravity. In this way,
43
(a) (b)
Figure 5.7: Helmet Accelerometer (a), and Chest Accelerometer (b).
no moment would be applied to the vehicle, resulting in suspension loads. The center of
gravity was found for the combined system of the occupant and vehicle. To find the center
of gravity of the system the occupant and vehicle were hung from two points at the top
of the vehicle. A plum hung from each of these points would create two intersecting lines.
The intersection represents the center of gravity, as shown in Figure 5.8. The engine deck
location is an ideal location to load the frame due to its ability to handle structural loads,
so no additional structural enhancement was needed. Tabs were used to connect the load
cell to the frame, as shown in Figure 5.9.
With the tabs in place, a method was created to load the frame in a repeatable fashion.
It was not essential that the pulse be ideal or exactly a sinusoidal curve since an approx-
imation to an analytical model was not the goal. The goal was to apply known loading
data and see how the simulation matched the real event. As such, a repeatable method was
developed so that seat belt friction would have consistent magnitude. The occupant and
44
Figure 5.8: Detail of Method used to find Center of Gravity
(a) (b)
Figure 5.9: Detail of Frame Load cell and attachment
vehicle were loaded by the inertia of the system in motion reacting with the force applied
by an elastic strap attached to an immobile structure. A load cell in line with this elastic
strap provided the method by which the load history was recorded. This method is detailed
in Figure 5.10. The initial testing velocity was similar in magnitude to a persons jogging
speed, which produced clean and repeatable data, so no other speed was deemed important
to study.
45
5.2.2 Calibration
The load cells were calibrated for the conditions they were in. These conditions included
the supply voltage, attributes of the data acquisition system, and the ambient temperature
given the summer season. Since the load cell gave accurate results for a given load range, it
was decided to calibrate the load cells in two steps. First every time the load cells were to be
used, they would be zeroed for the ambient conditions. Second the load cells were calibrated
individually by applying a known load to them and recording the change in output voltage.
To give an example, the output of a load cell at rest with the given data acquisition system
is shown in Figure 5.1.
Figure 5.10: Detail of Experimental System
The reason there are multiple bands of values is due to the power supply. The power
supply for this acquisition system is a 10 volt regulator, LM 7810, manufactured by National
Semiconductor. This power supply is a switching regulator, and thus is assumed to be the
46
Table 5.1: Plot of Data with Load cell at Rest
Figure 5.11: Plot of Typical Load vs. Time
47
reason for the different bands of voltages. It is clear that there is a central band of voltage
where the majority of the data points are, and this is used as the zero. If such a clear
banding was not present, a statical method would have to have been done. A histogram
could have been used here to find the value of the zero point [2]. While still connected to
the data acquisition device, the load cell is then connected to the testing apparatus. The
load cell calibration apparatus is shown in Figure 5.12 and is detailed in Figure 5.13.
Figure 5.12: Calibration Rig
This device allows many different load cells to be tested in tension or compression.
The belt load cells were tension only cells. With the known weight of the bar and adding
additional weight at known intervals, the force applied at the load cell is easy to compute.
An example of the data used to determine the load cell properties is given in Figure 5.14.
In this data, the approximate zero is seen just below the numeric zero. This value
48
Figure 5.13: Calibration Rig Detail
Figure 5.14: Plot of Load cell Voltage
49
does not drift any sizable amount. There is some excitation of the natural frequency of the
bar before it settles on the exact value for the weight. A table was created with the known
load and the recorded voltage. The resulting plot of this table is shown in Figure 5.15.
Figure 5.15: Plot of Volts vs. Newtons for Calibration
This result means that the lap load cell was calibrated at 1.00854E-05 Volts per New-
ton. All subsequent calibrations of the other load cells showed similar linear equations with
R squared values above 99%. Using this method to determine the properties of the load
cells, accurate load histories could be recorded.
With adequate methods for calibrating the data acquisition system, experiments could
be run. However a consistent methodology needed to be adopted to ensure accuracy. This
50
methodology incorporated the following steps: record baseline values, load body in vehicle,
begin recording, accelerate vehicle, decelerate vehicle, and record data.
5.2.3 Belt testing
Figure 5.16: INSTRON - 4500
The properties of the seat belts in the car were determined experimentally for the
loading condition. There was no data from the manufacturer on the load versus elongation
curve. The seat belts were tested in the Textile Engineering Department at Auburn Univer-
sity on an INSTRON - 4500 machine, shown in Figure 5.16. The belt was attached to the
loading rig via hydraulic clamps shown in Figure 5.17. The maximum load applied to the
seat belt was 2000.00 N (450.00 lb) and was applied in one second. This load provides a large
range of data without increasing the load to a point where the belt will slip in the mounting.
This machine clamped the belt with minimal slippage and produced a table of data of
51
Figure 5.17: Detail of Belt Mounting
52
Table 5.2: Plot of Experimental Results of Load vs. Elongation
the load applied versus the elongation. The gage length of the belt was 152.40 mm (6.00
in). The strain rate of the belt was 300.00 mm/min (0.1969 in/sec). It should be noted
that after the test was over, the machine held the distance constant. It was noticed that
the belt relaxed itself at a rate of .001 Newtons per second, giving an indication of the rate
that the belt fibers re-align. The results of the test are shown in Figure 5.2.
This table shows the relationship between the load applied and the strain output.
The dashed line represents the values in the example files that came with MSC.Dytran.
The solid curve represents the data from the experiment, and the black triangles represent
the values input to the simulation in a TABLED1 bulk data entry. The example data con-
tinues on to a much higher load, but only has three data points, two of which are present
on the table. The new set better represents the loading characteristics of the belt. The
53
loading and unloading events are acknowledged to be different, however for the magnitude
of the forces in this case, they are assumed to be the same.
5.2.4 Cases Run and their Application to the Simulation
Prior to running experiments to obtain data for the simulation, tests had to be run
to ensure the fidelity of the data. As such, accelerometer placement was varied as well as
sampling frequency to determine that no fidelity was being lost. The sampling frequency
was determined to be 2000 Hz, which when divided up amongst 5 channels of input would
give a per channel frequency of 400 Hz. This means that each second of data has 400 data
points, and since the loading event is 300 milliseconds long, that means that there are 120
data points in each curve. A visual representation of these data points are provided in
Figure 5.11.
The belt tension matrix involved three different belt tension levels with three different
accelerometer locations. The three belt tension levels were: loose belts, self tight belts,
and very tight belts. Although the specific load is detailed below, loose belts were defined
as having no tensile load on them, they were free to move somewhat; self tight belts were
defined as the highest tensile load the belts could have from the driver?s adjustments; and
very tight belts were defined as belts that were tightened externally by a person outside of
the car. These three cases were run for three cases of accelerometer placement. These three
cases were the accelerometer: connected to the frame, the helmet, or the chest. The frame
accelerometer was always placed at the top of the roll hoop right in front of the firewall.
The helmet accelerometer placement was on a bracket attached to the helmet. The chest
54
placement was on a plate that was taped to the driver?s chest.
The validation work done for the occupant and vehicle simulation is for the load case
in which the system is decelerated from the aft of the vehicle in a single direction with no
rotations. This load case was simple to experiment and easy to reproduce in a simulation.
The flexibility of the solver allows for more complicated load cases, however these cases
were out of the scope of this research. These cases might represent matching loads and
accelerations for a dynamic motion like a jump, or determining the impact characteristics
of the system with a tree. The results of the validation for this load case are shown in the
following chapter and provide information on the limitations of the simulation.
55
Chapter 6
Results
The results of the modal validation and the dynamic validation methods in the previous
chapter are presented here. The results of these two validations show what parts of the
simulation are accurate and the amount of error for parts that are not accurate. It is
important to know if and by how much the simulation may over or under predict the
solution.
6.1 Modal results
The frame of the Baja SAE vehicle transfers the load due to the applied force to
the inertial masses. The simulated model must have a dynamic behavior similar to the
experimental model. If the stiffness of the frame is too low or too high, the amount of force
transferred to the occupant by the frame may not be correct. The modal analysis compares
frequencies and mode shapes of the simulated frame versus the experimental frames to show
that the stiffness and mass have been accurately modeled.
6.1.1 Natrual Frequencies of the Experimental Frame
The natural frequencies of the frame were found through applying an impulse load to
the frame and then recording the response in different places with an accelerometer. That
data was then converted via Fast Fourier Transform from the time domain to the frequency
domain, producing peak responses at specific frequencies. In order to know where to place
the accelerometers, the finite element modal analysis was done first. The results showed
56
distinct places were the structural response was highest for each mode. Many of the ac-
celerometer locations will record the response of many frequencies. In other positions the
accelerometers will be at a vibration node, and have small displacements for that frequency.
The positions of the accelerometers are shown in Figure 6.1 to aid in comparing the posi-
tions with the locations of peak deflection in the NASTRAN modal analysis shown later in
Figure 6.7.
Figure 6.1: Position of the accelerometers in relation to the experiments.
At every position, the frame was struck in a fashion so as to excite the natural fre-
quency associated with that position. An example would be for the first two positions (they
are collinear), which exhibit a pitch mode in one direction and a yaw mode in another, both
57
directions would be excited independently. For the first few three frequencies, the motions
were able to be seen with the naked eye, but for the higher frequency modes, it was not
able to be seen. The Fast Fourier Transforms were computed with a generic MATLAB code
[10]. A scaling factor was applied to the set so the frequencies could be better seen.
(a) (b)
Figure 6.2: FFT of data from position 1 (a), and position 2 (b).
Figure 6.2, shows the FFT of both position one and position two. Position one is a
pitch mode, and so with the accelerometer on the nose of the frame, oscillations in the
pitch direction have the greatest amplitude. It has a high response at an isolated frequency
of 7.97 hz, which is unquestionably the 1st mode. However, referencing the MSC.Nastran
results Table 6.4, the results for the 1st mode should be a bit higher than 9 hz. This shows
the utility of positioning the accelerometer in a way to isolate a specific frequency. Position
two is a yaw mode, and is the accelerometer in position 1 turned ninety degrees in order
to isolate the yaw frequency of 9.85 hz. The forces applied in the Y direction excited the
second and third modes, and it is clear that the second mode has the highest response.
58
There is also a response from the sixth mode, at 72.28 hz. For position two, the sixth mode
should represent a vibration node of no displacement, however this result would seem to
indicate that there is enough lack of symmetry to produce a significant response.
(a) (b)
Figure 6.3: FFT of data from position 3 (a), and position 4 (b).
Figure 6.3, shows the FFT of both position three and position four. For position three,
the accelerometer was placed at the top of the firewall, near the intersection with the roll
halo. The frequency 14.75 Hertz has the highest magnitude, indicating that it is the third
mode. At this accelerometer position, the second and sixth modes show high response.
Position four located the accelerometer at the center of the rear shock tube in order to get
the fourth mode?s rocking motion as shown in Figure 6.7. The response is dominated by the
third mode, and the response of the fourth mode is barely present with almost no response
at 54.95 hz. The sixth mode is also present.
Figure 6.4, shows the FFT of both position five and position six. The placement of
59
(a) (b)
Figure 6.4: FFT of data from position 5 (a), and position 6 (b).
the accelerometer at position five was at the firewall mid-plane; this position should have
high response to mode five and low response to six. The results show that mode five, at
68.34 hz, is indeed resonated, however not to the degree expected, mode three dominates
the motion. Although mode six should not have been present, a very small response for six
is shown at 71.85 hz. Mode three should specifically be absent, but it has the highest re-
sponse. It is proposed that the impact that drives the modal response of the system deflects
it enough that vibrational nodes are moved to a degree that those frequencies show up on
the accelerometer. Also mode three has a very strong vibration that can be seen with the
naked eye, so it can overpower other modes. The accelerometer at position six was placed
on the front halo tube specifically to be excited in the side to side direction. The results
of the FFT show that mode six, which has shown up consistently in earlier results, barely
shows up as a peak on the side of mode five.
60
(a) (b)
Figure 6.5: FFT of data from position 7 (a), and position 8 (b).
Figure 6.5, shows the FFT of both position seven and position eight. The accelerom-
eters at position seven were placed on the upper 2/5ths of the front bracing tube. Those
at position eight were placed near the steering wheel bracket. Position seven shows the
highest response at frequency 88.69 hz, which is mode seven. It is interesting to note that
in addition to the first few bending modes, this position also picked up many high frequency
modes. Position eight also shows a peak at mode eight, at a frequency of 91.52 hz.
Figure 6.6, shows the FFT of position nine, which had the accelerometer placed on the
diagonal bracing of the roll halo. The accelerometer was mounted to this tube with ties,
not with the heavy accelerometer bracket as was in all the other tests. This was due to
the size of the tube it was attached to at this position. Note that the FEA modal analysis
specifically for this mode also does not have extra point mass as well. This position should
get high responses from the higher modes. This was the case, as mode nine at 108.4 hz had
the highest response, and there was also small response from modes four and five.
61
Figure 6.6: FFT of Position 9
The plots of the frequency response data are used to create a table with natural fre-
quencies versus accelerometer position, which the max and min values are provided in Table
6.1. Since the accelerometer and its support bracket represent a mass of 0.6 kg (1.3 lb),
the frequency of vibration for certain modes will change, and using the frequency response
data the amount of variation for each frequency can be seen. This change happens due an
increase in mass for a constant stiffness. The experimental frequency data is compared to
the simulated data in the next section.
6.1.2 Modal Analysis of the Simulated Frame
The modal analysis of the simulated frame was be done in several ways, in order to get
a range of values that represent valid solutions. Three analyses were done, comparing the
formulation of the simulation, the modeling of the masses, and the modeling of the con-
straints. Comparing the formulation of the simulation involved comparing the frequency
results between a lumped mass matrix and a coupled mass matrix. This range of values
62
represents the change in frequency due to different formulations of the mass matrix, and as
shown in Table 6.3 the change in frequency is small.
It was necessary to know the effect of adding the mass of the accelerometer bracket
to the system. Nine simulated cases were run, in which a point mass representing the ac-
celerometer bracket was placed in a different position corresponding to those in Figure, 6.1.
This analysis compares the frequency change by repositioning the accelerometer bracket.
As noted in the section above, this bracket is also repositioned in the experimental modal
analysis. The maximum and minimum frequencies are shown in Table 6.2. In comparing
these two tables to each other, Table 6.1 and Table 6.2, the frequencies of the lowest modes
do not match well.
The goal of the final analysis was to determine what effect the assumption of a rigid
constraint would have on the frequencies. The table that the frame is connected to is as-
sumed to be rigid, but if that assumption was not valid, the effect had to be known. A
simulation was done that included the attachment table as part of the structure, and the
result was that the first three natural frequencies dropped frequency significantly. The fre-
quency results are documented in Table 2. Without more modal experiments with different
boundary conditions, it is not possible to say that the exclusion of the attachment table is
a bad assumption, but it is a possibility. A comparison of the finite element modal solution
to the experimental modal solution is shown in Table 6.4.
The experimental frequencies and relative magnitude of each were output by taking
63
Figure 6.7: Finite Element Modal Solution Fixed at Rear
64
accelerometer data and converting them to Fast Fourier Transforms. A range of frequencies
were found for each mode. The frequencies from the MSC.Nastran runs with the bracket
in different positions are documented in Table 6.2.
Table 6.1: Table of experimental frequency changes
Without the bracket a lumped run and a coupled run were done to use as a bound. The
results of it are shown in Table 6.3. Note that the difference in frequency for the bracketed
runs is from 0.22 hertz to 12.12 hertz. The difference between the lumped and coupled with
no bracket is 0.0003 hertz to .0628 hertz. The difference between the bracketed runs is at
least an order of magnitude larger. Since the bracketed runs are also more realistic to the
experiment, they will be used for comparing the results. A comparison of the maximum
values and the minimum values of the brackets runs are shown in Table 6.4.
6.2 Dynamic results
The dynamic validation done compared the simulation?s seat belt loads and accelera-
tions to those of the experiment. A comparison is made between the forces in the shoulder
65
Table 6.2: Table of simulated bracketed runs
66
Table 6.3: Table of Lumped Frequencies vs. Coupled Frequencies
Table 6.4: Table of Experimental Frequencies vs. Nastran Frequencies
67
belt and lap belt, the acceleration of the head and chest, and the overall body motion. The
force input into the simulation was a reduced set of the experimentally determined load. An
example of a typical load is shown in Figure 6.8 (a), with a detailed view shown in Figure
6.8 (b). The values for the loading were input into MSC.Dytran in a tabular form and are
plotted in Figure ??.
(a) (b)
(c)
Figure 6.8: Typical load history of the frame load cell (a), and a detailed view (b);
TABLED1 load (c).
68
6.2.1 Low-Friction Belt Experiment and Simulation
Figure 6.9: The FEM element position
The locations of the load cells in the experiment are shown in Figure 6.9; while the
locations of the elements that represent those load cells are shown in Figure 6.10. Note
that four elements are depicted in the previous figures so that the difference in forces due
to friction on the body can be shown. For clarity, all plots show three cases where the peak
value was relatively high, average, and low. The effects of belt pretension are shown in
the Appendix 2. The results from the experiments, will be shown in the following order:
experiments with zero friction, loose belts, and tight belts. Detailing the conditions in each
69
Figure 6.10: Load cell physical location
70
cases, the zero friction case represents an effort to reduce the effects of friction as much as
possible. This was done by placing layers of wax paper between the belt and the person and
the seat and the person as shown in Figure 6.11. In this experiment the belts were tight with
a preload in the shoulder belts beginning at 25 Newtons. The loose belt case represented
the average driver in the vehicle, restrained with belts that have no preload. In this way,
the body has to move further before engaging the belts. The tight belt case represented a
restrained driver with the most possible preload. Although the amount of preload fell as
the belts were strained, the preload began at a load of 133 N for the first case, and fell to 56
N for the last three cases. The results of the low friction belt experiment show a multi-peak
Figure 6.11: Detail of wax paper to provide low friction surface
response that is repeatable and is specifically a consequence of the low friction. For this
case, comparing the experiment with the simulation shows good agreement in magnitude,
71
but little agreement in shape. In particular, the multi-peak affect shown in the plots of the
experiment should show up in the simulation. It is unknown why the shoulder belt had a
high frequency oscillation. For the same case, the lap seat belt had no such artifact, most
likely due to it being well constrained between the torso and the leg.
The lap belts show a very clean response in the experiment, with a maximum magni-
tude of 600 N (134 lb). The shape of the loading is very different from the shoulder belts,
and is very similar to the shape of the cases with friction. This may be because the lap belt
had much greater contact with the body than the shoulder belts did. Even with the wax
paper to reduce friction, the contact did not allow the loading to change. A secondary force
peak is noticeable approximately 200 msec after the main loading pulse. This second pulse
is also in the experiment and represents the occupant oscillating between the belts and the
seat.
6.2.2 Low Tension Belt Experiment and Simulation
The low tension experiments represent runs where the belts had no initial force on
them. These experiments are shown in Figure 6.14. The shoulder load cell had a maximum
force of 500 N (112 lb), and the simulated belt force had a maximum of 600 N (134 lb). For
the shoulder belt loads, the simulation had a very similar pulse shape to the experiment,
however it was elongated by 100 msec. Both results show a plateau of 25 msec before the
maximum peak. For the lap belt loads shown in Figure 6.15 neither the magnitude of the
load nor the shape of the load match.
72
(a) (b)
(c) (d)
Figure 6.12: The zero-friction, shoulder belt results for the Experiment (a), with detail (b),
and the Simulation (c), with detail (d).
73
(a) (b)
(c) (d)
Figure 6.13: The zero-friction, lap belt results for the Experiment (a), with detail (b), and
the Simulation (c), with detail (d).
74
(a) (b)
(c) (d)
Figure 6.14: The low tension, shoulder belt results for the Experiment (a), with detail (b),
and the Simulation (c), with detail (d).
75
(a) (b)
(c) (d)
Figure 6.15: The low tension, lap belt results for the Experiment (a), with detail (b), and
the Simulation (c), with detail (d).
76
6.2.3 High tension belt experiment and simulation
The high tension belts had an initial load of around 75 N (17 lb). As shown in Figure
6.16, the experimental shoulder belt loads have a duration of blank and have a peak magni-
tude of approximately 325 Newtons (73 lbf). The simulation results have a peak magnitude
of over 600 N, or double the recorded loads in the experiment. In the experimental results,
there are smaller peaks at approximately 600 and 800 msec. This result is duplicated in
the simulation, whereupon it shows peaks at 700 and 800 msec, these peaks are spaced
much closer together. A possible explanation for this result can be the interaction of the
human with the system, since the human being is an active controller it is possible that
the body motion was being damped, which would extend the time of the secondary peaks.
Another explanation is that there is strong interaction between the seat contact and the
belt contact on the body. Since the body is rigid in this simulation, the belts and seat must
take up all of the deformation, thus making the frequency of the contact higher. The lap
belt loading shows a much closer result than the other belts. Comparing the simulation to
the experiment, both in Figure 6.17, the simulation is within the maximum and minimum
values recorded in the experiment at 450 Newtons (100 lbf). The general shapes of the
two are similar, with both having an abrupt increase to maximum load, followed by a more
gradual unloading. The body induced oscillating is also present.
6.2.4 Effect of friction coefficient on seat
The friction between the seat and the person is unknown in every case except the low
friction case, where wax paper separated the body from the seat. In all other cases, the
friction was determined by contact between cloth and plastic. A simulation was run to
77
(a) (b)
(c) (d)
Figure 6.16: The high tension, lap belt results for the Experiment (a), with detail (b), and
the Simulation (c), with detail (d).
78
(a) (b)
(c) (d)
Figure 6.17: The high tension, lap belt results for the Experiment (a), with detail (b), and
the Simulation (c), with detail (d).
79
analyze the effect of increasing the seat coefficient of friction from .12 to .5. In early work
with friction between the belts and the body, it was found that between .20 and .50 friction,
the contacts ?locked,? which means they maintained a high contact force when one was not
necessary, see Appendix ??. In maintaining the belt friction constant and increasing the
seat friction, the same effect of ?locking,? happened. In this case, the peak magnitude of the
force also went down compared to the other data sets. Thus friction does play an important
role in determining the belt loads, so this is a place where the data was insufficient.
(a) (b)
Figure 6.18: The effect of seat friction on lap belt loads (a), and shoulder belt loads (b).
6.2.5 Head acceleration
The acceleration data for the occupant?s head is separated into three groups, corre-
sponding to the three cases of the belts: low friction, low tension, and high tension. The
response of the head will be less exact due to the rotation of the accelerometer, but the
order of magnitude of the results should be similar. For the low friction case, the peak
accelerations in the experiment were approximately 6 G?s in deceleration. The simulation
80
over-approximates this number by 1G, however the shape of the acceleration pulse well
matches the experimental results. It matches in terms of the duration of the pulse at 200
msec. The result of approximating the neck as a spring is the oscillation shown in Figure
6.19, part (c). Since the human body?s head is actively controlled, little oscillation is shown.
The accelerations in the Z-direction show similar shapes, however there is an unknown is-
sue with the simulation history. The acceleration history goes positive for a short period,
which probably indicates that the contact routine had trouble converging on a solution and
resulted in a positive force.
For the case of low tension belts, the simulation over predicts the magnitude of the
acceleration of the head by 2 G?s. Although the plots are very similar to the low friction
plots in terms of the overall shape, there is a discrepancy. The smaller peak before the
larger one in the experimental data was assumed to be a larger magnitude response of the
oscillation that was in the experimental data. However, comparing Figures 6.21 and 6.22,
both simulation plots show an opposite response beginning at time 460 msec, showing that
this is an artifact of the simulation, and not an agreement.
The head accelerations for the high tension belt case show roughly the same mag-
nitude and shape as the previous cases. This would seem to indicate the belt tension does
not have a strong effect on head accelerations under these conditions. In this case, the simu-
lation shows no artificial peak like in the previous two cases, and shows better agreement in
the shape of the data. Both the simulation data and the experimental data show a plateau
immediately preceding the highest peak, and an inflection soon after the peak.
81
(a) (b)
(c) (d)
Figure 6.19: The zero-friction, head X-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d).
82
(a) (b)
(c) (d)
Figure 6.20: The zero-friction, head Z-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d).
83
(a) (b)
(c) (d)
Figure 6.21: The low tension, head X-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d).
84
(a) (b)
(c) (d)
Figure 6.22: The low tension, head Z-acceleration results for the Experiment (a), with detail
(b), and the Simulation (c), with detail (d).
85
(a) (b)
(c) (d)
Figure 6.23: The high tension, head X-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d).
86
(a) (b)
(c) (d)
Figure 6.24: The high tension, head Z-acceleration results for the Experiment (a), with
detail (b), and the Simulation (c), with detail (d).
87
6.2.6 Chest accelerations
The chest acceleration data provided is for the typical case. In the X direction, the
accelerations are over-predicted by the simulation by 1G, and the duration is similar between
the experiment and the simulation. A large spike in the data is attributed to contact
problems. In the Z direction, the acceleration is over predicted by approximately 4G?s, and
has a similar spike in it that is attributed to contact problems.
6.2.7 Motion of the vehicle
The motion of the frame in the Z direction will be ignored. This is due to a physical
difference between the experiment and the simulation. The experiment had contact between
the tires and the ground, which are similar to springs and dampers between the ground and
the frame. The simulation has a single point constraint in the Z direction at the four shock
points, as well as constraints in the Y direction at all the suspension attach points. Note
the results for the experiment in the Z direction have upper and lower bounds of 1.5 to -1.5
G, signifying that little major acceleration took place in the up and down direction.
6.2.8 Gross Body Motion
The gross motion of the human body in the experiment and the simulation should
match well for the simulation to be valid. The motion of the body is consistent amongst all
the simulated runs, even if the results of the seat belt loads are not. Motion capture was
not a priority, so there are limited pictures in which to use for comparison of the simulation
and the experimental occupant. There are three sets of pictures for both the simulation
and the experimental occupant, shown in Figure 6.31.
88
(a) (b)
(c) (d)
Figure 6.25: Typical chest X-acceleration results for the Experiment (a), with detail (b),
and the Simulation (c), with detail (d).
89
(a) (b)
(c) (d)
Figure 6.26: Typical chest Z-acceleration results for the Experiment (a), with detail (b),
and the Simulation (c), with detail (d).
90
(c) (d)
Figure 6.27: Plot of acceleration vs. time from accelerometer (a), with detail (b).
Figure 6.28: Plot of acceleration vs. time for point on vehicle frame.
91
Figure 6.29: Plot of velocity vs. time for point on vehicle frame.
Figure 6.30: Plot of position vs. time for point on vehicle frame.
92
The first set of pictures shows the unloaded cases for both. The occupant in the
experiment has a different arm position than the dummy in the simulation. In both the
simulation and the experiment, the occupants are resting flush against the firewall of the
vehicle. In the second set of pictures, the acceleration is building up to it?s peak. Both
bodies show movement away from the firewall, a downwards pitch to the head, and motion
of the arms. The head movement shows how the neck allows the head to translate forward
somewhat before a significant downward pitch of the head. The arms have moved upwards
in both simulations, however in different ways. In the simulation, the arms have no contact
interaction with the body and are allowed to pass through the body. As such, the arms
begin translating forward and rotating upwards, very different from the simulation. In the
experiment, the arms are much better constrained by the driver, but also translate forward
and upwards. This can be seen by comparing the first two sets of experimental photos, by
which it can be shown that in the first set, there is a triangular gap between the arm and
the leg at the elbow; in the second set, this gap is gone. Also notice that the wrists in the
experimental photo have changed position, which signifies that the arm is sliding up the leg.
Note that in the experiments, the driver was conscious and was thus actively controlling
the motion of the body. The arms were constrained by holding the steering wheel. In the
simulation, the arms had no such constraint, and although none was desired, the closest
correlation would have been to use the ATB input file to provide a very high locking force
to keep the joint from rotating [7]. In the third set of pictures, the experiment shows that
the body has regained contact with the firewall, the head has a large downward pitch, and
the arms have traversed around three inches up the leg (based on the movement of the
93
watch). The hands no longer contact the steering wheel, further signifying the translation
of the arm up the leg.
94
(a) (b)
Figure 6.31: Occupant response Simulation (a) and Experiment (b)
95
Chapter 7
Conclusions
The occupant and vehicle interaction simulation works well for this specific load case.
This simulation poorly matches the magnitude of the loads, in general it over-approximates
them, but the shape of the loading is matched well. With the lack of fidelity in the seat, and
modeling issues with the human body, there are several reasons the model could have an
error in magnitude. The model presented is a way to assess whether changes in a structure
can better protect the human body. It is a way to effect changes in design of the frame
structure and see the changes in a relative fashion.
96
Chapter 8
Future Work
This computer simulation has been validated for a specific case. To make it more
robust, further validations must be made to detail an operational envelope in which the
simulation is accurate. Further work with a person would involve matching gross body
motion in the simulation with a more complex event, like jumping an obstacle. Using load-
cells to record the suspension data (the load into the frame), the model could re-create
the jump and the gross body motion could be compared. Other validation would have
to be done without a person due to the high accelerations, but with the mass added to
the system in another fashion. These validations would include accelerating the Baja SAE
vehicle to a known speed, and impacting it into a rigid obstacle of known shape like a tree
or concrete divider. In this way the material properties of steel can be modified such that
the simulation has the same deformations as the experiment. The occupant and vehicle
interaction model opens the door to many different fields of study. Study into frame design,
occupant protection, restraint harness design (seat and seat belts), energy-absorbing front
bumpers, frame failure, and more.
97
Bibliography
[1] Digges, K. H., ?Recent Improvements in Occupant Crash Simulation Capabilities of
the CVS/ATB Model,? SAE Document: 880655.
[2] Doebelin, E. O., EngineeringExperimentation : Planning,Execution,Reporting.
New York:Mc-Graw-Hill, Inc., 1995.
[3] Fasanella, E. L., and Jackson, K. E., ?Best Practices for Crash Modeling and Simula-
tion,? ARL-TR-2849.
[4] Grimes, W. D., ?Using ATB in Collision Reconstruction,? SAE Document: 950131.
[5] Huanining, C., Rizer, A. L., and Obergefell, L. A., ?Pickup Truck Rollover Accident
Reconstruction Using the ATB Model,? SAE Document: 950133.
[6] Huanining, C., Rizer, A. L., and Obergefell, L. A., ?ATB Model Simulation of a
Rollover Accident with Occupant Ejection,? SAE Document: 950134.
[7] Huanining, C., Rizer, A. L., and Obergefell, L. A., ?Articulated Total Body Model
Version V User?s Manual,? ASC-98-0807.
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TheFiniteElementMethodforEngineers. Fourth Edition. New York: John Wiley &
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[9] ?Input Description For the Articulated Total Body Model ATB-V.1,? December 1998.
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[12] MSC.Dytran c?2005r3,UserprimesGuide. MSC.Software Corporation, 2006.
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98
[16] da Silva, M. M., de Oliveria, L. P. R., Neto, A. C., and Varoto, P. S., ?An Experi-
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99
Appendices
.1 Contact Definition
Table 1: Contact card in MSC.Dytran
100
.2 MATLAB Fast Fourier Transform
Fs = 1000; % Sampling frequency
T = 1/Fs; % Sample time
L = 1000; % Length of signal
t = (0:L-1)*T; % Time vector
NFFT = 2\^nextpow2(L); % Next power of 2 from length of y
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2);
% Plot single-sided amplitude spectrum.
plot(f,2*abs(Y(1:NFFT/2)))
title(?Single-Sided Amplitude Spectrum of y(t)?)
xlabel(?Frequency (Hz)?)
ylabel(?|Y(f)|?)
1984-2007 The MathWorks, Inc.
101
.3 Modal solution with Table
Figure 1: Finite Element Modal Solution Including Table
102
.4 Effects of seat belt friction
(a) (b)
(c) (d)
Figure 2: Belt forces: lower belts .20 (a), upper belts .20 (b), lower belts .50 (c), upper
belts .50 (d).
103
Table 2: Frequencies of Modal analysis with table included in boundary condition
1987
104