Vehicle Crash Dynamics P13 potx

7.2 OCCUPANT MOTION UNDER IMPACT AND EXCITATION Occupant motion in the vehicle compartment is controlled by both the vehicle and restraint impactfactors.. 7.1 A Two!Degree!of!Freedom Occ

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 anddesign conditions Since an impact is a physical event that involves analyses of impulses and energycomponents, such as kinetic energy, energy absorption, and energy dissipation, the analyses requireboth the principle of work and energy and that of impulse and momentum Although both principlesare derived from Newton’s Second Law, they are not mutually exclusive when it comes to solvingproblems 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, theclosed-form formulas derived in Section 4.11 of Chapter 4 can be utilized to solve problems Casestudies, such as the dynamic principles of pyrotechnic pretensioner on the occupant responses, areinvestigated The preloading effect of a restraint system on the occupant response and ridedownefficiency are discussed Many crashworthiness topics related to single and multi-vehicle collisionsare analyzed by the engineering principles presented so far for determining the degree of crashseverity Applications of these principles to vehicle-to-vehicle compatibility, shear loading of truckbody mounts due to eccentric loading, and the methodology of accident reconstruction methodologyare also presented

7.2 OCCUPANT MOTION UNDER IMPACT AND EXCITATION

Occupant motion in the vehicle compartment is controlled by both the vehicle and restraint impactfactors Both factors complement each other in producing the occupant responses in a particular testcondition Since any vehicle produced needs to be certified to meet the federal vehicle safetystandard, 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 translationand rotational kinematics of the occupant in a crash The theory and effect of the pretensioner inimproving 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 restrainedoccupant model [1] is developed to simulate occupant motion and response in the event of a vehiclefrontal 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 theircombinations are incorporated in the model The occupant-vehicle contact surfaces are defined by theupper 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 Thevehicle compartment is defined by the inclinations and the locations of the upper and lower panels andtheir force deflection (F-D) data In the case of an air bag restraint system, the air bag F-D data iscombined together with the upper panel F-D characteristics

Fig 7.1 A Two!Degree!of!Freedom Occupant Model

M1: Lower mass (Hip),

M2: Upper mass (Chest)

X1: Lower mass displacement

Xv: Vehicle displacement (Crush)

L: Distance from link pivot to upper mass

L1: Distance from link pivot to head center

Ls: Distance from D-ring to upper mass

LL: Distance from lap belt anchor to tangent

point on hip circle

R1: Radius of hip circle

B1: Vertical distance from lap belt anchor to

center of hip circle

*1: Lap belt stretch

F0: Friction between hip and seat

FL: Knee and lower panel contact force

Fu: Effective torso and upper panel contactforce which produces a moment aboutlink pivot

K1: Lap belt stiffness

K2: Shoulder belt stiffness

H1: Horizontal distance from lap belt anchor

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 qi: (1) i = 1, qi = x1, the linear displacement

of the hip joint, and (2) i = 2, q2 = 2, the angular displacement of the upper torso The kinetic andpotential energies of the system are expressed in terms of the two independent variables as shown in

Eq (7.2)

Table 7.1 Definitions of Model Variables

By completing the partial differentiations with respect to the independent variables x1 and 2

shown in Eq (7.1), the equations of motion of the model in terms of the linear acceleration of the hipand 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 solutionsfor 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

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 beltF-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 thesubjects to be presented in the following sections

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 frontalrigid barrier test undergoes an impact process, while a restrained occupant undergoes an excitation bythe vehicle crash pulse and an impact at high speed test by the intruding toe board on the lowerextremities of the occupant The outcome of the impact can be quite different from that of theexcitation As an example, the occupant in a vehicle crash has the benefit of riding down with thedeforming vehicle structure, thus diverting some of the occupant energy away from interacting withthe 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 theoccupant dynamics in a vehicle-to-rigid barrier condition Except for the effect of vehicle intrusionand vehicle pitch, the sled test captures most of the effects of the vehicle crash pulse on the occupantresponse

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 beingtested In this section, the effects of a pretensioner on impact responses are presented The kineticrelationships 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 animpact By zeroing in the slack, the pretensioner in a system test reduces the torso deceleration whilethe 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

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) withand 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 occupantresponses, especially the chest g, is quite obvious The pretensioning effect is even more pronouncedfor 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 berestrained by the pretensioning force, FO, at time zero as shown in Fig 7.6 The magnitude of thepretensioning 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 modelare 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

Note: w/o : without; w/ : with

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 (M2 or M4) riding in a vehicle for the two cases,without and with a pretensioner, are shown in Fig 7.7 The restrained occupant decelerations vs timefor the two cases are also marked on the model The simulation results of the modeling aresummarized in Table 7.3 The responses of an occupant, such as the maximum displacement, restraintdeflection, restraint force, and restraint energy, are smaller in the model with a pretensioner (for M4)than in the model without a pretensioner (for M2) Therefore, overall, the crash severity of theoccupant 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

Force,klb

Restraint Energy,klb-ft

The occupant deceleration profile with a preload of 0.6 klb and an occupant effective weight of0.1 klb yields an initial deceleration of 6 g at time zero, as shown in Fig 7.8

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 thanthat without preloading The lower chest g in the preloaded case is also confirmed by the restraintforce-deflection curves for the two cases as shown in Fig 7.9 Both the peak force and energy of therestraint 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, Eo,

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 Forthe model with a pretensioner, : equals 54% This compares with 46% for the model without apretensioner The underlying reason for the higher ridedown efficiency is due to a larger force in theearly portion of the occupant deceleration curve that results in a higher ridedown energy density Thehigher occupant deceleration in the beginning of the crash pulse is attributed to the use of thepretensioner

Table 7.4 Output Responses of Models w/ and w/o Preload

Model

Eo , OccupantKinetic Energy, klb-ft

Ers ,RestraintEnergy, klb-ft

Erd ,RidedownEnergy, klb-ft

: , RidedownEfficiency, %

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 Therestraint system with and without pretentioner is impacted by a black tuffy (a body block) at a presetspeed For the test with pretensioner, it is assumed that the pretensioning takes effect at time zerowhen 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 andwithout preload as shown in Fig 7.10:

Fm , FNm : Maximum force developed without or with pretensioner, respectively,

*m , *Nm : Maximum deflection developed without or with pretensioner, respectively,

Fo : Preload at time zero,

*o : Initial belt stretch (or compression) due to preload

E, EN : Energy absorption without or with preloading, respectively

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 withoutpreloading are shown in Figs 7.12(a) and (b), respectively These relationships are defined by thePythagorian Rule It can be concluded that in a component test at a given impact velocity, the testobject in a preloaded condition is subjected to a higher impact force but with less deflection than thetest without preload

Depending on the test setup, the effects of the pretensioner on the dynamic responses of an objectcan be different In a component test setup, the impactor is propelled to a certain speed and impactsthe test component In a system test, such as in a vehicle-to-barrier or a Hyge sled test, an occupantundergoes both impact and excitation processes The excitation is due to the crash pulse of the vehicleand the impact between the occupant and restraint system is the second collision

The solutions of FmN and *mN can be further normalized by Fm and *m, respectively, as shown in

Eq (7.7)

Fig 7.13 Peak Load and Deflection Ratios w/ and w/o

Preload of A One-Mass Model

7.3.3 Transient Analysis of a Preloaded Model — Impact and Excitation

The dynamics of the preloading spring-mass model shown in Fig 7.10 can be formulated by asecond order differential equation The effect of preloading on the output responses can then bestudied using the closed-form solutions presented in the Section 4.11 of Chapter 4

The forcing function (excitation) in (1) of Eq (7.8) is a constant in the second-order differentialequation The preloaded g-force, Fo, produces the preloaded deflection, *o If the preloaded forceequals the weight of an object in a horizontal impact, the corresponding deflection is then the same

as the static deflection due to the weight of an object in a vertical drop test

Since the initial test speed of the impactor is vo, and the preloaded g-force acting on the mass is

Eo, the preloaded model is a special component test subjected to a constant excitation due to thepreload in addition to the impact

In Section 4.11, the impact and excitation of a Kelvin model are presented and a set of closedform solutions is presented The solutions for the model subjected to various pulses such as a TESW(tipped equivalent square wave), halfsine, or haversine pulse are expressed in terms of homogeneousand particular solutions In general, the initial conditions are a*, the initial acceleration due toexcitation, v*, the velocity due to impact, and d*, the relative displacement

(7.10)

Using the solution formula for the TESW shown in Eq (4.88) and Table 4.11, one gets the outputtransient acceleration of the mass as shown in Eq (7.9) Note that a* = E is a constant decelerationwhich will be shown due to the equivalent preloading, and v* = vo is the initial impact velocity

The maximum g-force in the component test consists of two acceleration components, shown in(1) of Eq (7.9) One acceleration component is v*Te, attributed to the impact, and the othercomponent, E, is attributed to the excitation caused by preloading

Case Study: In a component test, a test object with an effective weight of 100 lbs is propelled to a

speed of 15 mph The restraint stiffness is assumed to be 500 lbs/in The object is tested under tworestraint conditions: One model in Fig 7.10 has no preload, and the other has a preload of 300 lbsobtained by precompressing the spring 0.6 inches We propose to perform the transient analysis forboth models and to identify the parameters that affects the output responses

Using the formula shown in Eq (7.9), the output acceleration components due to the impact andexcitation are computed and shown in Eq (7.10)

The timing, tg, that the maximum acceleration incurs can be found from (1) of Eq (7.10) and isshown in Eq (7.11).

Shown in Fig 7.14 are two output acceleration components and one resultant accelerationcomputed by the closed-form formulas shown in Eq (7.10) Additional two curves superimposed onthe first three curves are from the numerical method using the CRUSH II model Note that themaximum resultant acceleration of 30.2 g occurs at 33 ms In this component test at 15 mph, thesingle-mass model without preloading (impact only without excitation) yields a maximum acceleration

of 30 g which is slightly lower than that with preloading

7.4 CENTRAL COLLISIONS

Two approaches are used in the analysis of central collisions One uses the relative motionconcept to analyze the total crush energy absorbed and dissipated in the two-vehicle collision, and theother uses a fixed-frame reference to relate the total and individual crush energy to the crash severity

in terms of barrier equivalent velocity (BEV)

It will be shown that the concept of an effective mass system is very useful in simplifying theexpression for the energy absorption in a vehicle-to-vehicle impact (VTV) In a rigid barrier test, theenergy absorbed by the vehicle structure is ½ mv2 It can be shown that in a two-vehicle impact, theenergy absorbed by the combined structure is also ½ me p2, where me is the effective mass and p is therelative approach velocity

Fig 7.15 Two-Particle Impact to Determine Impact Velocity

Any crash event involves not only impact and excitation, but also energy absorption and loss Incollisions among multiple vehicles, the crush energy absorbed by each vehicle determines the crashseverity for that vehicle Although, the principle of work and energy and the principle of impulse andmomentum are derived from Newton’s Second Law of Motion, they are not mutually exclusive when

it comes to solving dynamic collision problems In the following two-bob impact problem, although

it involves energy transfer between two events, the momentum principle must be used (notdiscretionary) to account for the energy loss during the collision

7.4.1 A Collision Experiment

In an experiment, a ping-pong ball exits from a toy gun and strikes a stationary fishing bob, asshown in Fig 7.15 The masses of the ball and bob are m and M, respectively, and the coefficient ofrestitution between them is e After impact, the bob swings up to a maximum height, where the angle

is "° Derive the closed-form formula for the muzzle velocity of the ping-pong ball, vm, and thepercentage of energy loss (with respect to the initial kinetic energy of the ball) during impact

Case Study (Exercise): Before proceeding to solve the general problem, we propose to solve a special

case in order to review basic principles Given the following information: L = 12 inches, " = 30°,mass ratio of M/m = 3.0, and e = 0 (using a Velcro pad attached to the ball and bob), determine theinitial impact velocity of the ball and the percentage of the energy loss due to impact (Answer: 8 mphand 75%)

Hint: Note that if only the conservation of energy is applied to the two events (before and afterimpact), this will lead to a substantially lower initial impact velocity because the energy loss occurredbetween the two events is not accounted for

Impacts involve generally energy loss, which occurs in two phases: a deformation phase and arestitution phase In the deformation phase, the crush energy is absorbed by the engaging structures,and in the restitution phase, a portion of the energy absorbed is returned as rebound energy The finalenergy loss, termed as the energy dissipation, is equal to energy absorption minus rebound energy

It will be shown in this chapter that the total crush energy depends on the effective mass of the twomasses and the closing speed, i.e., the relative approach velocity of the two masses The generalproblem shown in Fig 7.15 is solved for the initial impact velocity of the ball and the energy loss.The solution procedures are shown in Eq (7.12)

Fig 7.16 Normalized Impact Velocity of Mass m

The initial velocity of mass m, vm, normalized by the square root of 2gh, is plotted against massratio for five levels of coefficients of restitution, e, and shown in Fig 7.16 The percent energy loss,

%Eloss, during impact with respect to the initial kinetic energy can then be computed using (8) of Eq.(7.12)