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
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5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) David Fox
5d. PROJECT NUMBER
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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
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Public Release
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33
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Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18
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
Absorber construction
• 0.5 inch wide mild steel fins
• Connected with a mild steel web
• Sandwiched between mild steel surface panel and rigid armor
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
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
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
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
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
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
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
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
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)
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
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
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
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)
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)
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
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
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
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
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
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
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
Kriging
p
Y krige == fJ k Jk ( X ) + Z ( X ) k==l
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
Goodness-of-fit estimates
Maximum Error= max Ykrige,i- Y factoriaZ,i
( ) 1/2
RMSE = L Y krige, i - Y factorial, i
. n l
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
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
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
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
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
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.
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