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Analysis of Automotive Safety Issues Related to Depowering of Airbags

Using Finite Element and Lumped Mass Models

By

Ahmad Noureddine

B.S. M.E. June 1987, The University of Tennessee, Knoxville

MS May 1989, The University of Tennessee, Chattanooga

A Dissertation submitted to

The Faculty of

The School of Engineering and Applied Science

of the George Washington University in partial satisfaction

of the requirements for the degree of Doctor of Science

May 17, 1998

Dissertation directed by

Dr. Nabih E. Bedewi

Associate Professor of Engineering and Applied Science

and

Dr. Kennerly H. Digges

Research Professor of Engineering and Applied Science



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DM! Number: 9831537

UMI Microform 9831537Copyright 1998, by UMI Company. All rights reserved.

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ABSTRACT

Current airbag design in the United States is influenced by motor vehicle safety

standard FMVSS 208 o f the Code of Federal Regulations. This standard requires the airbag

to protect an unbelted 50th percentile Hybrid IE dummy in a 30 mph crash into a rigid barrier.

In order to meet this standard, the airbag has to be fully inflated in approximately 25

milliseconds and maintain an adequate pressure after occupant impact. The level of

aggressiveness required for this rapid inflation has proven harmful and sometimes fatal to

occupants who happen to get in the way of the inflating airbag.

Depowering the airbag is being considered as a means of reducing unintended injuries

due to airbag inflation. Depowering can have different results due to the complexity of the

crash environment: occupants can vary in size and seating position, vehicle interiors

incorporate different designs for energy absorption, and crash pulses can vary depending on

vehicle size, impact speed, and type of objects impacted.

This research investigated all the parameters involved using finite element based

computer simulations. A model of the Hybrid EH crash dummy was developed and used -in

conjunction with a folded airbag model and a vehicle model- to perform the simulations. In

addition, a lumped mass model that represents the airbag as a spring damper system was

developed to give more insight on the issues involved. The results indicated that some

drivers involved in low severity/late deployment crashes may experience higher chest gs

than those involved in 35 mph high severity crashes. Reducing the inflation rate by 25%

reduced chest gs by 20 to 25%. However reducing the inflation rate further had marginal

benefits while it increased the risk of chest contact with the steering wheel. The results also

indicated that a minimum clearance of 2 to 4 inches is required between the airbag and driver

at time of deployment to avoid airbag induced injuries.

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TABLE OF CONTENTS

ABSTRACT ii

TABLE O F CONTENTS iii

LIST OF FIGURES vi

LIST OF TABLES ix

INTRODUCTION I

1.1 The Search for a Better Restraint System 11.2 Developing the Necessary Tools for Analysis j1.3 Research Achievements 41.4 The Need for Finite Element Based Computer Simulation in Crash

Analysis and the Issue of Reliability 51.5 A Brief Overview of LS-DYNA3D 71.4 General Discussion of Material Models and Element Formulation 151.5 Contact Algorithms 161.6 Analysis Procedure and Text Organization 17

THE DEVELOPMENT OF THE HYBRID HI MODEL 19

2.1 Introduction 192.2 The Chest Model 21

2.3 The Head Model 25

2.4 The Head-Neck Model 27

2.5 The Lumbar Spine Test 34

2.6 The Knee Test 35

2.7 Joint Modeling 36

THE AIRBAG MODEL 41

3.1 Introduction 41

3.2 Concept of a Supplemental restraint System 43

3.3 Airbag Volume Calculations Using Element Geometry 46

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6.3.5 Benefits to Older Population6.3.6 Analysis Based on Statistical Data

102102

7 THE CRASH EVENT AS A LUMPED SPRING MASS SYSTEM 104

7.1 Introduction 1017.2 The Lumped Chess Model 1067.3 The Airbag Lumped Mass Model 107

7.3.1 Determining an Equivalent Airbag Spring Constant 1097.3.2 Determining a Damping Coefficient for the Airbag 110

7.4 Determining K n and C [2for Any Inflation Rate and Applications 112

8 SUMMARY, CONCLUSIONS, AND FUTURE WORK 115

8.1 Summary 115

8.2 Conclusions 1188.3 Future Work 118

REFERENCES 119

APPENDICES 124

A. A Brief history of Automotive Safety 124

A.1 The Unsolved Problem 125

A.2 The I890s 125A.3 The Pre-World One Era 126

A.4 The 1920s 127A.5 Internal Design for Safety: The 1930s 128

A.6 Limit of Human Tolerance: The 40s 128

A.7 Understanding the Collision 129A.8 Accident Investigation and Data Collection 130

A.9 Regulating the Industry 130

A.10 The I960s Rush for Safety Design 132A .l l The 1970s and Beginning of Airbag Era 132

B. A Runge-Kutta Program to Solve a System ofSimultaneous Differential Equations 134

C. 5th Percentile Hybrid HI Dummy ProtectionReference Values 13 8

D. Hybrid HI Dummy External Dimensions and Assembly

Weights 140

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LIST OF FIGURES

Figure 1.1 A Car-to-Car Simulation Using Finite Elements 6

Figure 2.1 The Hybrid HI Dummy 192.2 FE Model o f the Hybrid EH Dummy 212.3 Hybrid EH Dummy Chest 222.4 FE Model o f the Hybrid EH Chest 232.5 Dummy Position for Standard Impact Test 232.6 Ribcage Deformation of the Finite Element Chest Model 242.7 Resistance Force: Test vs. Simulation 252.8 Chest Centerline Deflection: Test vs. Simulation 25

2.9 Dummy Head External Dimension and Reference Frame 262.10 Head Drop Test 272.11 Head Drop Test Deceleration: Test vs. Simulation 272.12 FE Hybrid EH Dummy Neck Model 292.13 Hybrid HI Dummy Neck 292.14 Neck Pendulum Test Set-Up 302.15a Neck Pendulum Test:Extension 322.15b Neck Pendulum Test:Flexion 322.16 Pendulum Deceleration in Extension: Test vs. Simulation JJ2.17 Nodding Joint Bending Moment in Extension: Test vs. Simulation 33

2.18 D-Plane Rotation in Extension: Test vs. Simulation JJ

2.19 Pendulum Deceleration in Flexion: Test vs. Simulation JJ2.20 Nodding Joint Bending Moment in Flexion: Test vs. ?rmulation JJ2.21 D-Plane Rotation for Flexion: Test vs. Simulation JJ

2.22 Lumbar Spine Test 34

2.23 Results of Test vs. Simulation for the Lumbar Spine Test 352.24 Knee Test Simulation 362.25 Results of Simulation for the Knee Impact Test 362.26 Spherical and Cylindrical Joints in LS-DYNA3D 37

2.27 Load Curves Characterizing the Hybrid EH Joints 39

Figure 3.1 Time Line Showing Sequence of Events in Airbag Deployment 42

3.2 General Schematic of a Supplemental Restraint System 43

3.3 Crash Sensor Operation Principle 44

3.4 A Typical Pyrotechnic Airbag Inflator 45

3.5 Free Body Diagram of the Airbag Control Volume 48

3.6 Airbag Folding Patterns for Different Makes 51

3.7 Details of Foding Patterns for the overlapped Fold Usedin This Model 52

3.8 Free Body Diagram of a Typical Airbag Fabric Element 53



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3.9 Front and Side Views of the Simulated Folded Bag 54

3.10 Airbag Deployment: Test vs. Simulation (Front View) 563.11 Airbag Deployment: Test vs. Simulation (Side View) 57

Figure 4.1 Vertical Alignments: Bag-on-Head, Bag-on-Chest?and

Bag-on-Neck Respectively 604.2 Inflation Curves Used for Analysis 614.3 Effect of Inflation Rate on Head Acceleration 64

4.4 Effect of Inflation Rate on Neck Extension 64

4.5 Effect of Inflation rate on Neck Axial Loads 65

4.6 Effect of Inflation Rate on Chest Acceleration 654.7 Effect of Inflation Rate on Rib Deflection 66

4.8 Effect of Initial Separation on Head Acceleration 67

4.9 Effect of Initial Separation on Neck Axial Loads 674.10 Effect of Initial Separation on Neck Moments 68

4.11 Effect of Initial Separation on Chest Acceleration 68

4.12 Effect of Initial Separation on Rib Deflection 694.13 Effectof Initial Relative Velocity on Chest Acceleration 70

4.14 Effect of Initial Relative Velocity on Rib Deflection 71

4.15 Inertial Effect of Airbag Deployment on Chest gs 72

4.16 Inertial Effect of Airbag Deployment on Rib Deflection 72

4.17 Inertial Effect of Airbag Deployment on Reaction forces 734.18 Steering Column Characteristics of a 1985 Volvo 744.19 Chest gs Comparison Between a Rigid Column and

a More Realistic Column 75

4.20 Chest Deflection Comparison Between a Rigid Column

and a More Realistic Column 75

Figure 5.1 A Simple Impact Problem of Two Moving Bodies 77

5.2 A Simple Spring Mass System Representing the Impactof Two Moving Bodies 78

5.3 Simulation Set Up For Dummy and Vehicle Interior 805.4 Crash Pulse for the 30 mph Baseline Test 81

5.5 Velocity Time History of Vehicle eg for the 30 mph Baseline test 825.6 Chest Acceleration: Test vs. Simulation 825.7 Rib Deflection: Test vs. Simulation 835.8 Head Acceleration: Test vs. Simulation 83

5.9 Right Femur Load: Test vs. Simulation 84

5.10 Effect of Inflation Characteristics on Chest gs 895.11 Effect of Inflation Characteristics on Chest CenterlineDeflection 89

Figure 6.1 Airbag Inflation Rates Used in Simulation 936.2 Airbag Pressure Response in 30 mph Crash 946.3 Dummy Displacement in 30 mph Crash 96

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6.4 Chest Injury Measures for Five Crash Modes 99

Figure 7.1 Spring-Damper System Representing the Airbag, Chest, andCrash Pulse 104

7.2 The Lumped Mass Thorax Model Under a Blunt Impact 1067.3 Finite Element Simulation to Determine Spring Characteristics

of Airbags 1087.4 A Typical Kinematics Plot o f the Isolated Dummy Thorax

Impacting the Airbag 1097.5 Determining an Equivalent Airbag Spring Constant 1107.6 Determining an Equivalent Airbag Damping Coefficient 1107.7 Determining Ar from a Lumped Mass System 112

7.8 Spring Constants and Damping Coefficients as a Functionof Inflation rates 113

7.9 System Response for Different Airbag Inflation Rates 114

Figure A. 1 A 1901 Oldsmobile Runabout 126

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LIST OF TABLES

Table 2.1 Dummy Finite Element Model Joint Description 382.2 General Finite Element Model Description 40

Table 4.1 Unintended Fatalities Caused by Airbags 594.2 Results of Simulation for the Head Centered on Module Cases 624.3 Results of Simulation for the Chest Centered on Module Cases 624.4 Results of Simulation for the Neck Centered on Module Cases 634.5 Results for the Case Where the Dummy Has an Initial

AV of 2 m/s (7 mph) and Module Fixed 704.6 Results for the Case where Module Is Free to Move; Chest

Is Centered on Module with 0 mm Separation 714.7 Results for the Case Where Dummy Has an Initial AV of 2 m/s

and Module Attached to a Volvo Like Steering Column 74

Table 5.1 Input-Output Relationships Around The Baseline 87

Table 6.1 Simulation Results - 30 mph Barrier Crash 956.2 Simulation Results - 20 mph Barrier Crash 976.3 Crash Types and Deployment Timing For Inflation Rate Study 986.4 Simulation Results - 100% and 75% Inflation Rates 99

Table 7.1 Values for Ar for Two Inflation Rates and Two Initial Speeds 111

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efficient design of the vehicle interior and restraint system would minimise injury to

occupants by controlling the energy exchange of the second collision (occupants

impacting vehicle interior).

A typical restraint system today is composed of seat belts and one or more

airbags. The effectiveness of seat belts has been widely accepted. While the

webbing stiffness of seat belts varies between manufacturers, their performance has

not been controversial. On the other hand, the overall effectiveness of airbags have

been proven but their level of aggressiveness is still under debate. In the United

States for instance, airbags are designed to protect an unbeltedoccupant in a 30 mph

frontal crash into a rigid wall. In Europe and the rest of the world, a smaller less

aggressive airbag is used since it is only designed to protect beltedoccupants. The

present American design of the airbag has the advantage of reducing the risk of

injuries to occupants involved in higher severity crashes but can produce unintended

injuries to out-of-position (OOP) [5] occupants involved in low severity crashes.

Due to its reduced size -and energy level- thepresentEuropean design is less likely

to be effective for unbelted occupants and those involved in more severe crashes but

less harmful to OOP occupants.

Recent legislation in the United States allowed manufacturers to depower

airbags after several incidents where airbag deployment caused unintended fatal

injuries in low severity crashes. The debate over this issue was intense and

continues among researchers, lawmakers, and the general public. The goal of this

research is to use mechanics-based computer simulation to study the issues

surrounding the depowering of the airbag. The effects of the most common form of

depowering which involves the reduction o f the mass flow rate of the inflating gas-

is investigated. The effects of other parameters that come in contact with the

occupant or airbag, such as the steering column and knee board, are also studied.

These parameters are studied separately and in conjunction with the airbag inflation

levels. Crash environments for these studies include static tests, the 30 mph

FMVSS-208 standard test, 16 mph late deployment/low severity tests, 35 mph

barrier and car-to-car crash tests.

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1.2 Developing the Necessary Tools for Analysis

In order to study the effects of depowering and related parameters using

numerical tools, three models were needed: a vehicle model, an airbag model, and a

crash dummy model. Validated finite element models that represent a number of

different cars and trucks were available through the National Crash Analysis Center

(NCAC) and other organizations [6]. In addition, a finite element model of a

generic folded airbag was available. However, the few finite element models of the

Hybrid HI dummy that existed at the time were proprietary and could not be used.

The dummy models that were accessible were lumped mass models [7] [8]

[9]. Researchers used these models successfully in conjunction with seat belts. The

use of lumped mass models was practical with belts since belt loads can be

represented as point loads applied to the dummy at specific geometrical locations.Furthermore, with seat belts, no interaction occurs -except for the anchor points-

between them and the vehicle interior.

With the increased use of airbags in the nineties, and specifically to

perform depowering studies in this research, it was necessary to develop a validated

finite element model of the dummy. In response to this need, a dummy model that

incorporates enough details and flexibility to allow interaction with the distributed

nature of airbag loads was developed and validated. This model is comprised of

15,000 rigid and flexible elements and features full joint characterization. The

model was validated for frontal crashes and is available for other researchers to use.

A driver side airbag model that is folded and fitted to a steering wheel was also

validated. The dummy and airbag models were combined together in a vehicle

interior set-up with simplified components. The vehicle set up can be given the

weight o f a car and the velocity time history of a crash event. The components of

this vehicle set-up that can be easily varied include the steering wheel, steering

column, knee board, toe pan, seat, and windshield.

The combination of validated models of the crash dummy, an airbag, and a

vehicle interior with the ability to modify any number of parameters provides an

inexpensive and useful research tool to study current automotive safety issues and

explore experimental ideas.

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1.4 The Need for Finite Element Based Computer Simulation in

Crash Analysis and the Issue of Reliability

For years, computer aided engineering (CAE) has played an essential role in

the design and performance analysis of automobiles. More recently, computer

models have been developed for crash analysis. These models are based on the

finite element method and are used to analyze vehicle crashworthiness, occupant

kinematics, restraint system performance, and roadside hardware design evaluation.

Due to the destructive nature of crash tests, the use of computer models in

crash simulation becomes essential in the design process of the automobile. A

future goal of computer modeling is to replace Anthropomorphic Test Devices

(crash dummies) with full scale human models. Biomechanic research has already

produced sophisticated models of volumetric soft and hard tissue components.Progress is also being made in the areas of characterizing more complex, life-like

behavior such as muscle activation and material properties of brain fluids. Full

scale human models pose a challenge since they require large number of elements

due to the complexity o f the geometry, but more importantly, due to the difficulties

in material characterization [10].

Finite element models rely on proper geometric representation of the

physical object. In the process of discretization, the geometry is divided into

elements connected together via nodes (Figure 1.1). The number of elements for a

given geometry or domain determines the mesh density. Limited by round-off

errors, the accuracy of the solution is a function of mesh density. Accordingly, to

accomplish more accuracy, crash models are rapidly increasing in size and

complexity. Figure 1.1 is an example of a car-to-car collision with Hybrid HI

dummies and airbags. The size of this model is well in excess of 150k elements.

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Figure 1.1 A car-to-car crash simulation using finite elements.

The issue of reliability rises whenever a mathematical model is used to

represent a dynamic physical phenomenon. An understanding of the limitations of

any solution is important. The analysis based on a mathematical model can only

predict a phenomenon that is contained in the model. The reliability is then defined

with respect to the phenomenon to be predicted and with respect to the

mathematical model chosen. For example, researchers develop different vehicle

models for frontal impact, side impact, or rear impact. Each model is only expected

to be reliable when used within its intended purpose. In general, the reliability of a

finite element model is defined as one that gives reasonably accurate results under

any boundary conditions, loading, or material properties [11].

Many finite element codes have been developed to solve a variety of

engineering problems. Although the concept of the finite element method is unique,

many finite element-based codes can be implemented in ways that make them more

appropriate for specific applications. A popular code for solving the highly

transient non-linear dynamic problems encountered in crash analysis is DYNA3D[12]. This code was originally developed at the Lawrence Livermore National

Laboratory and became the basis for many commercially available crash codes such

as LS-DYNA3D [13], PAM CRASH [14], and RADIOSS [15]. These codes are

used around the world for crash analysis, metal forming, and other impact

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applications. LS-DYNA3D was available for use in this research and was used to

run the simulation analysis. The major characteristics of this code are briefly

presented in the following section.

1.5 A Brief Overview of LS-DYNA3D

The crash models developed in this work were constructed using different

preprocessors and the analysis was performed using the finite element code LS-

DYNA3D. LS-DYNA3D is an explicit 3D Finite Element code for analyzing large

deformation responses o f solids.

The governing equations are derived from the virtual work principle. The

virtual work is defined as the work done on a particle by all forces acting on the

particle while this particle is given a small virtual displacement. This virtual

displacement can not violate the constraints and the forces are held constant as the

particle is given the displacement. The virtual work for a deformable body having

surface tractions T, body forces b , an acceleration u , and under going a virtual

displacement Suis given as [16]:

SWvirt = 7)(v)Suid S dutdu (1-3.1)

using Cauchys formula:

T r = T ijVj (1.3.2)

where 7(v) are the components o f the stress vectors for any interface, r -are the

components o f the stress tensor, and vy are the direction cosines o f the unit normal

of the interface where the traction force is desired, combining the terms under the

triple integrals, the virtual work becomes:

5W,in = j] \ ( bi ~P Ui)5u(d u + ^ T ' j v f a d S . (1.3.3)

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Now using Gausss theorem:*

JI{.(V ) / u= o-3-4)

Equation (1.3.3) becomes:

* * * = - P Ui)Suidu+ W l i r ^ j d v . (1.3.5)

Now taking the partial derivative of the term inside the second integral:

= f J l t b ' - p u O f y d v + f fo (T iJ(&ii )J +Tij'j dui )du (1.3.6)

and rearranging:

3Wvirt = W lib i -p u i + T qJ dU id v + W^TqidUiXjdv (1.3.7)

The first integral vanishes since the term in parenthesis is the momentum equation.

This equation is derived simply from Newtons law for a mass dm:

d f= dm V (1.3.8)

where f is the sum of total traction forces 7(v) and body forces bt on a mass dm .

Integrating this equation over an arbitrary domain having a volume Vand surface S

and using tensor notation:

u(pdu (1-3.9)

using Cauchys formula (equation 1.3.2) and Gausss theorem (equation 1.3.4)

successively on the second integral, and collecting terms, this equation becomes:

J T J / ^ - p u ^ T y j )d v= 0 (1.3.10)

Ga usss theorem is a generalized form o f the more familiar divergence theorem where the tens or is

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and since the domain of the integral is arbitray it can be concluded that:

bi +rij. j - p u i =Q (1-3-11)

this is the equation of motion in inertial form.

Now going back to equation (1.3.7) and using the equation of motion

(1.3.11), the equation for virtual work becomes:

SW,ir, = JJIrii (* / ) . ;dv (1-3.12)

Equating equation (1.3.12) to equation (1.3.1), rearranging and noting that

(Su() j =S (uLj) = Ss{ j defines the principle of virtual work:

H I b,Su,dv+ T^Su,dS= H I ZydSjjdv+ JJp u id u ^ u (1.3.13)

where 8sj is a kinematically compatible strain field.

In essence, what this equation says is that the external virtual work (left side

of equation (1-3.12) must equal the internal work (first term of right side) plus the

acceleration term (second term of right side). If the problem is static, the 2ndterm of

right side vanishes, whereas for rigid bodies the first term of the right side becomes

zero.

In the more general form, a dissipative term JJc m Su^duis added to

equation (1.3.13). The dissipative term takes into account energy losses. Adding

this term and rearranging equation 1.3.13), it becomes:

jJX bM dv + j T ^ S u ^ S - \ \ \rpuiSuid u - \ \ \ c u i8iiidv= W^T ^e^du

(1.3.14)

= JJV. d A

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first degree (i.e. vector): H l d i v V d v



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The finite element method makes use of the above equation (1.3.14) by

manipulating this mathematical relationship using geometrical approximations.

Following the process of discretization, where the body is divided into finite

elements, this method transforms equation (1.3.14) into matrix form where it can be

solved using a computer. In matrix form, equation (1.3.14) becomes:

\ \ [ m S u } r d o + l [ T M {du}Td S \\ [p [ i] { d u} Td u - \ \ [ c [u ] { d u } Td u

J * J [r /y] {8 }T d v (1.3.15)

The nodal coordinates of each discrete element (linear, triangular,

rectangular, equilateral, etc ....) is defined by the preprocessor. Interpolation or

shape functions [A/] are used to relate the displacement field for an element to the

nodal displacement for the element {d). For a three dimensional element, the

displacement field is expressed as:

u{ x ,y ,z ) = [u] = [N]{d} (1.3.16)

and

[] (1-3-20)

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while the strain is related to the nodal displacement as:

\_Se} = {B}{Sd}r (1.3.21)

The matrix form of equation (1.3.15) then becomes:

( l \ i l b tN Y u + \ [ T l' \ N V S - \ \ [ p [ N m m d u - \ \ l < i N m { N - \ d u \Sd)T =

J J J ( [ ] [ 3 M S ] Y S d f d v (1.3.22)

Next, several of the parameters in equation (1.3.22) are grouped together:

{q) = l \ [ m N o + ^ ' [ N y s (1-3.23)

[ M \ = \ [ l p [ N f [ N Y v (1.3.24)

[ C ] = \ \ l ^ N f { N V o (1.3.25)

where {q} is normally associated the external forces, [M] is called the mass matrix,

and [C] is called the damping matrix.

Also, the right hand side o f equation (1.3.22) can be written as:

W l i D m w m d u = [ d][b v v w =[ Km (1.3.26)

Equation (1.3.24) can now be written as:

[M] (d) +[C] {d} +[.K] {d} = {q} (1.3.27)

Up to this point the governing equaitons were discretized in the spatial domain. The

next step is to discretize equation (1.3.29) in the time domain and express at time n

as:

[M]{d}n+[C]{d}n H K \{ d }n ={q}n (1.3.27a)

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The finite difference method is used here. The choice of step size and a

particular finite difference method determines whether the solution will be implicit

or explicit. In the finite difference method, a time dependant differential equation is

transformed into an algebraic equation. Taylor series expansions are used to

express the displacement field at two adjacent time points. The two equations aremanipulated to obtain the first and second derivatives in discrete forms:

W U ={


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W +l J & t 2{q} -M *[K]{d}n+ [M ](2 {flf} - {d } _ ,) + M Q { _ ,V 2.

*

(1.3.32)

The problem with equation (1.3.32) from a standpoint of large problem

applications as the ones encountered for crash simulations is that it requires the

inversion of the non-diagonal damping matrix [C ]. This matrix inversion requires

iterative solutions that involve tremendous storage requirements. This method of

solving the matrix equations is called implicit.

In order to overcome this difficulty, the time discretization of equations

(1.3.28) through (1.3.31) will be manipulated in such a way that an equation

expressing [{


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-m+{d}.i)+^r(w.-w,i)+ma = {?>Ar Ar

(1.3.35)

From equation (1.3.35), a new expression for the updated displacement field can be

obtained:

w +. =

[M]-'(a/2{?> + (2 [M ]- aF[X]-A/ [C]){rf} -( [W ] + A/[C]){rf}_,)

(1.3.36)

The difference between equations (1.3.36) and (1.3.32) might seem trivial but

mathematically the difference is very important.

In summary, implicit methods of integration use full time step intervals for

time discretization. Furthermore, implicit methods use the forward difference

operator to obtain the algebraic equations. The result is a set of equations that are

independent of the time step but require iterations for convergence of the solutions.

Implicit methods then require a large amount of computer storage and lend

themselves to static analysis.

In the explicit method however, the velocity is discretized at half-time

intervals while displacement and acceleration are discretized at full-time intervals.

The successive use of the central difference dynamic operator leads to a set of

algebraic equations where only the diagonal mass matrix needs to be inverted.

Solution of this system of equations is trivial and does not require the formulation of

global stiffness matrix and thus reduces computer storage. The disadvantage of the

explicit method however, is that it puts an upper limit on the time step A t (due to

lagging the velocity by a ha lf time step) for stability requirements. A simple form

of the stability requirement is the Courant-Friedrichs-Lewy criteria:

A LAt < (1.3.37)

c

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where Lis the characteristic length of the element and c is the speed of sound or

speed of wave propagation. In other words, The numerical time step must be

smaller than the time needed by the shock wave to cross the element.

In crash simulation, it is common for an average minimum side length of an

element to be 5 mm and considering the speed of sound o f steel materials to be 5000

m/s, the minimum time step is approximately 1 microsecond (ps). The small time

step required for stability increases running time but it may be justified because

large distortions of the structure over relatively short duration may require a small

time step regardless of stability. Accordingly, the structural states can be

determined at many discrete points in time in order to allow for an accurate tracing

of the complex physical phenomena that occur during a crash. In addition, given

that an average 1 ps time step is needed for reasonable running time, a minimum

element characteristic length of 5 mm becomes the limiting factor for accurate

representation o f crash model geometry.

1.4 General Discussion of Material Models and Element

Formulation

LS-DYNA3D incorporates about 80 material models that are capable of

representing a range of material types from simple elastic to more complex ones

such as multi-layered composites and crushable honeycomb. Implementing user

defined material models is also possible in this code. Additionally, gases can be

modeled in this code using equations of state. This option is mentioned here to

show versatility of the code but no gas dynamics problems are handled in this work.

Many element types are also available. Beam, shell, thick shell, and solid

elements are formulated using a choice of algorithms. Each algorithm is useful or

preferred for a particular application. The choice of method for element

displacement representation, distribution of element mass into the nodes, stress and

strain update, reference frames, the number and location of integration points make

each formulation technique different.

Computational efficiency is the most important parameter in choosing a

particular element formulation. Because of its computational efficiency, the

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Belytschko-Lin-Tsay shell element is the most popular element and is used as the

default shell element. This particular shell element is formulated in such a way that

it does not put any restriction on the magnitude of the elements rigid body rotation.

Rather the restriction is imposed on the element strain. This makes it suitable for

use on vehicle exterior under impact similar to a crash environment

As an example of what is involved in element formulation, the Belytschko-

Lin-Tsay element is briefly described here. A reference coordinate system is made

to deform with the element. The displacement of any point in the element is

partitioned into a mid-surface displacement (nodal translation) and a displacement

associated with the rotation of the element fibers (nodal rotation). The velocity o f

any point in the shell is also partitioned in a similar maimer and according to the

Mindlin theory o f plates.

1.5 Contact Algorithms

Several contact types are available in LS-YNA3D. The user specifies slave

and master surfaces and the direction of no penetration. More advanced contact

types allow the user to specify materials. All contact algorithms depend heavily on

advanced geometrical manipulation. In contact algorithms, nodes of the slave

surface are checked for penetration against master segments at every time step.

When a node is determined to have penetrated a master segment, a force is applied

between the slave node and its contact point on the master segment. This force is

called in LS-DYNA3D and throughout this work as the interface force. This force

can be output inx, y,or z direction or as a resultant force. The magnitude of this

force is proportional to the amount of penetration and a stiffness factor that depends

on element geometry and element properties. This force can be thought of as an

interface spring:

f s= ~lk ni (1.5.1)

where / is the amount of penetration determined from geometry, n is a normal

vector to the master segment, and ki is the stiffness factor. The stiffness factor of

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an element is defined in terms of bulk modulus Kt , element face area Afand

element volume Vt , and a scale factor s :

(1.5.2)

This interface force is added to the slave node.

An equivalent force f lmis applied to the nodes comprising the master

segment. The magnitude of this force is:

(1.5.3)

Where h( is a factor that distributes the force into the nodes comprising the master

segment depending on the node location and segment orientation.

1.6 Analysis Procedure and Text Organization

Having defined the scope of this work and the method to be used, an outline

of this dissertation follows. Chapter 2 introduces the Hybrid HI dummy model and

its components and discusses the correlation with the physical Hybrid IE. Chapter 3

presents the airbag model and its finite element basis and describes the operation of

the supplemental restraint system. Chapter 4 addresses the issue of depowering as it

is related to reducing injuries to out-of-position (OOP) occupants, and investigates

the other parameters involved in OOP situations. Chapter 5 deals with the effect of

depowering and other pertinent design parameters on injury level requirements of

the Federal Motor Vehicle Safety Standard (FMVSS) 208. Chapter 6 investigates

the effect of inflation rates on occupant kinematics and chest injury measures under

a wide range of realistic crash modes. Chapter 7 introduces lumped mass models of

the Hybrid m dummy chest and the airbag and uses these models to characterize the

airbag at any inflation level as a spring damper system. Chapter 7 provides a

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summary of results and conclusions. Appendix A is a brief overview o f automotive

history while the rest of the appendices provide additional information on pertinent

subjects.

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CHAPTER 2

THE DEVELOPMENT OF THE HYBRID El DUMMY

MODEL

2.1 Introduction

The Hybrid HI dummy is an anthropomorphic test device that mechanically

represents the human body (Figure 2.1). By mimicking the geometry, weight, inertia,

jo int stiffness, and energy absorption characteristics of humans, anthropomorphic test

devices are expected to simulate human response when exposed to a crash environment.

Basic instrumentation on the dummy that is required for FMVSS-208 compliance testing

include head and chest uniaxial accelerometers, a chest rotary potentiometer, and uniaxial

femur load cells. While earlier dummies were not instrumented and were only expected

to test the integrity of seatbelt systems and possibility of ejection, todays dummies are

far more sophisticated. Recent dummies used for research and development can produce

over 80 signals measuring accelerations, forces, displacements, and joint moments in all

pertinent locations.

Figure 2.1 The Hybrid IE dummy [17].

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The meaningfulness of the numbers obtained from dummy instrumentation and

their interpretation as to the level of injury they represent goes to the heart of dummy

design. Once dummies are given the pertinent physical characteristics ofhumans, their

behavior is expected to represent -in a general and crude sense- human behavior.

Engineers ascertain the correspondence early in the development stage by correlating

specific test results obtained from cadavers and dummies.

The human chest for example is a major area of concern in automobile accidents.

To develop a dummy with exact chest would obviously be impossible due to durability

requirements of mechanical parts, the complexity o f geometry and more importantly due

to the unknown properties of human bones, muscles, and other live tissues. Rather,

engineers developed a dummy chest made from plastics, metals and viscoelatic polymer

materials. The dummy chest is calibrated by a test in which the chest of the dummy is

subjected to a blunt impact by a 23.4 kg, 6 diameter pendulum having an initial velocity

of 6.7 m/s. The response of the chest in this test must be similar to human response. Key

parameters such as the deflection time history of the chest centerline and the load applied

are compared. Materials that make up the submodel, their properties, or their shapes are

modified until an acceptable response corridor is achieved. The results are then

correlated and the dummy chest is then said to be biofidelic.

The process of correlating results o f simulated dummies (Figure 2.2) with actual

dummies is identical to the process used in correlating human test results with actual

dummies. In both cases, a certain level o f confidence is to be established between the

actual object and a simplified representative of it. Fortunately, in the process of creating

computer simulation models, repeatability, reproducibility, ease and accuracy of initial

set up, are inherently solved problems. The process of correlating data between actual

tests and simulation tests is commonly referred to as validation.

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Major parts of the finite element model are validated here. The process of

validation ensures that results obtained using the model would reflect, to a certain degree

of accuracy, the results that would have been obtained if the physical model were used.

Figure 2.2 FE model of the Hybrid EH dummy.

The rest of this chapter is devoted to describing several tests that were performed

on the physical dummy as part of design specification or biofidelity assurance. The tests

were then simulated using the finite element model. Results of tests vs. simulations are

then presented for comparison and proof of validation.

2.2 The Chest Model

The Hybrid HI dummy chest model consists of a rib cage covered by a removable

jacket and bolted to a welded steel spine. The ribcage consists of six steel ribs of unequal

dimensions and contoured to approximate human form (Figure 2.3). A layer of

polyviscous damping material is bonded to the inside o f the ribs to provide the proper

dynamic response in blunt frontal impact. Leaf springs help control bending of the ribs at

their narrow attachment to the spine. In the front, the open-ended ribs are connected

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together by inner and outer vertical stiffeners. Horizontally the ribs are all connected to

an aluminum sternum by a thick plastic plate and a urethane bib. A sternum pad helps

distribute the weight and a jacket enhances the human like appearance o f the dummy.

All the above parts are included in the finite element model thorax shown in

Figure 2.4 with the bib and jacket removed for illustration purposes. The geometry of

these parts is accurately represented using the original dummy engineering drawings.

The sternum is modeled as an elastic material with properties of aluminum. The ribs

damping materials and sternum pad are modeled as solid elements with viscoelastic

material properties. The rest of the parts are elastic materials with properties of steel (see

Table 2.2 at the end of the chapter for a complete list of materials and their properties).

Figure 2.3 Hybrid HI dummy chest.

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Figure 2.4 FE model o f the Hybrid III chest.

To validate the chest model, the standard thorax impact test was followed (Figure

2.5). Details of this procedure are described in part 572 of the Code o f Federal

Regulation. In this test, the dummy is seated on a flat surface without back and arm

support and the angle of the pelvic bone is set to 13. The midsagital plane o f the dummy

is centered along the centerline of the pendulum. The probe in the centerline o f the

pendulum is set to coincide with a point .5 " below the number 3 rib. The pendulum,

which weighs 23 kg, is allowed to impact the chest at a speed of 6.7 m/s. The probe is

guided during impact so that no significant vertical, lateral, or rotational movement is

allowed. The simulation is set up to be identical to the real test shown in Figure 2.5.

Figure 2.6 shows deflection patterns of the dummy ribcage under impact loading.

Figure 2.5 Dummy position for standard impact test.

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The behavior of the system is then compared with test results to confirm a

correlation between the two. The standard specifies that the resistance force be 5525

350 Newton, the chest centerline deflection relative to the spine be 68 5 mm. The

overall curves for centerline deflection time history and for the resistance force areplotted for both test and simulation as shown in Figures 2.7 and 2.8.

J ..S. T CI ' / v / .V i .Wv* W'.iuijw:tr>. 4 iL'.fKftt - I V V ' . t / .T V .

"igure 2.6 Ribcage deformation o f the finite element chest model.

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7000

~ 5000

3000

O. 1000

20 40 60-1000

Time (ms)

Figure 2.7 Resistance force: pendulum test vs. simulation

E

40coo


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left euryon to right euryon) 155 mm 2.5, and the maximum head circumference above

the brow line 572 mm 5.

n

r.zTOtergfg

N S i i < ! ^ p r 9 r f M a

.v-A-'-'.^..^ guitri(anions ,

v?rS*2

Figure 2.9 Dummy head external dimension and reference frame [18].

Experimental results on head weight suggest a weight of 4.54 kg for the average

male head. The eg location of the head would have the coordinates (-76.2 mm, 0 mm, -

12.7 mm) relative to the reference system shown in Figure 2.9. The mass moment of

inertia about a lateral axis passing through the eg is determined as .00238 kg-m-s2.

The head drop test is a simple test used to compare dummy head dynamic

response relative to biomechanical data. In this test the head is suspended in a tilted

position such that the lowest point on the forehead is 13 mm below the lowest point on

the nose while the midsagittal plane is kept vertical (Figure 2.10). The head is dropped in

this configuration from a height of 376 mm and allowed to impact a rigid plate with a

closing speed of 2.7 m/sec. Part 572 of the Code of Federal Regulation specifies that the

peak resultant acceleration of the eg be no less than 225 gs and no more than 275 gs.

Figure 2.11 shows a comparison between head center of gravity acceleration time history

of test and simulation [19],

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Figure 2.10 Head drop test

250


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Two end plates are molded in and used to attach the neck to the head and torso. A steel

cable is bolted between the end plates and used to limit axial loading of the neck.

The geometry o f the neck is asymmetric in the anterior posterior plane in order to

provide more bending resistance to flexion (forward rotation) than extension (backward

rotation). Additionally, horizontal slits in the anterior mid section of the rubber elastomer

further reduce resistance to extension without affecting flexion. The base of the neck is

bolted to a neck bracket, which in turn is bolted to the thoracic spine. The combination of

rubber and vertebral plates give the neck flexibility in its motion relative to the upper

torso.

Except for the neck cable and the holes drilled at the end of the slits, all features

of the Hybrid HI neck are included in the finite element model (Figure 2.13). Ignoring

the neck cable in the finite element model has minor effect since the cable would only

interfere with the performance of the neck if it were to over-stretch.

On the other hand, not including the holes in the neck (which are presumably

made to prevent the rubber material from splitting) may stiffen the response of the neck

in extension. The neck rubber material is modeled as solid elements with viscoelastic

material properties. The aluminum vertebrae are modeled as rigid material with the

correct weight. The rigid vertebrae and the viscoelastic elements are merged together. A

contact is specified between the horizontal slits for proper flexing motion.

The occipital condyle joint between the head and neck is modeled as a pin joint

between the upper neck plate and base of the head. The load curve defining moment

resistance of this joint is obtained from the literature [20] and described in Table 2.1.

The new version o f the dummy under developm ent does include the neck holes.

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Figure 2.12 FE Hybrid HI dummy neck

Figure 2.13 Hybrid HI dummy neck

The finite element model for the head-neck complex is validated against the neck

calibration test as described in the Code of Federal Regulation. In the test, the Hybrid EH

head neck assembly is mounted upside down on a 27.6 kg rigid pendulum as shown in

Figure 2.14. The pendulum is released from a height and is allowed to swing and impact

a block of aluminum honeycomb. The height is such that the tangential velocity

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Figure 2.14 Neck pendulum test setup.

at the pendulum accelerometer centerline at the instance of contact with the honeycomb is

23.0 .4 ft/sec for flexion and 19.9 .4 ft/sec for extension. The code specifies ranges

for pendulum deceleration, occipital condyles moment, and head D-plane rotation at

certain intervals. Simulation of the pendulum test was performed in a modified manner.

Instead of impacting the dummy with the honeycomb block -the purpose of which is to

give the pendulum a stepped acceleration pulse- the pendulum was given this pulse as a

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velocity time history. Figure 2.15 below shows the simulated pendulum test head-neck

kinematics in flexion and extension while Figures 2.16 through 2.21 shows correlation

between test and simulation. Simulation results show reasonable agreement with test

results. Some deviations are observed -especially in D-plane rotation in extension- but

the values were within the acceptable corridor of performance. The differences could be

due to the deceleration of the pendulum, the modeling of slits in the neck rubber, or the

material properties of the rubber material itself.

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(ax' -\ v . .

ngure 2 .15a Pendulum test: extension igure 2.15b Pendulum test:flexion

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^ggtg^srmglg.^5

0

5

-10

-15

-20

-25a.0 15 30 45 60

Time (ms)

Figure 2.16 Pendulum deceleration in extension:

test vs. simulation.

o -10

| -15

-20

| -25-30

40

Time (ms)

7igure 2.19 Pendulum deceleration in flexion: test

vs. simulation.

50

o

-50as

Z -100

0 25 50 10075 125Time (ms)

7igure 2.17 Nodding joint bending moment in

extension: test vs. simulation

1 srmuiMtonfeTestI--.' - l i

80

40

z-40

-80

-120

0 12040 80

Time (ms)

7igure 2.20 Nodding joint bending moment in

flexion: test vs. simulation

:Testf iSimulatrorr

Q

3oDC

0cJOCL1Q

0

-20

-40

-60

-80

-100

1250 50 10025 75

Time (ms)

Figure 2.18 D-Plane rotation for extension: test vs.

simulation

;S|nujaBfflr agnjest

us

-40

-80

120

Time (ms)

igure 2.21 D-PIane rotation for flexion: test vs.

simulation

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2.5 The Lumbar Spine Test

The simulated lumbar spine shown in Figure 2.22 represents a 45 curved member

made of rubber (polyacrylate elastomer). The curved lumbar spine allows the dummy to

assume a slouch position with the proper eye location in order to better simulate a human

placed on a vehicle seat [21]. For lateral seating stability, Two steel cables pass through

the lumbar spine and attach to the end plates. Though the cables provide lateral stiffness,

they do not interfere with the dummys fore and aft flexibility and they are not included

in the FE model. The geometry of the lumbar spine is modeled accurately and taken from

engineering drawings of the Hybrid III dummy.

In order to model the flexibility of the lumbar spine properly, a procedure found

in reference [22] was followed. This reference describes a test where a moment (pure

bending) ramp function is applied at the top plate of the spine while the base is rigidly

mounted on a vertical structure. This test was simulated here and the result is shown in

Figure 2.23. The simulation curve shows reasonable correlation with the test at small

rotations but tend to be stifter with large rotation. The new version of the dummy

incorporates a better material model for the spine and correlates better with test results.

However the current lumbar spine model is acceptable since it compares well with other

published simulation results [23] while the standard does not specify a range o f values.

Figure 2.22 Lumbar spine test

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250

Simulation -a- test

200 -

i 150 -

| 100 ..

50 -

25

Rotation (degres)

Figure 2.23 Results o f test vs. simulation for the lumbar spine.

2-6. The Knee Test

The knee assembly and particularly the kneepad are important parts of the Hybrid

HI design since they influence the calculated femur load. In the finite element model, a

pin joint between the femur and the lower leg is used to represent articulation motion

between the two. The physical knee assembly also allows translation at this joint. But

the finite element model does not incorporate this feature since it is only useful when the

load is applied below the knee [24]. The characteristics of the knee pads, however,

influence the amount of force transmitted by the pendulum impact test.

According to the knee impact test described in the Code of Federal Regulations,

the knee assembly is detached from the dummy and rigidly connected to a large mass as

shown in Figure 2.24. A 5-kg mass pendulum is used to impact the kneecap at a speed

of 2.26 m/s. The test specifies that the resultant force on the knee be between 4700 N and

5800 N. In the finite element model, the parameters of the viscoelasic pad material were

adjusted to give a reasonable correlation with the test requirements. Since test data was

not available for the time history of the impact forces it was only possible to show that

the peak impact force from simulation (5200 N) does fall in the specified corridor

(between 4700 N and 5800 N) as mentioned above. The time history of simulation is

presented in Figure 2.25.

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Figure 2.24 Knee test simulation

7000

5000

4)O

3. 3000utm3 1000

-1000

Time (ms)

Figure 2.25 Results of simulation for the knee impact test.

2.7 Joint Modeling

The subparts of the finite element model are assembled together using a

combination of joint definitions and torsional springs. A joint definition is used to

constrain the motion of two parts relative to each others while a torsional spring is used

to apply the correct stiffness. LS-DYNA3D supports the use of nine different joint

definitions. However, only the two joints shown in Figure 2.26 are used in this model:

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spherical (used between the pelvis and femur) and revolute (or pin) used on all other

joints.

Revolute jointSpherical joint

Figure 2.26 spherical and cylindrical joints in LS-DYNA3D [25]

The way joints are defined between two rigid bodies is through the use of two

local coordinate systems. Three nodes that are attached to the rigid body using extra

nodes for rigid bodies define each coordinate system. Two of the nodes define the

rotational degree of freedom of the joint. Each pair of local coordinate system is initially

coincident. As external loads are applied, a resisting torque will counteract using the

torsional springs load curves of moment vs. angle (Figure 2.27). A torsional spring axis

is made to coincide with that of a joint allowing it to define the stiffness of the joint.

Joints in LS-DYNA3D are designed to allow for stiffness definition. However, the use of

torsional springs with zero joint stiffness was found to give better results. Torsional

spring stiffness values are obtained from published reports on Hybrid m dummies and

their finite element models [26] [27]. Table 2.1 below lists all the joints used, their local

coordinate systems and stiffness values while Table 2.2 lists all the materials used, their

properties, and their number designations.

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joint # type

Materialsconnected Description of materials

local coord.Sys.# used

TORSIONAL SPRING*

material #. elem. #, &load curve #

I revolute 24 & 23 L foot*L lower leg I & 2 I

2 revolute 23 & 22 L lower leg ->L femur 3 & 4 2

j spherical 22 & 25 L fem ur pelvis (y axis) 5 & 6

3 (y axis)

20 ( x axis)

21 ( zaxis )

4 revolute 46 & 47 R foot > R lower leg 7 & 8 4

5 revolute 47 & 48 R lower leg -+R femur 9 & 10 5

6 spherical 48 & 25 R femur >pelvis (y axis) 11 & 12

6 ( y axis)

22 ( x axis)

23 ( z axis)

7 revolute 45 & 44 L hand L forearm 13 & 14 7

8 revolute 44 & 42 L forearm > L upper arm 15 & 16 8

9 revolute 42 & 43 L upper arm -> L sh. bracket 17 & 18 9

10 revolute 43 & 37 L sh. Bracket - L shoulder 19 & 20 10

II revolute 37 & 29 L shoulder -* L clavicle 21 & 22 11

12 revolute 29 & 26 L clavicle -+thoracic spine 23 & 24 12

13 revolute 49 & 50 R hand > R forearm 25 & 26 13

14 revolute 50 & 51 R forearm -> R upper arm 27 & 28 14

15 revolute 51 & 52 R upper arm -> R sh. bracket 29 & 30 15

16 revolute 52 & 38 R sh. Bracket -*R shoulder 31 & 32 16

17 re vo lute 38 & 30 R shoulder >R clavicle 33 & 34 17

18 revolute 30 & 26 R clavicle thoracic spine 35 & 36 18

19 revolute 53 & 13 head neck 37 & 38 19

Table 2.1 Dummy finite element model joint description



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Load curve Nos 1 & 4 Load Curves 10,11,16, & 17

c

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P A R T

Tauruspart #

weight

(kg)

material

type

Element

typePoissons ratio

densitykg/m3

youngs orbulk mod

ulus MPA

GO

MP

A

Goo

MPA

# o f

elem.

head 53 4.51 elastic Shell .3 rigid 200e3 400

head sidn 19 elastic Brick .499 4e-10 100 364

neck disks 9-13 Brick rigid 458

neck rubber 17 Viscoelas. Brick 2.1e-9 113 4.3 3.5 1232neck bracket 27 Shell rigid 66

clavicle L 29 1.9 Shell rigid 254

clavicle R 30 1.9 Shell rigid 254

shoulder L 37 2.08 Shell rigid 273

shoulder R 38 2.08 Shell rigid 273

shoulder

bracket L43 .32 Shell rigid 58

shoulderbracket R

52 .32 Shell rigid 58

shoulderpadding

15 .5 Brick 208

upper arm L 42 2.09 Shell rigid 164

upper arm R 51 2.09 Shell rigid 164

u. arms skin 20 Brick 284

forearm L 44 1.73 Shell rigid 88

forearm R 50 1.73 Shell rigid 88

f. arms skin 21 Brick 192

hand L 45 .586 Shell rigid 384

hand R 49 .586 Shell rigid 384

thoracicspine

26 17.6 Shell rigid 575

ribs 1-6 31-36 .28

ea.

elastic Shell .31 7.9e-9 200e3 * 1028

ribs damp,

materials

1-6 .05

ea.

Viscoe last. Brick .7e-9 1010 10

5

5 764

leaf springs 41 .3 Elastic Shell .31 7.9e-9 200e3 192

rib stiffeners 40 .2 Elastic Shell .31 7.9e-9 200e3 68

sternum 39 Shell 86

Jacket 8 1.3 Elastic Brick .499 .7e-9 4.35 1315

bib 28 .1 Elastic Shell .3? 7.9e-9? I00e3 563

lumbar spine 7 .9 1.8 Viscoelast. Brick I.3e-9 230 6.6 5.5 572

pelvis 25 19.8 Shell rigid 420

pelvis skin 14 .40 Elastic Brick .499 3e-9 4.35 132

upper leg L 22 6.23 Shell rigid 254

upper leg R 48 6.23 Shell rigid 254

knee cap L 16 Viscoelast. Brick ,33e-9 300 40 3 102

knee cap R 18 Viscoelast. Brick .3e-9 300 40 3 102lower leg L 23 3.29 Shell rigid 252

lower leg R 47 3.29 rigid 252

foot L 24 1.25 Shell rigid 142

foot R 46 1.25 Shell rigid 142

Table 2.2 General finite element model description

All Viscoelas tic materials are modeled with a delayed time t=0.5 seconds

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CHAPTER 3

THE AIRBAG MODEL

3.1 Introduction

Since 1988, it is estimated that 56 million airbags were fitted in vehicles and

800,000 of them were deployed. The result is a total saving of 1664 lives in addition to

reducing severe injuries. In 1997 when all cars will be equipped with airbags, it is

expected that 3000 lives will be saved annually due to airbag deployment alone [28].

Federal regulation FMVSS-208 influences major aspects o f airbag system design.

FMVSS-208 requires manufacturers to show that injury levels for an unbelted 50th

percentile Hybrid III dummy does not exceed a specified level in a 30 mph frontal crash

test into a rigid wall [29]. Figure 3.1 shows a time line schematic of factors involved in a

typical 30 mph crash which involves airbag deployment.

In the 30 mph crash test, the dummy is seated in normal position that corresponds

to mid-setting seat adjustment so that an average distance between the bag and dummy is

predetermined. In order for the airbag to perform well, it has to be fully inflated jus t

before occupant impact. The relative distance and relative velocity between the dummy

and airbag module in the initial stages of the crash determine the speed of inflation.

Another factor that affects the speed of inflation is sensing time. Sensors that trigger

airbag deployment via the ASDM (Airbag System Diagnostic Module) require an

additional period of time to determine a definite crash event.

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Figure 3.1 Timeline showing

42

t=l5 ms: ASDM has just confirmed a crash

t=20 ms: Airbag breaks cover

t=30 ms: Dummy moved slightly

t=40 ms: Dumm y to airbag contact

t=50 ms: Airbag fully inflated (60 Liters)

of events in airbag deployment.



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It can be concluded from Figure 3.1 that current driver-side airbag technology

requires producing 60 Liters of gas in about 45 ms from the time o f initial impact.

Generating this volume of gas at this speed requires an explosion like phenomenon. Gas

generation is accomplished via the inflator. The inflator is normally housed inside the

airbag module and must provide the airbag with predetermined gas flow characteristicsfor optimum occupant protection.

3.2 Concept of a Supplemental Restraint System

Inflater module

diverter

Steering column fassembly

Figure 3.2 General schematic of a supplemental restraint system [30].

The diagram shown in Figure 3.2 describes one type of a supplemental restraint

system. The first task of the system is to react to an impact and issue an electrical signal.

Crash sensors are designed to accomplish this task. Crash sensors are electromechanical

devices mounted in several front areas of a vehicle and are designed to trigger at a

deceleration that is equivalent to a 16 - 19 mph crash into a rigid barrier. Most sensors

use some type o f inertia switching mechanism: a ball held captive by a magnet would roll

forward under impact closing the contacts (Figure 3.3). This device has to be extremely

reliable. It is normally sealed in a can and some of its parts are gold plated.

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Figure 3.3 Crash sensor operations principle

Most cars use five sensors: two at the radiator support, one at each front fender

apron, and one in the passenger compartment, some cars like the Chrysler system shown

in Figure 3.2 use only two sensors in addition to a safing sensor. The safing sensor helps

the ASDM (Airbag System Diagnostic Module) confirm the magnitude and/or direction

of forces involved in an impact. In general, sensors are interlocked and at least two

sensors have to issue a signal before a system can trigger a deployment.The ASDM is responsible for issuing the final signal for deployment. Several

types of algorithms and criteria are used to make the final decision to deploy the bag.

The difference can be found between car makes, car sizes, and countries. Research in

this area is intensive and designs are constantly changing to achieve most efficient and

safest systems.

From the ASDM, the signal goes to the inflator module housed in the steering

wheel. The igniter inside the module is a two pin bridge device that allows the applied

current to arc as it crosses its two pins. The spark created ignites a charge of gas (often

called squib) containing zecronic potassium perchlorate (ZPP) or boron potassium nitrate

(BKNO3). A small quantity of these highly exothermic materials helps ignite the sodium

azide (NaNs) solid propellant. The combustion of sodium azide generates nitrogen gas

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that fills the bag. Oxidizers and binding agents are mixed with the gas generating

propellant in order for the combustible products to form a slag that can be captured by the

filters. Nitrogen gas produced by combustion is filtered and cooled as it exits the inflator

through holes cut all around the inflator body [31]. The process just described is for a

pyrotechnic inflator. Figure 3.4 shows a schematic of such an inflator.

Autoignitionc h a r g e -Igniter charge- / ^

Diffuserscreenassembly

Label

Figure 3.4 A typical pyrotechnic airbag inflator [31].

After exiting the inflator, Nitrogen gas enters the bag and the process o f filling the

bag begins. The airbag cover breaks at a specified pressure, usually occuring the first 5

ms after ignition. Nitrogen gas then enters the airbag. The driver-side airbag itse lf is a

60 to 70 cm diameter (the passenger-side airbag is much bigger) coated nylon bag. It is

folded several times to fit inside the steering wheel assembly. When fully inflated, the

airbag volume -under standard temperature and pressure- reaches about 60 Liters (2.5

ft3). The process of filling the bag itself with gas takes about 20 ms.

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3.3 Airbag Volume Calculations Using Element Geometry

Analysis of the inflation phenomenon requires breaking the process into several

control volumes. The last control volume in the thermodynamic analysis is that of the

airbag itself. The airbag is defined as membrane shell elements representing the fabric

material. The position, orientation, and surface area of every element is computed at

every time step. The control volume is then defined as that volume enclosed by the

surfaces of the shell elements [25]. The divergence theorem, with simple manipulation,

is used to compute the control volume as follows: the general form of the divergence

theorem is:

(3.3.1)

where

F=M (x ,y, z)i+ N(x, y, z ) j +P(x, y, z)k (3.3.2)

is an arbitrary vector field, Nis a unit vector normal to the element surface, and

divF= dM/ dx+ dN/ dy + dp/ dz. ^

Since F is an arbitrary vector, it is chosen as F =xi for simplification, hence

(3.3.3)

divF= 1. (3.3.4)

The divergence theorem then becomes:

control volume = V.

(3.3.5)

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Numerically, the volume is then approximated using a summation over the element

where xiis the average x coordinate value, is the direction cosine between the element

normal and thexaxis, and Aiis the surface area o f each element.

In order to avoid numerical errors associated with the direction cosine of an

element becoming nearly zero, the x axis is not chosen as the integrating direction.

Rather, this direction is chosen parallel to the maximum moment of inertia of the surface.

In the simple airbag model, the gas inside the control volume is assumed ideal

with uniform pressure and temperature. The mass flow rate of the gas entering the airbag

from the inflator is assumed to be given as a function of time. The input gas temperature

is also an input to the model and is typically reported by inflator manufacturer. Exit areas

and fabric material porosity are also specified. The principal parameter of interest is the

pressure inside the airbag. Determining the pressure inside the bag requires the following

calculations:

equation of state (Gamma Law; to be discussed below) derived from thermodynamic

relations o f an ideal gas under adiabatic expansion

conservation o f mass

external forces due to contact with dummy or vehicle interior as well as pressure

gradient with surrounding

internal forces from tethers, fabric membrane forces, and fabric self contact

input gas temperature, density, and other thermodynamic properties such as Cp

(specific heat at constant pressure) and Cv (specific heat at constant volume).

A diagram of the airbag model is shown in Figure 3.5. m designates mass flow

rate while m is the total mass inside the bag. P, V, and T represent the pressure, volume,

and temperature respectively. This model is the simple airbag model. It does not take

into considerations the je t effects. Jet effects can have significant influence in cases

surfaces :

(3.3.6)

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where the dummy interacts with the deploying bag [32]. But they are not known to

influence normal airbag deployment.

Inflator

m,P,V,T

mi,

external

Figure 3.5 Control volume parameters in the airbag model

3.4 Equation of State for Pressure Volume Relationship

The specific heats at constant pressure and at constant volume are defined as:

C = ( 0 A / 3 7 % , (3.4.U)

and

Cv =(dU/ BT ) L (3.4.1b)

It can be proven [33] that for a perfect gas, the internal energy and enthalpy are

independent of all properties except temperature. Hence, Cpand Cv can be written as

and

C=(,dh/dT%

Cv = (dU /dT \

(3.4.2)

(3.4.3)

Enthalpy is defined as:

h=U+P V (3.4.4)

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and in differential form:

dh = dU+PdV (3.4.5)

Using equation (3.4.2)

Cp =dU/dT + PdV /dT

Dividing by Cv and noting that k=C/Cvand Cv=dU/dT:

(3.4.6)

0dUtdT)(3.4.7)

Or

PdV = (Jc- l)dU (3.4.8)

Integrating both sides:

PV = (k - l )U (3.4.9)

Now dividing both sides by the mass.

P - p (k - l )u (3.4.10)

Wherep is the density and uis the specific internal energy.

This equation is known as the Gamma Law" and determines the pressure volume

relationship for an ideal gas mixture. The pressure can now be determined if the density

(or volume) and the specific internal energy are also known.

3.5 Control Volume Analysis of the Airbag Model

The control volume is defined as described earlier. The specific internal energy is

calculated from the energy balance across the control volume. Since the mass flow rate

of the entering gas and its temperature are known, the energy entering the bag is simply:

The energy out is a function of the mass flow rate exiting the bag. The mass flowrate of the gas exiting the bag through the vent holes and fabric leakage is defined in

Reference [34] as:


(3.5.1)

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mcu, =(C mK ,+ C l!atAu


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3.6 Airbag Folding and Finite Element Implementation

Several patterns are used for folding airbags. The most popular ones are shown in

Figure 3.6 below. The effect of folding patterns on airbag performance has not been fully

determined. Some manufacturers however claim that their folds can reduce neck

moments that might result from airbag deployment [35]. But what researchers have

found is that skin abrasion caused by airbags is directly related to the speed (leading edge

velocity) at which the surfaces of the inflating bag slap occupants. This speed, which

incidentally averages 200 mph [36] is in turn influenced by folding patterns.

Tethers are used on some airbags. By connecting the base of the airbag (which is

anchored to the module) to the opposing end, they control the shape and size of the bag.

Although this was the original purpose of tethers, researchers have found that they can

also reduce abrasions. Tethers limit the extension of the bag to an average of 10 to 13inches compared to an average of 15 to 20 inches for non-tethered bags [37].

Figure 3.6 Airbag foldingpatterns for different makes [37].

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The airbag used in this work is tethered and it is folded similar to the

overlapped design as shown in Figure 3.7. No attempt was made here to model other

folds or to determine a fold that provides better protection. Modeling the folds is a

complex phenomenon and falls beyond the scope of this work.

Figure 3.7 Details of folding patterns for the overlapped fold used in this model [38].

The pressure inside the bag, multiplied by an area segment contributes a force that

becomes an external force applied to the dummy or other car interiors through the fabric.

A free body diagram of an airbag element is shown in Figure 3.8. The fabric material

itself is modeled as membrane shell elements and can not carry bending or shear. From

the free body diagram it becomes obvious that when the airbag is being deployed, hence

the velocity of fabric element is high, inertial forces become significant. Conversely,

after full deployment, inertial effects become negligible.

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8/13/2019

analysis of automotive safety issues related to depowering of airbags using finite elements and...

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