instrumentation techniques for measuring large high rate strains with sg

8/13/2019 Instrumentation Techniques for Measuring Large High Rate Strains With Sg

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TECHNICAL REPORT ARBRL-TR-02573

INSTRUMENTATION TECHNIQUES FOR MEASURINGLARGE, HIGH RATE STRAINS WITH FOIL0Oq RESISTANCE STRAIN GAGESN

Sl Edward J. Rapacki, Jr."August1984

OUSRMY RM MENT RESEARCH ND DEYE[OPMENT CENTERBALLISTIC RESEARCH LABORATORY

ABERDEEN PROVING GROUND, MARYLAND

Approved for public release distribution unlimited.

-;6

84 09 13 071


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Destroy this report when it is no longer needed.Do not return it to the originator.

Additional copies of this report may be obtainedfrom the National Technical Information Service,U. S. Department of Commerce, Springfield, Virginia22161.

The findings in this report are not to be construed as an officialDepartment of the Army position, unless o designated by otherauthorized documents.

The use of trade names or manufacturers' nartes in this reportdoes not constitute indorsem~ent of any commercial product.


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UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (fhen Date Entered)nL;r~ ,. ~m~ I lvOD~ m 'i''raeN'P 'r't'READ INSTRUCTIO1SREPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM1, REPORT NUMBER .2. GOVT ACCESSION No 3. RECIPIENT'S CATALOG NUMWERTechnical Report ARBRL-TR-02573 2hI, l/ _ __/4. TITLE (and SutfJtle) 5. TYPE OF REDORT & PERIOD COVEREDINSTRUMENTATION TECHMIQUES FOR MEASURING LARGE, FINALHIGH RATE STRAINS WITH FOIL RESISTANCE STRAINGAGES 6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(e) 5 CONTRACT OR GRANt NUMBERfo)

Edward J. Rapacki, Jr.0, PFRFORMING ORGANIZATION NAME AND ADDRESS i0. PROGRAM ELEMENT, PROJECT, TASKUS Army Ballistic Research Laboratory AREA WORK UNIT NUMBERSrATTN: DILXBR-TBD 1L161102A143Aberdeen Proving Cround, .D 2100.55066II. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATEUS Army Ballistic Research Laboratory August 1984ATTN: DRXBR-OD-ST 13. NUMBEk OF PAGESAberdeen Proving Ground, MD 21005-5066 53T4 MONITORING AGENCY NAME & ADORESS(It different from Controltlng Office) IS. SECURITY Ct.ASS. (of thl reportIINCLASSI FlED

15o, DECL ASSIFICATION/DOWNGRADINGSCHEDULE16. DISTRIBUTION STATEMENT of thle Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT of the absttct entered in Block 20, If different fronm eport

Is. SUPPLtMENTARY NOTES

IS. KEY WORDS Cofltirwo an reverse side It necessary dnd Identifyy block numottrInstrumentation Strain Cage Power DensityPulse ExcitationWheatstone Bridge Impact Test Facility InstrumentationStrain GagesHigh Strain-rate Response

M0 AMYrAC? (4die Sov0000 ei,6 tit ,eceemy md Idwait by block amborInstrumentation for measuring large, high strain rate strains with foil typeresistance strain gages was designed, constructed and evaluated in terms ofsignal to noise ratio, strain rate response characteristics and overall accuracyof measurement. Complete design procedures and component specifications for theWheatstone bridge, pulsed power supply ant control circuit, as well as calibra-tion and data reducltion procedures are includej. The apparatus has a signal tonoise ratio up to six times that which can be obtained with conventional straingage signal conditioning equipment, and can measure to t. .20 strain at strainDO I M m a of 9NOV 05 TE UNCLASSIFIED

SECURITY CLASSIFICAT-f Q;1 THIS PiGE (Wpm Dote Eu'lerd)


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UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE(Wton Dat&Smtered)

rates up to 104 s-1 over a 35 to 200 microsecond sample time. The overallaccuracy of measurement is t (1.4 percent e + 375 microstrain), with 110microstrain resolution. Pulsed power density limits for annealed constantanfoil strain gages were also investigated and are reported.

IL

UNCLASSI FI I'DSFCURITY CL ASSIFICATION OF THIS PAGEi$.,, V)at& ntred


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TABLE OF CONTENTS

PageLIST OF ILLUSTRATIONS ..................... ...................... 5

I. INTRODUCTION........................ ............................ 7II. DESIGN CONSIDERATIONS ..................... ...................... 7

A. STRAIN GAGES..... ..................... .. .. . 7B. WHEATSTONE BRIDGE ................... ....................... 8C. PULSE POWER SUPPLY.............. ....................... ... 13D. CONTROL CIRCUIT ................. ........................ ... 15

III. PERFORMANCE TESTS ................. ......................... ... 15A. EXCITATION VOLTAGE STABILITY ........ .................. 1.B. RESPONSE TIME ................... ........................ .. 20

IV. CALIBRATION AND DATA REDUCTION .......... ................... ... 23V. SUMMARY ....................... .............................. ... 26

ACKNOWLEDGMENT ................... .......................... .. 28REFERENCES ...................... ............................ ... 29APPENDIX A: OPTIMIZING PULSE EXCITITATION LEVELS FOR CONSTANTANFOIL STRAIN GAGES .......... ................... ... 31APPENDIX B: TIME DOMAIN PRE-EVENT TRIGGER FOR CONSTANT VELOCITY

IMPACT SYSTEMS ............. .................... .. 37APPENDIX C: SAMPLE CALIBRATION AND STRAIN DAT A REDUCTION ..... ... 43DISTRIBUTION LIST ................ ........................ ... 47

Accvq';ton For

A I

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LIST OF ILLUSTRATIONSFigure Page1. Mathematical Schematic of Wheatstone Bridge Network ........... 92. Mathematical Schematic of Gage to Bridge Coaxial CableTermination. . . . . . .................... 93. Normalized Bridge Output Voltage vs Change in Resistance of

120.0 Ohm Gage ..... ................. . . . . . . . . 124. Schematic Diagram of Pulse Power Supply and Wheatstone BridgeCircuit. . ....... . . . . . . . . . . . . . 0 . . . . . .. 145. Schematic Diagram of Control Circuit for Pulse Power Supplies

and Oscilloscopes. ......................... 166. Output Characteristic of Switching Transistor. The Envelope

Indicates the Permissable Variaticn of Collector Current andCollector-Emitter Voltage for the Excitation Voltages Givenby the Right Hand Ordinate ........ ............. 18

7. (a) Pulse Duration Control Signal, (b) Excitation and c)Bridge Output voltage, 15 Volt Zener Diode; (d) Excitation and(e) Bridge Output Voltage, 30 Volt Zener Diode, vs Time. . . . . 21

8. Self-Contained Pulse Power Supply and Bridge. The BNC PlugPermits Direct Connection to an Oscilloscope. Both the PowerSupply and Switch Batteries are Mounted on the Bottom of theDevice .......... ......... ............................. 27

A-I. Zero-Shift vs Excitation Time. (a) Reference Baseline, 5WMetal Film Resistor as Gage Substitute. Power Densities of(b) F.1107, (c) 0.2038, (d) 0.6526, (e) 1.3490 and (f) 1.8381W/mm in Annealed Constantan Foil Strain Gage Mounted onSteel ............... .............................. 34

A-2. Apparent Strain Zero-Shift Rate vs Pulsed Power Densitj forAnnealed Constantan Foil Strain Gage . ............. 36

B-i. Schematic Diagram of Time Domain Pre-Event Trigger Circuit . . . 40

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I. INTRODUCTIONResistive element transducers, such as strain gages, manganin pressure

gages and nickel temperature sensors are used extensively in experimentalstress analysis. The variable of interest (deformation, pressure, ortemperature change) causes a change of sensor resistance, which must bemeasured. Using the sensor as an arm of a Wheatstone bridge network is themost sensitive circuit for measuring these often small resistance changes.Often too, these measurements must be made in environments where electrical"noise" may be severe enough to distort or obscure the signal of interest,even after proper grounding and shielding techniques have been employed.Greater signal strength is required also when digital signal acquisitiontechniques are used because of the inherent loss of voltage sensitivity andresolution. The ease of data acquisition and reduction, however, make digitaltechniques very desirable, particularly for multiple channels of single,transient events. Signal strength, and hence signal to noise ratio (S/N),canbe improved by increasing the excitation voltage of the bridge; however, powerdissipation capability of the sensor and allowable thermally induced driftplace constraints on the maximum allowable continuous excitation voltage. 2

Pulse excitation of the sensor allows higher excitation voltage withoutthe attendant difficulties of continuous high power dissipation. The tech-nique can be used whert a relatively short duration (up to a few hundredmicroseconds) measurement is required or where a series of short sample time,intermittent measurements is satisfactory.

This report describes the design of a Wheatstone bridge, power supply andassociated control circuitry for use with pulse excited resistive elementtransducers. The specific application was the measurement of high rate, postyield strains with foil resistance strain gages on long rods undergoing highvelocity impact. Performance tests, calibration and data reduction proceduresand an overall error analysis are included.

II. DESIGN CONSIDERATIONSA. Strain Gages

Foil resistance strain gages are available in a multitude of alloys, gagelengths and geometries. The measurement of very high rate (>104 s- ), post-yield strains up to 20 percent, however, requires short gage length and a veryductile alloy. Micro-Measurements cype EP gages, which are an annealed'Ralph M4oi-ris, (;h,:7, O anvt sh ezdinq Techniq:w.s in ln.,3trznentation- 2nded., John Wi ey an. 7ns, Inc., New York, Chichester, Bine, 2bron 'o, ld/'.

Measurements Group, Inc., Optimizinj ,,traiz (,a~e Excitation LeveZs, Technical,Note No. TN-502, Ralcigh, NC, 1979.

7

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constantan foil on a polyimide backing were chosen. Sharpe 3 shows that 1.57mm gage length foil gages have response characteristics comparable to dynamicoptical strain gages, whose gage lengths are as short 9s 0.127 mm and Hauverand Melani report that they can respond to compressive strains in excess of20 percent. Initial, unstrained resistance was 120.0 ohms to simultaneouslymaximize bridge sensitivity and facilitate proper termination of the gage tobridge connecting cable. Both single element and planar rosette gage patternsare usable; stacked rosettes are not recommended for high power excitation dueto their decreased power dissipation capability. 2

B. Wheatstone BridgeThe Wheatstone bridge network, Figure 1, consists of one active arm R

which includes the gage resistance Rg, and connecting cable and gage leadresistance Rx. The remaining arms (R2 , R3 , and R4) provide a network tobalance the bridge for an initial null output and provide proper terminationfor the connecting cable used. R5 is the input impedance of the outputvoltage measuring device, an oscilloscope. Ein is a constant DC excitationvoltage from a low impedance source. By necessity, pulsed excitation requiresthe bridge be used in the unbalanced condition, the theory of which, for5example, is shown by Perry and Lissner. Referring to Figure 1, bridge outputvoltage is given by

E tR 1RR_2out in R1 + R4 2 +R 3

if R5 is an infinite impedance. For finite values of RS, the output voltageis attenuated, and the measured output is

RSmeas E ut (2)

3 W. N. Sharpe, Jr., Dynamic Plastic Response of Foil Gages, ExperimentalMechanics, Vol. 10, No. IC, October 1970, pp. 408-414.

4G. E. Hauver d A. Melani, Strain-Gage Techniques for Studies of ProjectileBehavior During Penetration, Ballistic Research Laboratory Memorandum ReportNo. ARBRL-MR-03032, February 1981. ADA 098660

5C. C. Perry and H. R. Lissner, The Strain Gage Primer. McGraw-Hill Book Co.,Inc., New York, Toronto, London, 1955, pp. 48-ci.

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- Ein +0

R3 R2

Eo-- R5

Figure 1. Mathematical Schematic of Wheatstone Bridge Network.

ZE

R2 R3

Zo R4I.R (IMg)Figure 2. Mathematical Schematic of Gage to Bridge Coaxial Cable

Termination.9


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where

Z=R +(R 1 + R2) (R3 + R4 )S1 + R2 + R3 + R4 (3)

by the rules for parallel conductors. If the second term of Eq. 3 is much,much smaller than R5 Z t R5 and E E to a very close approximation.uhalr h 5 5 n meas ouNote that if a coaxial cable is used to connect bridge output to the oscil-loscope, R5 should be the cable's characteristic impedance. This makesboth terms of Eq. 3 of the same order of magnitude, and considerable (and forlarge variations of R1 , non-linear) attenuation of Eout occurs. Thus, directconnection of bridge output to a high impedance (one megohm) input, sanscable, is preferred.

Depending on the type of high strain rate experiment being performed, thegage to bridge connecting cable may need to be quite long. Cable selection isdone at this stage of the design because the bridge completion resistors andpower supply form the cable termination, which should be the characteristicimpedance. Figure 2 shows what the gage cable "sees" as impedance Z at thebridge end. If the impedance of the voltage source, ZE is assumed negli-gible, Z0 R4 for values of R4 much less than one megohm.

Differentiating Eq. 1 with respect to gage arm resistance R1 yields anexpression for bridge sensitivity, which should be maximized. It can be shownthat this is achieved when R4 = R1 , approximately 120 ohms. Thus, cablecharacteristic impedance should be close to this value. Also, low attenuation(air-spaced) cables are preferred. Thus, the choice is limited to RG-63/U(125 ohm) and RG-62/U (93 ohm) coaxial cable. The latter was chosen becauseof its ease of handling (smaller diameter), ready availability, and decreasedcost. Signal transmission characteristics of both cables are comparable,while bridge sensitivity is decrtased orily 1.5 percent using 93 rather than125 ohms for R4 .

Before power dissipation specifications for the bridge completion resis-tors can be determined, maximum excitation voltage must be established. Theprimary consideration is gage stability. Reference 2 provides guidance inthis matter, but an experimental determination of maximum excitation voltageunder which tolerable gage resistance instability occurs should be performed.The resistance instability manifests itself as "apparent strain. that is, apurely temperature induced change of gage resistance. Pulsed excitation forshort periods causes non-equilibrium heating of the gage grid material, back-ing, glue line and substrate specimen material. Apparent strain vs temp-erature curves supplied by gage manufacturers cannot be used as correctionfactors because their tests are performed at equilibrium temperatures.Appendix A details power dissipation limits for pulse excited annealed

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constantan foil strain gages mounted on steel. A power density (PD) of 0.235W/mm2 causes bridge output to drift approximately 0.3 microstrain permicrosecond of excitation. The active area of the grid (Ag, gage length Xgrid width, mm ) is used in the calculption, aid acceptable excitation voltageis given by Eq. 4.

xAED g(R Rin R g x 4) 4)

The use of strain gages with gage lengths longer than 3.18 mm and grid widthsin -xcess of 4.57 mm would be inconsistant with the dynamic measurementrequirements, thus the remaining bridge and power supply components aredesigned for a maximum operating voltage of 36 volts, while 15 volts is usedfor the 1.57 mm square gages. Continuous excitation would limit the voltageto about 5.5 for this size gage, thus S/N is improved by a factor of betterthan 2.7.

Equation 1 shows that bridge output can vary because of resistance changesin Rg, the intended measurement, and changes in any of the bridge completionresistors. For this reason, high stability, low noise resistors with fastrisetime characteristics are desired. Deposited metal film resistors meetthese requirements, and have the power dissipation capability needed. Forexample,R 4, which is 93 ohms, requires a short term power rating in excess of14 watts; this situation arises should the gage become shorted. A ten watt,50 percent overload for five seconds maximum, metal film resistor is availablein a heat sinkable standard TO-3 package at modest cost. The upper bridge armresistors, R2 and R3are chosen to make the second term in Eq. 3 muc, muchsmaller than one megohm, yet large enough to keep current drain on the powersupply small. Additionally, portions of these two resistances must beembodied in a tapped potentiometer to initially oalance the bridge. A tenturn, wirewound potentiometer provides good balance resolution if the variableportions of R2 and R3 are about ten percent of their total values. Values of690 and 515 ohms were used for the fixed portions of R2 and R3 ,respectively,using one watt metal film resistors. The balanctng potentiometer is 100 ohms,two watt, with eight microhenry inductance. By Eqs. 1 thru 3, bridge outputvoltage is attenuated less than 3.5 x 10-3 dB. Nominal impedance of thebridge is 185 ohms when balanced for a 120 ohm gage. The balancing sensitiv-ity is such that a 120 ohm gage can be balanced to 0.010 ohms, or45 micro-strain. Figure 3 is a graph of normalized bridge output vs change of gageresistance and can be used to estimate expected signal levels for givenresistance changes and excitation voltages.


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C. Pulse Power SupplyThe pulse power supply is of the voltage regulated, capacitive discharge

type. See Figure 4 for schematic diagram. The voltage to which the capacitoris initially charged (the desired excitation voltage) is regulated by a fivepercent tolerance zener diode. Capacitor size requirements depend upon th edegree of discharge voltage stability required and pulse duration. Stabilityrequirements are directly related to the bridge output voltage resolution.,which must be on the order of the balance resolution. For the bridgedesigned, the minimum output resolution should be0.8mV. This is the minimumresolvable with an 8-bit digital oscilloscope on the 100 mV scale, and is0.4 percent of full scale. Bridge output voltage for constant load should beconstant to this percentage extent, as should excitation voltage due to thedirect proportionality. Pulse duration requirements greater than 200microseconds were not anticipated, so a 470 microfarad electrolytic capacitor,discharging into a nominal bridge load of 185 ohms, provides the requiredvoltage stability over this time. Batteries are used to charge the capacitorsince the power supply must float with respect to ground when single-endedamplifiers are used. This also eliminates cross-talk problems associated witha common charging supply when multiple channels are used. Charging resistors(15 K-ohm) are chosen to minimize battery drain while supplying sufficientcurrent so the zener diode regulates properly, and initial charge up time isreasonable, about 60 seconds.

An NPN Si power transistor (2N3441)6 is used as the switch to turn th ebridge excitation voltage on and off. Current flows from the capacitor thruthe transistor as collector current, IC' to the bridge load. Sufficient basecurrent, IB1 must be provided so the power transistor is conducting in its lo wforward impedance range over the expected range of I The base current isprovided by a nine volt battery thru the phototransistor of an optocoupler7.(TIL117) in a modified Darlington configuration. The resistance-capacitancenetwork in the base current circuit limits the rate of IB' and provides a soft start for the power supply. This soft start is required because highcurrent slewing rates, even thru small reactances in the bridge circuit,produce back emf overshoots-at the bridge output. -- These overshoots cansaturate sensitive oscilloscope preamplifiers to the point where instabilityand drift seriously affects the measurement. The soft start does increase theturn-on response time, (see Performance Tests, below) but this can be dealtwith by trigger control circuitry, described below.

6 Radio Corporationof America, Inc., Power Transistors1 Databook -No. SSD-2040,Somerville, NJ, 1974, pp. 109-115.

7Texas Instruments, Inc., The Optoelectronics Data Book for Design Engineers5th ed., Dallas, TX 1978, pp. 114-118.The RG-62/U coaxial cable presents the largest unbalanced inductance in thebridge circuit, 0.41u 1/rm. Thus, even modest cable lengths can add signifi-cant reactance.

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22.5V 9VDPST

5 n 15K1 390a1N3024A 15V) "t

b M341.- 1 UR TO.F0WV 5

r_I- -IC3,T11.117,OUTPUT7, 1O E DU TFigure 4. Schematic Diagram of Pulse Power Supply and WheatstoneBridge Circuit.

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The optocoupler provides the necessary ioolation between the floating basecurrent circuit and the common pulse duration control signal. The controlsignal is the forward current thru the photodiode of the optocoupler and is atimed DC pulse.D. Control Circuit

The control circuit schematic for the pulse power supply and oscilloscopetrigger is shown in Figure 5. It is a sequential timer using MC1455P18integrated timing circuits, and the input trigger requirement is compatiblewith TTL levels. (A time-domain pre-event trigger circuit that is useful fortriggering instrumentation in impact tests is described in Appendix B.) Anegative edge trigger at the 47 picofarad input coupling capacitor triggerstimer ICI and 2. ICI sources current to the 2N3441 power transistor base, andthe collector current is the control signal. The power transistor is usedbecause it was desired to control up to 14 pulse power supplies simultaneously,requiring more current than the timer IC itself could source. The duration ofthe control signal is variable from 5 to 450 microseconds and is controlledby the 25K-ohm potentiometer. IC2 provides a delay of 10 to 300 microsecondsbefore IC3 is triggered, which provides a > +10vdc signal to trigger theoscilloscopes and/or other instrumentation. This delay between power supplyturn-on and oScilloscope trigger allows the power supply and bridge circuit tostabilize before recording any of the output signal, thus conserving recordlength and providing a common timing reference point.

III. PERFORMANCE TESTSThe performance tests on the power supply, switching circuit and bridge

were performed using a five watt, one percent tolerance, 120 ohm metal filmresistor as a substitute for the strain gage. This allowed a broad range oftests to be performed without concern for limitations imposed by the straingage itself. Except where noted, all tests were performed in situ, that is,pulsed on with the control circuit and the Wheatstone bridge was the load. Thegage substitute was connected to the bridge with 14 meters of RG-62/U coaxialcable, which added 2.55 ohms series resistance to the gage arm. The desiredrange of strain measurement is 20 percent, the upper limit of epoxy-basedstrain gage adhesives. Strain t, is calculated using

1 (5)

where R is the resistance of the strained gage, and R is the initial,g ounstrained resistance. This expression for strain results when (2 + t) is8 MotoroZa, 111., L Dltc ''amed Ciroudts, Ser'es C, Phoenix, AZ, 1979, pp.

6-44 - 6- 0.


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VCC (12V)62-25K

0 A-,-82N3441 TIMER2 No 6,71

.R-5.RG58/U ( 5 jO.015FPULSE POWER68 ./ASUPPLY CONTROL TSIGNAL

100 K620-25K

47pF 4a "TRIGGER TIMER

22K

7 ]4. 8100K>TIMER

6,7RG58/U 3No 3

0 SCOPE 0.0/FTRIGGER 0.01, FSIGNALFigure S. Schematic Diagram of Control Circuit for Pulse Power

Supplies and Oscilloscopes.16


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used as the gage factor (G.F.) in the well-known expression aR/R = G.F. crelating resistance change and strain. The usual convention of positivetensile and negative compressive strain is followed. The gage manufacturersuggests, and independent tests confirm,0 that this non-linear gage factoris correct for large strain. Thus, gage resistance may vary unidirectionallydown to 76.8 ohms and up to 172.8 ohms from 120.0 ohms. Under theseconditions, bridge load range is 152.2 to 222.6 ohms. These values are usedas the maximum load excursions affecting excitation voltage stability.A. Excitation Voltage Stability

Two factors affect excitation voltage stability: a) the exponentialvoltage decay of the discharging capacitor, and b) the variation ofcollector-emitter voltage across the switching transistor as collector currentchanges. The measurement of compressive strains compounds these two factorsbecause as bridge load decreases, current requirements increase, whichhastens voltage decay and increases collector-emitter voltage. The firstfactor is easily determined, the second depenJs on the output characteristicsof the transistor type, which must be measured.

The base current available is 7.5 milliamperes and Figure 6 showscollector current, IC vs collector-emitter voltage, ECE A d', ade resistancebox was the load, the capacitor charged to 36 volts, and pulse duration was100 microseconds for these measurements. Differential amplifiers were used tosimultaneously measure E and the voltage across the load. The outputcharacteristic curve show that the transistor conducts with low forwardimpedance (1.0 to 4.4 ohms) over the range of 20 to 210 milliamperes. Notethat this impedance variation destroys the gage cable termination by less thanfive percent. The combination of excitation voltage and bridge load, tuinclude maximum excursions, however, should be such that I is within thisrange. Also shown in Figure 6, as the right hand ordinate, is the excitatiorvoltage applied across a 185 ohm balanced bridge load corresponding to thecollector current iodicated.

Hauver and Melani4 report that total recording times of 150 microsecondsare required to completely record the strain-time histories of some impactexperiments. This, in addition to the 30 microseconds required for stabili-zation of the power supply and bridge circuit after, turn-on, necessitates aminimum pulse width of 180 microseconds. Table 1 tabulates the range ofoperation to allow this pulse width for several common zener diode voltages.The allowable ranges are calculated by limiting the change in ECE plus thevoltage decay over the pulse width indicated to less than or equal to 0.4percent of the excitation voltage. The m, asurement of tensile strainspresents no limitations to the desired limit of 20 percent because the two9M1easurements Group, [ha., High HZonqation StrIain Me, iirments, Technical Tip

No. TT-605, Raleigh, ,NC , i983.10 R. E. Franz, Thc Aleaeuremcnt of Large Stra-.ns with Foil Resistance StrainGages, Bal liatic, R xx az oh Laboratory Technical Repol-t No. ARBRL-TR-O2.ld9,August 193,. ADA 133 68?

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i 3002N3441 Si NPN

2 5 I s =7.5 mn

40200

30150

-20100 20

50 10

0 000 0.5 1.0Ect (V)

Figure 6. Output Characteristic of Switching Transistor, The envelopeindicates the permissable variation of collector current andcollector-emitter voltage for the excitation voltages given bythe right hand ordinate.

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b 0 0) C 0 0 0 0 0 0 c Lo C j CP\ co

- 0 0 0 0 0 0 0 0 0 0wa N~ N~ N~ N~ N~ N~ N~ N~ N~ N~ N~ N N~

(a03 00 00 c3 00 00 OD 03 00 00 00 00 00

'0 0 ') 00 0 '.0 '0% 0% 0r '0 ON a'

L03 00 L0 03 m 03o 1E - - .- - -- - - -

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factors affecting voltage stability tend to negate each other. The use ofexcitation above 22 volts, however, places some restriction on the magnitudeof compresive strains which can measured and still insure excitation voltagestability. The allowable ranges of collector current and collector-emittervoltage lie within the envelope surrounding the characteristic curve in Figure6.B. Response Time

The turn-on response time of the power supply and bridge circuitdetermines the usable window of the pulse width, and is taken as the timerequired for excitation voltage and/or bridge output to reach its steady statevalue under constant load, whichever is longer. Figure 7a shows the controlsignal to the photodiode used to switch the power supply on and off. The10.32 volt signal has a rise time of less than 100 nanoseconds and a pulsewidth of 198.75 microseconds. Also shown is the point at which the controlcircuit triggers the oscilloscopes in normal operation, 30 microseconds aftercontrol signal turn-on. The input signal to the control circuit (Figure 5)was used as the trigger in these tests, and this is taken as zero time. Thebridge was statically balanced by applying five volts continuous DC excitationwhile monitoring output with a microvolt null detector.

The excitation and output voltage waveforms (Figure 7b and 7c) using a 15volt zener diode (capacitor voltage 14.470) show mid-pulse excitation voltvewas 14.355 volts and was within 0.4 percent of this value from 29.5 to 219.5microseconds. The output voltage was 0.0 0.8 mV (the minimum resolvable)from 21.0 to 241.0 nicroseconds. The usable window is determined by exci-tation voltage stability and the response time is 29.5 mi'croseconds. Asimilar test using a 30 volt zener diode (capacitor voltage 28.530) showsmid-pulse excitation was 28.201 volts and met 'he stability criterion from21.5 to 212.0 microseconds (Figure 7d), and output voltage was stable from26.5 to 227.0 microseconds (Figure 7e). Here, the usable window is determinedby output voltage stability. In both cases, however, the 30 microsecond pre-trigger is adequate time for the device to stabilize. Note that the exci-tation for both voltages remains on longer than the control signal. This isdue to the capacitor in the switching transistor base circuit sourcing currentafter control signal turn-off, and transistor storage time. The true usablewindow of pulse width is, however, 30 microseconds after control signal turn-on to control signal turn-off.

The over-/undershoots of the bridge output voltages are due to the exci-tation voltage slewing rates acting uton reactances in the bridge load, andnot due to the absolute magnitude of excitation because balanced bridge outputis independent of excitation magnitude. Note that the peaks coincide with thesteepest portions of the excitation voltage waveforms, i.e.,at the highestslewing rates, and that the magnitude of the peaks increases with excitat ionvoltage. These magnitudes of approximately 20 millivolts should not overdrivean amplifier ; however, hard turn-on of the power supply with 36 vol t exci-tation produces an. undershoot of 110 m illivo lts, which could be detrimental.In contrast, hard turn-on of a balanced bridge in which no coaxial cable isused produces an overshoot of only 7 millivolts. hus the cable is the mostreactive element of the bridge, and very long cables may severely degradeoverall performance.

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> 10ULU 0

> lO - (b)LU

0

10

-10 (c)LU -20 -30

> 20LU o

20-- 10 -E 0

o 10 (e)LU -200 100 200

t (/S)Figure 7. (a) Pulse Duration Control Signal, (b) Excitation and (c) BridgeOutput Voltage, 15 Volt Zener Diode; (d) Excitation and (e) BridgeOutput Voltage, 30 Volt Zener Diode, vs Time.

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The slewing rate of current in the bridge which causes reactance inducedinstabilities to occur in the output can be used to estimate the strain-rateresponse characteristics of the bridge circuit. For this determination, aninstability is defined as an induced voltage greater than the input noiselevel departing from the steady state condition. Specifically, this is anoutput of greater than 0.8 millivolts departing from the null balanced output.

Current in the gage arm of a balanced bridge is given by

n/~ Rg +1g = E + Rx +R 4 ) (6)

and slewing rate by

9 ~ =R Ei4) +i(Rg + R + in =-E. x 4 Eg in + R 4+)2 R R +g + 4 Rg x R4 (7)

In the tests illustrated in Fijure 7, all derivatives of resistance withrespect to time are zero, and Ein was + 0. 2 3v/ps at the onset of outputinstability for both voltages investigated. Thus the maximum magnitude of Iis 1.067 x 103 A/s. During the usable window of the pulse width, the secondterm of Eq. 7 is on the order of unity, and thus is negligible. Duringdynamic straining, only R is non-zero, and this term can be expressed ingterms of strain rate, i by differentiating Eq. 5. The maximum apparent strainrates to which the bridge can faithfully respond in terms of both strain andstrain rate is given by

i.1 jgjm~x Rg + R +R)1m = 2E (R RP (8)

where IgJmax is experimentally determined for a given type bridge and cabledesign. Higher excitation voltages and increased bridge sensitivities tend todegrade strain rate response capabilities. Because bridge sensitivity is

22


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non-linear for a quarter-bridge arrangement, the rate response characteristicsare a function of the level of strain also, being less for compressive strainsand greater for tensile strains, than the zero-strain value. The apparatusdescribed here should respond to apparent strain rates of 104 s-I at 20percent compressive strain, provided excitation is 16.5 volts or less.

The position of the gage arm in the bridge is such that excessive realstrain rates will cause bridge output to indicate greater resistance changesthan have actually occurred due to strain. Apparent strain rates, asdetermined from the slopes of strain vs time records, will also be in error.If these apparent strain rates are greater than tnose determined to beacceptable by Eq. 8, the dtata analyst should suspect that errors in strainmagnitude are also presen .. Apparent strain rates are always less than realstrain rates, however, because of gage length resolution.

IV. CALIBRATION AND DATA REDUCTIONRaw, time resolved strain data for each gage is obtained by Eq. 9

E(t) R(t)/R -g (9)

These can be further reduced by correcting for angular misalignment of thegage axis with the intended axis of measurement, transverse sensitivity, 1 2and applying the appropriate rosette analysis, all of which are beyond thescope of the present report. R is measured directly using a digital multi-0meter in four terminal resistance modes; R is determined by using measuredgbridge output voltages in an algebraically manipulated form of Eq. 1. Circuitconstants must be either directly measured or calculated based on calibrationdata. Two assumptions are made in reducing both the calibration and testdata: 1) the excitation voltage is constant over the measurement window, thatis, variation of Ein with respect to resistance and time is negligible, and 2)that bridge balancing sensitivity and output voltage resolution are such thatthe bridge may not be initially perfectly balanced. Both assumptions aresupported by the performance test data.

Calibration data are obtained for each power supply/bridge circuit bymeasuring bridge output voltages for three known resistances of R1 : RIB. RIC1 1Measurements Group, Inc., Errors Due to Misalignment of Strain Gages, Tech-

nical Note No. TN-511, Raleigh, NC, 1983.

1Measurements Group, Inc., Errors Due to Triesverse Sene'i ,ity in StrainGages Technical Note No. TN-509, Raleigh NC, 1982.

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data reduction and shows the accuracy is actually on the order of the reso-lution of the measurement scale.

V. SUMMARYA pulsed power supply and Wheatstone bridge circuit for measuring large,

high strain rate strains with foil type resistance strain gages has beendesigned, constructed and evaluated for overall performance. The unit has asignal to noise ratio up to six times better than conventional strain gagesignal conditioning equipment and can be used to measure static strains bydiscrete sampling or dynamic strains at rates up to 104 s- over a sampletime of 35 to 200 microseconds. Strains to 20 percent can be measured withan overall accuracy of (1.4 percent e + 375 microstrain). The compact,self-contained unit (10.5cm L x 6.Ocm W x 8.Ocm H, 250g) shown in Figure 8connects directly to an oscilloscope, and a simple trigger control circuit,also described herein, is the only additional equipment required. Thus, theunit is well suited for field testing, as well as laboratory applications.The complete design specifications included allow the unit to be adapted foruse with other types of resistive element transducers, such as pressure gagesand temperature sensors.

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eoSTNDS

OFF

TRIG GAGE

Figure 8. Self-Contained Pulse Power Supply and Bridge. The BNC plug permitsdirect connection to an oscilloscope. Both the power supply andswitch batteries are mounted on the bottom of the device.

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ACKNOWLEDGMENTThe author extends his appreciation to Mr. Konrad Frank and Mr. Robert E.

Franz for helpful discussion concerning electronics and strain gage metrology,respectively.

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REFERENCES1. Ralph Morrison, Grounding and Shielding Techniques in Instrumentation,2nd ed., John Wiley and Sons, Inc., New York, Chichester, Brisbane,Toronto, 1977.2. Measurements Group, Inc., Optimizing Strain Gage Excitation Levels,Technical Note No. TN-502, Raleigh, NC, 1979.3. W. N. Sharpe, Jr., Dynamic Plastic Response of Foil Gages,Experimental Mechanics, Vol. 10, No. 10, October 1970, pp. 408-414.4. G. E. Hauver and A. Melani, "Strain-Gage Techniques for Studies ofProjectile Behavior During Penetration," Ballistic Research LaboratoryMemorandum Report No. ARBRL-MR-03082, February 1981. AD.4 0986605. C. C. Perry and H. R. Lissner, The Strain Gage Primer, McGraw-Hill BookCo., Inc., New York, Toronto, London, 1955, pp. 48-51.6. Radio Corporation of America, Inc., Power Transistors, Databook No .SSD-204C, Somerville, NJ, 1974, pp. 109-115.7. Texas Instruments, Inc., The Optoelectronics Data Book for DesignEngineers, 5th ed., Dallas, TX, 1978, pp. 114-118.8. Motorola, Inc., Linear Integrated Circuits, Series C, Phoenix, AZ, 1979,pp. 6-44 - 6-50.9. Measurements Grc.ip, Inc., High Elongation Strain Measurements, TechnicalTip No. TT-605, Raleigh, NC, 1983.

10. R. E. Franz, "The Measurement of Large Strains with Foil ResistanceStrain Gages," Ballistic Research Laboratory Technical Report No.ARBRL-TR-02519, August 1983.ADA 13368711. Measurements Group, Inc., Errors Due to Misalignment of Strain Gages,

Technical Note No. TN-511, Raleigh, NC, 1983.12. Measurements Group, Inc., Errors Due to Transverse Sensitivity in StrainGLe~s, Technical Note No. TN-509, Raleigh, NC, 1982.13. N. Cook and E. Rabinowitz, Physical Measurement and Analysis,

Addison-Wesley Publishing Co., Reading, 1963, pp. 29-35.A-i. Measurements Group, Inc., Temperature Induced Apparent Strain and GageFactor Variation in Strain Gages, Technical Note No. TN-504, Raleigh,

NC, 1976.B-I. D. F. Merritt and C. E. Anderson, Jr., X-Ray Trigger Predictor:Automatic Electronic Time Delay Device for Flash X-Ray Systems,"Ballistic Research Laboratory Technical Report No. ARBRL-TR-02284,January 1981. ADB 056362


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APPENDIX AOPTIMIZING PULSE EXCITATION LEVELS

FOR CONSTANTAN FOIL STPAIN GAGES

31

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APPENDIX AOPTIMIZING PULSE EXCITATION LEVELS FOR CONSTANTAN FOIL STRAIN GAGE S

The Measurements Group, Inc., publication, Optimizing Strain Gae2Excitation Levels, provides an excellent summary of the factors affectingchoice of excitation level for strain gages, and includes recommended powerdensity ranges based on the level of accuracy required and the heat sinking

capability of the substrate to which the gage is bonded. The recommendedpower densities are for conti jous excitation, however, and are intended tominimize zero-shift due to apparent strain within the level of accuracy stated.

Apparent strain is a temperature induced change of gage resistance, andunder equilibrium temperature conditions, errors due to apparent strain can beA-icorrected. During pulse excitation, however, thermal equilibrium betweenthe grid material and the substrate is not achieved due to the low thermalconductivity of the gage backing. Consequently, the grid material is heated,but cannot expand in the plane of the gage. It may expand out-of-plane.however, effectively increasing the cross-sectional area of the grid. Sincethe resistance R(ohms) of a conductor is given by

R = p L/A (A-1)2

where A - cross-sectional area, cmL - length, cmp resistivity, ohm-cm

increasing A causes resistance to decrease. Thus, compressive apparent strainis indicated when the grid becomes heated.Power density is a convenient parameter when discussing strain gage

excitation levels because it takes into account variations in instrumentationdesign and gage geometry, as well as excitation voltage. The power to be2dissipated in the gage grid is I Rg, where I is the current passing thruthe gage, Eq. 6. Power density is simply this power divided by the activearea (gage length x grid width) of the gage. Appaient strain zero-shift maybe calculated from bridge output voltage zero-shift.

Tests were performed on annealed constantan foil strain gages to determineapparent strain zero-shift vs pulsed power density. The specific gage testedwas a Micro-Measurements EP-08-062AK-120, bonded with methyl-.2-cyanoacrylateto a 1.2 mm wall, 24.7 mm O.D. AISI 1020 steel tube. A 0.025 mm polyurethaneprotective coating was applied over the installation, in accordance with thegage manufacturers recommendations. The steel substrate was chosen asA-lMeasurements Group, Inc., Temperature Induced Apparent Strain a;d Gage

Factor Variation in Strain Gages- Technical Note No. TN-504, Raleigh,NC, 1976.

33

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0

(b)

(c)

I0

10E0w 0 I I I I I I I I I

0 100 200t /AS)

Figure A-1. Zero-Shift vs Excitation Time. (a) Reference Baseline, S W MetalFilm Resistor as Gage Substitute. Power Densities of (b)0.1107, (c) 0.2038, (d) 0.6526, (e) 1.3490 and (f) 1.8381 W/m2in Annealed Constantan Foil Strain Gage Mounted on Steel.

34


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typical, and has "good" heat sink capability. The gage was connected to apulse power supply/Wheatstone bridge circuit of the type described in thisreport with 25 cm of RG-62/U coaxial cable. Zener diodes ranging from 10 to43 volts regulated excitation voltage, which was pulsed on for 200 micro-seconds. Actual pulsed excitation voltages across the bridge were measureddirectly to 5 millivolt accuracy, while bridge output voltages were measuredto 50 microvolt accuracy.

Zero-shift vs excitation time for several power densities is shown inFigure A-i. After the 30 microseconds required for circuit stabilization,zero-shift increases at nearly constant rate for each power density, and therate of zero-shift increases with power density. The rate of zero-shift doesdecrease somewhat with time, however, as heat generated in the grid is con-ducted to the substrate. This, of course, occurs more rapidly for higher gridtemperatures. It is expected that for very long excitation times, the zero-shift would stabilize as the grid reached thermal equilibrium.

The rate of zero-shift was assumed constant, and the data reduced toapparent microstrain per microsecond of excitation using Eqs. 15, 16, and 9,and assuming initial balance. These zero-shift rates are plotted vs powerdensity in Figure A-2, and the error bars indicate the uncertainty. A linearleast squares fit was performed on the data, and the result is the solid line.Of interest is the intersection of the line with the power density axis,0.0568 W/mm2, corresponding to zero zero-shift rate, and hence, no zero-shift.

This is in the range of 0.031 - 0.078 W/mm , indicated on the figure, recom-mended by the gage manufacturer as the maximum continuous power densities. 2

To use the curve for estimating optimum pulse excitation levels, theallowable zero-shift rate must be determined. This is the strain measurementresolution divided by total excitation time, pel/us. The power density canthen be read from the curve, and excitation voltage calculated by Eq. 4. Themeasurement resolution using this excitation should be re-evaluated to deter-mine if the power density is acceptable. A word of caution concerning use ofthis curve is in order. The data were obtained using short (200 microsecond)pulse widths, good substrate heat sink capability and a strain gage with 08self-temperature compensation (S-T-C). (Thermal coefficient of expansion 8ppm/ F (14.4 ppm/ C).) For much longer pulse widths, the rate of zero-shiftmay be inversely proportional to substrate thermal conductivity. The S-T-Cnumber also affects the slope of the line in Figure A-2. Lower thermalexpansion coefficients (S-T-C number) allow greater power densities for agiven zero-shift rate and vice versa. Because quarter bridge output and thestrain reduction used are both non-linear, extrapolation to much higher powerdensities is not recommended without verification of applicability.

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-2.5

-2.0

,,,..

u -1.5

I-.it

0o -1.0L

-0.5

0.00.0 0.5 1.0 1.5

POWER DENSITY (W/mm 2 )Figure A-2. Apparent Strain Zero-Shift Rate vs Pulsed Power Density forAnnealed Constantan Foil Strain Gage.

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1.. . I .11- o 4 -MR... .. . ..

APPENDIX BTIME DOMAIN PRE-EVENT TRIGGER FOR

CONSTANT VELOCITY IMPACTSYSTEMS

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APPENDIX BTIME DOMAIN PRE-EVENT TRIGGER FOR CONSTANT VELOCITY IMPACT SYSTEMS

The acquisition of transient experimental data requires precise triggeringof instrumentation to insure recording the events of interest. An automatic,electronic time delay trigger device, developed by Merritt and Anderson, B- isuseful in impact studies because it provides a trigger at or just beforeimpact. The device is a TTL up/down counter, and operates in this manner.Two passive circuits that detect the passage of a projectile or fragment arespaced a distance X along the projectile's line of flight, the second adistance 2X from the target. When the projectile arrives at the firstcircuit, the counter starts incrementing one count for each pulse provided bya 1 MHz oscillator. Upon projectile arrival at the second circuit, thecounter stops incrementing, and starts decrementing one count for each two1 MHz pulses. Thus, it takes the counter twice the time to decrement to zeroas it did to count up. A projectile travelling at constant velocity will taketwice the time to travel a distance 2X as it does to travel IX, so it willreach the target at the same time the counter returns to zero. A comparatorcircuit detects the return to zero and outputs a trigger pulse.

The developers state that spacing the target 'slightly' greater than twicethe inter-detection-circuit spacing from the second circuit will provide atrigger before impact. This is space domain pre-event triggering, and theamount of time before the event depends on the amount of this 'slightly'greater spacing and the projectile velocity. If time domain pre-eventtriggering is required, as for example to allow pulsed instrumentation tostabilize, either the velocity must be known beforehand to calculate thedistance, or an alternative device must be developed. This appendix describesa modification to the original trigger predictor circuit to allow time domainpre-event triggering.

Merritt and Anderson provide an excellent description of the detailedoperation of the device, and the reader is directed to their report. Theentire circuit diagram, Figilre B-I, with the modification is included here,however, for clarity and completeness, and Table B-I lists the integratedcircuits used.

In the original design, the 12 bit binary counter, IC8, 9 and 10, has eachoutput register Q connected to an inverter, IC6A-F and IC7A-F. The inverteroutputs, which are open collector, are all tied together and to a single 1K-ohm pull up resistor. When any counter register is in the high logic levelstate, i.e., counter not at zero, the corresponding inverter output is in thelow logic level state, and the pull up current is sunk to ground. So output ofthe paralleled inverters is high only when all counter registers are zero.The low to high transition when the counter decrements to zero triggers amonostable multivibrator, (not shown in schematic) which provides a triggerpulse. Also, an output to reset the STOP flip-flop, ICIA, to prevent decre-menting past zero is provided to prevent subsequent retriggering.B-1D. F. Merritt and C. E. Anderson, Jr., X-Ray Trigger Predictor: Automatic

Electronic Time Delay Device for Flash X-Ray Systems, Ballistic ResearchLavoratory Technical Report No. ARBRL-TR-02284, January 1981. ADB 056362

39PRECEDING PAGE BLANK-40T FILLMD


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>lu lcg) +U ujb r, - N d 0a 0 0 V) zC) tu '0 < zo N ZL FZZ=)C4 CV) z :*co zLn ujA A C4

CVca -4uatlu ICD-ju u u Go L)01

001- Tj O 13 ZL01 10 U) -4.

Cc) k0 LLJ C; Ne(L Z = , I- U)D 4-A A CY Ao- >.) Ij -Ln q . M:= tn >LL ALO, + Qj'0 z

L -Niu ICDC9 N a.01 %0

CY Nu 10 u 0. r:300 0 0a kn Im9D C14 uC14z co Ng E936 10 >Lr) aDA A U. 4-4

11 r) -1 ciC-4 41V-to K cdu-410 m Lu 4-)tA 0 Cd

co 01) 00 U.1 504 04 ae10M ice Wa UA

01 10a to to 4

0 1wItA Ice b4lixu NOC;A In In UA10 C%4 LU Q-00 In 01 U.1 -0

C14 C14C14 v>In m+ +40


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TABLE B-I. ICs USED IN PRE-EVENT TRIGGER DEVICEIC No. Type No. FunctionlA-B,4 SN7474 D-type, positive edge triggered

flip-flop2A-D SN7408 2-input positive AND gate, totem pole

output3D-E, 5A-F SN7404 Inverter, totem pole output6A-F, 7A-F SN7405 Inverter, open collector output8,9,10 SN74193 Positive edge triggered, 4-bit binaryup/down synchronous counter11A-C, 12C-D SN7400 2-input positive NAND gate, totem pole

outputThe modification involves splitting the inverter outputs with a diode andproviding pull up current to both parallel inverter circuits thru 1 K-ohm

resistors. Current cannot flow cathode to anode, so when the counter regis-ters corresponding to those inverters tied to the cathode side are zero,output is high regardless of the state of the registers on the anode side.Conversely, current may flow in the opposite direction, so output of their . ers tied to the anode is low when any register is high. Thus twooutputs are available, one from the anode side when the counter has decre-mented to zero, and another from the cathode side. The time before zero thatthe cathode side goes high depends on the number of registers n tied to theanode side, and is given by

Si-12 Ali 1 (B-1)

where 4 s the period of the oscillator providing decrement pulses. In thiscase n is 4 and 41 s 2 microseconds, so pre-event time is 30 microseconds.IC11A-C comprise the output section, replacing the monostable multi-vibrator in the original device. The output of IC11A is used to reset the

STOP flip-flop in a fashion similar to the original version of the circuit.IC11C provides the pre-event trigger signal, a TTL level high to low traas-ition. IC11B is used as a low active OR gate to enable output. One input,pin 5, is normally high, the other, pin 4, is low only when the STOP flip-flophas been triggered. Thus IC11A and IC11C are enabled only during decrementingof the counter.

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The output may be manually triggered by momentarily causing pin 5 of IC11Bto be low. This is done with the flip-flop switch comprised of IC12C and Dand the resistance-capacitance circuit. The manual trigger can be used forpre-shot testing and calibration of other instrumentation.

To insure that the desired amount of pre-event time is obtained, thecounter must increment to at least all registers associated with the anodeside of the diode. The time is given by Eq. B-I, where 4 is the period of theincrement pulses, 1 micrcsecond. The projectile velocity and detectioncircuit spacing must be such that 15 microseconds or more "count up" time isobtained. This is not a severe limitation unless velocity is very high orcircuit spacing is very small. If this situation is not met, the circuit willstill trigger, but the pre-event time will be only twice the count up time.

Timing accuracy of the device is limited by the asynchronicity of theSTART and STOP pulses with the oscillator pulses. Incrementing, the uncer-tainty is zero to +1 count and decrementing, zero to -1 count for a totaluncertainty of 3 microseconds. Thus, the pre-event trigger can occur between27 and 33 microseconds before impact. One hundred tests show the uncertaintyis random, with a mean pre-event time of 30.1 .1 microseconds and a standarddeviation of 1.5 microseconds. The uncertainty could be decreased by using ahigher frequency oscillator, but this would necessitate additional counterbits to retain the counting capacity.

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APPENDIX CSAMPLE CALIBRATION AND STRAIN

DATA REDUCTION

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APPENDIX CSAMPLE CALIBRATION AND STRAIN DATA REDUCTION

A typical calibration and simulated strain data reduction was performed,with total pulse durations of 200 microseconds and the bridge output voltagesmeasured at mid-usable-pulse-width, 115 microseconds after turn-on. Theactual excitation voltages, not normally directly measured during calibration,were measured with an oscilloscope with a differential preamplifier for com-parison with the calculated value. The most general case of the bridge beingslightly unbalanced initially was used in the example. A five watt, 120 ohmmetal film resistor was used as a gage substitute and connected to the bridgewith 14 meters of RG-62/U coaxial cable. A nominal 15 volt zener dioderegulated the excitation voltage. Table C-i shows directly measured cali-bration resistances and bridge output voltages needed to calculate the circuitconstants, as well as the measured excitation voltages. Table C-2 shows thecalculated circuit constants based on the data of Table C-i. The calculatedexcitation and baseline bridge output voltages are in excellent agreement withthe measured values.

To test the strain data reduction procedure, several compressive strainsimulations were performed. Precisicn metal film resistors were inserted inparallel with the gage substitute to simulate a gage under strain, and thebridge output measured on several oscilloscope scales, each with differentresolution, to test the validity of calibration on one scale and signal mea-surement on another. The resistance of the "gage under strain was measureddirectly, and this value used to calculate the actual strain. The calcu-lated strain and uncertainty were determined from output voltage and reso-lution lim it. The difference between the two determinations is the error. SeeTable C-3.

The error associated with these measurements is on the order of th eresolution of the measurement scale. Calibrating on a high resolution scaleprovides more accurate circuit constants, and the scale may be changed to

accommodate the expected range of measurement without loss of calibration.

45FRECED1Z PAoS BLANK-1OT FThU


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TABLE C-i. MEASURED CALIBRATION CONSTANTS

R (M) Eout mv) Ein (v)

R = 119.6640R4 = 92.9686RIB = 122.274 EB = -15.3 13.825R1T = 124.725 ET = +52.0 13.835R1C = 119.880 EC = -82.4 13.840

TABLE C-2. CALCULATED CIRCUIT CONSTANTS

R (29) R (2/M) Rdum 1) Roffset ()) Ein (v) Ebase (mv)

2.610 0.56918 122.825 -0.551 13.826 -15.23

TABLE C-3. DATA REDUCTION AND COMPARISON WITH ACTUAL STRAINEs + res (mv) Cale res ,At) act (ME)a Error pe)

-50.4 + 0 .8b -5306 120 -5443 -137-52.8 + 1.6 -5667 + 241 -5443 +224

-150.4 + 1.6 -20211 + 241 -20121 +90-48 * 16 -4945 2406 -5443 -448

-144 + 16 -19265 2406 -20121 -856-1488 16 -198435 2406 -198779 -344

a+S3bSame scale and resolution as calibration measurements

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Space Administration ATTN: Dr. Arfon JonesLyndon B. Johnson Space Center 420 Wahara WayHouston, TX 77058 University Research ParkSalt Lake City, UT 84108

Aeronautical Research Associates 3 California Institute ofof Princeton, Incorporated TechnologyATTN: Ray Gogolewski Division of Engineering and1800 Old Meadow Rd., #114 Applied ScienceMcLean, VA 22102 ATTN: Dr. J. Mikowitz

Dr. E. SternbergHoneywell, Inc. Dr. J. KnowlesDefense Systems Dikision Pasadena, CA 91102ATTN: Dr. Gordon Johnson600 Second Street, NE 1 University of DenverHopkins, MN SS343 Denver Research Institute

2 Orlando Technology, Inc. ATTN: Dr. R. RechtATTN- Dr. Daniel Matuska P. 0. Box 10127Dr. John J. Osborn Denver, CO 80210P.O. Box 855Shalimar, FL 32579 Rensselaer Polytechnic Institute

ATTN: Prof. E. H. LeeProf. E. KremplProf. J. Flaherty

Troy, NY 121811 Southwest Research InstituteATTN: Dr. Charles Anderson

8500 Culebra RoadSan Antonio, TX 78228

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DISTRIBUTION LISTSOrganizat ion C Organization

2 Southwest Research Institute 2 Forrestal Research CenterDepartment of Mechanical Aeronautical Engineering Lab.Sciences Princeton UniversityATTN: Dr. U. Lindhholm ATTN: Dr. S. LamDr. W. Baker Dr. A. Eringen

8500 Culebra Road Princeton, NJ 08540San Antonio, TX 78228 1 Harvard UniversityUniversity of Dayton Division of Engineering andUniversity of Dayton Rsch Inst Applied PhysicsATTN: Dr. S. J. Bless ATTN: Prof. J. R. RiceDayton, OH 45469 Cambridge, MA 02138

7 Brown University 2 Iowa State UniversityDivision of Engineering Engineering Research LaboratoryATTN: Prof. R. Clifton ATTN: Dr. G. NariboliProf. H. Kolsky Dr. A. SedovProf. L. B. Freund Ames, IA 50010

Prof. A. NeedlemanProf. R. Asaro 2 Leligh UniversityProf. R. James Center for the ApplicationProf. J. Duffy of MathematicsProvidence, RI 02912 ATTN: Dr. E. Varley

Dr. R. Rivlin3 Carnegie Mellon University Bethlehem, PA 18015Department of MathematicsATTN: Dr. D. Owen 1 New York University

Dr. M. E. Gurtin Department of MathematicsDr. B. D. Coleman ATTN: Dr. J. KellerPittsburgh, PA 15213 University Heights

New York, NY 100532 Catholic University of AmericaSchool of Engineering and 1 North Carolina State University

Architecture Department of Civil EngineeringATTN: Prof. A. Durelli ATTN: Prof. Y. HorieProf. J. McCoy Raleigh, NC 27607Washington, DC 20017

1 Pennsylvania State UniversityEngineering Mechanical Dept.ATTN: Prof. N. DavidsUniversity Park, PA 16802

2 Rice UniversityATTN: Dr. R. Bowen

Dr. C. C. WangP. 0. Box 1892Houston, TX 77001

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Southern Methodist University 1 University of DelawareSolid Mechanics Division Dept of Mechanical EngineeringATTN: Prof. H. Watson ATTN: Prof. J. VinsonDallas, TX 75221 Newark, DE 19711Temple University 1 University of DelawareCollege of Engineering Dept of Mechanical and Aerospace

Technology EngineeringATTN: Dr. R. M. Haythornthwaite, ATTN: Dr. Minoru TayaDean Newark, DE 19711Philadelphia, PA 19122

2 University of Kentucky4 The Johns Hopkins University Dept of Engineering MechanicsATTN: Prof. R. B. Pond, Sr. ATTN- Dr. M. Beatty

Prof. R. Green Prof. 0. Dillon, Jr .Prof. W. Sharpe Lexington, KY 40506Prof. J. Bell

34th and Charles StreetsBaltimore, MD 21218

2 University of HoustonTulane University Department of MechanicalDept of Mechanical Engineering EngineeringATTN: Dr. S. Cowin ATTN: Dr. T. WheelerNew Orleans, LA 70112 Dr. R. Nachlinger

Houston, TX 770043 University of CaliforniaATTN: Dr. M. Carroll 1 University of IllinoisDr. W. Goldsmith Dept. of Theoretical andDr. P. Naghdi Applied Mechanics

Berkley, CA 94704 ATTN: Dr. D. CarlsonUrbana, IL 61801University of CaliforniaDept of Aerospace and 1 University of Illinois

Mechanical Engineering Science ATTN: Dean D. DruckerATTN: Dr. Y. C. Fung Urbana, IL 61801P. 0. Box 109La Jolla, CA 92037 1 University of Illinois atChicago CircleUniversity of California College of EngineeringDepartment of Mechanics Dept. of Materials EngineeringATTN: Dr. R. Stern ATTN: Dr. T. C. T. Ting504 Hilgard Avenue P. 0. Box 4348Los Angeles, CA 90024 Chicago, IL 60680University of California at University of Kentucky

Santa Barbara Dept of Engineering MechanicsDept of Mechanical Engineering ATTN: Dr. M. BeattyATTN: Prof. T. P. Mitchel Prof. 0. Dillon, Jr.Santa Barbara, CA 93106 Lexington, KY 40506

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University of Maryland Aberdeen Proving GroundDepartment of Mathematics Dir, USAMSAAATTN: Prof. S. Antman ATTN. DRXSY-flCollege Park, MD 20740 DRXSY-MP, H. CohenCdr, USATECOMUniversity of Minnesota ATTN: DRSTE-TO-FDept of Aerospace Engineering Cdr, CRDC,AMCCOM

and Mechanics ATTN: DRSMC-CLB-PAATTN: Prof. J. L. Erickson DRSMC-CLN107 Akerman Hall DRSMC-CLJ-LMinneapolis, MN 55455 Dir, MTDATTN: STEAP-MT-GUniversity of Pennsylvania S. WaltonTowne School of Civil and

Mechanical EngineeringATTN: Prof. Z. HashinPhiladelphia, PA 19105

4 University of TexasDepartment of Engineer' igMechanicsATTN: Dr. M. SternDr. M. Bedford

Prof. RippergerDr. J. T. Oden

Austin, TX 78712University of WashingtonDept of Aeronautics andAstronauticsATTN: Dr. Ian M. Fyfe206 Guggenheim HallSeattle, WA 98105

2 Washington State UniversityDepartment of PhysicsATTN, Dr. R. Fowles

Dr. G. DuvallPullman, WA 99163

2 Yale UniversityATTN: Dr. B. T. Chu

Dr. E. Onat400 Temple StreetNew Haven, CT 06520

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instrumentation techniques for measuring large high rate strains with sg

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