Vehicle Crash Dynamics P14 ppsx

Only in the fixed barrier test condition or when the stiffness ratio equals the mass ratio, will BEV or crash severity index be the same as V or crash momentum index.. The crash severit

Fig 7.28 A Non-linear Two-Mass Impact Model

In general, it is the BEV (not the ) V) that describes the VTV crash severities in a complete manner Only in the fixed barrier test condition or when the stiffness ratio equals the mass ratio, will BEV (or crash severity index) be the same as ) V (or crash momentum index) This relationship can

be proved by simply making Rm = Rk and substituting into Eq (7.52) Then BEV1/Vclose = ) V/Vclose

= 1/(1+Rm).

7.6.3 Crash Severity Assessment by a Power Curve Model

This section presents a model with power curve force deflection, as shown in Fig 7.28 The model is used to assess the crash severity of a mid-size passenger vehicle in a vehicle-to-vehicle test The velocity change and fixed barrier equivalent velocity (BEV) of a 1985 Merkur which is struck from the front by a NHTSA Moving Deformable Barrier (MDB) at 70 mph will be estimated This test, a central collinear impact, was conducted at Calspan Corp under a contract to NHTSA The crash severity of the Merkur will then be analyzed and compared with that of NCAP (New Car Assessment Program) at a 35 mph rigid barrier test condition.

7.6.3.1 Power Curve Model and Methodology

Power curve force-deflection model can be utilized to perform the following tasks: (1) impact modeling, with loading and unloading simulations, (2) computations of the barrier equivalent velocity (BEV), and (3) velocity change (V.C.) of a vehicle during impact.

Modeling of the two-vehicle impact was effected using a two-mass and two-EA (non-linear-spring Energy Absorber) model This was used for both validation and prediction The model simulates vehicle-fixed barrier and vehicle-vehicle impacts In the vehicle-fixed barrier impact, only one set of data for the subject vehicle is specified The other set of data for the second vehicle in the model is simply the mirror-image of the first set Note that in the vehicle-fixed barrier impact, the velocities of the two vehicles are equal and opposite The mass and velocity of the two vehicles are defined as follows:

m1, m2: masses of struck and striking vehicles, respectively.

V1: initial velocity of struck vehicle.

V2: initial velocity of striking vehicle.

7.6.3.2 Power Curve Force-Deflections

A power curve describing the force-deflection characteristics of the energy absorber of vehicle

i is defined as:

F = kiDni Where

F: force level of the energy absorber.

D: deflection of the energy absorber.

ki, ni: stiffness and power factors of vehicle i, respectively.

The test data for (1) the NHTSA MDB used in the vehicle side impact tests, and (2) the Merkur's frontal fixed barrier certification tests at 35 mph and the NCAP test are shown in Table 7.6

Fig 7.29 NHTSA Moving Deformable Barrier (MDB)

Force/Deflection Characteristics

Fig 7.30 Simulated ‘85 Merkur XR4 Frontal Structure

Characteristics

Table 7.6 Merkur Test Data at 35 mph Rigid Barrier Tests

Crash Test No Test Weight, lb Dynamic Crush, in @ ms Static Crush, in

The power curve formulas for both MDB and Merkur are obtained that approximate the force-deflection characteristics of both structures (see Figs 7.29 and 7.30 ) They are:

NHTSA MDB: F = 29.86D.47 , and Merkur: F = 21.50D.44

where F is the force level in klbs and Dis the deformation in inches.

Since both k (stiffness coefficient) and n (power) for the MDB are larger than those for the Merkur, MDB is definitely stiffer than the Merkur structure.

The first stage of simulation computes the maximum dynamic crush and the fixed barrier equivalent velocity of each vehicle The structural unloading properties are taken into account, which yields the static crush in the second stage of simulation.

Fig 7.31 Individual Crush Energy and BEV

(7.58)

(7.59)

Following the schematic shown in Fig 7.31 , the BEV can be computed In the loading phase of

a vehicle-vehicle impact, the structure of each vehicle undergoes a process of absorbing kinetic energy The amount of absorbed energy (crush energy) in each vehicle depends on its structural characteristics The energy absorption reaches its maximum when both vehicles reach the common velocity, where the maximum deformation (or dynamic crush) of each vehicle occurs Since the vehicle structure is not perfectly plastic, part of the energy absorbed is transformed into kinetic energy due to spring back effect when unloading occurs For the numerical methods on the power curve loading and unloading simulations, the reader is referred to Sections 5.6.1 and 5.6.2 of Chapter 5.

The crush energy absorbed by the vehicle structure up to the dynamic crush can then be computed By equating the crush energy to that absorbed by the subject vehicle in a fixed barrier impact, one obtains the fixed Barrier Equivalent Velocity of the subject vehicle (BEV).

7.6.3.3 Computation of Barrier Equivalent Velocity (BEV)

Consider one of the two vehicles (Vehicle i): Ei is the maximum dynamic crush energy absorbed

by the vehicle in a vehicle-vehicle impact, where:

By equating Ei to the energy absorbed by the subject vehicle in a fixed barrier impact, one obtains:

(7.61)

where BEVi is the barrier equivalent velocity of vehicle i and mi is the mass of the subject vehicle i.

Case Study: For the struck vehicle (i=1), BEV1 is computed as follows:

The velocity change ( ) V) of each vehicle involved in the two-vehicle impact can be computed either by using a numerical searching technique during the simulation or by the application of the conservation of linear momentum Note that the sum of the absolute values of the velocity changes

of the two vehicles is equal to the “closing speed” of the two vehicles — or the relative approach velocity of the two vehicles.

It should also be noted that ) V of a vehicle in a two-vehicle impact is not necessarily the same

as the BEV (fixed barrier equivalent velocity) As mentioned in Section 7.6.2, the ) V and BEV of

a vehicle are the same only when mass ratio equals stiffness ratio of the two vehicles The analytical computation of the BEV of a vehicle in a two-vehicle impact involves the application of the principle

of work and energy in addition to the principle of impulse and momentum.

The dynamic responses of the striking and struck vehicles are shown in Table 7.7 The dynamic crush and BEV of the Merkur are 32.7 inches and 40.6 mph, respectively The estimated characteristic length of Merkur equals 32.7/40.6 = 0.81 inches/mph Compared to the Merkur test data at 35 mph

in rigid barrier tests shown in Table 7.7 where the characteristic length is about 0.80 inches/mph, the model’s prediction is fairly reasonable.

Table 7.7 Dynamic Responses of Merkur and MDB

Under the test condition where a NHTSA MDB (moving deformable barrier) strikes a mid-size passenger car (Merkur) at 70 mph, the velocity change of Merkur (32.7 mph) is less than NCAP test speed of 35 mph However, based on the actual crush from the test, Merkur suffered a greater damage than that in the NCAP tests at 35 mph Based on the power curve model simulation, the BEV of Merkur is 40.6 mph as shown in Table 7.7

Therefore, in order to achieve the same crash severity for the Merkur as that in NCAP rigid barrier test, the striking speed of MDB should be scaled back from 70 mph to about 60 mph.

Fig 7.32 A Damage Boundary Curve

7.7 VEHICLE ACCELERATION AND CRASH SEVERITY

The acceleration of a vehicle involved in a two-vehicle collision is an indicator of crash severity Using the relative acceleration response of an effective mass system shown in Eq (4.70) in Section 4.9.1.1, the acceleration of the subject vehicle can be derived Eq (7.62) shows the acceleration of the subject vehicle as a function of relative approach velocity, mass ratio (rm = m1/m2) , structure natural frequency, and damping factor It should be noted that the acceleration of the subject vehicle

is not governed by its own initial velocity; rather, it is governed by the relative approach velocity of the two vehicles.

7.7.1 Damage Boundary Curve

To assess crash severity, a method adopted in the packaging industry called Damage Boundary Curve (DBC) [6] is used in the following crashworthiness analysis Based on the effective mass and effective stiffness in assessing the impact severity, DBC defines the threshold of crash severity that the packaged components (such as a computer and peripheral products) can sustain without incurring damage The specification is expressed in terms of peak acceleration (due to stiffness effect) and velocity change (due to mass effect) as shown in Fig 7.32 Any impact condition sustained by the product which is above and/or to the right of the curve is in a damage zone If the impact condition

is below and /or to the left of the curve, it is a safe condition.

Fig 7.33 Transient Velocity and Deceleration of a Product at

Two Impact Speeds

Case Study 1: A product (component) is protected by a cushion material with stiffness given by a

natural frequency of either 3 or 4 Hz It is further assumed that the impact speed of the component striking a fixed barrier is kept at a constant 15 mph Plot the transient velocity and acceleration responses and locate the two points on a DBC plot.

Using the transient and major response formulas shown in Section 4.5.1 in Chapter 4, the transient responses of the two tests are shown in Fig 7.33 Both velocity curves between time zero and the time

of dynamic crush have the same velocity change of 15 mph However, the timings at the dynamic crush is 84 ms with the softer cushion (3 Hz) and 62 ms with the stiffer cushion (4 Hz) The peak sinusoidal deceleration is 13 g with the softer cushion and 17 g with the stiffer one.

Since the two points of the tests (15 mph, 13 g), and (15 mph, 17 g) have the same ) V, they are located along a vertical in a DBC plot.

7.7.1.1 Construction Steps for DBC

Step 1: Determine the critical velocity change for a product Using a drop test setup, the product is

dropped from a given height onto a pad of known stiffness The test is repeated with increasing drop test height until the product is damaged Record the data points in terms of peak acceleration and velocity change Circle the damage data point as shown in Fig 7.32 The critical velocity change, ) vc is the velocity change of a point immediately preceding the damage point A vertical line is drawn through ) vc.

Step 2: Replace the pad with a softer pad and choose a drop height such that the velocity change

exceeds ( B /2) ) vc By using this new velocity, the new test point will be located on the flat part of the lower right portion of DBC Conduct a series of drop tests at the chosen drop height with an increasing pad stiffness for each succeeding test The data points in terms of peak acceleration and velocity change are recorded Circle the damage data point The critical acceleration, Ac, is the acceleration of a point immediately preceding the damage point A horizontal line is drawn through Ac

Step 3: Round off the corner between the vertical through ) vc and the horizontal through Ac By

fitting part of an ellipse between the two points ( ) vc ,2Ac) and (( B /2) ) vc ,Ac ), finish the final DBC construction.

Fig 7.34 DBC Curves for a Fuel Shutoff Switch of a Full-Size Vehicle

7.7.1.2 Mechanic Principles of DBC

The mechanic principles of DBC involve the transient response of a two-mass system subjected

to an impact The two-mass system has been analyzed by an effective mass system in Section 4.4.4, Chapter 4 The impact response of a subject mass is controlled by its momentum (x-axis of DBC, due

to the mass ratio) and energy absorption (y-axis of DBC, due to the stiffness ratio) relationship Since the momentum principle describes the gross motion of the system, the impact duration is controlled

by the natural frequency of the system From Eq (4.81), the contact (or impact) duration is inversely proportional to the undamped natural frequency.

Velocity change is the product of acceleration and impact duration Given a velocity change on the DBC, the point that has a higher acceleration will have a shorter impact duration and the point that has a lower acceleration will have a longer one Similarly, given an acceleration on the DBC, a smaller velocity change will have a shorter impact duration and a larger velocity change will have a longer one.

Case Study 2:

For a vehicle where the fuel is delivered to the engine by an electric fuel pump, a fuel shutoff switch is installed either in the trunk or in the passenger compartment The switch is designed to shutoff the fuel supply when the impact severity in a certain impact mode is severe enough A typical fuel shutoff switch is a mechanical device similar to the ball-in-tube (BIT) safing (or confirmation) sensor with a magnet to provide the bias g-force Similar in function to the BIT safing sensor, the amount of damping in the fuel shutoff device is negligible

A typical DBC of the fuel shutoff switch used in a full-size vehicle is shown in Fig 7.34 The DBC is plotted in terms of deceleration and contact duration The product of the two quantities yields the velocity change There are two outer DBC curves shown in the top and bottom of the plot When the deceleration is in the “must actuate region,” the crash severity is the highest; while the deceleration

is in the “must not actuate region,” the severity is very low.

The two curves with indices A and B were obtained from tests Curve A is based on a test where

a full-size vehicle struck a rigid barrier at 35 mph Curve B is based on both a test where a full-size vehicle was hit in the rear by a mid-size car at 50 mph, and a test where the full-size vehicle was hit

in a frontal 50% offset by a mid-size car.

Fig 7.35 Specific Stiffness vs Characteristic Length

(7.64)

7.7.2 Crash Severity Assessment in Vehicle-to-Vehicle Compatibility Test

7.7.2.1 Vehicle Crush Characteristics

Fig 7.35 shows the crush characteristics of three vehicles in a fixed barrier test condition The characteristic length (c/v, in/mph) of the full-size car is the largest, followed by the mid-size car and then the truck/SUV The relationship between the specific stiffness (K/W, lb/in/lb) and characteristic length (C/V, in/mph) has been shown in Eq (4.26) This relationship is repeated in Eq (7.63), and plotted in Fig 7.35

It has been shown in Section 4.5.2.5, Chapter 4, that in a vehicle-to-vehicle impact, the relative magnitudes of the mass ratio and stiffness ratio of two vehicles are determined by the specific stiffness

of each of the two vehicles.

Since the specific stiffness of the truck is larger than those for either of the two cars, as shown

in Fig 7.35 , the relative magnitudes of the mass ratio and stiffness ratio between the truck and car can

be determined as shown in Eq (7.64) (a repeat of Eq (4.31) in Chapter 4).

In order to show the differences of the crash severity index and crash momentum index clearly

on a 3-D plot, the mass and stiffness ratios in the two expressions have been inverted Substituting

rm = 1/ r'm and rk = 1/ r'k in the respective expression, they become the ones shown in Fig 7.36 The two crash indices of the subject vehicle #1 are now expressed in terms of the mass ratio, r Nm and stiffness ratio r Nk of vehicle #2 to #1.

Fig 7.36 Closing Speed Comparison Based on ) V and BEV

Fig 7.37 Truck to Full-Size Car Compatibility Test — Case 1

The crash severity index is not equal to the crash momentum index in general, as shown in Fig 7.36 The two indices are equal to each other when the mass ratio equals the stiffness ratio This condition exists when the two surfaces shown in Fig 7.36 intersect along the diagonal of the base.

The closing speed will be determined such that the full-size car would have the same ) V and BEV of 35 mph as in a rigid barrier test.

Table 7.8 Closing Speeds Based on 35 mph Rigid Barrier Test (BEV|1 and ) V|1=35 mph)

Case

#

vehicle-to-vehicle

rmN

m2/m1

rkN

k2/k1

vclose, mph

on

) V

based

on BEV

w1,

klb

k1/w1, klb/in/

klb

k1, klb/in

w2 , klb

k2/w2 , klb/in/

klb

k2 , klb/in

In a rigid barrier test, the striking speed of a vehicle is the same as ) V in the deformation phase and is also the same as the BEV If the barrier impact speed is set at 35 mph, then the closing speed based on the momentum formula is 64 mph, while that based on the energy absorption formula is only

54 mph Consequently, using the ) V momentum method overestimates the closing speed by almost 20% In Case 2, a full-size car strikes a mid-size car as shown in Fig 7.38 The closing speed is determined in such a way that the subject mid-size vehicle m1 would yield a BEV or ) V of 35 mph,

as in the rigid barrier test.

Fig 7.38 Full-Size to Mid-Size Car Compatibility Test — Case 2

(7.65)

From Table 7.8 for case 2, rmN > rkN, the closing speed based on the momentum formula is 62 mph, while that based on the energy absorption formula is 70 mph Consequently, using the )V momentum method underestimates the closing speed by about 11% in this test condition.

7.7.2.2 Vehicle Peak Responses

In the vehicle-to-vehicle test shown in (a) of Fig 7.38 , the subject vehicle m1 absorbs a certain amount of the total crush energy during an impact This energy absorption is equal to that absorbed

by m1 when it impacts on a rigid barrier at a speed of BEV1, as shown in (b) of Fig 7.38

It will be proved that the peak sinusoidal deceleration of vehicle m1 in the two-vehicle impact shown in part (a) is the same as that vehicle-rigid barrier test in part (b) of Fig 7.38

The right hand side of (3) of Eq (7.65) is the peak sinusoidal acceleration of vehicle #1 in a rigid barrier test where the impact speed is BEV1 and the circular natural frequency of vehicle #1 is T1 The left hand side of (3) is the peak sinusoidal acceleration of vehicle #1 in the vehicle-to-vehicle test Consequently, as long as the crash severity index is used in establishing the crush energy relationship between the vehicle-to-vehicle (VTV) and vehicle-to-barrier (VTB) tests, the peak sinusoidal acceleration of the subject vehicle will be the same in both VTV and VTB tests.

Note that the magnitude of the effective stiffness (or mass) expressed in terms of individual stiffness (or mass) is shown in Fig 7.39 The magnitude of ke becomes larger when both k1 and k2 are larger (e.g., k1 = k2 = 10, ke = 5) and the magnitude of ke becomes smaller when both k1 and k2 are smaller (e.g., k1 = k2 = 2, ke = 1) Similar relationship applies to the effective mass By knowing the magnitudes of the effective mass and stiffness, the change in vehicle response in a two-vehicle impact can be quickly assessed.