Vehicle Crash Dynamics P4 ppsx

Nevertheless, the analysis points out the unique features of the FEW coefficients in the non-perpendicular barrier tests where the coefficients can be manipulated and the crash severity

Fig 2.32 Crash Pulse Data Points (from Fig 2.17)

(2.34)

The power rate densities based on the original FEW coefficients and the all-negative coefficients for the three full-size vehicle tests are shown in Figs 2.30 and 2.31, respectively Note that in Fig 2.31, the must-activate tests, #2' and #3', are well separated from the #1 test after the introduction of the all-negative coefficients

In crash severity analyses using power rate density (prd) and FEW coefficients, it has been assumed that the FEW coefficients be given before the prd computation The application of the methodology to real time sensing application, however, needs to be explored further Nevertheless, the analysis points out the unique features of the FEW coefficients in the non-perpendicular barrier tests where the coefficients can be manipulated and the crash severity can then be distinguished

2.4.5 Use of Pulse Curve Length in Crash Severity Detection

An algorithm using the curve length concept to analyze vehicle crash severity is explored here Its purpose is to test its usefulness in discriminating non-perpendicular impacts, such as the rigid pole test, and for meeting the desired sensor activation criteria Since curve length of a crash pulse depends

on how the crash pulse is filtered, the use of the same filtering technique for different impact modes

is necessary In the algorithm based on the curve length concept, it is postulated that the curve length

of the crash pulse in a “softer” impact, such as an 8"-diameter rigid pole test, is longer than that in the perpendicular rigid barrier tests

The computation of the curve length, )L, of a given crash pulse can be carried out using the notations shown in Fig 2.32 and algebraic relationships shown in Eq (2.34):

The test data from the four mid-size vehicle tests shown in Table 2.6, filtered by a Butterworth

100 Hz cutoff frequency, are shown in the previous Figs 2.24 and 2.25 These are analyzed for the curve length comparison as shown in Fig 2.33 Note that at any given time, #3 test, a 14 mph rigid

Fig 2.33 Pulse Curve Length vs Time from Four Sets of

Crash Data Filtered at 100 Hz

Fig 2.34 Pulse Curve Length vs Time from Four

Sets of Crash Data Filtered at 300 Hz

barrier test, has the longest curve length However, the curve length of #4 test, a 17 mph center pole must-activate test, is sandwiched between the two must-not-activate tests of #1 and #2 There exists

no curve length relationship that would cause the sensor to activate for the #4 must-activate test condition

A similar analysis was carried out using a higher Butterworth filter cutoff frequency of 300 Hz and the curve length comparison is shown in Fig 2.34 The curve length of each of the four tests filtered at 300 Hz is longer than that filtered at 100 Hz The conclusion is the same that an algorithm using the curve length concept is not sufficient to discriminate the crash severity of the must-activate center pole test from the other must-not-activate tests

2.4.6 FEW Analysis on Body Mount Attenuation

In a body-on-frame vehicle, Fig 2.35, the body or cab is fastened to the frame by body mounts One type of truck body mount, shown in Fig 2.36, consists of rubber bushings on the top and bottom

of the frame bracket, plus a bolt and retainer A typical rubber bushing is made of Butyl, a man-made rubber There are four body mounts on each side frame and two front end sheet metal (FESM) mounts Body mounts are designed to carry the horizontal impact load in an impact, and to isolate the noise, vibration, and harshness (NVH) from entering the passenger compartment during driving

Fig 2.35 Truck Body on Frame Fig 2.36 A Typical Body Mounton a Body-on-Frame Vehicle

Fig 2.37 Frame Wideband Data

The impact responses of the frame and body of a truck in a 31 mph rigid barrier test will be analyzed using the FEW method The dynamic performance of the body mounts in attenuating the frame pulse to the body can be better understood using analyses in both the time and frequency domains The frame responses are shown in Figs 2.37!2.39 and the body responses are shown in Figs 2.40!2.42 Note the differences in the response intensity and peak response location between the frame and body

2.4.6.1 Frame Impulse Attenuation by Body Mount

The frame, body, and body mount impact performances of a truck in a 31 mph rigid barrier test are analyzed The wideband data of the frame and body crash pulse are shown in Figs 2.37 and 2.40, respectively Note the frame pulse contains higher frequency contents and magnitudes than those for the body pulse The filtered frame and body data sets using a Butterworth 2nd-order filter at a roll-off frequency of 100 Hz are plotted in Figs 2.38 and 2.41 Figs 2.39 and 2.42 show the coefficients of FEW, which approximate the frame and body pulses, respectively The number of coefficients, n, is

100, and the fundamental frequency, f, is equal to 2.91 Hz, which is based on the pulse duration of the test data

For comparison purposes, the filtered frame and body data sets shown in Figs 2.38 and 2.41 are combined and shown in Fig 2.43 The initial frame impulse can be approximated by a halfsine with duration and magnitude of about 7 ms and 71 g, respectively The corresponding velocity change of the impulse is )v = 014×7 ms × 71 g = 7 mph (see the closed-form shown in Table 2.7) The impulse frequency of 1000 ms/(2×7 ms) = 71 Hz dominates the frequency spectrum as shown in Fig 2.39 Due to body mount attenuation (see Section 3.5.1 in Chapter 3), only a small fraction of frame impulse is transmitted to the body

Fig 2.38 Frame Data Filtered by Butterworth at 100 Hz

Cutoff Freq

Fig 2.39 FEW Coefficients for the Frame Data

Fig 2.40 Body Deceleration Wideband Data

Fig 2.41 Body Data Filtered by Butterworth at 100 Hz

Cutoff Freq

Fig 2.42 FEW Coefficients for the Body Data

Fig 2.43 Frame and Body Filtered Crash Pulses

(Butterworth rolloff freq = 100 Hz)

Fig 2.44 Frequency Spectrum Magnitude of Frame

and Body Filtered Crash Pulses

Fig 2.45 A Sensor Module bracket

Those FEW coefficients shown in Figs 2.39 and 2.42 are converted to positive spectrum magnitudes and combined in Fig 2.44 From these figures, it is evident that the peak frame g-loading

is attenuated before it is transmitted to the body by the body mounts Shown in Fig 2.39, the spectrum magnitudes of the frame, between 70 and 100 Hz, reflect the decelerations of the initial shock impulse and the subsequent oscillatory signals However, due to the effect of body mount attenuation, the body does not carry any significant crash pulse components with frequency content above 30 Hz

2.4.7 FEW Analysis on Resonance

In the previous section, FEW was used to analyze and display the frequency contents of a crash pulse and the magnitudes of their spectra It will be shown that the FEW approach can also be used

to identify and remove certain frequency content, such as resonant frequencies, during a component design process Therefore, using the FEW approach, an existing crash pulse can be re-synthesized to include or exclude certain frequency content for the purposes of design analysis

Since removing the resonant frequency in a Fourier Series expression is equivalent to strengthening the component where the resonance occurs, it provides a quick way of evaluating a crash pulse free of resonance during a component redesign process

2.4.7.1 Air Bag Sensor Bracket Design Analysis

In evaluating the performance of an air bag system with a single point electronic crash sensor (ECS) in a van in an 8 mph rigid barrier impact, a mounting bracket supporting the ECS module was designed as shown in Fig 2.45

Fig 2.46 Coefficients of Fourier Equivalent Wave at ECS

Module

Fig 2.47 Bracket 100 Hz Resonance

The bracket, a stamped sheet metal with three segments, was installed at the center line tunnel near the dash panel An accelerometer, mounted on top of the module, recorded the deceleration (shown as A1(t) in Fig 2.49)

Frequency Domain Analysis of Resonance

A FEW analysis shows the FEW coefficients, ai, of the crash pulse, where i ranges from 1 to n The total number of coefficients, n, used in the analysis is 100 with a fundamental frequency, T, of 4.24 Hz, as shown in Fig 2.46 The maximum magnitude of the coefficients occurs between i = 22 and i = 25, where resonance occurs It should be noted that the magnitude and sign of the pair of coefficients #22 and #25 are about the same but opposite in sign; so are those of the pair of #23 and

#24 Therefore, these four coefficients as a group cancel out their effects on the signal generation, and yield the resonance shown in the transient response

Time Domain Analysis of Resonance

Since both ends of the bracket are fixed to the floor pan, the bracket behaves as a four-bar linkage with flexible joints between the segments The resonance of the bracket at about 100 Hz is mainly due

to the vibration of the flexible bracket excited at its own natural frequency

To visualize the transient response of the resonance, the Fourier expression using the four coefficients ranged from i = 22 to i = 25 is plotted and shown in Fig 2.47

Fig 2.48 Velocity and Displacement Changes of the

Resonance A2(t)

Fig 2.49 Composition of Accelerometer Data at

ECS: Signal A1 and Resonance A2

Shown in Fig 2.48 are the first and second integrals of the resonance deceleration The magnitudes of the velocity and displacement changes are fairly small even though the resonance deceleration magnitudes are fairly large

Since resonance is an undesirable vibration in the signal detection, the removal of the resonance will not affect significantly the contents of the signals such as velocity and displacement changes

2.4.7.2 Re-synthesis of a Crash Pulse Without Resonance

Re-synthesis of a crash pulse is a process in which the resonance is removed, and the crash pulse

is reconstructed using the FEW approach Before making a new and stiffer bracket to test the ECS performance, the original crash pulse, A(t), shown in Fig 2.49, is decomposed into two sets, signal A1(t) and resonance A2(t)

Fig 2.50 Velocity and Displacement of the FEW With and

Without Resonance A2(t)

A2(t) is identified by observing the group of the FEW coefficients (i = 22 to 25) whose magnitudes are the largest, as shown in Fig 2.46 Note that the coefficients in the second half of the group (i = 24, 25) are approximately mirror images of those in the first half of the group (i = 23, 22) The effect of mirror imaging of the FEW coefficients of the resonance set is that the signal due to each

of the coefficients cancels out The first and second integrals of the resonance A2(t); (velocity and displacement changes) is very small Therefore, the signal contribution due to the resonance is also small

By subtracting the resonance A2(t) from the original crash pulse A(t), the re-synthesized pulse

A1(t) is thus obtained, as shown in Fig 2.49 The integrals of the re-synthesized pulse A1(t) are compared with those of the original pulse (A) Comparison of the first integrals, )v, between the original pulse, A(t), and re-synthesized pulse, A1(t), shows very little difference, as shown in Fig 2.50, even though a large oscillation from the resonance is removed Similarly, the difference of the second integrals, )d, between the original and re-synthesized pulses is also very small The underlying reasons are attributed to the first and second integrals, )v and )d, of the resonance, A2(t), which are very small as shown in Fig 2.50

2.4.8 Trapezoidal Wave Approximation (TWA)

The deceleration of the TWA starts with zero deceleration at time zero and rises along a constant slope, e, until it reaches a constant deceleration A at time T1, as shown in Fig 2.51 The constant deceleration extends from T1 to Tm, when the maximum deformation occurs Since there are two unknowns, T1 and A, two equations based on two boundary conditions are needed The two boundary conditions for the barrier impact are (1) the velocity at Tm being equal to zero and (2) the displacement

at Tm being equal to the test dynamic crush The derivation and the solution for the two unknowns are shown as follows TWA is a useful crash pulse approximation when the kinematics occurring in the beginning of test pulse duration can be well duplicated In that early portion of the crash, structure deformation and energy and air bag sensor crash performance can be accurately assessed by the TWA

2.4.8.1 Deriving the Closed-form Solutions for TWA Parameters

The derivation of the TWA parameters is preceded by the kinematic relationships in the deformation phase (Step 1) Thereafter, the boundary conditions are applied to derive the solutions (Step 2) The two-step procedure is shown as follows

Fig 2.51 Trapezoidal Wave Approximation and Its

Integrals

(2.35)

(2.36)

(2.37) Trapezoidal Wave Approximation (TWA) and Kinematic Relationships–Step 1

Trapezoidal Wave Approximation (TWA) and Kinematic Relationships–Step 2

(2.39)

Fig 2.52 Bi-Slope Approximation (BSA)

Case Study:

A test was conducted of a mid-size passenger car in a 31 mph rigid barrier impact The crash pulse at the left rocker panel at the B-post is shown in Fig 2.53 The TWA and the integrals are shown in Figs 2.53!55, along with those for the BSA (Bi-Slope Approximation) Note that the test velocity and displacement boundary conditions at Tm= 86.5 ms are satisfied by the TWA

2.4.9 Bi-slope Approximation (BSA)

In the Trapezoidal Wave Approximation (TWA), there are two consecutive line segments of which the slopes are e and zero, respectively In the Bi-Slope Approximation (BSA) shown in Fig 2.52, there are also two consecutive line segments but with finite slopes of e and f Since there are three unknowns in the BSA, the ramp-up time of T1 and two slopes, e and f, it needs three boundary conditions for a solution In addition to the two boundary conditions for the TWA, which are the velocity at Tm equal to zero and the displacement at Tm equal to the test dynamic crush, the third boundary condition is for the displacement at Tc, the centroid time of the test crash pulse

There are three unknowns: T1, e, and f The three boundary conditions for BSA are:

1 Velocity at Tm= 0

2 Displacement at Tm = test dynamic crush

3 Displacement at Tc = test displacement at centroid time

The procedures used to determine these unknowns (A, e, f) of BSA are shown in Eq (2.40)

2.4.9.1 Comparison of Test Pulse, BSA, and TWA

The rear-loaded crash pulse of a truck in a 35 mph rigid barrier test was used in Section 2.3.6.1 for the ASW, ESW, and TESW analyses All three approximated pulses have two boundary conditions The crash pulse shown in Fig 2.12 is re-plotted and shown in Fig 2.53 for the BSA (Bi-Slope Approximation) analysis The solutions of BSA which have three boundary conditions are as follows:

C (dynamic crush) = 29.7 in B (deceleration at Tm) = !24.1 g

A (deceleration at T1) = !20.8 g

In the BSA, in addition to satisfying the two boundary conditions for the velocity and displacement at Tm (83.4 ms), the third boundary condition of the displacement at Tc (48.1 ms) is also satisfied, as shown in Fig 2.55 Also shown in the figures are the responses for the Trapezoidal Wave Approximation (TWA)

Based on the closely approximated velocity curves shown in Fig 2.54, the comparison of energies for the test, TWA and BSA, should be fairly close