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Crash Pulse and Kinematics |
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1 | (1) |
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Vehicle Impact Modes and Crash Data Recording |
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1 | (3) |
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Accelerometer Mounting and Coordinate Systems |
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3 | (1) |
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Digital Filtering Practice Per SAE J211 and ISO 6487 |
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4 | (17) |
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Relationship Between Two Points in a Frequency Response Plot |
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8 | (1) |
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Chebyshev and Butterworth Digital Filters |
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9 | (2) |
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Filter Type, Deceleration Magnitude, and Phase Delay |
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11 | (6) |
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Moving Window Averaging and Equivalent Cutoff Frequency |
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17 | (1) |
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17 | (2) |
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Equivalent Cutoff Frequency |
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19 | (2) |
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Basic Kinematic Relationships |
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21 | (12) |
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Computing Acceleration from a Velocity-Displacement Curve |
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21 | (3) |
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Particle Kinematics in a Gravitational Field |
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24 | (1) |
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24 | (5) |
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Slipping on an Incline - Down Push and Side Push |
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29 | (3) |
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Calculation of Safe Distance for Following Vehicle |
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32 | (1) |
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Impact and Excitation: Vehicle and Sled Test Kinematics |
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33 | (5) |
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Vehicle Kinematics in a Fixed Barrier Impact |
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33 | (1) |
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Unbelted Occupant Kinematics |
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34 | (1) |
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Kinematics Based on Accelerometer Data |
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35 | (2) |
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Kinematics Based on Crash Film Records |
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37 | (1) |
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Vehicle Crush, Sled Displacement, and Crash Pulse Centroid |
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37 | (1) |
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Vehicle and Occupant Kinematics in Fixed Object Impact |
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38 | (5) |
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Vehicle Kinematics in Different Test Modes |
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38 | (2) |
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40 | (1) |
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Occupant Kinematics in Different Test Modes |
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41 | (2) |
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43 | (5) |
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Use of Residual Energy Density in Air Bag Sensor Activation |
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44 | (1) |
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Time Requirement for Air Bag Sensor Activation |
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45 | (1) |
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Vehicle-Occupant-Restraint (VOR) Interaction |
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45 | (3) |
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Case Study: Single Vehicle-Tree Impact Accident |
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48 | (5) |
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Analysis of the Recorder Crash Data |
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49 | (3) |
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Frequency Spectrum Analysis for Electronic Crash Sensing |
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52 | (1) |
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Application of a Residual Energy Density Algorithm |
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53 | (1) |
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53 | (14) |
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Restraint Specific Stiffness and Onset Rate of Occupant Deceleration |
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54 | (1) |
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Occupant Response in the Restraint Coupling Phase |
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55 | (4) |
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Maximum Occupant Response, Timing, and Onset Rate |
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59 | (1) |
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Vehicle, Occupant, and Restraint (VOR) Analysis Charts |
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60 | (1) |
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3-D Contour Plots of the Occupant Response and Timing |
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60 | (2) |
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Vehicle, Occupant, and Restraint (VOR) Analysis Charts |
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62 | (4) |
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VOR Trend Analysis Based on Car and Truck Test Results |
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66 | (1) |
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Occupant Ridedown Analysis and Energy Management |
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67 | (16) |
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71 | (1) |
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Equations of Motion and Energy Density of a Crash Mode1 |
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72 | (1) |
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Ridedown, Restraint Energy Densities, and Timings |
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72 | (2) |
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Validation of Energy Density Model in High Speed Crash |
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74 | (1) |
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74 | (1) |
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75 | (3) |
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Contour Plots of Ridedown Efficiency and Occupant Response |
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78 | (2) |
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Restraint Design with Constant Occupant Deceleration |
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80 | (2) |
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Design Constraint arid Trade-Off |
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82 | (1) |
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83 | (2) |
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Crash Pulse Characterization |
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85 | (1) |
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85 | (6) |
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Displacement Computation Without Integration |
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86 | (1) |
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Centroid Time and Characteristics Length |
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87 | (1) |
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Construction of Centroid Time and Residual Deformation |
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88 | (1) |
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Centroid of a Quarter-Sine Pulse |
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89 | (2) |
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Residual Deformation of a Quarter-Sine |
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91 | (1) |
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Pulse Approximations with Non-Zero Initial Deceleration |
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91 | (13) |
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ASW (Average Square Wave) |
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91 | (1) |
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ESW (Equivalent Square Wave) |
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92 | (1) |
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93 | (1) |
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Tipped Equivalent Square Wave (TESW) - Background |
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94 | (1) |
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Derivation of TESW Parameters |
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95 | (1) |
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Deformation and Rebound Phase |
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96 | (1) |
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Construction of TESW Parameters |
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97 | (1) |
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Relationships Between TESW and ASW |
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98 | (3) |
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Kinematic Comparisons of Test Pulse and Approximated Pulses |
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101 | (1) |
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101 | (3) |
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104 | (1) |
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Pulse Approximations with Zero Initial Deceleration |
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104 | (41) |
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Fourier Equivalent Wave (FEW) |
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104 | (1) |
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FEW Sensitivity Analysis with Boundary Conditions |
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105 | (1) |
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Kinematics and Energy Comparison |
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106 | (3) |
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Use of FEW and Power Rate Density in Crash Severity Detection |
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109 | (1) |
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Discrimination of Pole Impact Crash Severity |
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109 | (3) |
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Use of All Negative FEW Coefficients in Pole Tests |
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112 | (3) |
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Use of Pulse Curve Length in Crash Severity Detection |
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115 | (1) |
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FEW Analysis on Body Mount Attenuation |
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116 | (1) |
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Frame Impulse Attenuation by Body Mount |
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117 | (3) |
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FEW Analysis on Resonance |
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120 | (1) |
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Air Bag Sensor Bracket Design Analysis |
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120 | (2) |
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Re-synthesis of a Crash Pulse Without Resonance |
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122 | (1) |
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Trapezoidal Wave Approximation (TWA) |
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123 | (1) |
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Deriving the Closed form Solutions for TWA Parameters |
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123 | (2) |
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Bi-slope Approximation (BSA) |
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125 | (1) |
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Comparison of Test Pulse, BSA, and TWA |
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126 | (2) |
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Harmonic Pulses - Background |
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128 | (2) |
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130 | (3) |
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133 | (2) |
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Comparison of Halfsine and Haversine Pulses |
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135 | (1) |
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Response of Air Bag Sensor to Harmonic Pulses |
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136 | (2) |
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138 | (1) |
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Gas-Damped Sensor Mathematical Relationship |
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139 | (1) |
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139 | (3) |
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142 | (2) |
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Application of HIC Formula in Head Interior Impact |
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144 | (1) |
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145 | (2) |
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Crash Pulse Prediction by Convolution Method |
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147 | (1) |
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Transfer Function Via Convolution Integral |
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148 | (9) |
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Convolution Method and Applications |
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149 | (1) |
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Solution by the Least Square Error Method |
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150 | (1) |
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Matrix Properties and Snow-Ball Effect |
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151 | (3) |
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Case Studies: Computing Transfer Functions |
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154 | (3) |
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Transfer Function and a Spring-Damper Model |
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157 | (5) |
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FIR Coefficients and K-C Parameters of a Spring-Damper Model |
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158 | (2) |
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Transfer Functions of Special Pulses |
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160 | (2) |
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Belted and Unbelted Occupant Performance with Air Bag |
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162 | (8) |
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Test Vehicle and Occupant Responses |
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163 | (3) |
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Truck #1: Unbelted Occupant with Full-Powered Air Bag |
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166 | (1) |
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Restraint FIR Model Validation Using Test Results |
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167 | (1) |
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Filtered Signals of FIR Coefficients |
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167 | (1) |
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Response Prediction using TWA |
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168 | (1) |
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Truck #2: Belted Occupant with Depowered Air Bag |
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168 | (1) |
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Restraint Transfer Function Validation |
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168 | (1) |
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Response Prediction Using TWA |
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169 | (1) |
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Response Prediction Using Fourier Equivalent Wave (FEW) |
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169 | (1) |
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Body Mount and Torso Restraint Transfer Functions |
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170 | (11) |
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Body Mount Characteristics and Transient Transmissibility |
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171 | (2) |
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Types F and T Body Mount Transfer Functions |
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173 | (1) |
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Body Response Prediction of Truck T with Type F Body Mount |
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174 | (1) |
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Frame Impulse Duration and Transient Transmissibility |
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174 | (1) |
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Testing Frame Rail for a Desired Impulse Duration |
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175 | (1) |
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Torso Restraint Transfer Functions |
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176 | (1) |
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Vehicle and Belted Occupant Performances in Trucks F and T |
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176 | (3) |
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Truck T Response Prediction with Truck F Restraints |
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179 | (2) |
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Effect of Sled and Barrier Pulses on Occupant Response |
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181 | (2) |
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183 | (1) |
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Response Inverse Filtering (RIF) |
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184 | (8) |
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Forward Prediction by Finite Impulse Response (FIR) |
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184 | (2) |
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186 | (1) |
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Crash Pulse Prediction using FIR and RIF |
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187 | (1) |
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Transferring [X] to [Y] with [H] |
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187 | (1) |
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Transfer [Y] to [X] with [H] |
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188 | (1) |
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Transferring [Y] to [X] using [IF] |
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189 | (1) |
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RIF Application in Frame Pulse Prediction |
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190 | (2) |
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192 | (1) |
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Basics of Impact and Excitation Modeling |
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193 | (1) |
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Impact and Excitation - Rigid Barrier and Hyge Sled Tests |
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193 | (8) |
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Vehicle and Sled/Unbelted Occupant Impact Kinematics |
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197 | (1) |
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Vehicle-to-Barrier Displacement Model |
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197 | (2) |
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Unbelted Occupant Kinematics |
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199 | (2) |
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Ridedown Existence Criteria and Efficiency |
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201 | (11) |
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Vehicle and Occupant Transient Kinematics |
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201 | (1) |
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202 | (1) |
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202 | (1) |
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Derivation of Ridedown Existence Criteria |
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202 | (1) |
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202 | (1) |
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203 | (41) |
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Application of Ridedown Existence Criteria |
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244 | |
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Case Study - High Speed Crash |
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204 | (1) |
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Case Study - Low Speed Crash |
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205 | (1) |
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Occupant Response Surface and Sensitivity |
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205 | (1) |
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Restraint Design Optimization by Response Contour Plots |
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206 | (1) |
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Sensitivity of Occupant Response to ESW |
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207 | (1) |
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Sensitivity of Occupant Response to Dynamic Crush |
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208 | (1) |
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Statistical Regression of Test Data and Mode1 Responses |
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209 | (1) |
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Response Prediction and Ridedown Efficiency |
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210 | (2) |
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Basics of Spring and Damper Dynamic Modeling |
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212 | (4) |
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Spring and Damper Elements |
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213 | (1) |
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Properties of Viscoelastic Materials and Damping |
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214 | (1) |
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Equivalent Viscous Damping |
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214 | (1) |
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2-Mass (Vehicle-to-Vehicle) Impact Model |
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214 | (1) |
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Dynamic Equivalency Between Two-Mass and Effective Mass Systems |
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215 | (1) |
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Vehicle to Barrier (VTB) Impact: Spring-Mass Model |
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216 | (9) |
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216 | (2) |
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Design and Trend Analysis |
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218 | (1) |
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218 | (1) |
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218 | (1) |
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Estimating Time of Dynamic Crush, Tm |
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219 | (1) |
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Response Properties as a Function of V and C |
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220 | (1) |
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Mass and Stiffness Ratios in vehicle-to-vehicle Impact |
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220 | (1) |
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Effect of Test Weight Change on Dynamic Responses |
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221 | (4) |
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Spring-Mass Occupant Model Subjected to Excitation |
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225 | (10) |
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Response Solutions due to TESW and Sinusoidal Excitation |
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226 | (1) |
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Model with TESW Excitation, (E + j t) |
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227 | (2) |
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Sine Excitation (E sin ωt) |
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229 | (3) |
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Model Response due to Sinusoidal Displacement Excitation |
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232 | (3) |
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Vehicle-To-Vehicle (VTV) Impact: Spring-Mass Model |
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235 | (7) |
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Crash Pulse Approximation by TESW and Sinusoidal Waves |
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235 | (1) |
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Relative Motion Analysis (An Effective Mass System) |
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235 | (2) |
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Individual Vehicle Response Analysis |
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237 | (1) |
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Comparison of Sinusoidal Wave with Test Crash Pulse |
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238 | (1) |
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Truck and Car Occupant Responses due to Halfsine Excitation |
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238 | (2) |
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240 | (2) |
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242 | (9) |
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A Damper-Mass System (without Oscillatory Motion) |
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243 | (1) |
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The Maxwell Spring-Damper Model |
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244 | (1) |
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Alternate Method: Zero Mass Between Maxwell Spring and Damper |
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244 | (2) |
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Transition and Infinite Damping Coefficients |
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246 | (1) |
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Transition Damping Coefficient, c* |
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246 | (1) |
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Infinite Damping Coefficient, c=∞ |
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246 | (1) |
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Model Response Characteristics with Transition Damping Coefficient |
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247 | (4) |
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Impact on Kelvin Model-Vehicle or Component |
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251 | (14) |
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Transient and Major Responses of Kelvin Model |
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251 | (1) |
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Underdamped System (ζ < 1) |
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252 | (2) |
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Critically Damped System (ζ = 1) |
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254 | (1) |
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Overdamped System (ζ > 1) |
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255 | (1) |
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Normalized Response Comparisons of Three Damping Systems |
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256 | (1) |
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Factors Affecting the Pulse Shape of System with Various Damping |
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257 | (3) |
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260 | (3) |
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Coefficient of Restitution and Damping Factor (ζ) |
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263 | (1) |
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264 | (1) |
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Damping Factor and Natural Frequency From Tests |
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265 | (4) |
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Conversions of the Stiffness and Damping Coefficient |
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267 | (1) |
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Application to SUV and Sedan Frontal Structure Properties |
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267 | (2) |
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Excitation of the Kelvin Model - Occupant and Restraint |
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269 | (5) |
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General Crash Pulse Excitation by Fourier Series |
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272 | (1) |
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Testing the Haversine Excitation |
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272 | (1) |
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Effect of Restraint Damping Control on Occupant Response |
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273 | (1) |
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274 | (1) |
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Response Prediction by Numerical Methods |
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275 | (1) |
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Hybrid Model - A Standard Solid Model |
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275 | (8) |
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276 | (1) |
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Dynamic Response and Principles of Superposition |
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277 | (1) |
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Combination of Two Hybrid Models |
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278 | (2) |
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Dynamic Equivalency between Two Non-Isomorphic Hybrid Models |
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280 | (2) |
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Dynamic Eguivalency in Transient Kinematics and Crush Energy |
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282 | (1) |
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Two Mass-Spring-Damper Model |
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283 | (9) |
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Solutions of the Characteristic Equation |
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284 | (3) |
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Vehicle Displacement Responses in Fixed Barrier Impact |
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287 | (2) |
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Application in Pre-Program Vehicle Structural Analysis |
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289 | (2) |
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Application in Post-Crash Structural Analysis |
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291 | (1) |
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Natural Frequencies in Two-Mass System |
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292 | (6) |
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Formulas for the Natural Frequencies |
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293 | (1) |
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Decoupling of a Two-Mass System |
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294 | (1) |
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Natural Frequency Ratio and Stiffness Computation |
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294 | (1) |
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Add-On or Splitting of a Spring-Mass Model |
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295 | (1) |
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Doubled-Up of a Spring-Mass Model |
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295 | (1) |
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Splitting of a Spring-Mass Model |
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296 | (2) |
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Numerical Searching Techniques |
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298 | (3) |
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Imbedded Random Search (IRS) |
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298 | (2) |
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Newton-Raphson Search Algorithm |
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300 | (1) |
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Loading and Unloading Simulation |
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301 | (6) |
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301 | (1) |
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Unloading Phase Simulation |
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302 | (1) |
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Model with Power Curve Loading and Unloading |
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303 | (1) |
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Unloading Parameters k', n', and xi in Reloading Cycle |
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304 | (2) |
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Deceleration Contributions of Spring and Damper |
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306 | (1) |
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A Lumped-Parameter Model - Crush II |
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307 | (10) |
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Simple Structure Force-Deflection Table |
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307 | (1) |
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Push Bumper Force-Deflection Data |
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308 | (4) |
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Basic Operation of EA Types |
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312 | (2) |
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Basic Operation of CV Factor (Velocity Sensitive Factor) |
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314 | (1) |
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Coefficient of Restitution, Static, and Dynamic Crush Relationship |
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314 | (1) |
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1-mass Model with Elasto-Plastic Spring |
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315 | (2) |
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Side-Impact and Frontal Offset Models |
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317 | (8) |
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318 | (2) |
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320 | (1) |
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Basic Concepts in Offset Impact Modeling |
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320 | (1) |
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Full Barrier and Frontal Offset Test Results |
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321 | (2) |
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Modeling the Full Barrier and Frontal Offset Tests |
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323 | (1) |
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Optimal Vehicle Structure for Both Full Frontal and Offset Tests |
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323 | (1) |
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An Offset Lumped Mass Model |
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324 | (1) |
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325 | (2) |
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Impulse, Momentum, and Energy |
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327 | (1) |
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327 | (3) |
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Impulse and Momentum for a Single Particle |
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328 | (2) |
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Impulse and Momentum for a System of Particles |
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330 | (1) |
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Center of Gravity and Motion Theorem |
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330 | (11) |
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Location and Motion of Center of Mass |
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331 | (1) |
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Conservation of Momentum and CG Formula |
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332 | (1) |
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333 | (3) |
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Use of CG Motion Theorem in a Three-Car Collision Analysis |
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336 | (5) |
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Impulse and Circle of Constant Acceleration |
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341 | (12) |
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Derivation of Acceleration at Point Q |
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342 | (2) |
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Circle of Constant Acceleration (COCA) |
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344 | (1) |
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Construction of COCA Given the Acceleration Ratio, c |
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345 | (1) |
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346 | (3) |
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Determination of the Direction of Acceleration, aQ |
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349 | (1) |
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COCA Evaluation of Impact Severity |
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349 | (2) |
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Given the Coordinates of Point Q, Find the Acceleration Ratio c |
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351 | (1) |
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Distributed Loading by Superposition |
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352 | (1) |
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Principle of Work and Energy |
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353 | (15) |
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Applications using Principle of Impulse, Momentum, and Energy |
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354 | (2) |
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Drop Test and Impact Using a Spring Having Finite Weight |
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356 | (1) |
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Drop Test on a Weightless Spring |
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356 | (1) |
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Drop Test Using a Spring Having Finite Weight |
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357 | (2) |
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Horizontal Impact on a Bar/Spring |
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359 | (1) |
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Vertical Impact on a Beam/Spring |
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360 | (1) |
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Rebound Criterion in a Two-Mass Impact |
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360 | (2) |
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Separation Kinematics in a Multi-Mass Impact |
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362 | (1) |
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Separation Kinematics in a 3-Vehicle Collision |
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363 | (1) |
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COR, Times of Dynamic Crush, and Separation Time |
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364 | (1) |
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Coefficient of Restitution and Stiffness in Vehicle Crashes |
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365 | (3) |
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Vehicle Inertia Properties and Critical Sliding Velocity |
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368 | (11) |
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368 | (2) |
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Moment of Inertia Using Trifilar Pendulum Method |
|
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370 | (3) |
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Moment of Inertia Using Swinging Pendulum Method |
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|
373 | (1) |
|
Critical Sliding Velocity (CSV) |
|
|
374 | (1) |
|
Derivation of CSV Formulas |
|
|
374 | (2) |
|
Normalized CSV Equation and Applications |
|
|
376 | (3) |
|
|
|
379 | (7) |
|
Rollover Dynamics of a Rigid Vehicle in a Steady Turn |
|
|
379 | (2) |
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Rollover Detection and Threshold Criterion of a Rigid Vehicle |
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|
381 | (1) |
|
Transient Rollover Dynamics of a Rigid Vehicle |
|
|
382 | (1) |
|
Transient Rollover Without Lateral Acceleration |
|
|
383 | (1) |
|
Transient Rollover With Lateral Acceleration |
|
|
384 | (2) |
|
Rollover and Yaw Detections |
|
|
386 | (1) |
|
Eccentric Loading on Vehicle Rollover |
|
|
386 | (8) |
|
Vector Method for Eccentric Loading Analysis |
|
|
386 | (2) |
|
Rollover Kinematics Using the Vector Method |
|
|
388 | (2) |
|
Conditions for a Vehicle to Stop Rolling Following Rollover |
|
|
390 | (4) |
|
|
|
394 | (1) |
|
Crash Severity and Reconstruction |
|
|
|
|
|
395 | (1) |
|
Occupant Motion Under Impact and Excitation |
|
|
395 | (4) |
|
Two-Degree-of Freedom Occupant Model |
|
|
395 | (3) |
|
Effect of Seat Belt and Pretensioner on Occupant Kinematics |
|
|
398 | (1) |
|
Preloading on an Occupant |
|
|
399 | (8) |
|
Modeling Pretensioning Effects in a System Test |
|
|
399 | (4) |
|
Modeling Pretensioning Effects in a Component Test |
|
|
403 | (2) |
|
Transient Analysis of a Preloaded Model - Impact and Excitation |
|
|
405 | (2) |
|
|
|
407 | (9) |
|
|
|
408 | (2) |
|
Relative Motion During Impact |
|
|
410 | (2) |
|
Kelvin's Theorem, Total Crush, and Dissipated Energies |
|
|
412 | (1) |
|
|
|
413 | (2) |
|
|
|
415 | (1) |
|
|
|
416 | (4) |
|
Case Study 1: Central Collision |
|
|
419 | (1) |
|
Case Study 2: Non-central or Offset Collision |
|
|
420 | (1) |
|
Use of ΔV and BEV in Crash Severity Assessment |
|
|
420 | (9) |
|
|
|
422 | (1) |
|
Compatibility by Equal Crash Severity Index |
|
|
423 | (1) |
|
|
|
424 | (1) |
|
Crash Severity Assessment by a Power Curve Model |
|
|
425 | (1) |
|
Power Curve Model and Methodology |
|
|
425 | (1) |
|
Power Curve Force-Deflections |
|
|
425 | (2) |
|
Computation of Barrier Equivalent Velocity (BEV) |
|
|
427 | (2) |
|
Vehicle Acceleration and Crash Severity |
|
|
429 | (6) |
|
|
|
429 | (1) |
|
Construction Steps for DBC |
|
|
430 | (1) |
|
Mechanic Principles of DBC |
|
|
431 | (1) |
|
Crash Severity Assessment in Vehicle-to-Vehicle Compatibility Test |
|
|
432 | (1) |
|
Vehicle Crush Characteristics |
|
|
432 | (2) |
|
|
|
434 | (1) |
|
Velocity and Energy Distributions in Two-Vehicle Impact |
|
|
435 | (8) |
|
|
|
435 | (6) |
|
Lumped Mass Modeling on Crash Severity |
|
|
441 | (2) |
|
|
|
443 | (3) |
|
Modeling the Vehicle-To-Vehicle Compatibility Test |
|
|
446 | (6) |
|
Models with Same Effective Stiffness |
|
|
446 | (4) |
|
Models with Different Effective Stiffness |
|
|
450 | (2) |
|
Accident Reconstruction Methodology |
|
|
452 | (10) |
|
|
|
452 | (3) |
|
Vehicle Size and Stiffness Coefficient Categories |
|
|
455 | (1) |
|
Computing Stiffness Coefficients, Intercept and Slope |
|
|
456 | (1) |
|
Stiffness Coefficient Comparison Between Data Base and Crash Tests |
|
|
457 | (1) |
|
Four-Way Plot of Stiffness Coefficients and Responses |
|
|
457 | (2) |
|
Non-Linear Crush Profile and Force Deflection Data |
|
|
459 | (1) |
|
|
|
459 | (1) |
|
Elasto-Plastic Force Deflection |
|
|
459 | (1) |
|
Estimate of the Impact Severity and Sensor Performance in a Van Impact |
|
|
460 | (1) |
|
Estimate of the Vehicle Impact Severity |
|
|
460 | (1) |
|
Estimate of the Sensor Performance |
|
|
461 | (1) |
|
|
|
462 | (1) |
| List of Figures |
|
463 | (12) |
| Unit Conversions |
|
475 | (2) |
| Index |
|
477 | |
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