Conservatism Implications of Shock Test Tailoring for

Multiple Design Environments

Thomas J. Baca

R. Glenn Bell

Susan A. Robbins

N88- 13611

Specification of a mechanical shock test requires an en-gineering decision concerning the relationship between thelaboratory and field shock environments. Once a method ofshock characterization is selected, test conservatism becomesa measure of the degree to which the laboratory test is moresevere than the operational environment of the structurebeing tested. This paper describes a method for analyzingshock conservatism in test specifications which have beentailored to qualify a structure for multiple designenvironments. Shock test conservatism is quantified forshock response spectra, shock intensity spectra and rankedpeak acceleration data in terms of an Index of Conservatism(IOC) and an Overtest Factor (OTF). The multi-environmentconservatism analysis addresses the issue of both absoluteand average conservatism. The method is demonstrated in acase where four laboratory tests have been specified toqualify a component which must survive seven different fieldenvironments. Final judgment of the tailored testspecification is shown to require an understanding of thepredominant failure modes of the test item.

INTRODUCTION

Tailoring test specifications for shock-hardened components requires an engineerto relate the laboratory test environment to the field shock environment in the mostmeaningful way possible. This process is critical since "overtesting" may requireexpensive design modifications to the component, while "undertesting" will sustainuncertainty regarding the survivability of the component in the field. Thefundamental problem becomes one of operationalizing the analyst's engineeringjudgment about test conservatism into a consistent and quantitative methodology.This process is complicated further when the component must survive more than onefield environment. An engineer typically utilizes data measured from the operationalshock environment as the basis for selecting the qualification test method and testlevel. Test conservatism is a measure of the degree to which this tailoredlaboratory shock environment exceeds the field environment. Even though it is rarelyevaluated in a quantitative manner, a level of test conservatism is implicit in everytest specification. In this paper, a method is presented and demonstrated for

This work was performed at Sandia National Laboratories and supported by the U. S.Department of Energy under contract DE-ACO4-76DPO0789.

_'RI_P_,I)ING PAGE BLANK NOT FILMED

29

https://ntrs.nasa.gov/search.jsp?R=19880004229 2018-04-18T23:06:37+00:00Z

assessing conservatism in shock test specifications tailored for multiple fieldenvironments.

Description of the conservatism analysis procedure will be presented by example.Shock data for an electronics package subjected to both operational and laboratorymechanical shock tests will be analyzed in the course of performing the conservatismassessment. The discussion will cover: i) the original tailoring of the the testspecification considering multiple environments; 2) the initial evaluation ofconservatism; 3) the specification of a level of conservatism for judging an overtestcondition; 4) the identification of overtest and undertest conditions; and 5) and theinterpretation of the results in terms of possible failure modes of the component.

SHOCK TEST TAILORING

A common shock test tailoring procedure [i] is based on matching the absoluteacceleration shock response spectra (SAA) [2] of the field data and a laboratory testinput. If multiple field environments exist, then the test is specified to have aSAA spectrum which envelops the SAA of the field data. For the component beingdiscussed in this paper, the field design environments consisted of six measured andone analytically predicted responses of the component in its longitudinal (X) andlateral (Y) axes. Figures IA and IB show the ensemoles of SAA spectra for theseenvironments. The field environments are denoted with regard to the fact that theyare either derived from blast (B) or nonblast (NB) environments. These operatingenvironments include: i) three different impulsive shock tests (NBI, NB2, NB3); 2)one induced thermo-structural response (NB4); 3) two blast tests (B1 and B2); and oneanalytical prediction of a different type of blast loading (B3). Envelopes showingthe distinction between the blast and nonblast environments are shown in Figures 2Aand 2B. In general, the blast environments dominate the low frequency range (i.e.,100 Hz to 1000 Hz), while the nonblast environments control in the high frequencyrange (i.e., 1KHz to 10 KHz). All of the data were lowpass filtered at i0 KHz and a20 ms duration were analyzed for each record.

A resonant plate shock test technique [3] was chosen as the test method. Thistechnique produces high level, two-sided shock inputs which are more similar to thefield data than a one-sided haversine pulse which is generated using a drop tableshock machine [4]. Two resonating plates were chosen with primary resonantfrequencies of 250 Hz and 3000 Hz. The component test specification required thatthe component survive shocks on the low and high frequency plates in both the X and Yaxes. Figures 3A and 3B show a comparison of SAA spectra for the field and testenvironments. The test designation is a three letter code denoting: the resonantplate used (H for the high frequency plate and L for the low frequency plate); thecomponent axis aligned with the test input direction (X or Y); and the orientation ofthe accelerometer at the base of the component during the test (× or Y). Forexample, HYX is the measured X axis input during the Y axis high frequency platetest.

These tests were judged to be acceptably tailored given the constraints ofseeking a minimum number of different test setups, and accepting partial envelopingof the X axis shock spectra in the high frequency range. Note that the X axis highfrequency range controlled selection of the high frequency plate test while the Yaxis low frequency data primarily influenced tailoring of the low frequency platetest.

3O

SAA

1(34 .........

#-RE ......."_"°-"

S • • _:.o-Jo_....._S • .._,'.p . • .-.-_.. to

s s • s • *o"

s • • _:.':.'.""0 .. ,,N

o• • o• ._0 •

S 1 G2 _-'o-;_'-.-,r._.E / ..'.;"/

_...<-...s

G :_:" ":'"s °

IGI ........

lg 2

i i l w i | i i-

_,: _..,.o.,, .."-..,,. -e' "....-'',.-_..-.¢.

o.,. /_'_-, " ....... -• .¢-.:_.s ...... "._.... _'.

,.._,_"._.[",'_.,c_ "_%,_:," --'---_.-av_ -jr --.- .# • • '-

BLAST NONBLASTB1--- NBI-'-B2 .... NB2 ....B3--- N63 ....

NS4 ......* I | l I I I l

193 1G 4

FREOUENCY HZ

FIGURE 1A.COMPARISON OF × A×IS SAA RESPONSE FIELD DATA

(DAMPING=G._S)

S 1G4AA

RE 103SP0NS 102

E

G 101

_- | ! • i . | i i

- o-

; ..._.. _,'," "_

-_ ._ "- _'._,;-:..'"" Js . .,t..."

ss = " _"

.... ,,,. •

,,-,- #. o•- ..,

s -S •

...... _ o o"

o'_-.

• -_, • s -'i d • " $_ - - C"_'F _:-L""_'_'v', "'""" "'"

-..-.. --._ j'-° oo"

_AST NONSLAST

81--- NBI---B2 .... NB2 ....B3--- NS3 ....

NB4 .....• i t | t | t

102 183 I_ 4

FREOUENCY H2

FIGURE 18.

COMPARISON OF Y AXIS SAA RESPONSE FIELD DATA(DAMPING=_._S)

31

SAA

11_4

RE 103SP0NS 102E

G lgl

EBLASY .... ""

NONBLAST ....

i i I i i I i i.

/

I I I I I I I l I I I I I I I I

102 103 104

FREOUENCY H2

FIGURE 2A.

COMPARISON OF BLAST _ NONBLAST X AXIS SAA FIELD DATA ENUELOPES(DAMPING=B.OS)

S 104

AA

RE 103

SP0

NS 102

E

G1_ 1

• • • , , , • •

BLASTNONBLAST ....

t

ijs_ p_oSJ_ts "l

I | I i | I i i | i i i | | i i

102 103 IB 4

FREOUENCY HZ

FIGURE 2B.COMPARISON OF BLAST _ NONBLAST Y AXIS SAA FIELD DATA ENUELOPES

(DAMPING=B._S)

32

SAA

RESP0NSE

11_4

G 1131

._ • . • • l v v l

d _ B_ J _,.

: o_W_ oo. _°

1{32

i • l i . , • v-

o.:'"'"' ' !

FIELD--LXX ........HXX ----HYX ....

i i i n l | i I

1G 3 104

FREQUENCY HZ

FIGURE 3A.

COMPARISON OF X AXIS SAA FIELD DATA ENUELOPE AND THREE TEST INPUTS(DAMPING=_._S)

SAA

1134

RE 183

SP0NS 182

E

G181

.°"°... ...... ..-"" %-.

• _'°se"

• %°.._

S S

.....#

I

#

FIELDLYY ........HYY --- -HXY ....

|l i . i . i I i l i i i

18 2 18 3 18 4

FREQUENCY HZ

FIGURE 3S.COMPARISON OF Y AXIS SAA FIELD DATA ENUELOPE AND THREE TEST INPUTS

(DAMPING=8.BS)

33

MULTIPLE ENVIRONMENT SHOCK CHARACTERIZATION

Even if the shock test is specified on the basis of the SAA spectrum, it is notnecessary to restrict the conservatism assessment to that sole shockcharacterization. The advantages of utilizing alternative shock characterizationshave been demonstrated in previous studies of shock conservatism involving singlefield environments [5-8]. Primary attention will be focused on the shock intensityspectrum (SIS) which is a plot of the contribution of each frequency band shown tothe overall rms acceleration of the shock transient [8]. The SIS has the advantageof being a direct indicator of frequency content of the shock signal, while the SAArepresents the single degree of freedom response to the shock transient as a functionof the natural frequency of the SDOF resonators. Additional mention will be made ofthe ranked acceleration peaks, with particular attention being paid to the highestpeak value (TPKI) as a meaningful shock characterization.

These shock characterizations were computed using the SHARPE computer code [5,8]for all of the field and laboratory test data. The blast and nonblast envelopes ofthe X axis field test SIS spectra are given in Figure 4. Note the lack of frequencycontent in the blast data above 3000 Hz. A comparison between an envelope of all ofthe field data and the lab test data is shown in Figure 5. The predominant frequencyof the low frequency plate is shown to actually be at 180 Hz. The question ofstatistical variation of a shock environment characterization must also be consideredprior to the conservatism analysis. This is a difficult question because of thepaucity of field data normally available at the time the test is specified, so it israrely answered. Since all seven field environments considered in this study weredifferent, each field environment characterization is considered as an average valuehaving a coefficient of variation of 0.15. This introduces a variability factor intothe field data which may be optimistic (i.e., it may be difficult to verify theaccuracy of the measured or analytical data with this degree of refinement), butprevious studies [8] indicate that this is a reasonable value. The statisticalvariation of the laboratory tests was dealt with by repeating each test ten times.Mean values and standard deviations were also calculated by the SHARPE code for theensembles of laboratory test data.

CONSERVATISM CRITERIA

The index of conservatism (IOC) [5] provides a quantitative criterion forevaluating shock conservatism. Calculating the IOC for a particular shockcharacterization C requires that the mean and standard deviations of the field and

test be provided by the analyst. Representing the mean values as CT and _ , and thestandard deviations as oT and o F where T and F denote the lab test and fieldenvironments, respectively, the-iOC is defined as:

CT - CFIOC ....

y OT2 + OF2 o M

(I)

where M is the mean margin of conservatism and o, is the standard deviation of themargin of conservatism. Figures 6 and 7 depictMthe relationship between these fieldand test environment parameters. These figures also emphasize the fact that when themean margin of conservatism is zero, the mean field and test environments are thesame on the average, but some of the time there is an overtest or an undertest.

34

S!S

RESP0NSE

IG 3

I{32

IO I

1{3 °

sLAs'T ......NONBLAST ....

i"-I __

i :°.o I__ o

L.*

-2;.ii

* • | | • J • I

, I

I I

'' i!--1 t...

'!3_ t_7"" I

i

* | = I I I I

1{32 1{33" 1{34

FREOUENCY HZ

FIGURE 4.

COMPARISON OF BLAST _ NONSLAST X AXIS SIS FIELD DATA ENUELOPES(DURATION={3.{32)

SIS

RESP0NSE

1{3 3

1{32

1(aI

1{3{3

1{3-I

! • ! u I J u u J v i ! i w J i:

, .. ,--, - "-:"" .'.t

- . $,...

2

_,_! ..... -._)FTFI 13- : " ...... i

LXX ........ --',:..}"" i..i ....... :: HXX - - -" HYX ....

i i i l 1 l i i i 1 I l i i I i

1{32 1{33 1{34

FREQUENCY H_

F IGURE S.COMPARISON OF × AXIS SIS FIELD DATA ENUELOPE AND THREE TEST INPUTS

( DURAT ION={3. {}2 )

35

Pc(CJ

N

CF CT

Figure Probability Density Functlonsof Field and Laboratory TestShock Environments

PM(m)

Figure 7 Probability Density Functionof the Margin of Conservatism M

36

Initially in this study, a test is considered conservative if the IOC is greater thanzero. This criterion is the basis of a conservatism binary index (CBI ) which isdefined for N different field tests under study: J

IO lOC < 0CBI = ' 3 j : Z,N (2)

J I I, lOCi > o

Once the CBIj is calculated, these values are combined in a quantity called themultiple environment conservatism ratio (MECR) given by:

CBI

J=1 JMECR =

(3)

Thus, a MECR value of one indicates that the test was always conservative, and azero value would indicate that the laboratory test was never conservative for any ofthe field environments. The MECR ratios were computed for SAA and SIS data collectedas X axis inputs to the component in the three lab tests and the seven field tests.This data is shown in Figures 8A and 8B. Figure 8A shows that the low frequency testcovers the field data up to 1300 Hz. The high frequency tests are conservative foronly 70 to 80 percent of the tests at frequencies above 1500 Hz. The MECR for SIS inFigure 8B reveals a frequency range between 950 and 1100 Hz where none of the testswere conservative. Both plots indicate that the Y axis test is comparable to the Xaxis test in providing an X axis input to the component.

SPECIFYING CONSERVATISM REQUIREMENTS

While the MECR ratio indicates whether the test was nominally conservative, itdoes not indicate the degree to which an overtest or an undertest was experiencedduring the test. This can only be done once the analyst has selected a desire_ levelof conservatism for the test. Specifying the desired level of conservatism involvesselecting an IOC value and then calculating an overtest factor (OTF) [8] defined as:

OTF -_ , IOC : I (4)

CT,I

where _T'" is the mean characterization of the test data which will produce

the desired IOC value of I. In other words, the OTF indicates how many times greater

the mean test characterization was that_ it had to be to satisfy the conservatism

criterion. The OTF is calculated assuming that _T varies linearly and that oT

37

MEC

R

1.4

1.2

1.

.S

..4

.2

0.

LXX ........HXX ----HYX ....

..................................................#'--i._:'-'_ A- _'_ .., .,"._

- ii "._; v,V

_',,_ ; ,, ;';--C -, ; • :';

", _ ',' .,:: .

•, _.'i ....... ; - "' ';'T'. ', ,' ; ::..........

-- \% • _ a "._'! _-, , ...-

%

:,f' ,'_ .... ,i • , ", _ , , ,,,

1G2 113:3 10 4

FREOUENCY HZ

FIGURE SA.MERC FOR X AXIS SAA RESPONSE

(DAMPING=G.gS)

MEC

R

1.4

1.2

1.

.S

.S

.4

.2

G.

LXX ........HXX -- ---HYX ....

-_.--;---,---- f-_

_ i. I I • _. I Io | : I i- _ I •• ..... ;¢-. -, ,.,_ !, I ;, : I _ !

; I;_ :. I ,.,:':,- i . I ;'

I !l • "- ! | ,'

_ i ...j ,• " t _ • I

t _ i , i,l,t

1132 1133

FREOUENCY H2

F IGURE SS.

;--'--i,'-'__.-_ ._-_ ;--I I . I I

_..o

::..... :. ..........:•" t" t i i I i

t'IECR FOR X AXIS SIS RESPONSEC DURATION=G. G2)

1134

38

remains constant regardless of a change in _T" An overtest occurs if OTF is greaterthan one. An OTF less than one indicates an undertest.

OVERTEST ANALYSIS

Assuming that an IOC of one is the desired degree of shock test conservatism,the OTFs for SAA and SIS were computed for each combination of field test and labtest. The minimum of these OTF curves are shown in Figures 9A and 9B. Significantovertesting is apparent in both plots at the resonant frequencies of the high and lowfrequency plates.

In order to get a closer look at where the overtest and undertest is occurring,a multiple environment overtest ratio (MEOR) can be defined:

OBIj

j:1MEOR :

N (5)

where N is the number of field environments and the overtest binary index is given

by:

I O, OTFj < IOBI = j : l,N (6)

J I i, OTFj _> i

The MEOR plots for SAA and SIS are shown in Figures IOA and lOB, respectively.Note the general similarity between Figures IOA and B and the MECR plots in Figures8A and 8B. The plot amplitudes have decreased in the MEOR curve where the lab testsare only marginally conservative. Figures IIA and lIB portray the SAA and SIS MEORratios for the Y axis tests. The Y axis tests indicate that the desired level ofconservatism was reached for nearly the entire SAA spectrum (Figure 11A). The Y axisSIS spectrum MEOR ratio, however, reveals a significant area of undertest in the 900to i000 Hz region.

FAILURE MODEL BASIS FOR INTERPRETING RESULTS

Final interpretation of the conservatism analysis results obtained so farrequires the analyst to assume a failure model for the component being tested. Forexample, if the component has a failure mode in the X axis associated with a certainfrequency, the analyst looks at Figures 9A or 9B to determine the value for theminimum overtest factor at that frequency. If an overtest occurs, considerationmight be given to modifying the test input accordingly. If an undertest is observed,then Figures IOA or IOB indicate what percenta'e of the field tests experience anundertest at this frequency.

39

D8UER

BTES

T4

o

.°

/\ LXX ........HXX - --HYX

F o°° °'°°;

A "% °" ;°° ;

C2 " . ;"....-

T ... .. _ ¢,,,_. p ._.

R {3 '::::-:';'::=:'i "'_'=i'';:';'-':_''''" , "'_......,'"'r"r',","_

102 1G 3 Ig4

FREOUENCY HZF IGURE 9A.

COMPARISON OF X AXIS SAA OTF MINIMUMS FOR THREE TEST INPUTS( DAMPI NG ={3.{35 )

0UER 2{3

TEST

1{3FACT0

R 13

LXX ........HXX ---HYX ....

_1"_ ..;-_,.,: . _-'c_ _.... --I

102 1{33

FREOUENCY H2FIGURE 9B.

i'-" I'_;

,'-:.-";'"'5 ......

1{3 4

COMPARISON OF X AXIS SIS OTF MINIMUMS FOR THREE TEST INPUTS(DURATION={3.{32)

4O

ME0R

1.4

1.2

1.

.8

.S

.4

.2

8.

LXX ........HXX ---HYX ....

.......................................... . :. ,.r- _) .,"_"" ,, _ ., k

"-...... ,..; _- .- -% "_. :. ,- \ : i ',,:., ',.v_'_'.,:.

I O

..... " _ #,/ - :."o I

',_, : ;_....

*t I , ,_,,'l t .l t _ . #. I w • i " s

182 1(33

i," i i i i i

1G 4

FREQUENCY HZFIGURE 1GA.

MEOR (10C=1) FOR X AXIS SAA RESPONSE(DAMPING=G.GS)

ME0R

1.4

1.2

I.

.8

.S

.4

.2

O.

LXX ........HXX -----HYX ....

--_:,.......,'-_"',: :"', [---]/-_q..... , :, -_ :-; r-'--I ;--';. ,-',,,.... _ ,,--

s I s : w • !,_j __.: . ! J :__, :' ! L. e 5-..'

'il,: i :i ;- _ , _,__*. :.: , : ' _5

; ;1 : ! ,';' ,' '., • ¢..;.J : ; I t. # ¢

- '" " ' " : I_] 'ii , • , _ "-...,-.:_ ,.!,:.... I i-.'.-,.-.'--; , ; :: : : I

,t|

10 2 1133 18 4

FREQUENCY H2

FIGURE 18S.MEOR (IOC=I) FOR X AXIS SIS RESPONSE

( DURAT I ON =G. 132 ) "

41

i i I I I i I I | I i i i i i i i

1.4 - LYY ........ -HYY ----

1.2 - HXY ....

. IV ,E 8 / _ -0 _ ...... _ :, /_R 6 / , :, -, -

A: '.4 : • _'" -

.2 - _ z -.............• A £

G. , , i _. ..... n . :'; .......

i_ 2 i_ 3 1G 4

FREOUENCY H2FIGURE 11A.

MEOR (IOC=I) FOR Y AXIS SAA RESPONSE(DAMPING=G.GS)

1.4

1.2

1.M

E .S0

R .S

.4

.2

8.

FREOUENCY HZ

FIGURE 118.

MEOR (IOC=I) FOR Y AXIS SIS RESPONSE(DURATION=8.GZ)

42

When the sensitivity of the component is not well understood, another approachis to summarize the conservatism data by assuming a general type of failure model,such as a brittle displacement sensitive structure or a fatigue/multicycle sensitivestructure. The conservatism analysis in the X axis is summarized in Tables I and Iifor each of these failure models. Table IA and Table IIA present overtest andundertest weights as bar charts and weighted OTF numerical values for each of thefield/lab test comparisons. The overtest weight WTO is given by:

WTO =

KDoi

i=1

LZ_ Dajj=l

(7)

where:Doi = ith abcissa delta increment where an overtest

condition exists for the shock characterization

Daj = jth abcissa delta increment for the shockcharacterization

K = total number of abcissa overtest delta increments

L : total number of abcissa delta increments.

For discrete characterizations like ranked peaks, the WTO is the ratio of the

number of ranked peaks which were an overtest to the total number of ranked peaksunder study. For frequency domain characterizations, the WTO is the ratio of the

cumulative frequency range where an overtest condition occurred to the total

frequency range being considered. An undertest weight WTU is defined in a parallel

manner. Note that WTO and WTU must sum to one. The shaded rectangle is positionedin the bar depending on the relative values of WTO and WTU. Complete undertest is

indicated by a shaded box shifted entirely to the left, and complete overtest is

indicated by a shaded box situated on the right end of the bar chart. This display

of the data offers the analyst the opportunity to see the range of test conservatism.The weighted OTF values OTFw are shown on each side of the bar chart and are definedas:

OTFw =

_' K_i OTFii=1

WTO *

WTU *

K

L-KOTFi

i:1

L-K

OTFi >__1

OTFi < I

(8)

43

TABLE IA.

SUMMARY OF OV_ FACTOR WEIGHTS AND WEIGHTED 0TF_BRrlTLE AND DISPLACEMENT SENSITIVE STRUCTURES

I LXX m HXX _ HYX [%..:..

132

133

NBI

NBa

NB3

NB4

MAX pgAK G

o._ r------BI o.oo I I,,,_,,;,,.,,,_

o.oo r----- msu_ml

0.00 L__._ i I

0.0O _ I,,,,u_uulo.0o r------ ,mmml0.0O r---_ mmml

o.oo L__ rmmm_Jm,;

0.0O r------- _0.55 m0._ f----- _

0.0o r------- _

0._ t_._..___ [ i

0.0o L__--- _,mmu_

0._ I_.._____ _

0.45 _

0.08 m_uuu.u,,,uO.O0 t_____ Iwm;_d

0.00 I._ I0.00 L--------- UIIIIUUUI_[_0.98 _ ------]

IJM32.g3.39

1.15

_.512.58

1,553253.45

0.00

,121124

1.142.49

0.000.00

1.01

1.092.360.00

SAA IO0-Ioo0 tg

0.0O m 5.320.47 g"'""'"'"; ---I 0.01026 _ _ 0.00

0.O9 _ _ 3.350.3_, ,,m,m,mm, ' I 0.00o2.1 _ -----'n o.0o0.00 I'-'_-I_II "I79

0.6_ m,l,mnumlm I 0.000.37 __ 0.0O

0.00 _ mmmm 17220.40 _ _ O.9'70.50 _ I------I 0.16

0.o0 _mm 11."/30.40 L ""mumu"eli I 0.300.50 __ 0.O2

0.00 _ Nll 10.810.57 l__n_i h_tx...__...J 0.0"70.57 _ --------J 0.00

0.00 r---"_mnl 11.22OKo,8 I_ _ 0.1'70.57 _ _1:'_I 0.37

SISI00-I000

o.,o____i__i_ ,,.m,O.25 _ _ 5,18

0.10 _ _ 0.(13

0.14 _ _ 123/025 _ _ I.IPSO.2O _ r------10JO

o.r¢ _ _Z] 20.0o025 I_]l_l _ l_.oe02.4 _ _ I.,?.9

O.IS _ _ 20.0O0.12 OI _mE] 9.920.13 __ |.13

o.m_---_mm:::::_ ,_

0.14 _ L"_0.24 0.0O

0.19 20.00

025 _ 4.430.40 0.36

0.18 17.03

0.32 _ 2.2202.5 4.43

TABLE IB.

SUMMARY OF OV_ FACTOR WEIGHTED AVERAGESBRITrLE AND DISPLACEMENT SENSITIVE STRUCTURE_

[ LXX m HXX HYX Ittllllllilllllllill

SAA 100-10(30 HZ

ALL

B

NB

MAX PgAK G

o.14 _ 2._/

0.o_ U IA0

0.0O _ 3.020.00 314

020 05¢3]

O_ _ 1.5,?.

0 25 I_ 1.21

00! •I • 0.610.51 Gill _ 0260.44 •1 • 0.08

003 •11 51400.49 _ • 01 _

01 _ _ _ O .O0

01 _ i • 12.69

0.53 Gill_ 0.45

056 I_ 0.14

SIS 100-I000 H_

0.18 I1• 18.05

0.23 _ m 5.360.23 III _ !.14

0.14 • II 15.740.25 _]TI_] 8.4102.1 Ill _ 0.80

0.18 •III 1628

0.21 rrrr_ 4.570.25 I_ _ 1.48

44

_GLHAL PAkGE I_

L_X)R QUA_TABLE I IA.

_u'MMARY OF OVL_'T_S'I'FACTOR W_G'HTS AND WEI_FATIGUE AND MULTICYCLE SENSITIVE S'I'RUCI3JRES

LXX ml HXX HYX l_m ['tglflflll:ltllfil

BI

132

133

NBI

NB2

NB3

NB4

M_X 5 PEAK G

0.33 _ _ O.83

OJ9 L......--_l _mJ._l |..,_

O.00 r------ _ 2.10

0.4g __ 0.44

0.18 _ _J_a_l 1.210.00 r---'--" _ I.'/o

O.lg _ _ 1.100.00 L_____ _... 1.870.00 r-------- _

0A3 maim _ 0.oo0.41 i u...m,..11 I 0240..54 _ a_____.J 0.25

0.10 _ _ 0._

0.00 _ 1.66

0._ 2.04

0.43 0.000.63 0.000.56 020

0.,30 064

0.17 _ 1_0.63 0.00

0.00 I'---"-- m 1.500.00 L-...--_ ua,uu_ 2790.00 _ Immma 0.05

0.00 I----'---" mlllmm LI4

0.00 L.-.-.-- "_ 2.120.00 1"_m 2.32

o.oor_-" m 1.5_0.00 I _,.u,,,,t_l 0.2_0.00 r-------- m 3.45

0..5,5 _ --"----1 0.00

0.00 ! """""""" 1.020.00 1 _ LI2

0.00 I-'--'--- I !.130.00 I ""'"""' 1.230.73 _ _ 0.00

0.45 Immm "-'----1 0.0O0.83 .m,m,,,.,m I 0.00

0_1 _ _ 0.0O

0.00 I_" m 1.10

0.80 I._ luuu,m.nm, 2.050.03 _ "'--'-'I 0.00

024 _ !.33

0.0_ g.g3

0.0_ 8.86

020 l._0.05 8.680.05 7.94

0.00 20.800.06 _ _ 20.000.06 _ _ 20.00

0.1:' _ r------1 5.'n

0.,,21 _ _ 5.130.|7 [_ li_ 1.64

0.17 __ 0.040.05 U-'-'_l _ 5.0"/0.05 E::::::::_ :ml_l:J

0.10 _ "-"-'-1 3.010._ I::1_ _ 2.14

O.,?.5 _ _ 0._1

0.|0 BImB -'--"--'1 1.830.15 _ _ 5.300.35 _ _ 2.14

TABLE IIB.

SUMMARY OF OVERTEST FACTOR WEIGHTED AVERAGESFATIGUE AND MULTICYCLE SENSITIVE STRUCTURES

[ LXX m HXX _ HYX I,:._::%_'TW,.¢;_

ALL

B

NB

MAX 5 PEAK G

0.34 • • 0.570..23 _] _ 1.11

020 I¢ f4 I.,23

0.34 • II O.'r9

0.12 I_ D I._0.00 I_ _I 2.03

0.33 • IE 0.400.30 nn _1 0:'18

0.43 I_ _ 01 _

RMS OVERALL

0,14 Bl • O.g20.12 _ [] 1.78

0.,35 I_ [] 1.42

0.00 El • 1.400.00 [] _I 2."r20.00 B U 2.94

0.25 • II 0.56021 rm _ 1.070.62 [] _1 0.28

ALL SIS_

0.1__4.83

0.13 _]_I_ 8.030.14 I¢ 6.0g

o.18 • 7..53

0.0_, _ 12.870.05 12.2"/

0.17 2.80

0.19 m 4.410.21 2.51

45

where L and K are defined above. The weighted OTF reflects both the amplitude of theOTF and the range over which either an undertest or an overtest occurs. Zero valuesof OTFw indicate that either WTO or WTU was zero for that range of the shockcharacterization. It should be noted that nonzero weighted overtest factors havebeen limited to values between 0.05 and 20 in an effort to keep extremely largeovertest values from dominating summary averages of the weighted OTFs in Tables IBand lIB. These summary averages provide a measure of overall overtest or undertestcharacterized into three summary groups: all of the tests, the blast tests, and thenonblast tests. A review of these tables indicates that even though absoluteconservatism is not achieved for all of the shock characterizations, the analyst isin a position to make a quantitative statement about the degree of overtest orundertest in an average sense. The low frequency X axis shock test is quiteconservative for brittle and displacement sensitive structures as indicated in TableIB.

The high frequency content of the X and Y axes tests results in their achievingthe desired level of conservatism for fatigue and multicycle sensitive components.

CONCLUSION

Conservatism analysis techniques have been described and demonstrated in thispaper which address the complication of trying to make a laboratory test qualify acomponent for use in multiple field environments. Quantitative measures areintroduced which show when tests are conservative in both an absolute and averagesense. Both the degree of undertest and the degree of overtest are tracked in thisprocedure. Alternatives to shock spectra are shown to give additional conservatisminformation to the engineer which may be crucial in determining the suitability of ashock test specification. The desired level of conservatism used in the analysis isalways clearly stated, and can be modified to meet the requirements of the designengineer. Specifically, knowledge about the failure modes of a component may lead tolower level test specifications which do not meet the original criterion ofenveloping shock spectra, but which can be rigorously shown to be conservative interms of another shock characterization. Greater insight into the significance ofthe functional outcome of the test (i.e., did it break because the design is too weakor because the test specification is too conservative ?) and detailed knowledge ofhow the test specification can be altered to achieve a desired level of testconservatism are two significant benefits of performing a conservatism analysis.Future use of these techniques will produce qualification test inputs which venturebeyond the realm of engineering judgment, and enter the state of soundly tailoredtest specifications founded on quantifiable measures of conservatism.

46

REFERENCES

i •

o

.

•

B.

•

•

0

S. Rubin, "Concepts in Shock Data Analysis," Shock and Vibration Handbook, Second

Edition, C. M. Harris and C. E. Crede, eds., New York: McGraw-Hill, 1976, pp.23-1,30.

R. D. Kelly and G. Richman, Principles and Techniques of Shock Data Analysis, TheShock and Vibration Information Center, USDOD, SVM-5, 1969.

N. Davie, "The Controlled Response of Resonating Fixtures Used to SimulatePyroshock Environments," Shock and Vibration Bulletin, Vol. 56, Part 3, 1986, pp.119-124•

I. Vigness and J. R. Sullivan, "Shock Testing Machines," Shock and Vibration

Handbook, Second Edition, C. M. Harris and C. E. Crede, eds., New York: McGraw-

Hill, 1976, pp.26-1,19.

T. J. Baca, "Characterization of Conservatism in Mechanical Shock Testing of

Structures," SAND82-2186, Sandia National Laboratories, 1983.

T. J. Baca, "Evaluation and Control of Conservatism in Drop Table Shock Tests,"ShocK and Vibration Bulletin, Vol. 53, Part I, 1983, pp. 163-176.

T. J. Baca, "Alternative Shock Characterizations for Consistent Shock Test

Specifications," Shock and Vibration Bulletin, Vol. 54, Part 2, 1984, pp.i09-130.

T. J. Baca and T. D. Blacker, "Relative Conservatism of Drop Table and ShakerShock Tests," Shock and Vibration Bulletin, Vol. 56, Part I, 1986, pp. 289-298.

47