INVESTIGATION OF

REPORT No. 388

THE DIAPHRAGM-TYPE PRESSURE CELL

By THEODORFITELEODORSEX

SUMMARY

This report relate8 to carious improrement8 in theprocess of ‘wrwfacture of the N. A. C; A. ~tandard pres-wre cell. Like most pressure recording den”ces employ-ing thin diaphragm, they would in general 8how con-~“derable change in calibration with temperature and a180some change of calibration with time or aging effect.Some instruments exhibited cmwiderable internal frictimt.

It tom established that the temperature dependence ofthe stijfness wag due to diference in the thermal expan-sivity between the diaphragm proper and the supportingbody of the cell, and conrenieni method8 for its compensa-tion hare been dereloped. The diaphragm i-s furnishedwith a small central bushing of a di~erent metal, and it i-spossible to determine a w“ze of this bu~hing which giwthe diaphragm exactly the 8mme ih-wn.al expansivity asthe cell body.

It was further established that the internal hysteresisin the diaphragm w of a negligible magnitude and thatthe obwred lag was due, primarily to the force of thehairspring on the sQIlu8 point. The redtant adoptionof weaker hair8pring8 made it possible to extend the u8efulrange of the instrument con~”derably downward. Sati8-factoy insirument8 hating a range of les8 than 3 inche8of water were made pwsible.

Ii we found that the tendency to change calibrationunlh time was cawed, to a great extent, by in.sqj%”entclamping of the diaphragm. % adoption qf doublecopper gasket8 improred this condition.

The required diaphragm thickness and the dem”rablerate of mechanical magnification hare been determined onthe ba8i8 of 8ereral hundred te3t8.

INTRODUCTION

This report was prepared by the National AdvisoryCommittee for Aeronautics. It giws the results of asystematic inwdigation undertaken at the LangleyMemorial Aeronautical Laborato~ during the falI of1929. The investigation is rather general in its scope.The actual experimental work is, however, contked toteds on the N. A. C. A. standard instruments. Theseinstruments, developed by the technical stafl of thecommittee, are of a very simple and rugged design. ,The pressure cell is sho&n in-F~ge 1. ‘it eonsik,essentitiy, of a flat, circular diaphragm or membrane,A, tightIy stretched and securely ciknped along itscircumference. The unsupported diameter of the

I1

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diaphragm is appro.simately 1% inches, and the thick- _ness is of the order of 0.001 inch to 0.006 inch. The - --?.-motion of the diaphragm is transmitted by a smallsteel pin or stylus, E, to a rotatable mirror, F. Thedistance between the @ of the stylus and the wds .,=of the mirror shaft k from 0.010 inch to 0.050 inchj .-—approximately. For the present purpose it will be _-.“sufhient to stats that the actual deflection of thediaphragg is reproduced on a greatly ma=gnitiedscaIe “-by mew of a beam of light reflected from the mirror. .-The maximum ma=@ication employed is somewhat inOXCB of 1,000.

~The Iight beam k arranged so as to form a sharimage of the source on a graduated scale for diref

A Fhf ffWti d@%wy?B M&d caseC .5Yeei‘washer

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observation, or on a revolfim fiim for recording pur-poses. The pr-ure cell carries a small stationaryreference mirror, 1+. (See iig. 1.) For rLmore completedescription of the instrument, see N. A. C. A. TeclmicalNote No. 64 by F. H. h’orton. @eference L)

Because the diaphragm instrument is almost entirelyfree from mass effects, it is indispensable as a pressure-memmring device in alI investigations performed onairplanes in fli@t. The acceleration in tiolent maneu-vers may, at times, amount to more than 10 g. If thisacoekation happens to be perpendicular to the dia-phragm, it is equivalent to a pressure of approximately0.2 inch of water on the most frequently employeddiaphragm of 0.002 inch thickness. & the range ofthis diaphragm is about 20 umhes of water, the aboveerror is seen to amount to but one per cent of the fuU-

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508 REPORT NATIONAL ADVISORY

scaIe deflection. This error may, however, easily becompensated for by counterweights on the mirror staff,if necessary.

Contrasted to this and to other desirable qualities,it is also well known that instruments employing thindiaphragms as an integral element very often aresubject to a number of peculiar effects of quite anobscure nature, In fact, the behavior of some dia-phragms is so erratic that one nay, at-a fist glance,

COMMITTEE FOR AERONAUTICS

(1) Compensation of temperature effects(2) Removal of frictional effects.

It was known that the prmure cells usually showeda change in reading with temperature. The effectwae very pronounced. Figures 2, 3, 4, 5, and 6 givean impression of the situation at the time the foUowinginvestigation was started. The temperature eflectamounts to as much as 30 per cent of the scale range.The calibration curves taken at different temperature

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Cdlcededh ITF. Dlapbmgmatretahed

be tempted to believe that they me subject to no lawsat all.

The purpose of the following study was to producesuch information as would increase the general know]-edge regarding the behavior of the diaphragm and thepredictability of its performance, The study was, forpractical reasons, directly focused on the two followingproblems :

do not, in general, intersect at zero, as might kmex-pected, but at some quite different- pressure, Thezero point is, consequently, subject to a change withtemperature. (See @s. 13 and 14.) In some casesthe curves do not intersect at all (see fig. 16), or theyintersect beyond the range of the calibration. (seefigs.15and 17.) The trouble increases rapidly withthe sensitivity of the ceil.

1.NV3STIGA’I’ION OF THE DLAPERAGM+lTPE P13ESSURE CELL 509

in this paper an attempt is made to analyze thecauses of this phenomenon. It will be indicated hwhat extent the prediction and prevention of thecondition is possible.

Even more troubiwome than the temperatureeffect is the internal friction in the celIs. The authorhas gone to great detail in tracing the origin of the lag,

nature will be more or less touched upon. NTotwith-stan~~ the very simple desigq of the cell, it wasfound to furnish quiti a rich fieid for investigation.

METHODS OF CALIBRATION

The instruments exe usua~y allowed to age for atleast one day. They are then put through individual

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or dead motion, in the N. A. C. A. instrument. This crdibrations at three Merent temperatures. Theeffect is$however, only of importance for -iery sensi- caLibrationsare taken in the following succession:tive cells, instruments hamng a full rmge of less than (1) Room temperature.about 3 inches of water. The sources of the interred (2) – 15° c.friction were aaalyzed. As a rwdt, the most desirable (3) Room temperature.condition ccndd be definitely established, resulting in (4) + 53° c.considerable improvement. (5) Room temperature. “

A number of related probkms which, naturally, The instrument is kept at each desired temperaturearise in connection with an investigation of this for one-half hour prior to exposure to insure an even

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510 REPORT NATIONAL ADVISORY

and correct temperature. In each case readings aretrtkenboth for increasing and for decreasing pressureover the full range. The deflections are recordedphotogmphicdly on a nondistorting fiIm. This pro-cedure has been followed in the present investigation.

THEORY OF Diaphragms

It wns soon established that most of the difficultiesmentioned above could be traced back to the dia-

COMMITT%E FOR AERONAUTICS

where p is the uniform pressure.t is the thickness,r is the radius,W is the deflection at the center,E is Young’s Modulus of Elasticity,~ is Poisson’s Ratio.

It wiU be noticed, in particular, that the only col]-strmtof the materiaI appearing in the expression is the

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phragm itself. Unfortunn.tAy, there does not@ thepresent time, exist any general theory of stretchedcircular diaphragms. We me, however, able to drawa number of conclusions from pmticulm cases forwhich the solutioIu~are known.

The classical theory of thin diaphragms gives forthe case of a circular phme dinphragm clamped atthe circumference:

(1)

so-crdled plate modulus ~~. It seems, then, quite

consistent to draw the conclusion that any observedtemperature dependency of the characteristic curvesis, necessarily,,caused by changes in the plate moduluswith temperature.1 This latter variability is, in turn,attributed to “cold working of the diaphragm, or todefective elasticity.” (See for instance Journal of the -: -. :=

1There is a slfght dependencybroughtabout by CtMIIgWin lln~ dlmefio~ Of

the dkiphmgmwith tsmpwature. The magnltnde19negligible.

INVESTIGATION OF THEl DLKFHRAGM-TYPE PRESSURE CELL 511

Royal Aeronautical Sooiety, Number 210, VolumeXXXII, June, 1928, p. 444. Reference 3.)

A rather interesting study, relating directly to thisquestion, is given in the N. A. C. A. TecbnicaI ReportNo. 165, by M. D. Eersey. (See paragraphs 21–22,on temperature compensation. Reference 4.) Wequote from thk paper:

departure in mechanical desiggj such as to satisfy equa-tion (15) for any given vrdues of a, & and 7.”

Mr. Eersey’s discussion is, however, mtricti togeometrically sir&ihrcases, which fact is clearly pointedout. b order to satisfy this requirement, in the caseof a rigidly olamped diaphragm, when the temperatureis subject to change, it is necessary that the diaphragm

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FIG_GEE6.–AWpeed calfbratiom IMrnment No. 149. Ce.@a No. 0-2S0(n=)

“The question whether intrimic compensation ispracticable remainsasanimportsnt one for future study,but the conditions to be satisfied have been ardyzedabcme. It is conceivable that compensation might besecured either .by diwovering alloys wbic.h satisfyequation (15) i for a given value of C; or conversdy bydeveloping a suitable vslue of C through some radical

ZFortbesakeof brevfty, It wflljnst be *W thatequation(M),wnfdningtbasymbo~C,~,&~d T,wwntklly, givesthe mndltion of a cmwt!lntPM YnafrtfoJ.

and the casing have the wm.e coemnt of thermalarpansion. All that needs to be done in order to secure —temperature compensation of any tiects of the pIatemodulus is to ciolate this restriction of geometricalsinihrity with respect to temperature.

It is aIso quite conceivable that the large tempera-ture coeflkients which are iometimes observed are dueto departure from similarity, caused by hwli of homo-geneity with respect to thermal expansion, rather than

512 REPORT NATIONAL ADVISORY

by artificial conditions presumably affecting themoduli of elasticity.

Mr. Hersey states, for instance, that the coe&ientof stiflness for a soft iron disk, supported freeIy on asharp, brass ring, amounts to – 6 per cent per degreecentigrade, or, in other words, that the stiffness isdoubled for every 16 degre~ centigrade. A large

COMMITTEE FOR AERONAUTICS

tit place, the formula is correct for sm.ulldeflectionsonly, so as to secure proportionality between stressesand Etraine, as required. This fact is, howevor, noemential limitation on its genertd value, We hav~, inmost cases, a straight-Iine rdation between pressureand central deflection, Moreover, we me primarilyinterested in utihzing the formula in predicting the

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FIGUBE6.–Mr-qwed oaIfbratIon. InWrmnentNo. ML CaWUIeNo. - (RPM

temperature coefficient of the moddi of elasticity hae,on the other hand, not been observed directiy. Theconclusion arrived at in this investigation is that thestifbss is cm”ticaUydependent upon 8muU irregularities

in the diaphragm proper, and on the relatioe expan..sionof the diaphragm to the enclo8ure, when chunped.

LIMITATIONS OF THE CLASSICAL FORMULA FORDEFLECTION OF THIN DL4PHItAGhfS

Ih order to emphasize the condition referred to abovewe will subiect eauation (1I b a closer studv. In the. . .,. –“-— –__

slope of the curve at zero pressure, independent ofany deviation that may appear at larger prmsures.

By diBerentiation of equation (l), we obtain as‘(stiffness” at zero pressure, the exprcsion:

dPlt3EP—.‘=d~’=~l–ti% (2)

Examination of the calibration curves of Figures 2to 6 will disclose the fact that the stfiness S is aboutdoubkd, as the temperature is inoreased from -15°to + 53° cent&ade. The expression (2), on the other

INVESTIGATION OF TEE DIAPDRAGM-TYPE PRESSURE CELL 513

hand, should be almost a constant as far as the tem-perature is concerned. The contradiction is expkinedby the fact that the formula (2] is Iimited to the caseof the so-called inextensionaI strain. That is, theneutral plane of the diaphragm is assumed free fromstrain. (Reference 5.) The dibration curves inthe FQures 2 to 6 were taken on standard N. A. C. A.instruments with stretched diaphragms. The expltma-tion of the rather bafbg temperature dependency isthus forced upon us:

lt is due to chunge8 in the Mid-strain in the dia-phragm, which, in turn, are due to a difference in thethermal expansion of the diaphragm and the cell body.

To recapitulate: In formula(2) the following assump-tions are made:

(I) Diaphragm homogeneousand isotropic.

(2) ; small.

(3) No initial strain.(4) Diaphragm phne.For the pressure cdl, conditions 1 and 2 are

satisfied.Condtiian 3 is violated, owing to rehdiw expansion,

except for one definite due of the temperature.Condition 4 must, for practical reasons, be given

some consideration. The slack 0.00125-iich dia-phragm is sti~er than the 0.002-inch, owing ta regularstar-shaped buckling caused by soldering on the cen-tral bushing. (See TabIe II of diaphragm data.)

It has been found, from long experience with thinpressure diaphragms, that it is necewuy to stretchthe diaphragm at least to a certain extent. Theexplicit reason for this procedure is to avoid a ‘fdoublezero.“

Expression (2) is useful in giwing the ultimate sen-sitivity that can be expected for given dimensions of adiapbra=gn. The actual thin diaphragm will, owingto violation of conditions 3 and 4, show a stifhsof up to 30 times this Iirniting value. (See fig. 2.)Tbia question is vitil in connection with what hasbeen termed “sensitive cek.”

TEE APPROXIRIATETHEOBY OF STEETCKEDR1E31-BRANES

The classical theory of the unstretched cirmdardiaphragm chunped aIong its edge and subjected to auniform fluid pnwmre, gives the following differential

(See Fuller and John&m, p. 434, eq. 11.) The leftside represents the fluid pressure on a circular ring ofradius z and the right side repr-ts a pure shear@force at the edge of this ring. (See fig. 7.) Themernbrme being unstretched, there is no taugentiaIforce. The above equation admits of an exact solu-tion:

Y==* (d– 2A?) where A is a constant.

If, however, we assume an initial tmsion Tin thediaphragm, we have:

where the fit right side member indicates the pressurecarried by the outward tension on the ring of radius x.

The solution of this reIation is very importaut, b+cause it would furnish means of predicting the initialstiffn~ of the membrane for any arbitrary value of theinitial tension. The exact solution has not been found.In order to obtain at least some information as to thetendency of the effect we will limit ourselves to thecase where the initial tension may be considered small.

..-

—

Y

For smaII initial str~s we apply an approximate —-

expression for the first right-hand member in the”above equation. We have

.—

.y=$(x4-2?W), y== -;+

and

S!!=4 4&–.@x) = –*(#–r%)dx 32(

which actuaUy is correct only for zero initial stress.

Replacing ~~ in the fit right-hand member of the

above equation by this approximate vahe, gives:

The solution of this equation follows. ‘We write

where

L= –8@5’ and M= –e ~.m%–l 6Rearranging:

.—

514 REPORT NATIONAL ADVISORY COMMF.PTEE FOR AERONAUTICS

Integrating:

@+LF);=L:+M(,,+;,,)+c,

MuMplying by x:

@+ LP):-z:+M(w’’+y’) +cxo

Integrating:

(P+@$=L~+Jl(zY’)+C~ +D,(but D= O).

Dividing by x:

(P+ Lr9:-Lg+M!/’+c;”

To~detern~ineC we have tlmt y’= Owhen x= r:

(p+ Lr’);=L~+ 0;s

C=(p+Lr’)$-L&=p$ +L;”

Replacing G!

@+LR):=L~+Mv/+(p;+L;);.

Rearranging and integrating:

( ‘+L%+@+L~%+E ‘E=O)My=–L&– P~

We obtain y~ by putting z= r and further reintro-

duce L = – 8tT9

,.4

lVith

P&5T2

–M+tT3F

or

.

-Q at the center equaIs:. . .~tlal ‘tIffness dy~

that is, the original stiflness as given by formula (2)appears to have been magnified by the factor:

ma–l 5 r 2

()1+~,#’~ ~

For a slack membrane, T= O,and the result is identimlwith that given in formula (2).

This result is instructive, for it shows how the stiff-ness depends on the initial tension T. Now, this tm-aion is proportional to the temperature, and w-e havethe result that the stiffncm is a linear function of thotemperature, as could be expected. It will bc observedthat the thinnest diaphragms are the ones that. S11OWthe greatest temperature effects.

The above formula gives onIy the initird stiffness, orstiffness at zero pressure. It is possibIe to derive amore generaI form. (See page 8 of British Aeronau ti-cal Research Committee Reports and Memoranda hTo.113!3.)

EXPERIMENTALVER1F1CATIONOF THE CAUSE OFTEMPERATURE DEPENDENCY OF THE STIFFNESS–ADOPTED METHOD OF COMPENSATION

Following Up the conclusion that the only causecapkble of producing. the observed large tompcraturecoefli.cient was the possible dMercnce in thermalexpansivity of the diaphragm relative to the ceLfbody,a number of experiments were resorted to. In fact,a considerable number of trials were run before thisconclusion was definitely accepted as being corrcc t.In the Figures 2 to 6, it is noticed that the ternpcraturccoe.ilRientof stitlneseis positive; the stitTncssincrmsestith temperature. This fact is awounted for by theassumption that the thermal expansivity of the mwn-brane is leas than that of the cell body. A phosphorbronze diaphragm was subsequently inserted in thesteel ‘body of the cell. The expected reversal of thetemperature dependency appeared. (See fig. 8.) Thecoefllcient-is here negative, and appca~ to bo aboutfour_imes greater than in the preceding case.

The author then adopted the procedure of employ-ing a diaphragm composed of two metaIawith differentcoefficients of expansion, and so arranged as to givethe diaphragm, as a whoIe, the same expansivity as thesupporting body. The pressure diaphragms alreadycarried a %e-inch central steeI bushing. Aa a firstattempt this bushing was made of brass and incremedto % inch in diameter. The result of the calibrationis shown in Figure 9. The instrument is overcom-pensated, The n~~t trial was made with a M-inchbrass bushing, This calibration is reproduced inFigure 10. This instrument is undercompenaated to

IiXVESTIGATION OF TEE DIA.PHIL4G31-TYPE PREsslJRE CELL 515 .-.

the same degree as the preceding one was overcom- was discovered that this internal friction was broughtpensated. Consequently, a %-inch bushing vm.s about in a different manner.employed. The restdt is shown in Figure 11 and, with It millbe seen from the schematic drawing, Figure 1,further improvements in the technique, in Figure 12. that the mirror is kept in position by a hairspring.The temperature dependency is here entirely taken The hairspring consisted of nine convolutions of phos-care of for the entire range between —15° and + 53° phor bronze -wire,the cross section of which was aboutcentigrade. 0.003 by 0.016 inch. This tiny spring adds consider-

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FRICTION IN PRESSURE CELLS-AGING EFFECTS

One of the obstacles in making a good low-pressurecell of the type in question is the appearance of Iag ordead motion. The 0.00125 diaphragm would showas much as %inch ~’double zero.” (lurioualy enough,it was found that this dead motion had nothing to dowith hystemis in the diaphragm, as might have beenexpected. Mter considerab~e e~erimental work it

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able stiffness to the diaphragm-spring combination.We wiLIindicate the numerical value of this sti17n-.

By st.i.tTnessis meant the hydrostatic pressureneeded to give a central deflection of the diaplmagmof one unit. Tbie is in accordance with the mathe-matical definition in fornda (2). As is customary,the units used in the following are inches of water forthe pressmre and inches for the defkction. The

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FIQvm lZ-AkdPmd dibmtbn. IMtmmnt No. m. CM No. Z30(ha). O.OIWdlophragrm W flangebraai bushing. TWO0.04Wannmled mpmr uaake~, 20”HKI 0!

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FIavm 14.—Air*pad cdbzntlan. In$hvanant No. 180. CmpmdeNa. G-=. Center dlatume r.-O.fmYJ.Mxe rnbkr E&et removedand oo~ guk~ khnd

I

INKESTTGATION OF THE DIAP~GM-TTPE PRESSURE CELL 519

stHn~ S accordingly is expressed as inches of waterper inch detledion.

The angdar stdlness of the above spring was de-termined directly as M=O.190 gram cm per radian.If the stylus is kwated at a distance r. from the ti of

J&xthe spring, the latter exerts a force of ~ on it, where

a isthe angle of angular cornpr~=ion of the spring.

This gives a stiflness reduced to the stylus of SO=%.

Tilth the given value of M, and with rOequal to theadopted minimum of 0.010 inch or 0.0254 cm, weobtain :

In the limiting case of a slack diaphragm, the effect ofa single central force is equivalent to four times theeffect of an evenly distributed load of the same msg.

nitude. Hence, AS.equals 1,180 -& for equivalent

evenly distributed load. This due c&responde to astimss of 1.23inches water per inch deflection. Thisvalue is high beyond expectation. A glance at tiediaphragm data in Table II shows why any attempts

0

-.2

-.4

-.60 -2 .4 .6 -8 /0 [2 ,4 ,6 ,8

Pressureainchesofwafer

FIGURE15.—M- capmls h-o. leO. 0.00%’dtapbrsgmw’ stcsdboskdmg.scmwsdOnto dfaPbrs@m.6ty109OLW~fromsenti. Ad@ted to 1.6’1OfW&r

to use this spring with a slack diaphragm were un-successful.

I The stiffnws of the 0.00125-inch diaphragm as usedamounts to onIy 87 imchesof water per inch deflection,

.——

-.

R-essu-e,inchesofwaferR(imu16.—AfF-sPe&capsubsNo. 0-1S0. O.MWdiSpbE@l 1%#’brssabnsb@.wldsre&

Bnsbfogpresssdsf& sdddng ta relievestislmpeofdispbrsgm. Adjusfedto3“ ofwatersk@lS O.OIWfrom Csnb?r

so that in this case approsimateIy 60 per cent of the.

force is transmitted through the styIus point to theback of the mirror shaft, and from there on through

—-

tihe bearings. This condition is highly undesirable.Not only is the effecti~e deflection reduced, but the fric-tional forces reach an appreciable relative magnitude.

--.—

The spring was usually given an initial angular de-flection of about 45 degrees, or somewhat less thanone radian. Referring to the above value of equiva-lent stiffness of the spring, we fid that this force isapproximately equaI to one inch of water. The valueof the force ren@ns fairly constant owr the range ofthe instrument owing to this large inititd deflection.This internal force on the stylus and bearings is re-

.. — .,

sponsible for a considerable part of the observed lag.‘I’here is, howe-wr, another oondit.ion bat causes an

amplification of the kg when S’ is small. Wlm.n theforce on the stylus is large compared to the internalforces in the diaphragm, considerable lateral motionof the stylus point, rdative to the mirror axis, willtake place, due to bendhg of the diaphragm. Thislatter effect explaine why the observed deviations al-ways would be much larger for slack diaphragms.

As a remedy against this dead motion it was con-cei-red that it would be necessary to employ weakerhairsprings or less initial tension then -wasusurdly em-ployed. The last scheme was resorted to for sometime. The hairspring was given an initial angularcompression of only about 15°, instead of 45°. Thk

520 REPORT NATIONAL ADVISORY

experiment made it quite evident that the friction wasmainly due to the spring. The friction diminished,M expected, and, moreover, it-became evident that the

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FIGURE17.—Mr-spwdcdibretion. Instrument No. l!H. Capsuleh’o.103. 0.00!2’dfapbragmH“ sf.edbnehlngwltb 0.010”dentfdrubberbetween flangeof buehing and dlapbragm on both eides. Centerdletancq r,-O.011”. Fiber geekek. Stretohd by blowlng breath011 dliaphrwn

magnitude of the frictional lag changed tith the de-flection, due to the greater proportional change in thetransmitted force.

A new set of hairspringswas then obtained, whichshowed a stiflrms of 0.055 g om per radian, instmd ofthe previous type of 0.190 g cm. It is on the goodresults obtained with these winker hairsprings that thecontention was based that the actual hyster=is in thediaphragm proper is of negligible proportions. (Seefig. 18.) The quality of these inatrumente, as far asthe hysteresis is concerned, is coinparabIe with anyof the ordinary high-pressure types. The increasingand decreasing pressu.mreadings are marked by circlesand crosses respectively. The Iag is seen to benegligible.

%me instrument had a tendency $0 change theircalibration with time, This change would be mostpronounced just after the instrument was made up,but the changes would usually go on for severalmonths. It was suspected that this effect was due binsufficient cIamping of the diaphragm. It is seenfrom Figure 1 that the diaphragm is inserted betweenthe cell body proper and a steel gasket. It is obviousthat a slight inaccuracy in manufacture will cause the

COMMITIWE FOR AERONAUTICS

thin diaphragm to be clamped only partially along itsedge.

On introducing soft-and relatively thick capper gas-kets on both sides of the diaphragm instead of thissi@e steel gasket, it was found that this disagreeableeffect was removed. Two cells were calibrated atinteivds for a period of more than half a year as amatter of comparison. The cell employing coppergaskets was entirely superior. This method of clmnp-ing”has been adopted as standard in the FT.A. C. A.pre&ure c-ells. .,

LOW-PRESSURECELLS

The sensitivity of the instrument depends on:(1) The stiEfnessof the diaphragm;(2) The maetification.

As regards the magnification, the only variablo.ekwnen~affecting it is the distance Tobetween the stylus andthe mirror ati. The allowable minimum is largoly afunction of the workmanship, It was found that theinstrument worked perfectly well with this distancomade equal to one-hundredth of rm inch, Beyondthis limit, however, a lag wouId become cmidont andrapidly increase in magnitude, The magni~cation,defied as the ratio at the motion of the lighb~pot on

2.

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FIOUEE18.—Abme0dcaubration. In6tmmmntNo. Ed. Cell No. ~-~.0.MIZ5dfsphram with ~E” brassbusbinswith dautelrubber bdwwn fhn~ofbushingand d!epbragmonbotbsides. New hrdrepring. StretclmdWithheating iron. Adjueted to 0{” of watef

the @m ta the equivalent deflection of the diaphragmcenter, is given for the ~. A. C. A. instruments inTable It

INVESTIGATION OF TEE DLAYHWGM-TYPE PRESSURE CELL 521

Regarding the actmdly observed and the theoreti- on the theory that they might tend to minimize thecalIy expected stiffness (see fig. 20 and Table II), @ect of any radial corrugations which might be

-.—

Figure 20 is very instructive. Curve 1 represent5 the present. The stitbss persistently remained, however,.—

well-knom formula for a sIaok diaphragm.Curve 2 shows the actually obtained stiffness ~,- ygiven as an average of a great number of o S’a+ t

I‘b-sfre!ssof M

i~GWhlprlsqh

t

triaIs. The diaphragm was inserted with &care in a perfectly alack condition. The direct ~ _ p

effect of the soldered center bushing is given ~by the third column of Table II and is, in ~ / A

/ /‘itself, not veqy large. For instance, the 5/16- b ~inch bushing is theoretically responsible for 5 /

/only 21 per cent decrease in the defkction. ~ /It has thus nothing to do with the curioudy %~ / ‘

&&-Veagreat st.iffnees exhibited by the very thin ~ fw i&hfIy / ‘

diaphragms.erveo’ti~

%L-

sfrekhed v ~ membr- 5/~WZ

It will be noticed from F- 20 that the ~ ~membrcme

A . !/ - --thinnest diaphragm is not the most flexible. ~ l~i

i/ -

k fact the 0.004-inch membrane is ahnost 2 s=;&R#: . ~ -

!! o~ &’- -

as flexible as the 0.00125-inch. I?retiousIy, . .mthe author had been of the opinion that this @-

m .Wlhicknessof o@#rqw hches

effect was caused by small irregularities in FIGUBE21.-StiLbweaof the N. A. C. A. stend?xddlephragmsfzm

the diaphragms and that such irregularities Nom.-CurYe1sbowathetheoretIeaImInhnnm,curve4 tbe tbeordid msrbnmn of9tIKnem.

constituted an inherent quality of the thin diaphra~ I at not less than seven times the expected minimumand. as such. were bevond control. SeveraI means value.wek tried o~t in ord~r to “soften” the diaphragms I As

-1

Pmssqe, inchesofwafer

FIUUBE1%-ti+peedsdIbrstim.titroment No. 149. Low= _ No. O-MO. ~-~ ~ ~t BW=4 Wv==hd. 0.W4”dfmhwm U“ brrwbneblns.TWOmm= s=~e~. Sblus o.o~ fromeater. AdjustedtOIS”OfWS&. m ti~

without much success. It was thought that a ve~ i The

a substantiation of the calculated direct tiectof the center busbing, the author measured thesensitivity of a ceU containing a 0.002-inch dia-phragm with a very smalI center bushing. Anincrease in sensitivity of 15 per cent wasexpected. The resndt showed, however, thatit was doubled. This unexpected and greatlysurprising discovery furnished the expkmation.The “corrugations” were not a quality of thediaphragm mat&al, but were a necessary ccm-sequence of the method of mounting the centerbushing. The busbing is soldered on. Themelting point of the solder is around 300° centi-grade. This means that the diaphragm is subjectto considerable radial stretching in a directiontoward the center, the amount be@ proportionalto the size of the busling and to the differenceof the normal temperature and that of themeIthig point of the connecting metaI used.

What actually happens in the case of the thindiaphraa= is that it does not retain its originalshape, but assumes a “star” shape. H the edgeof the diaphragm is laid out on a phne it is nota straight line, but assumes a zigzag form. Thisremdt was followed up by the tA of a 0.002-inch diaphragm with no center bushing. Thatis, the bushing still was used but it was screwedon with rubber gaskets on each side of the dia-phragm, not being in any direct contact with thediaphragm proper. The calibration showed,beyond suspicion, that the contention was correct.sensitivity was increased five times. One and

.—

-.

I Onqumter inch~ of watir was needed for a deflec-good initiaI stretching might tend to-soften the dia- ,phragm. AIao, circumferential corrugations were tried , tion of the diaphragm of 0.00385 inch, or S= 324

.—.-~

sWoo-W~

522 REPORT NATIONAL ADVISORY

inches of water per inch dehotion, which vaIue ismuch closer to the theoretical minimum of 176.(See fig. 20.)

CONCLUSIONS

In this investigation, it is shown that pressure celkused for pressures above 3 to 4 inches of water can bemade independent of temperature effects for all pra~tical purposes. The serveral factors aflectkg theaccuracy of pressure cells, namely, temperaturedependency, aging eflect, internal hysterwis, magni-fication effects, and the physical properties of thindiaphragms, have been separately studied and methodsof compensation devised. The production of goodpressure cells for pressures below 3 to 4 inches ofwater is still, however, a matter of considerablemechanical dii%culty.

LANGLEY %IEMORIAL AERONAUTICAL LABORATORY,

NATIONAL AnVISORY COMMI~EE FOR AERONAUTICS,

LANGLEY FIELD, VA., Februury 3, 1931.

C~ FOR AERONAUTICS

REFERENCES

1. Norton, F. H.: N. A. C. A. Recording Air Speed .Vcter.l?. A. C. A. Technical Note No. 64 (1921}.

2. Love, A, E. ~.: A Treatise on the ?&thomatiotd Theory ofElasticity. Third edition, Cambridge University Press,P. 450 (1920),

3. Stewart, C. J.: llodern Developments in Aircraft Instru- ‘ments. The Journal of the Royal Aeronautic&l Society,No. 210, Volume XXXII (June, 1928).

4. Hersey, hf. D.: Diaphragms for Aeronautic Iuetrumenta.N. A. C. A. Technical Report No. 165 (1923).

5. FuUer, C. E., and Johnetq IV. A.: Af)pIied Mechanics,Volume 11. John W’iley & Sons (Inc.), New York (1919).

TABLE I

TABLE OF MAGNIFICATION OF THE N. A. C. A. STANDARD PRESSURE CELL

p?ablegivesthe ratio ofthe travel ofthe Ilght beamon tha Clmto the actonl dlsplawmentof the stylus]

Canta dfshnca rtOnfnehes) -.a010

+

c.015 flmo O.cco am. —

2-een~mt ........................................ .................- Soc aaa::E

la7l-eelfim*ent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..- 8% 42)Unoh distanceas u.wdin multlpfemamme~--------------------------- 005

2104W E m m

TABLE II

DIAPHRAGM DATA FOR THE N. A. C. A. PRESSURE CELL

TiI;c&ee

pbragm

Imhe9

a m125amaoo4

EO%xii!keedge clamped

N;cmtrgal

09176

1,410

87

L%i

Obearvede.tMneMat mm deflactlon TheOre4ntlffnes9at

—

●

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