CHAPTER 7 CRASH SEVERITY AND RECONSTRUCTION 7.1 INTRODUCTION In the development of a new vehicle platform, its crashworthiness is an important concern, and it is imperative to compare the impact severity of the vehicle and occupants under various test and design conditions. Since an impact is a physical event that involves analyses of impulses and energy components, such as kinetic energy, energy absorption, and energy dissipation, the analyses require both the principle of work and energy and that of impulse and momentum. Although both principles are derived from Newton’s Second Law, they are not mutually exclusive when it comes to solving problems involving impact and excitation. It will be shown that any crash event, modeled by either a single-mass or a multi-mass system, involves impact and/or excitation. Recognizing the existence of the impact and/or excitation, the closed-form formulas derived in Section 4.11 of Chapter 4 can be utilized to solve problems. Case studies, such as the dynamic principles of pyrotechnic pretensioner on the occupant responses, are investigated. The preloading effect of a restraint system on the occupant response and ridedown efficiency are discussed. Many crashworthiness topics related to single and multi-vehicle collisions are analyzed by the engineering principles presented so far for determining the degree of crash severity. Applications of these principles to vehicle-to-vehicle compatibility, shear loading of truck body mounts due to eccentric loading, and the methodology of accident reconstruction methodology are also presented. 7.2 OCCUPANT MOTION UNDER IMPACT AND EXCITATION Occupant motion in the vehicle compartment is controlled by both the vehicle and restraint impact factors. Both factors complement each other in producing the occupant responses in a particular test condition. Since any vehicle produced needs to be certified to meet the federal vehicle safety standard, it is not unusual to see a truck equipped with a pyrotechnic device or a pretensioner. This is because the truck in general is stiffer than a passenger car, and the pretensioner affects the motion of an occupant. The chest deceleration rises up earlier and the ensuing ridedown efficiency increases. In the following sections, a simple 2-dimensional occupant model is presented to show the translation and rotational kinematics of the occupant in a crash. The theory and effect of the pretensioner in improving the occupant crashworthiness are presented in the following sections. 7.2.1 Two-Degree-of-Freedom Occupant Model A generalized two-degree-of-freedom (TWODOF) dynamic model based on a simple restrained occupant model [1] is developed to simulate occupant motion and response in the event of a vehicle frontal collision. The TWODOF model and the variables used are shown in Fig. 7.1 and Table 7.1, respectively. Unrestrained and restraint systems, including lap, shoulder belts, air bag, and their combinations are incorporated in the model. The occupant-vehicle contact surfaces are defined by the upper and lower panels. The occupant body consists of a chest (upper mass) and a hip (lower mass). The chest is able to rotate about the link pivot, and the hip is able to translate horizontally. The vehicle compartment is defined by the inclinations and the locations of the upper and lower panels and their force deflection (F-D) data. In the case of an air bag restraint system, the air bag F-D data is combined together with the upper panel F-D characteristics. © 2002 by CRC Press LLC Fig. 7.1 A Two!Degree!of!Freedom Occupant Model M 1 : Lower mass (Hip), M 2 : Upper mass (Chest) X 1 : Lower mass displacement X v : Vehicle displacement (Crush) L: Distance from link pivot to upper mass L 1 : Distance from link pivot to head center L s : Distance from D-ring to upper mass L L : Distance from lap belt anchor to tangent point on hip circle R 1 : Radius of hip circle B 1 : Vertical distance from lap belt anchor to center of hip circle * 1 : Lap belt stretch F 0 : Friction between hip and seat F L : Knee and lower panel contact force F u : Effective torso and upper panel contact force which produces a moment about link pivot K 1 : Lap belt stiffness K 2 : Shoulder belt stiffness H 1 : Horizontal distance from lap belt anchor to hip center H 2 : Horizontal distance from D-ring to torso center 2: Angular displacement of body segment from vertical The model also simulates an unrestrained occupant impact. The derivation of the equations of motion of the "TWODOF" model is based on a lap and shoulder restraint system. The occupant undergoes the two-dimensional motion and is subjected to restraint interactions and external forces. The shoulder belt load is applied to the chest, and the lap belt load is applied tangentially to the hip circle. The lap belt is "wound up" on the hip as the chest rotates. The lap belt load is thus a function of the relative displacement of hip-to-vehicle and chest rotation. The dynamic solution of the occupant model is obtained using the LaGrange's Equations as shown in Eq. (7.1). The independent variables in the equation are q i : (1) i = 1, q i = x 1 , the linear displacement of the hip joint, and (2) i = 2, q 2 = 2, the angular displacement of the upper torso. The kinetic and potential energies of the system are expressed in terms of the two independent variables as shown in Eq. (7.2). © 2002 by CRC Press LLC Table 7.1 Definitions of Model Variables (7.3) (7.1) (7.2) (7.4) Where q i and Q qi are defined as follows: i1 2 q i x 1 θ Q qi –(F 0 + F L )–F u By completing the partial differentiations with respect to the independent variables x 1 and 2 shown in Eq. (7.1), the equations of motion of the model in terms of the linear acceleration of the hip and the angular acceleration of the chest are thus derived as shown in Eq. (7.3). Solving for the linear and angular accelerations in Eq. (7.3), one gets the closed-form solutions for the two accelerations as shown in Eq. (7.4). The model has been generalized to include the following main variables and features: 1. Chest force-deflection characteristics (see Fig. 7.2). 2. Seat friction and friction coefficient between shoulder belt and chest. 3. Restraint systems: unrestrained, lap, shoulder belts, air bag, and their combinations. 4. Lap and shoulder belt slacks. 5. Air bag deployment time. © 2002 by CRC Press LLC Fig. 7.2 Chest Force-Deflection Data Fig. 7.3 Vehicle Contact Surface Force- Deflection Curve Fig. 7.4 Unrestrained and Restrained Occupant Kinematics in a Crash 6. Chest and knee targets. 7. Upper and lower panel general F-D characteristics (see Fig. 7.3). 8. Linear belt stiffness (with minor program modification, non-linear belt stiffness or general belt F-D curve can be simulated). 7.2.2 Effect of Seat Belt and Pretensioner on Occupant Kinematics In a vehicle frontal crash, an unbelted occupant undergoes a free-flight motion until impacting on the vehicle interior surfaces, such as windshield, steering wheel, and instrument panel as shown in the left column of Fig. 7.4. The motion of an occupant without and with a pretensioner installed on the retractor anchor side or buckle side of the 3-point (lap and shoulder belt) restraint system is shown in columns 2 and 3 of Fig. 7.4, respectively. The dynamic effects of the pretensioner on the occupant dynamics are the subjects to be presented in the following sections. © 2002 by CRC Press LLC Fig. 7.5 Effects of Pretensioner on Occupant Responses 7.3 PRELOADING ON AN OCCUPANT Any crash event involves impact and/or excitation. A vehicle passenger compartment in a frontal rigid barrier test undergoes an impact process, while a restrained occupant undergoes an excitation by the vehicle crash pulse and an impact at high speed test by the intruding toe board on the lower extremities of the occupant. The outcome of the impact can be quite different from that of the excitation. As an example, the occupant in a vehicle crash has the benefit of riding down with the deforming vehicle structure, thus diverting some of the occupant energy away from interacting with the restraint system. The occupant response, such as chest deceleration, depends on the distribution of the remaining restraint energy. In a laboratory, a Hyge sled test is intended to replicate the occupant dynamics in a vehicle-to-rigid barrier condition. Except for the effect of vehicle intrusion and vehicle pitch, the sled test captures most of the effects of the vehicle crash pulse on the occupant response. In Section 6.6.4 of Chapter 6, the kinetics of a preloaded safety belt is briefly discussed. Depending on the test condition, it may have different effects on the dynamics of the subject being tested. In this section, the effects of a pretensioner on impact responses are presented. The kinetic relationships for both component and sled test conditions (due to excitation and impact) are described, respectively. 7.3.1 Modeling Pretensioning Effects in a System Test The main function of the pretensioner is to take out any restraint slack as early as possible in an impact. By zeroing in the slack, the pretensioner in a system test reduces the torso deceleration while the vehicle is undergoing the “deformation phase” and the occupant is undergoing “ridedown.” A summary of a series of tests conducted in the laboratory using a Hyge sled is shown in Fig. 7.5. © 2002 by CRC Press LLC Fig. 7.6 Restraint System w/ Pretensioner and F vs. D There are four factors in the tests, and two occupant responses (HIC and Chest G). The factors are (1) pulse: stiff and approximated square pulses, (2) driver and passenger, (3) with and without restraint slack (four inches), and (4) with and without pretensioner. A total combination of 8 tests were conducted and the chest g and HIC for each of the 8 tests are shown in the chart. Looking at the effect of pulse shape on occupant responses in Fig. 7.6, the square pulse is seen to be an idealized optimal pulse, the resulting chest g and HIC being lower than those of stiff pulse. Regardless of the type of pulse used in the test, the effect of the pretensioner on reducing the occupant responses, especially the chest g, is quite obvious. The pretensioning effect is even more pronounced for the cases where a stiff pulse was used and the occupant had a 4-inch restraint slack. Assuming that restraint slack is taken out as soon as the impact is initiated, the occupant will be restrained by the pretensioning force, F O , at time zero as shown in Fig. 7.6. The magnitude of the pretensioning force is assumed to be on the high side of 600 lbs. Using the CRUSH II model for a 30 mph rigid barrier test, the input data needed for the model are listed in Table 7.2. Note that the occupant weight of 100 lbs is an approximated effective weight of torso interacting with the restraint system. The model parameters for the vehicle, occupant, frame, and restraint (spring) are shown in Fig.7.7. Table 7.2 Input Data for Vehicle-Occupant Models w/ and w/o Restraint Preload Model, 30 mph Barrier Weight, klb Stiffness, klb/in Restraint Preload, F o klb Vehicle Occupant Frame Restraint w/o preload M1: 3 klb M2: 0.1 klb 3 0.5 0 w/ preload M3: 3 klb M4: 0.1 klb 3 0.5 0.6 Note: w/o : without; w/ : with © 2002 by CRC Press LLC Fig. 7.7 A Vehicle-Occupant Model w/ and w/o Restraint Preload Fig. 7.8 Pretensioner Effect on Chest Response The motion and chest g responses of an occupant (M 2 or M 4 ) riding in a vehicle for the two cases, without and with a pretensioner, are shown in Fig. 7.7. The restrained occupant decelerations vs. time for the two cases are also marked on the model. The simulation results of the modeling are summarized in Table 7.3. The responses of an occupant, such as the maximum displacement, restraint deflection, restraint force, and restraint energy, are smaller in the model with a pretensioner (for M 4 ) than in the model without a pretensioner (for M 2 ). Therefore, overall, the crash severity of the occupant in this system test with a pretensioner is less than that without a pretensioner. Table 7.3 Restrained Occupant Responses w/ and w/o Restraint Preload Model, 30 mph Barrier Occupant Restraint Peak Values Max.Displ., in @ ms Chest Decel, g @ ms Deflection, in Force, klb Restraint Energy, klb-ft w/o preload 35.3 @ 88 -44 @ 98 8.8 4.4 1.6 w/ preload 33.2 @ 90 -41 @ 104 7.1 4.1 1.4 The occupant deceleration profile with a preload of 0.6 klb and an occupant effective weight of 0.1 klb yields an initial deceleration of 6 g at time zero, as shown in Fig. 7.8. © 2002 by CRC Press LLC Fig. 7.9 Force vs. Deflection of Models w/ and w/o Preload (7.5) However, the final peak occupant deceleration of the preloaded model is about 3 g smaller than that without preloading. The lower chest g in the preloaded case is also confirmed by the restraint force-deflection curves for the two cases as shown in Fig. 7.9. Both the peak force and energy of the restraint system for the preloaded case are smaller than those of the non-preloaded case (see Table 7.3 for numerical values). To compare the occupant ridedown efficiencies for both cases, the occupant kinetic energy, E o , in the 30 mph test is computed in Eq. (7.5) and is equal to 3 klb-ft. The ridedown efficiencies, :, for both models have been computed and shown in Table 7.4. For the model with a pretensioner, : equals 54%. This compares with 46% for the model without a pretensioner. The underlying reason for the higher ridedown efficiency is due to a larger force in the early portion of the occupant deceleration curve that results in a higher ridedown energy density. The higher occupant deceleration in the beginning of the crash pulse is attributed to the use of the pretensioner. Table 7.4 Output Responses of Models w/ and w/o Preload Model E o , Occupant Kinetic Energy, klb-ft E rs ,Restraint Energy, klb-ft E rd ,Ridedown Energy, klb-ft : , Ridedown Efficiency, % w/o Preload 3 1.62 1.38 46 w/ Preload 3 1.38 1.62 54 © 2002 by CRC Press LLC Fig. 7.10 Component Impact Model without and with Preload Fig. 7.11 Force vs. Deflection of Impact Model w/ and w/o Preload 7.3.2 Modeling Pretensioning Effects in a Component Test In a component test on a seat belt restraint system, the test setup is shown in Fig. 7.10. The restraint system with and without pretentioner is impacted by a black tuffy (a body block) at a preset speed. For the test with pretensioner, it is assumed that the pretensioning takes effect at time zero when impact occurs. The corresponding initial stretch, * therefore depends on the initial preload. Let us define the parameters for the force-deflection curves for the component tests with and without preload as shown in Fig. 7.10: F m , FN m : Maximum force developed without or with pretensioner, respectively, * m , *N m : Maximum deflection developed without or with pretensioner, respectively, F o : Preload at time zero, * o : Initial belt stretch (or compression) due to preload. E, E N : Energy absorption without or with preloading, respectively v : Impactor speed We propose to derive the following relationships among the three forces, F m , FN m , and F o , and the three deflections * m , *N m , and * o , respectively. Based on the geometry in the force-deflection plots for the two cases, with and without a pretensioner, shown in Fig. 7.11, the area in the triangle OCD, and the area in the trapezoid OGEB are the energy absorptions. These two areas are the same and equal to the initial kinetic energy of the impactor. By equating the energies of the two areas, and rearranging the geometric terms, the relationships between the forces and deflections are then derived as shown by the formulas (3) and (4) of Eq. (7.6), respectively. © 2002 by CRC Press LLC (7.6) Fig. 7.12 Force and Deflection Relationships (a) w/o, and (b) with Pretensioner The geometric relationships among the forces and deflections in the cases with and without preloading are shown in Figs. 7.12(a) and (b), respectively. These relationships are defined by the Pythagorian Rule. It can be concluded that in a component test at a given impact velocity, the test object in a preloaded condition is subjected to a higher impact force but with less deflection than the test without preload. Depending on the test setup, the effects of the pretensioner on the dynamic responses of an object can be different. In a component test setup, the impactor is propelled to a certain speed and impacts the test component. In a system test, such as in a vehicle-to-barrier or a Hyge sled test, an occupant undergoes both impact and excitation processes. The excitation is due to the crash pulse of the vehicle and the impact between the occupant and restraint system is the second collision. The solutions of F m N and * m N can be further normalized by F m and * m , respectively, as shown in Eq. (7.7). © 2002 by CRC Press LLC [...]... BEV of vehicle 1 in case (2) is higher than in case (1) © 2002 by CRC Press LLC 7.6.1 Crash Severity Index The term BEV1/Vclose shown in Eq (7.52) is defined as the crash severity index of vehicle 1 (subject vehicle) in a vehicle- to -vehicle collision It is a measure of BEV experienced by the subject vehicle per unit of closing speed in a two -vehicle collision Fig 7.24 shows the value of the crash severity... 7.6.1.1 Compatibility by Equal Crash Severity Index Using the simple criterion, RmRk = 1, both vehicles in the vehicle- to -vehicle collision would have the same crash severity index (BEV/Vclose) Since FMVSS 208 mandates that every new vehicle has to be certified to meet the crash safety requirements in a 30 mph rigid barrier test, the corresponding closing speed for a vehicle- to -vehicle test can then be derived... 3-D Plot of Crash Severity Indices for Vehicles 1 and 2 © 2002 by CRC Press LLC Note that the crash severity indices for the two vehicles have opposite trends As far as the subject vehicle 1 is concerned, as the mass ratio Rm goes up, crash severity index goes down A similar trend exists for the stiffness ratio, Rk For the other vehicle 2, the trends are just opposite to those of subject vehicle 1 The... can then be derived as shown in Eq (7.57), (7.57) In a vehicle- to -vehicle compatibility test, the condition for both vehicles to have the same crash severity index, the vehicles should have the following attributes: the stiffness ratio of the subject vehicle to the other vehicle is inversely proportional to the mass ratio of the subject to the other vehicle Condition shown by (1) of Eq (7.57) is plotted... 7.6.2 Crash Momentum Index Another parametric relationship used in the analysis of vehicle- to -vehicle collisions deals with the change of momentum of a subject vehicle This relationship, )v1/vclose = 1/(1+Rm), derived and shown in Eq (7.27) of Section 7.4.4 and also in Eq (7.54) of Section 7.6, is plotted in Fig 7.27 Fig 7.27 Crash Momentum Index of Vehicle 1 in TwoVehicle Collision Unlike the crash. .. of a subject vehicle to closing speed is 0.5 For a special case (2), the other vehicle having the same weight but being two times as stiff as the subject vehicle, then Rm = 1, Rk = ½ = 5, and from Eq (7.52), the BEV of the subject vehicle is 0.58 of the closing speed The reason that BEV is higher for vehicle 1 is that the stiffer vehicle 2 imparts more damage and more crush energy on vehicle 1 Therefore,... those of subject vehicle 1 The two surfaces shown in Fig 7.25 for the two vehicles intersect within the ranges of mass ratio and stiffness ratio At the intersection of the two surfaces, the crash severity indices of the two vehicles are equal Therefore, in a vehicle- to -vehicle impact, the condition for both vehicles to have the same crash severity index or the same BEV is that the product of mass ratio... energy developed in a subject vehicle will be the same when the subject vehicle impacts a fixed perpendicular barrier at the BEV speed (given by Eq (7.52) for vehicle 1 or Eq (7.55) for vehicle 2) Two vehicle parametric constants are needed in this equation, the mass ratio and stiffness ratio of the two vehicles involved in the collision For a special case (1), two identical vehicles are involved in a... collision As an example, in a vehicle compatibility study, assuming the mass ratio of the subject vehicle to the other heavier vehicle is 0.5, the value of BEV1/Vclose shown in the base contour plot of Fig 7.24 is 0.67 when Rk (stiffness ratio of the subject to other vehicle) is 0.5 This crash severity index drops to 0.47 when Rk is 2 Therefore, in order to minimize the lighter vehicle crash severity index,... stiffness of the lighter vehicle and/or decreasing the stiffness of the heavier vehicle As shown in Eq (7.52), the stiffness ratio carries the same weight as the mass ratio when it comes to determine the crash severity of the subject vehicle Similarly, the crash severity index of vehicle 2 (i=2) can be plotted in terms of Rm and Rk The surface of this plot is superimposed with that of vehicle 1 (i=1) and . the occupant dynamics in a vehicle- to-rigid barrier condition. Except for the effect of vehicle intrusion and vehicle pitch, the sled test captures most of the effects of the vehicle crash pulse. energy absorption in a vehicle- to -vehicle impact (VTV). In a rigid barrier test, the energy absorbed by the vehicle structure is ½ mv 2 . It can be shown that in a two -vehicle impact, the energy. Velocity Any crash event involves not only impact and excitation, but also energy absorption and loss. In collisions among multiple vehicles, the crush energy absorbed by each vehicle determines the crash severity