Vehicle Crash Mechanics

VEHICLE CRASH MECHANICS......Page 2
PREFACE......Page 4
TABLE OF CONTENTS......Page 7
1.2 VEHICLE IMPACT MODES AND CRASH DATA RECORDING......Page 15
Table of Contents......Page 0
1.2.1 Accelerometer Mounting and Coordinate Systems......Page 17
1.3 DIGITAL FILTERING PRACTICE PER SAE J211 AND ISO 6487......Page 18
1.3.1 Relationship Between Two Points in a Frequency Response Plot......Page 22
1.3.2 Chebyshev and Butterworth Digital Filters......Page 23
1.3.3 Filter Type, Deceleration Magnitude, and Phase Delay......Page 25
A. Single-step and multiple-step function inputs......Page 27
B. Vehicle crash pulse and Driver chest deceleration......Page 28
1.3.4.1 Moving Window Averaging......Page 31
1.3.4.2 Equivalent Cutoff Frequency......Page 33
1.4.1 Computing Acceleration from a Velocity-Displacement Curve......Page 35
1.4.2.1 Car Jumping and Landing......Page 38
1.4.3 Slipping on an Incline -Down Push and Side Push......Page 43
1.4.4 Calculation of Safe Distance for Following Vehicle......Page 46
1.5.1 Vehicle Kinematics in a Fixed Barrier Impact......Page 47
1.5.2 Unbelted Occupant Kinematics......Page 48
1.5.2.1 Kinematics Based on Accelerometer Data......Page 49
1.5.2.3 Vehicle Crush, Sled Displacement, and Crash Pulse Centroid......Page 51
1.6.1 Vehicle Kinematics in Different Test Modes......Page 52
1.6.2 Vehicle Energy Density......Page 54
1.6.3 Occupant Kinematics in Different Test Modes......Page 55
1.7 KINEMATIC VARIABLES......Page 57
1.7.1 Use of Residual Energy Density in Air Bag Sensor Activation......Page 58
1.7.3 Vehicle-Occupant-Restraint (VOR) Interaction......Page 59
1.8 CASE STUDY: SINGLE VEHICLE-TREE IMPACT ACCIDENT......Page 62
1.8.1 Analysis of the Recorder Crash Data......Page 63
1.8.2 Frequency Spectrum Analysis for Electronic Crash Sensing......Page 66
1.9 RESTRAINT COUPLING......Page 67
1.9.1 Restraint Specific Stiffness and Onset Rate of Occupant Deceleration......Page 68
1.9.2 Occupant Response in the Restraint Coupling Phase......Page 69
1.9.3 Maximum Occupant Response, Timing, and Onset Rate......Page 73
1.9.4.1 3-D Contour Plots of the Occupant Response and Timing......Page 74
1.9.4.2 Vehicle, Occupant, and Restraint (VOR) Analysis Charts......Page 76
1.9.5 VOR Trend Analysis Based on Car and Truck Test Results......Page 80
1.10 OCCUPANT RIDEDOWN ANALYSIS AND ENERGY MANAGEMENT......Page 81
1.10.1 Energy Density Model......Page 85
1.10.1.2 Ridedown, Restraint Energy Densities, and Timings......Page 86
1.10.2.1 Test Energy Densities......Page 88
1.10.2.2 Model Energy Densities......Page 89
1.10.3 Contour Plots of Ridedown Efficiency and Occupant Response......Page 92
1.10.4 Restraint Design with Constant Occupant Deceleration......Page 94
1.10.5 Design Constraint and Trade-Off......Page 96
1.11 REFERENCES......Page 97
2.2 MOMENT-AREA METHOD......Page 99
2.2.1 Displacement Computation Without Integration......Page 100
2.2.2 Centroid Time and Characteristics Length......Page 101
2.2.3 Construction of Centroid Time and Residual Deformation......Page 102
2.2.3.1 Centroid of a Quarter-Sine Pulse......Page 103
2.3.1 ASW (Average Square Wave)......Page 105
2.3.2 ESW (Equivalent Square Wave)......Page 106
2.3.2.1 ESW Transient Analysis......Page 107
(2) Case Study: Pulse Shape and Centroid Location......Page 108
2.3.4 Derivation of TESW Parameters......Page 109
2.3.4.1 Deformation and Rebound Phases......Page 110
2.3.5 Construction of TESW Parameters......Page 111
2.3.5.1 Relationships Between TESW and ASW......Page 112
Case Study: Front and Rear Loaded Crash Pulses......Page 113
2.3.6.1 Rear-Loaded......Page 115
2.4.1 Fourier Equivalent Wave (FEW)......Page 118
2.4.2 FEW Sensitivity Analysis with Boundary Conditions......Page 119
2.4.3 Kinematics and Energy Comparison......Page 120
2.4.4.1 Discrimination of Pole Impact Crash Severity......Page 123
2.4.4.2 Use of All Negative FEW Coefficients in Pole Tests......Page 126
2.4.5 Use of Pulse Curve Length in Crash Severity Detection......Page 129
2.4.6 FEW Analysis on Body Mount Attenuation......Page 130
2.4.6.1 Frame Impulse Attenuation by Body Mount......Page 131
2.4.7.1 Air Bag Sensor Bracket Design Analysis......Page 134
Time Domain Analysis of Resonance......Page 135
2.4.7.2 Re-synthesis of a Crash Pulse Without Resonance......Page 136
2.4.8.1 Deriving the Closed-form Solutions for TWA Parameters......Page 137
2.4.9 Bi-slope Approximation (BSA)......Page 139
2.4.9.1 Comparison of Test Pulse, BSA, and TWA......Page 140
2.4.10 Harmonic Pulses – Background......Page 142
2.4.11 Halfsine Approximation......Page 144
2.4.12 Haversine Approximation......Page 147
2.4.13 Comparison of Halfsine and Haversine Pulses......Page 149
2.4.14 Response of Air Bag Sensor to Harmonic Pulses......Page 150
2.4.14.1 Sensor Dynamic Equations......Page 152
2.4.15 Head Injury Criteria......Page 153
(B) HIC Topographs of Other Simple and Test Pulses......Page 156
2.4.16 Application of HIC Formula in Head Interior Impact......Page 158
2.5 REFERENCES......Page 159
3.1 INTRODUCTION......Page 161
3.2 TRANSFER FUNCTION VIA CONVOLUTION INTEGRAL......Page 162
3.2.1 Convolution Method and Applications......Page 163
3.2.2 Solution by the Least Square Error Method......Page 164
3.2.3 Matrix Properties and Snow-Ball Effect......Page 165
3.2.4 Case Studies: Computing Transfer Functions......Page 168
3.3 TRANSFER FUNCTION AND A SPRING-DAMPER MODEL......Page 171
3.3.1 FIR Coefficients and K-C Parameters of a Spring-Damper Model......Page 172
3.3.2 Transfer Functions of Special Pulses......Page 174
3.4 BELTED AND UNBELTED OCCUPANT PERFORMANCE WITH AIR BAG......Page 176
3.4.1 Test Vehicle and Occupant Responses......Page 177
3.4.2 Truck #1: Unbelted Occupant with Full-Powered Air Bag......Page 180
3.4.2.2 Filtered Signals of FIR Coefficients......Page 181
3.4.3.1 Restraint Transfer Function Validation......Page 182
3.4.3.3 Response Prediction Using Fourier Equivalent Wave (FEW)......Page 183
3.5 BODY MOUNT AND TORSO RESTRAINT TRANSFER FUNCTIONS......Page 184
3.5.1 Body Mount Characteristics and Transient Transmissibility......Page 185
3.5.2 Types F and T Body Mount Transfer Functions......Page 187
3.5.3.1 Frame Impulse Duration and Transient Transmissibility......Page 188
3.5.3.2 Testing Frame Rail for a Desired Impulse Duration......Page 189
3.5.4.1 Vehicle and Belted Occupant Performances in Trucks F and T......Page 190
3.5.4.2 Truck T Response Prediction with Truck F Restraints......Page 193
3.6 EFFECT OF SLED AND BARRIER PULSES ON OCCUPANT RESPONSE......Page 195
3.7 OTHER APPLICATIONS......Page 197
3.8.1 Forward Prediction by Finite Impulse Response (FIR)......Page 198
3.8.2 Inverse Filtering (IF)......Page 200
3.8.3.1 Transferring [X] to [Y] with [H].......Page 201
3.8.3.2 Transfer [Y] to [X] with [H]\'......Page 202
3.8.3.3 Transferring [Y] to [X] using [IF]......Page 203
3.8.4 RIF Application in Frame Pulse Prediction......Page 204
3.9 REFERENCES......Page 206
4.2 IMPACT AND EXCITATION – RIGID BARRIER AND HYGE SLED TESTS......Page 207
4.2.1.1 A Vehicle-to-Barrier Displacement Model......Page 211
4.2.1.2 Unbelted Occupant Kinematics......Page 213
4.3.1 Vehicle and Occupant Transient Kinematics......Page 215
4.3.2.1 Method 1......Page 216
4.3.2.2 Method II......Page 217
4.3.3.1 Case Study – High Speed Crash......Page 218
4.3.4 Occupant Response Surface and Sensitivity......Page 219
4.3.4.1 Restraint Design Optimization by Response Contour Plots......Page 220
4.3.4.2 Sensitivity of Occupant Response to ESW......Page 221
4.3.4.3 Sensitivity of Occupant Response to Dynamic Crush......Page 222
4.3.4.4 Statistical Regression of Test Data and Model Responses......Page 223
4.3.4.5 Response Prediction and Ridedown Efficiency......Page 224
4.4 BASICS OF SPRING AND DAMPER DYNAMIC MODELING......Page 226
4.4.1 Spring and Damper Elements......Page 227
4.4.3 2-Mass (Vehicle-to-Vehicle) Impact Model......Page 228
4.4.4 Dynamic Equivalency Between Two-Mass and Effective Mass Systems......Page 229
4.5.1 Model Formulation......Page 230
4.5.2.2 Dynamic Crush Function......Page 232
4.5.2.3 Estimating Time of Dynamic Crush, Tm......Page 233
4.5.2.5 Mass and Stiffness Ratios in Vehicle-to-Vehicle Impact......Page 234
4.5.3 Effect of Test Weight Change on Dynamic Responses......Page 235
4.6 SPRING-MASS OCCUPANT MODEL SUBJECTED TO EXCITATION......Page 239
4.6.1 Response Solutions due to TESW and Sinusoidal Excitation......Page 240
4.6.1.1 Model with TESW Excitation, (E + j t)......Page 241
4.6.1.2 Sine Excitation (E sin wt)......Page 243
4.6.2 Model Response due to Sinusoidal Displacement Excitation......Page 246
4.7.1.1 Relative Motion Analysis (An Effective Mass System)......Page 249
4.7.1.2 Individual Vehicle Response Analysis......Page 251
4.7.3 Truck and Car Occupant Responses due to Halfsine Excitation......Page 252
4.7.4 Elasto-plastic Modeling......Page 254
4.8 A MAXWELL MODEL......Page 256
4.8.1 A Damper-Mass System (without Oscillatory Motion)......Page 257
4.8.3 Alternate Method: Zero Mass Between Maxwell Spring and Damper......Page 258
4.8.4.2 Infinite Damping Coefficient, c =.......Page 260
4.8.5 Model Response Characteristics with Transition Damping Coefficient......Page 261
4.9.1 Transient and Major Responses of Kelvin Model......Page 265
4.9.1.1 Underdamped System (.< 1)......Page 266
4.9.1.2 Critically Damped System (.= 1)......Page 268
4.9.1.3 Overdamped System (.> 1)......Page 269
4.9.1.4 Normalized Response Comparisons of Three Damping Systems......Page 270
4.9.2 Factors Affecting the Pulse Shape of System with Various Damping......Page 271
4.9.3 Hysteresis Loop......Page 274
4.9.4 Coefficient of Restitution and Damping Factor (.)......Page 277
4.9.5 Contact Duration......Page 278
4.10 DAMPING FACTOR AND NATURAL FREQUENCY FROM TESTS......Page 279
4.10.2 Application to SUV and Sedan Frontal Structure Properties......Page 281
4.11 EXCITATION OF THE KELVIN MODEL — OCCUPANT AND RESTRAINT......Page 283
4.11.1.1 Testing the Haversine Excitation......Page 286
4.11.2 Effect of Restraint Damping Control on Occupant Response......Page 287
4.12 REFERENCES......Page 288
5.2 HYBRID MODEL — A STANDARD SOLID MODEL......Page 289
5.2.1 E.O.M. for Hybrid Model......Page 290
5.2.2 Dynamic Response and Principles of Superposition......Page 291
5.2.3 Combination of Two Hybrid Models......Page 292
5.2.4 Dynamic Equivalency between Two Non-Isomorphic Hybrid Models......Page 294
5.2.4.1 Dynamic Equivalency in Transient Kinematics and Crush Energy......Page 296
5.3 TWO MASS-SPRING-DAMPER MODEL......Page 297
5.3.1 Solutions of the Characteristic Equation......Page 298
(II) Displacement components x12 and x22 due to s3 and s4, respectively......Page 299
Case 2: One pair of complex conjugate and two real and negative roots......Page 300
5.3.2 Vehicle Displacement Responses in Fixed Barrier Impact......Page 301
5.3.3 Application in Pre-Program Vehicle Structural Analysis......Page 303
5.3.4 Application in Post-Crash Structural Analysis......Page 305
5.4 NATURAL FREQUENCIES IN TWO–MASS SYSTEM......Page 306
5.4.1 Formulas for the Natural Frequencies......Page 307
5.4.2 Natural Frequency Ratio and Stiffness Computation......Page 308
5.4.3.1 Doubled-Up of a Spring-Mass Model......Page 309
5.4.3.2 Splitting of a Spring-Mass Model......Page 310
5.5.1 Imbedded Random Search (IRS)......Page 312
5.5.2 Newton-Raphson Search Algorithm......Page 314
5.6.1 Loading Phase Simulation......Page 315
5.6.2 Unloading Phase Simulation......Page 316
5.6.3 Model with Power Curve Loading and Unloading......Page 317
5.6.3.1 Unloading Parameters k\', n\', and xi in Reloading Cycle......Page 318
5.6.3.2 Deceleration Contributions of Spring and Damper......Page 320
5.7.1 Simple Structure Force-Deflection Table......Page 321
5.7.2 Push Bumper Force-Deflection Data......Page 322
5.7.3 Basic Operation of EA Types......Page 326
5.7.5 Coefficient of Restitution, Static, and Dynamic Crush Relationship......Page 328
5.7.5.1 1-mass Model with Elasto-Plastic Spring......Page 329
5.8 SIDE-IMPACT AND FRONTAL OFFSET MODELS......Page 331
5.8.1 Side Impact Model......Page 332
5.8.2.1 Basic Concepts in Offset Impact Modeling......Page 334
5.8.2.2 Full Barrier and Frontal Offset Test Results......Page 335
5.8.2.4 Optimal Vehicle Structure for Both Full Frontal and Offset Tests......Page 337
5.8.2.5 An Offset Lumped-Mass Model......Page 338
5.9 REFERENCES......Page 339
6.2 BACKGROUND......Page 341
Case Study: Batting A Baseball.......Page 342
6.3 CENTER OF GRAVITY AND MOTION THEOREM......Page 344
6.3.1 Location and Motion of Center of Mass......Page 345
6.3.2 Conservation of Momentum and CG Formula......Page 346
6.3.3 CG Motion Theorem......Page 347
6.3.4 Use of CG Motion Theorem in a Three !Car Collision Analysis......Page 350
Method 1: Simple Solution Using CG Motion Theorem......Page 351
Method II: In-Depth Analysis Using Momentum and Displacement Relationships......Page 352
6.4 IMPULSE AND CIRCLE OF CONSTANT ACCELERATION......Page 355
6.4.1 Derivation of Acceleration at Point Q......Page 356
Special Case......Page 357
6.4.2 Circle of Constant Acceleration (COCA)......Page 358
6.4.3 Construction of COCA Given the Acceleration Ratio, c......Page 359
Case Study 1: Slender Rod......Page 360
Case Study 3: Impulse to Ring......Page 361
Case Study 4: COCA with Various Acceleration Ratios......Page 362
6.4.6 COCA Evaluation of Impact Severity......Page 363
6.4.7 Given the Coordinates of Point Q, Find the Acceleration Ratio c......Page 365
6.4.8 Distributed Loading by Superposition......Page 366
6.5 PRINCIPLE OF WORK AND ENERGY......Page 367
6.5.1 Applications using Principle of Impulse, Momentum, and Energy......Page 368
6.5.2.1 Drop Test on a Weightless Spring......Page 370
6.5.2.2 Drop Test Using a Spring Having Finite Weight......Page 371
6.5.2.3 Horizontal Impact on a Bar/Spring......Page 373
6.5.3 Rebound Criterion in a Two-Mass Impact......Page 374
6.5.4 Separation Kinematics in a Multi-Mass Impact......Page 376
6.5.4.1 Separation Kinematics in a 3-Vehicle Collision......Page 377
6.5.5 COR, Times of Dynamic Crush, and Separation Time......Page 378
6.5.6 Coefficient of Restitution and Stiffness in Vehicle Crashes......Page 379
6.6.1 CG Height Determination......Page 382
6.6.2 Moment of Inertia Using Trifilar Pendulum Method......Page 384
6.6.3 Moment of Inertia Using Swinging Pendulum Method......Page 387
6.6.4.1 Derivation of CSV Formulas......Page 388
6.6.4.2 Normalized CSV Equation and Applications......Page 390
6.7.1 Rollover Dynamics of a Rigid Vehicle in a Steady Turn......Page 393
6.7.2 Rollover Detection and Threshold Criterion of a Rigid Vehicle......Page 395
6.7.3 Transient Rollover Dynamics of a Rigid Vehicle......Page 396
6.7.3.1 Transient Rollover Without Lateral Acceleration......Page 397
6.7.3.2 Transient Rollover With Lateral Acceleration......Page 398
6.8.1 Vector Method for Eccentric Loading Analysis......Page 400
6.8.2 Rollover Kinematics Using the Vector Method......Page 402
6.8.3 Conditions for a Vehicle to Stop Rolling Following Rollover......Page 404
6.9 REFERENCES......Page 408
7.2.1 Two-Degree-of-Freedom Occupant Model......Page 409
7.2.2 Effect of Seat Belt and Pretensioner on Occupant Kinematics......Page 412
7.3.1 Modeling Pretensioning Effects in a System Test......Page 413
7.3.2 Modeling Pretensioning Effects in a Component Test......Page 417
7.3.3 Transient Analysis of a Preloaded Model — Impact and Excitation......Page 419
7.4 CENTRAL COLLISIONS......Page 421
7.4.1 A Collision Experiment......Page 422
7.4.2 Relative Motion During Impact......Page 424
7.4.3 Kelvin’s Theorem, Total Crush, and Dissipated Energies......Page 426
7.4.4 Total Crush Energy......Page 427
7.4.5 Individual Crush Energy......Page 429
7.5 NON-CENTRAL COLLISIONS......Page 430
7.5.1 Case Study 1: Central Collision......Page 433
7.6 USE OF )V AND BEV IN CRASH SEVERITY ASSESSMENT......Page 434
7.6.1 Crash Severity Index......Page 436
7.6.1.1 Compatibility by Equal Crash Severity Index......Page 437
7.6.2 Crash Momentum Index......Page 438
7.6.3.2 Power Curve Force-Deflections......Page 439
7.6.3.3 Computation of Barrier Equivalent Velocity (BEV)......Page 441
7.7.1 Damage Boundary Curve......Page 443
7.7.1.1 Construction Steps for DBC......Page 444
7.7.1.2 Mechanic Principles of DBC......Page 445
7.7.2.1 Vehicle Crush Characteristics......Page 446
7.7.2.2 Vehicle Peak Responses......Page 448
7.8.1 Kelvin’s Theorem......Page 449
7.8.2 Lumped Mass Modeling on Crash Severity......Page 455
7.9 INTERMEDIATE MASS EFFECT......Page 457
7.10.1 Models with Same Effective Stiffness......Page 460
7.10.2 Models with Different Effective Stiffness......Page 464
7.11.1 Background......Page 466
7.11.2 Vehicle Size and Stiffness Coefficient Categories......Page 469
7.11.2.1 Computing Stiffness Coefficients, Intercept and Slope......Page 470
7.11.4 Four-Way Plot of Stiffness Coefficients and Responses......Page 471
7.11.5.2 Elasto-Plastic Force Deflection......Page 473
7.11.5.1 Estimate of the Vehicle Impact Severity......Page 474
7.11.5.2 Estimate of the Sensor Performance......Page 475
7.12 REFERENCES......Page 476
CHAPTER 1 CRASH PULSE AND KINEMATICS......Page 477
CHAPTER 2 CRASH PULSE CHARACTERIZATION......Page 479
CHAPTER 3 CRASH PULSE PREDICTION BY CONVOLUTION METHOD......Page 481
CHAPTER 4 BASICS OF IMPACT AND EXCITATION MODELING......Page 482
CHAPTER 5 RESPONSE PREDICTION BY NUMERICAL METHODS......Page 484
CHAPTER 6 IMPULSE, MOMENTUM, AND ENERGY......Page 485
CHAPTER 7 CRASH SEVERITY AND RECONSTRUCTION......Page 487
UNIT CONVERSIONS......Page 489