Development, optimization, and design for robustness of a ... · FMVSS 201 U energy absorber David...
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Development, optimization, and design for robustness of a novel FMVSS 201 U energy absorber
David M. Fox US Army RDECOM-TARDEC
COM: (586) 574-3844 DSN: 786-3844
Email: david.m.fox1 @us.army.mil
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1. REPORT DATE 15 MAY 2006
2. REPORT TYPE Briefing Charts
3. DATES COVERED 08-01-2006 to 25-04-2006
4. TITLE AND SUBTITLE Development, optimization, and design for robustness of a novel FMVSS201U energy absorber
5a. CONTRACT NUMBER
5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) David Fox
5d. PROJECT NUMBER
5e. TASK NUMBER
5f. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) U.S. Army TARDEC,6501 East Eleven Mile Rd,Warren,Mi,48397-5000
8. PERFORMING ORGANIZATIONREPORT NUMBER #15848
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) U.S. Army TARDEC, 6501 East Eleven Mile Rd, Warren, Mi, 48397-5000
10. SPONSOR/MONITOR’S ACRONYM(S) TARDEC
11. SPONSOR/MONITOR’S REPORT NUMBER(S) #15848
12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited
13. SUPPLEMENTARY NOTES For 2006 LS-DYNA INTERNATIONAL USER’S CONFERENCE
14. ABSTRACT briefing charts
15. SUBJECT TERMS
16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT
Public Release
18. NUMBEROF PAGES
33
19a. NAME OFRESPONSIBLE PERSON
a. REPORT unclassified
b. ABSTRACT unclassified
c. THIS PAGE unclassified
Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18
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Introduction
• Significant opportunity to improve vehicle occupant safety
• Reduce impact severity between occupant heads and vehicle interiors
• Rigid body panels
• Used plastic deformation of mild steel fins and cover sheet to absorb impact energy
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Absorber construction
• 0.5 inch wide mild steel fins
• Connected with a mild steel web
• Sandwiched between mild steel surface panel and rigid armor
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LS-DYNA absorber model
• Connected fin I web assembly to cover sheet using spot welds
• Used SPC to anchor fins at interface between absorber and rigid panel
• Type 13 contacts between the various assembly components
• Nominal 3 mm mesh
• Steel was modeled using MAT24
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Impact test simulation
• FMVSS 201U
• Component level, 10 inch X 10 inch surface
• FTSS v. 3.6 free motion headform
• 15 mph initial velocity
• 20° angle between velocity and surface
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Optimization problem
• Minimize crush space subject to the constraint that H IC( d) < 700
• Independent variables: - crush space
-spacing between fins
-shell thickness of fin, web, and cover sheet
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Head Injury Criterion (HIC)
HIC ==max t I ,t 2
2 .5
rtz a(r)dr J,l
HIC(d) == 0.75446 (HIC)+ 166.4
01 Typical Impact Event c 160r------"--'-------~---------,
----z-140
m12o c
2 100 co (i) 80 Q) (.) 60 (.)
~ 40 c ~ 20 ;:}
~ %~o.-oo2~o-.oo~4-o.o~oe-o.o-oa-o-.o1-0.0-12 -0.0-14-o~.o 1=eo=.o1=a~o.o2 <- timet (in seconds)
• HIC is used to estimate the severity of head impact events • HIC{d) is a correlation between free motion headform HIC and HIC for
a full 50th percentile dummy • In the expression for HIC, a(t) is defined as the resultant acceleration
as a function of time, t1 and t2 are any two points in time during the impact separated by not more than 36 milliseconds.
• Lower HIC is better, FMVSS 201 U requires that HIC(d) be less than 1000
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Optimization technique • Closely followed Stander and Craig (LS-OPT)
successive response surface method • Iterative sequence of linear least squares
response surfaces • Chose D-Optimal subsets of 33 full factorial
basis designs • D-Optimal subsets contained seven
combinations of the three design factors • 15 iterations of 7 runs each; 105 simulations
overall
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Convergence to optimum values
Initial Optimum
Crush space (inch) 0.875 0.8044 Fin spacing (inch) 0.875 0.9446 Fin I web I cover shell thickness (inch) 0.0285 0.02616 RIC( d) 737 699
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Convergence - crush space and
0.95
:2 0.9 (,.) c: -Cll ::I (ij 0.85 > ... Cll -c: ~ 0.8
0.75
0.7
• spactng
A / ~/ ~ I \ I
- -------, -- -
I \ I \
\ ~ '"-- ..... .....
v v
0 2 4 6 8 10 12 14 16
Iteration
1-+- Crush space -Fin spacing I
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Convergence - shell thickness
-.t:. () c:
0.029
0.0285
:.:;. 0.028 Q) :::J iU > s 0.0275 -c: Q) ()
::! 0.027 Q) c:
.ll:! ()
;s 0.0265 Qj .t:. en
0.026
0.0255
-
1\
\ \ I \ \ I \ v
0 2
A
~ /~ ..---_.._----,
~ ~ ~ ....... -a
4 6 8 10 12 14 16
Iteration
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Acceleration - time history for optimum design
160
140
120
- 100 ~ c: 0
~ 80 ... (I)
Gi (,)
lil 60
40
20
0
r
f\ ) 1\
\ l_ 1\. v \f\ I \
N \ \ \ ~ .....,
~ J 1"-----
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
time (s)
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Variability I robustness Cube Plot (data means) for HIC(d)
tB 1699.022 I
Spacing ~ ~--------
/ I
Crush Space
0.02485 0.8446
• 23 full factorial about optimum • Optimum design settings ± 5°/o
e Centerpoint
e Factorial Point
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Initial design interaction
Interaction Plot (data means) for HIC(d)
0.8974 0.9446 0.9918 0.02485 0.02616 0.02747
________. .___________
Crush Space
• • Or - -----o.--
.....
Spacing ~ •
Thickness
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Crush space- thickness interaction
§150 r----+----~4-~-~----r----+---~~ c: 0
~ Q)
~ 1 00 +----7f-+-t-'+-----l-() C'CS
0 ~---+----4---~~--~----+-~~~
0.002 0.004 0.006 0.008 0.01 0.012 0.014
t (s)
- low crush space- low th HIC(d)=818
- low crush space - hi th HIC(d)=756
-hi crush space - low th HIC(d)=709
hi crush space - hi th HIC(d)=688
• Lower shell thickness increases propensity toward "bottoming out"
• Lower crush space tends to increase mean deceleration
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y
HIC(d) = 688, first peak I I SAE J 1 000 Filtered Acceleration
Time=3.499797 ·•o..-------------,
100
- 80 s c: 2 ;;; a; c; .., ., 0
•O
1-·,1
o-l----.J~~~---.-------:--~.::::==;==--.--......,j o ooo2 ono.c- ono' oooa 001 001.2 oo,~ o.o1e- oo·a on:z
Time (s)
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HIC(d) = 688, second peak I I SAE J1 000 Filte red Acceleration
Time= 7.499736 ··~~.------------,
10D
1-.,1 y
20
+
~+----,.L~~~~~~--=-~ o ooo:: ooo..: oote oooa 001 oo1: oou o.C 1 ~ oo1s oo2 Time (s)
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Improve design Cube Plot (data means) for HIC(d)
m 1699.022 I
Spacing ~ ~--------
/ I
Crush Space
0.02485 0.8446
$ Centerpoint
e Factorial Point
• -5°/o increase in crush space should enable HIC(d) < 700 • Use 0.84 crush space face as starting point
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0.858
0.856
0.854
:2 .~ 0.852 -Q) (.)
[ 0.85 Ill
..c: Ill 2 0.848 u
0.846
0.844
0.842
v
0
Design improvement
/ ~
/ ~ r----/ - ._____
I I
I
1 2 3 4 5 6 7
Iteration
• Used interpolation process keeping spacing and thickness fixed • Found new crush space to ensure HIC(d) < 700 for nominal
parameter settings + 5°/o
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710
708
706
704
:0 u 702 ::I:
700
698
696
694
r ·-
1\
\
0
Design improvement
\ \
\
\ \ / -- ---------1 \ ~ ~ v
1 2 3 4 5 6 7
Iteration
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Improve design Cube Plot (data means) for HIC(d)
l699.022 I
Spacing ~ ~--------
/ I
Crush Space
$ Centerpoint e Factorial Point
• -5°/o increase in crush space should enable HIC(d) < 700 • Use 0.84 crush space face as starting point
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Improved design Cube Plot (data means) for HIC(d)
Spacing ~ ~--------
/ I
Crush Space
• New nominal design settings + 5°/o
EB Centerpoint
e Factorial Point
• Moderate(- 0.1 inch) increase in nominal crush space yields HIC(d) < 700
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Improved design interaction
Interaction Plot (data means) for HIC(d) 0.8974 0.9446 0.9918 0.02485 0.02616 0.02747
~ ~ Crush Space
. --- . -->---- >" - -
Spacing / •
Thickness
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Response surfaces for the improved design
• Sampled by means of uniform designs
• Developed response surfaces via Kriging
• Factorial simulation results were used to compare fidelity of Kriging response surfaces generated in various ways
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Kriging
p
Y krige == fJ k Jk ( X ) + Z ( X ) k==l
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Kriging models
• Compared results for surfaces generated with -constant
-first order polynomial
-quadratic polynomial
• Gaussian correlation function
• Three different sample sizes- 9, 17, and 30
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Goodness-of-fit estimates
Maximum Error= max Ykrige,i- Y factoriaZ,i
( ) 1/2
RMSE = L Y krige, i - Y factorial, i
. n l
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Comparison of maximum error
First Order Quadratic Sample size Constant Polynomial Polynomial
9 42.70 29.52 -
17 125.28 37.44 34.92
30 53.39 30.08 18.66
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Comparison of root mean square error (RMSE)
First Order Quadratic Sample size Constant Polynomial Polynomial
9 24.36 18.36 -
17 60.50 16.00 19.02
30 23.95 15.04 10.67
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Kriging model contours
Spacing = 0.95 (5°/o lower than nominal value)
0. 950 +-------'...___,.. __ ~......_____, __ __,...,.____;___;_,~"---'1,.~ 0.950 0.975 1.000
Crush Space 1.025 1.050
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Kriging model contours
{II {II (I)
1.050
1.025
.§ 1.000 u
~
0.975
0.950 0.950
Spacing= 1.00 (nominal value)
0.975 1.000 Crush Space
1.025 1.050
HIC(d)
• < 580
• 580 - 600
600 - 620
620 - 640 640 - 660
• 660 - 680
• > 680
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Kriging model contours
0.950 0.950
Spacing = 1.05 (5°/o higher than nominal value)
0.975 1.000 Crush Space
1.025 1.050
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Conclusions • It's possible to very efficiently optimize an energy
absorber design using - the LS-DYNA explicit finite element code - the successive response surface method algorithm
• Use of classic factorial techniques in combination with Kriging response surfaces can - guide improvement of product robustness - offer insight into the nature of a product and its performance
variability
• An enlightened combination of these techniques enables, if nothing else, valuable and relatively inexpensive insight into the feasibility and behavior of various design concepts.