A Primary DeadWeight Tester

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Volume 08 , Number 2, March-April 2 0 0 3

Journal of Research of th e National Institute of Standards an d Technology

[J. Res. Natl. Inst. Stand. Technol. 08 , 35-145 (2003)]

A Primary Dead- Weight Tester for Pressures (0 .05-1.0) M Pa

Volume 08 Number 2 March-April 2 0 0 3

Kamlesh Jain National Physical Laboratory,

N ew Delhi, India

Walt Bowers and James W. Schmidt National Institute of Standards an d Technology,

Gaithersburg, M D 20 8 99-8 360

[email protected]

[email protected]

Recent advances in technology on tw o

fronts, ) the fabrication of large-diameter

pistons an d cylinders with good geometry,

an d 2 ) the ability to measure the dimen-

sions of these components with high accu-

racy, have allowed dead-weight testers at

the National Institute of Standards an d

Technology (NIST) to generate pressures

that approach total relative uncertainties

previously obtained only by manometers .

This paper describes a 35 m m diameter piston/cylinder assembly (known within

NIST as PG-39) that serves as a pressure

standard in which both the piston an d the

cylinder have been accurately dimensioned

by Physikalisch Technische Bundesanstalt

(PTB). Both artifacts (piston an d cylinder)

appeared to be round within ±3 0 nm an d

straight within ± 1 0 0 nm over a substantial

fraction of their heights. Based on the

diameters at 2 0 °C provided by PT B (±15

nm ) an d on the good geometry of the arti-

fact, the relative uncertainties fo r the

effective area were estimated to be about

2.2X10"'(1CT).

Key words: ead-weight tester;

piston/cylinder assembly; piston gage;

pressure measurement; primary pressure standards.

Accepted: anuary 2 1, 2 003

Available online: ttp://www.nist.gov/jres

1. Introduction The pressure tandard n he tmospheric pressure

range t he ational nstitute f tandards nd

Technology (NIST) is presently established using mer-

cury manometers [1-4]. However, recent developments

in he abrication of large-diameter high-quality pis-

ton/cylinder assemblies an d recent advances in dimen-

sional metrology have llowed he pressure measure-

ment community to contemplate primary pressure stan-

dards

that

are

based

on

dimensional

measurements

of pistons an d cylinders whose uncertainties in generated

pressures could approach the best manometers.

The Pressure and Vacuum Group at NIST ha s recent-

ly cquired ne w imensional easurements f high

quality ro m hysikalisch echnische undesanstalt

(PTB) [5,6] ha t were taken from a piston gage with a

history going back about 12 years [7,8]. The ne w meas-

urements have yielded substantially reduced uncertain-

ties or th e effective area compared with th e previous

determinations. This gage ha s a relatively large diame-

te r (=35 m m ) , which means that PTB's stated uncertain-

ty on length measurements (±15 nm ) would allow th e

diameter of each piece to be determined with a relative

standard uncertainty ess ha n .5 x 10"', la). hi s

would ranslate o elative tandard uncertainty n

areaof 1.0x10 ,̂

(lo). Dimensional measurements llow direct determi-

nation of th e effective area of this gage without refer-

ring to another pressure standard fo r its calibration. Fo r

smaller diameter gages th e diameter of th e cylinder is

typically etermined y umbersome rocedure 13 5





invented y ohnson nd ewhall 9] hich s

described y eydemann nd elch 10] nd s

referred to s ontrolled clearance echnique. Other

equally mportant spects or th e ranslation of these

very accurate linear dimensions to an accurate effective

area are that both pieces constituting the present gage

possessed excellent geometry an d there was a relative-

ly small clearance between piston an d cylinder. These

three conditions, ) accurate dimensional measurement

capability from th e comparator at PTB, 2 ) good ge om-

etry of th e rtifact nd ) mall learance llows he

effective area when used as a pressure generator to be

determined ith elative tandard ncertainty u(A)/A«+1.4x10 ,̂(10).

A value or th e ffective re a distilled ro m all he

information n his eport grees with ecent value

obtained ia IST's ltrasonic nterferometer Manomet er (UIM) 11] within 2 .5 x 10"' an d it agrees

within 10" ' f imensional easurements er-

formed at NIST some years ag o [8].

Because NIST's Pressure an d Vacuum Group uses a

reference temperature of 23 °C whereas th e dimension-

al measurements were done at 2 0 °C it was necessary to

obtain an accurate value fo r th e thermal xpansion in

order no t to degrade th e accuracy when operating th e gage at 23 °C . A special oven/cooler w as constructed to

measure th e thermal expansion.

2. Apparatus For th e present measurements we used a piston an d a

close itting ylinder with arge 35 m ) iameters

made by th e Ruska Instrument Corporation'. (See Fig.

1. ) nown within NIST s G-39, oth piston nd

cylinder were made of tungsten carbide. When used as a pressure generator th e ssembly employs conven-

tional design with th e usual floating piston. A n impor-

tant feature of th e gage is that both piston an d cylinder

ar e ashioned ro m ingle blocks of tungsten arbide

rather than relying on bimetallic onstruction. With

careful handling w e expect this feature to provide good

stability over extended periods.

For th e dimensional measurements we relied on th e

relatively ew tate f he rt omparator t TB,

Certain commercial equipment, instruments, or materials are iden-

tified in this paper to foster understanding. Such identification does

not imply recommendation or endorsement by the National Institute

of Standards an d Technology, no r does it imply that the materials or

equipment identified re necessarily the best available or the pur-

pose.

PG39

Cylinder

Piston

Fig . chematic epresentation f he 5 m iston/cylinder

assembly. Both piston an d cylinder ar e made fiom single castings of

tungsten carbide.

Braunschweig Germany, which ha s he apability of

measuring both diameter an d straightness of cylinders using probe ontact echnique with high ccuracy.

Diameters via this omparator were obtained on both

piston an d cylinder [6]. Roundness measurements were

obtained using other equipment at PTB.

Other pecialized pparatus was used or uxiliary

measurements: ) n oven/cooler fo r measurements of

th e thermal expansion coefficient, ii) capacitance meas-

urements between th e piston an d cylinder fo r estimates

of th e revice width, nd iii) ultrasound fo r measure-

ments ofYoung's modulus of th e piston an d cylinder.

Rather than

ttempt to

determine

he

inear expan-

sion coefficient of the tungsten carbide material fo r th e

individual omponents ith aser nterferometry or

example, it was easier to use our expertise in pressure

metrology nd determine he real xpansion oeffi-

cient hrough direct omparison of pressure with

1 36





reference piston gauge. A temperature controlled envi-

ronmental chamber (oven /cooler) was constructed fo r

th e 35 m m piston/cylinder assembly an d base an d w as

used to accurately measure th e thermal expansion coef-

ficient of th e piston/cylinder assembly by placing PG -

39 nside he hamber an d using another piston gage

outside th e chamber as a reference. The chamber w as

capable of better than +0. 005 K stability. The tempera-

ture of th e chamber could be controlled between 10 °C

an d 40 °C using a Peltier element an d could be meas-

ured with a calibrated thermometer to better than +0. 02

K. With the piston /cylinder assembly inside, however,

th e hamber was perated nl y between 5 °C nd

40 °C in order to avoid possible damage to th e piston

an d ylinder. n eneral, onger emperature pa n

yields a mor e accurate expansion coefficient. Thermal

gradients within th e oven were estimated to be less than

+0.1 °C .

For revice idth easurements, apacitance

gauge with +0.1 nF resolution was used to measure th e

capacitance between th e piston an d cylinder in its pres-

sure column. One electrode was attached to th e base of

th e assembly an d electrically at th e same ground poten-

tial as th e cylinder. The other electrode w as connected

to th e to p of th e piston through a small cu p that con- tained a tiny amount of mercury in order to minimize

extraneous non-axial forces on th e cylinder assembly.

The apacitance method s urrently under investiga-

tion within th e Pressure an d Vacuum Group as a means

of measuring th e clearance in other gages.

For stimating Young's odulus, E, he peed f sound n he ungsten arbide iston w as easured

using an ultrasonic pulse launched at one en d of th e pis-

ton. From its reflection at th e other en d an d subsequent

return, he pulse wa s etected nd he otal im e of

flight was measured ro m which he peed of sound was determined. Young's modulus was obtained from

th e speed of sound, c, an d th e density p [12]:

E = pc\ 1 )

Similar measurements were made on th e cylinder.

planes, or four diameters on th e piston an d four diame-

ters on th e cylinder. All diameters were measured near

2 0 °C nd djusted o he eference emperature f 2 0 °C . A full se t of straightness data w as obtained from

both piston nd ylinder using he omparator. See

Fig. 2 .) Roundness data were obtained using a separate

device. (See Fig. 3. )

3.1 Direct Averages W e averaged th e diameters supplied by PT B fo r both

piston nd ylinder, nd hi s yielded values or he

areas of each component at th e reference temperature

2 0 °C :

Aop.2o = '^^p'/4 ̂

an d

7t(35.822 875 + 0 . 0 0 0 032)" m m V 4 ,

(2a)

Ao,2o = 7tA'/4 »7:(35.824 31 8 + 0 . 0 0 0 017)' m m V 4 ,

(2b)

Here D^ an d D^ are th e average diameters of th e piston

an d ylinder, espectively. he mbient ressure 1 atmosphere) ffective re a f he ssembly erived

from these measurements at 2 0 °C is:

' -^0p,20 * " ̂ 0c,20, )/2 = (1007.9251 + 0 . 0 0 1 2 ) mml

(3 )

The uncertainty listed represents a relative uncertainty

of 1. 2 X 1 0 " * (lo) t ambient pressure an d is obtained

from he ype ncertainty ro m he imensional

measurements oot um quared with he variance of

th e mean of th e diameters. (See Tables 1-3.) The type B uncertainties ere dded ogether lgebraically because these could be correlated. This area compares

very favorably with th e area obtained from dimensions

measured by th e NIST Precision Engineering Division

in 1989, (1007. 9 26 + 0. 011) m m ^ @ 2 0 °C [7,8].

3.2 Numerically Integrated Results 3. Characterization From Dimensional Measurements

The PT B measured he piston nd ylinder using

their elatively ne w tate-of th e rt omparator 5].

Diameters were measured long wo directrices tw o

longitudes, 0° to 180° an d 90 ° to 270°) fo r both pieces.

Diameters were obtained at tw o places in both vertical

A ll of th e nformation, bsolute diameters t our

places, oundness races t ive heights, nd traight-

ness traces at eight

angles was pu t together

in th e

form ofwhat is sometimes called a "birdcage" that represent-

ed the piston an d another se t of information to represent

th e cylinder. Cylindrical harmonics were then fit to th e

data n order o obtain nalytic unctions j^z,0) nd

rj,z,6) fo r th e surfaces where z is th e vertical coordinate

1 37





80

70

60

50 E E , 5 4 0 at 'o X

30

20

10

0

Straightness Traces PG-39 Cylinder

-0.8 -0.6 -0.4 -0.2 Deviations, [^m]

0.2 .4 0.6

Fig. 2 . traightness Traces of PG-39. Deviations from straight lines were measured at 0 °, 45°, 90°, 35°, 80°, 225 ° , 270 ° ,

315°, nd 360°. Straightness data were coupled with absolute diameters an d the roundness data to construct the traces in

this figure, which are referenced to an absolute scale.

138





Fig. 3. Roundness Traces of PG-39. Deviations ro m ircles were measured t levations 3.0, 8.75, 7.4,

56.25, an d 72.0 ) m m from th e bottom. Roundness data were coupled with absolute diameters an d the straightness data to construct th e traces in this figure, which ar e referenced to an absolute scale.

an d 6 is th e azimuth angle. Using r^(z,9) an d r^{z,6), a

numerical integration of forces acting over th e surface

of th e piston was performed with Dadson et al.'s work

serving as a guide [13]. These authors divide th e forces

into three categories, ) a basal force acting upward on

th e base of th e piston, 2 ) a vertical component of th e

normal forces acting on th e sides of th e piston if it is

other than

perfectly straight

an d vertical,

an d 3) a force

from viscous ga s flowing upward an d exerting a verti-

ca l drag on the piston.

3.2.1 The Piston Base, A ^ , ^ ^ The base area of th e piston, A f , ^ ^ „ w as obtained by a

numerical integration of th e analytical function rp(z,0):

Aase =-Jr;(0,0)^0 =1007.865 mm^ 4) where rîz = 0,6) is th e piston radius at th e base of th e

piston.

1 39





Table 1. Piston diameters PG-39 f fi 2 0 °C

Z)pi(0°) 3 5 .8 228 3 m m

Dp2(0°) 35.82293 m m

Opi(90°) 3 5 .8 229 0 m m

£>p2(90°) 35 . 82 2 84 m m

1s t Average

2 nd Average

Max. dev.

3 5 .8 228 8 m m

3 5 .8 228 75 m m

0. 00005 0 m m

3 5 .8 228 7 m m

1.40 X 0 m m / m m

Variance s

Variance of mean

/t(68.27%)=1.20

k*s/n

u(d„)

0. 00004 8 m m

0. 00002 4 m m

0. 00002 9 m m

0. 00002 9 m m

1.34

0.67

O .i Type A uncertainty Type B uncertainty

w ( r f p )

0. 00002 9 m m 0 .0 0 0 0 1 5 m m

0. 000032 m m

0.80 0.42

0.91

Table 2. ylinder diameters PG-39 @ 2 0 °C

D,i(0°) 35.82433 m m

Z),2(0°) 35.82432 m m

O,i(90°) 3 5 .8 24 3 0 m m

0,2(90°) 3 5 .8 24 3 2 m m

1s t Average

2nd Average

Max. dev.

35.82433 m m

3 5 .8 24 3 1 8 m m

0 .0 0 0 0 1 5 m m

35.82431 m m

0.42 X 0 m m / m m

Variance s

Variance of mean

/t(68.27%)=1.20

k*sln

0 .0 0 0 0 1 3 m m

0. 000006 m m

0. 000008 m m

0. 000008 m m

0.35

0.18

0.21

Type A uncertainty

Type B uncertainty

0. 000008 m m

0 .0 0 0 0 1 5 m m

0. 000017 m m

0.21

0.42

0.47

Table 3. auge effective area PG-39 @ 2 0 °C

A,s={A ̂+ A,)l2

Area Type A Type B" t o t ( ' 4 e ) =

1 0 0 7 . 8 8 4 5 mm 0 . 0 0 1 6 1 9 mm̂ 0 . 0 0 0 8 4 4 mm̂

1 0 0 7 . 9 6 5 6 mm̂ 0 . 0 0 0 4 2 5 mm̂ 0 . 0 0 0 8 4 4 mm̂

1 0 0 7 . 9 2 5 1 mm̂ 0 . 0 0 0 8 3 7 mm̂ 0 . 0 0 0 8 4 4 mm̂ 0 . 0 0 1 1 8 9 mm̂ 1 . 1 8

1 4 0





3.2.2 Shape Contribution S A ^ 3.2.3 Tiie Flow Contribution d4f The hange n p(z,9) with espect o height ntro-

duces an additional vertical force given by th e follow-

in g equation:

Z7l

^^s=ôj['-;(o.^)-'-;(A0)]d0/2

dn jjP(z)-^r^(z,e)d0dz.

(5 ) dz

Here PQ s th e pressure at th e top, Pi is th e pressure at

th e bottom of th e piston, an d P{z) is th e pressure as a

function ofheight within th e crevice an d L is th e length

of th e revice. The ontribution o he ffective re a

from th e shape of th e sides of th e piston is then:

The flow of ga s up through th e crevice between th e

piston an d cylinder contributes a drag force that m u s t

be accounted. Assuming Poiseuille flow in th e crevice

th e drag force is:

dP(z) 5F , » --J d0Jdzr ̂ ( z , 0 ) -̂ h iz , 0 ) (11)

Numerically integrating Eq . (11) using th e fitting func-

tions rJ(Z,Q) an d r^{z,6) with th e same pressure profile

as in th e previous section an d converting th e results to

fractional area gives:

5Af= 5FAPi -Po ) " +0 .0 449 mml (12)

dA,= dFJ{Pi-P,). (6 )

Numerically ntegrating he erivative f he itting

function, drjdz, s ndicated bove using pressure

profile, P{z), derived from th e Poiseuille flow equation

gives an increase in th e effective area:

&4,~+0.0167 mm ̂ (7 ) with respect to th e area at th e base of th e cylinder. The

pressure rofile as erived ssuming n verage

crevice width at each height

1 z;t hiz) = — \hiz,e)de, (8 )

where th e crevice width is h(z,9) = r^(z,9)-r^{z,9). n

Eq . 5) as ensity inear n ressure as lso assumed. In this case:

P(Z): L, p̂ -if\ z'

Kzf (9 )

where Pi an d /"o ar e th e pressures at th e bottom an d th e

to p of the crevice, respectively. The definite integral 4

is:

The drag force (since it is acting up-ward in this case)

will erve o ncrease he re a of he piston by n

amount of about 44.6 x 10"'.

Adding th e contributions from Eqs. (4), (7 ) an d (12)

gives:

A =^tase + 8A, + 5Af= 1007.9267 mml (13)

3.2.4 Uncertainty in tiie Numerical Integration of The principal uncertainty n he numerical alcula-

tion of ^ b a ^ ^ e , & 4„ & 4f arises from th e uncertainty in th e

dimensional easurements nd he implifying assumptions nvolved n alculating th e pressure pro-

file. A sensitivity check on the integration's dependence

on th e input parameters showed that th e uncertainty in

th e average radius of th e piston, u{r^, produced about a 0.43 X 1 0 " * uncertainty in th e area of th e gauge. A sim-

ilar check of th e uncertainty of th e derivative drjdz ~

0 .4 nm , showed about a 0. 19 x 1 0 " * contribution to th e

uncertainty n he ffective rea. imilar ensitivity

checks on the radius of th e cylinder, r„ an d drJdz, pro-

duced 0.42 X 10"" an d 0.30 x 1 0 ^ shifts in th e effective

area, respectively. With regard to th e calculation of th e

pressure profile, th e simplifying assumption of Eq . (8 )

wa s checked by assuming instead that:

L

':-[ dz' (10) Kz'f

h{z) = max[h(z,9)],

(14)

in Eq . 9) , with th e result that dA/A hanged by about

0. 1 X 1 0 " * mmVmm^. Several integrations were done in

which th e cylinder was rotated with respect to th e pis-

ton. his esulted n mall ifferences, 0 .1 5 x 1 0 " * .

14 1





Moving th e piston an d cylinder's vertical position rela-

tive to on e another by 3. 5 m m , resulted in a .0 x 1 0 ~ *

change in effective area. Root su m squaring th e seven

contributions o he uncertainty n he ffective rea,

namely, u{r^), u{drj(iz), M ( r p ) , u{drj(iz), u{h), u{9p) an d

M ( Z p -Zj.) adds an uncertainty of 1. 2 x 1 0 " * .

Lastly, with regard to th e flow contribution, another

model fo r the flow wa s assumed [14] . This mode l takes

into ccount ransition lo w within he learance nd

generally gives an effective re a slightly smaller than

th e oiseuille lo w odel. hi s lternative odel

resulted n n ffective re a .5 x 10" ' elow he

Poiseuille flow model. The average value of th e effec-

tive area fo r th e tw o models is:

(1007. 9 25 2+ 0. 002 2 ) mml (15)

W e have taken as an uncertainty fo r mode l dependent

crevice ffects, he tandard deviation obtained ro m

th e tw o models which is .8 x 1 0 " * . The uncertainty in

Eq . 1 5) s obtained by ombining he uncertainty of

th e numerical integration, 0 . 0 0 1 2 mm^, with th e flow-

model uncertainty, 0. 0018 mm^ in quadrature.

Note ha t he uncertainty given n Eq . 1 5) would

result in an uncertainty in generated pressure of 2 .2 x 1 0 " * P. his however, does no t nclude uncertainties

from mass loading an d other " in use" effects when used

in a secondary calibration.

Young's modulus nd Poisson's ratio 1 5] or obtained

from alibrations o other gages. W e obtained values

fo r Young's modulus ro m peed of sound measure-

ments on th e piston an d cylinder [12,16]. The speed of

sound w as measured ultrasonically nd ound o be

(6380 + 14 0) m /s or th e piston an d (6580 ± 146) m /s

fo r he ylinder la). ith aterial ensity f 14 X 1 0 ^ kg/m\ Eq . (1 ) yields Young's moduh of (5.70

± 0. 24) X 1 0 " a nd 6.06+ 0. 26 ) x 1 0 " a or he

piston an d cylinder respectively, (Ic?).

Jain et al. derived th e pressure coefficients fo r both

piston an d cylinder fo r this gage using elasticity theory

an d th e thick-wall formula [7]. (In that report th e gage

is eferred o s IST-9.) he y se d alue =

8.0 X 10"'^ Pa"' fo r th e pressure coefficient of th e gage.

No uncertainty was given but values from calibrations

to ther ages ield pread f values etween 2 .8 X 10"'^ Pa"' an d 5.18 x 10"'^ Pa"'. A n axi-symmetric

finite lement odel roduced alue 1 0 +2.0) x

10"'^ Pa"', based on a Young's modulus of 6. 0 x 1 0 " Pa

an d Poisson's ratio 0 . 2 1 8 . If one takes a square distribu-

tion ofvalues fo r b between th e lowest, 2 .8 x 10"'^ Pa"',

an d ighest alues, 0x10"'̂ a"', ne btains he

value:

Z ) = 6.4xlO"''Pa"', 1 7)

where th e standard uncertainty is 2.1 x 10"'^ Pa"'.

4. Auxiliary Measurements 4.1 Thermal Expansion Coefficient For operation of th e gage at temperatures other than

2 0 °C hermal xpansion oefficient or he piston/cylinder assembly's area is needed. With th e spe-

cial environmental chamber constructed to fi t th e gage,

a coefficient was found to be :

a =(8.754 +0.03) xlO"''/K, (16)

where he ncertainty epresents overage actor

{k= 1) . Thus when used near th e Pressure an d Vacuum

Group's eference emperature 3 °C n dditional

uncertainty of only (2 3 °C - 2 0 °C ) x (0.03 x 10^/K) =

0. 09 X 1 0 ^ is incurred.

4.2 Pressure Coefficient For operation of th e gage over th e intended pressure

range, (0.05 to 1.0) MPa, a pressure coefficient is need-

ed . t an be stimated ro m lasticity heory using

4.3 Clearance The learance, , etween he piston nd ylinder

ca n be determined using variety of techniques nd

although they do not provide direct help in reducing th e

uncertainty of th e effective area, based on th e dimen-

sional measurements, hese other measurement ech- niques an provide onsistency hecks on th e dimen-

sional easurements. rimarily, he adial learance

ca n be obtained from th e dimensions of th e piston an d

cylinder, secondly vi a fall-rate measurements an d third-

ly vi a capacitance measurements.

4.3.1 Via Dimensional Measurements The dimensional measurements ea d o n verage

clearance of :

/ 2 D i „ = (A -D^)/2 ~ (0.721+0.016) l^m, 1 8 )

where A n i m is th e clearance. The average diameters D^

an d /)p were determined from direct dimensional meas-

urements an d were listed earlier.

142





4.3.2 Via Fall-Rate Measurements Fall-rate easurements, nterpreted ith he Poiseuille flow equation fo r a uniform crevice [17,18],

were also used to obtain th e clearance:

12 RP^rjL dz

d t (P'-P:) (19)

Here r j is th e viscosity of th e pressure fluid (nitrogen),

R is th e radius of th e piston, L is th e engagement length,

PQ nd Pi are th e absolute pressures at th e to p an d th e

bottom of th e crevice respectively an d dz/dt is th e fall

rate. his ethod as ee n se d y olinar nd

Vatasso [19], by Dolinskii et al. [20] an d by Meyers an d

Jessup [21] .

The fall-rates at several pressures are listed in Table

4. The clearance hpî^ from Eq . (19) is listed in th e 4th

column. These values fo r th e clearance ar e seen to be

about 0 % igher ha n he alues btained ro m

dimensional measurement, j n i m , nd from capacitance

measurements, Q^^. See below.) However, lip-flow

phenomena have no t been aken nto ccount n Eq .

(19). Slip flow ha s been used before in the interpreta- tion f all-rate at a 22] nd an e mportant n

describing lo w n narrow hannels 23]. When lip

flow s aken nto ccount he pparent learance s

reduced by about 10 % :

h Ki

Slip

(i+6i:,„^/:„) ,1/3 (20)

where K ^ ^ ^ ^ is an accommodation coefficient taken to be

1.0 an d K^ is th e Knudsen number,

A an d where X is th e mean free path,

K (21 )

\6( RJ

2KM <P> (22)

Here R^ s he ga s onstant, is he hermodynamic

temperature, M is th e molar mass of th e ga s (Nj), j is

th e viscosity of th e ga s an d <P> is th e average pressure

in th e crevice. When Eqs. 2 0 ) with Eq . 2 1 ) are used

with A p o i s j from Eq . 19), values fo r h ^ n ^ result that are

about 0 . 8 0 0 + 0. 110) im. This s bout 0% arger

than j n im , bu t within he ombined uncertainty of th e

different techniques. Se e Table 4.

4.3.3 Via Capacitance Measurements Lastly, learances er e etermined sing apaci-

tance measurements [24]:

c a p ̂̂p̂ (23)

Here o s he permittivity of th e vacuum, K s he

dielectric oefficient of th e pressure luid nitrogen),

an d C is th e measured capacitance. For th e interpreta-

tion of th e capacitance measurements an ideal ge ome - try w as assumed, as w as th e case fo r th e interpretations

of th e fall-rate measurements using th e Poiseuille flow

model. Minimal efforts were made to shield extraneous

signals from th e capacitance gauge. After transients ha d

subsided, very stable operation was found with th e pis-

to n only in th e column an d pressurized to a value near

4 kPa. The piston was llowed o loat without pin-

ning. Values fo r the capacitance ranged between 91 nF

an d 96 nF. Most of th e time th e piston seemed to self-

center or ong periods s ndicated by he measured

capacitance, which is at a relative minimum when th e piston s entered. ro m im e o im e he values of

capacitance would increase dramatically indicating that

th e piston was drifting off center. When mor e weights

Table 4. all-rate measurements

Absolute

Po (kPa)

pressures

Pi

(kPa)

Fall-rates

dz/dt

(nm/s) ^Poise

(nm)

Clearances

''Slip

(nm)

95.1 19 3 4 54 ±63 93 5 ±130 849 ±120 95.1 19 3 38 5 ±53 8 8 4 ±125 79 9 ±110

10 0 24 1 4 94 ± 69 8 68 ±120 79 4 ±110

10 0 2 85 50 2 ± 70 810±115 74 4 ± 10 5

10 0 42 2 66 5 ± 93 76 2 ±110 71 2 ±100

14 3





were added, some configurations were found to be sta-

ble, hile thers ere nstable. he learances obtained ro m he apacitance easurements er e

found to be :

th e dimensional measurement within heir ombined

standard uncertainties.

Acknowledgments (0.725 + 0 . 0 2 0 ) |im. (24)

This is fo r a pressure of about 4 kP a generated by th e

piston only.

5. Summary

W e thank Dr . F . Ludicke of PT B fo r th e dimensional

measurements, an d Dr. Archie Miiller an d Dr . Charles

Tilford or omparisons ith he IS T ltrasonic

Interferometer Manometer. W e ls o hank Fred Long

fo r help with th e speed of sound an d with th e capaci-

tance measurements an d Jim H ouck fo r guidance in th e

early stages of this project.

W e have characterized a 35 m m dead-weight tester,

known ithin IST s G-39, sing imensions obtained from PTB. A n effective area was obtained by

averaging th e eight absolute diameters, four fo r th e pis-

to n an d four fo r th e cylinder.

In addition a numerical integration of forces over th e

surface of th e piston wa s performed an d yielded a value

about .6 X 1 0 ~ * higher ha n he imple verage. For

this ntegration, Poiseuille lo w was ssumed n he

crevice. A second numerical integration was performed

in which n lternative mode l or lo w was ssumed

[14] . In this case th e effective area was 0 .9 x 1 0 ~ * lower than he imple verage. Averaging he esults of th e

tw o numerical integrations yields an effective area

A ̂= (1007. 9 25 2 + 0. 002 2) mm ̂ (25)

an d is th e recommended value @ 2 0 °C . The tandard

uncertainty given here also covers th e averaged value

obtained from th e eight absolute diameters. For trans-

ferring this haracterization to other gages, uncertain-

ties from other sources will c ome into play an d are not

covered by this uncertainty. For use at temperatures other than 2 0 °C , th e thermal

expansion coefficient fo r th e effective area was meas-

ured n our aboratory n ontrolled nvironmental

chamber nd as ound o e = (8.754 + 0. 03 ) x

10^/K.

For use at higher pressures up to MPa, a pressure

coefficient w as stimated using variety of sources.

The recommended value is

6 = (6.4±2.1)xlO-''Pa- (26)

Auxiliary measurements (based on fall rates an d capac-

itances) were made on th e clearances between th e pis-

to n an d cylinder. These served as checks on th e dimen-

sional measurements. These measurements agreed with

6. References [1 ] . . uildner, . . timson, . . dsinger, nd . .

Anderson, Metrologia 6, -1 8 (1970).

[2 ] . . ilford nd . . yland, roc. I M E KO orld

Congress, Houston, Texas, 988; C. R. Tilford, Proc. Workshop

an d ymposium f he ational onference f tandards

Laboratories, 988.

[3 ] . E. Welch, R. E. Edsinger, B. E. Bean, an d C. D. Ehrlich, High

Pressure Metrology, G . F. Molinar, ed.. Bureau International de s

Poids et Mesures Monographic 89/1 1989) p. 81 .

[4 ] .L . M. Heydemann, C. R. Tilford, nd R. W. Hyland, .Vac.

Sci. Technol. 4 (1), 597-605 (1977).

[5 ] . Neugebauer, F. Ludicke, D. Bastam, H. Bosse, H. Reimann,

an d C. Topperwien, Meas. Sci. Technol. 8, 849-856 (1977).

[6] TB , [Report #5.31-99.148-1].

[7 ] . Jain, C. Ehrlich, J. Houck, an d J. K. N. Sharma, Meas. Sci.

Technol. 4, 24 9 - 25 7 (1993).

[8 ] alph C. Veale, Precision Engineering Division-NIST, Report

of Calibration M3565 (1989).

[9] . P . Johnson an d D. H. Newhall, Th e Piston Gage as a Precise

Pressure-Measuring nstrument, ransactions f he SM E

(1953) p. 304.

[10] . L. M . Heydemann an d B. E. Welch; Experimental

Thermodynamics, Vol. I, B. LeNeindre nd B. Vodar, ds.,

Butterworths, London (1975) pp . 47-201. [11] . Miiller, Private Communication.

[12] . E. Kinsler an d A. R. Frey, Fundamentals of Acoustics, 2 nd

Ed., John Wiley an d Sons, Inc., New York (1962).

[13] . S. Dadson, R. G P Greig, an d A. H om er , Metrologia 1 (2 ) 55

(1965).

[14] . W. Schmidt, Y . Cen, R. G Driver, W. J. Bowers, J. C . Houck,

S. A. Tison, an d C . D. Ehrlich, Metrologia 36 , 5 25 - 5 29 (1999).

[15] . M . Westergaard, heory f lasticity nd lasticity, Cambridge, Harvard University Press (1952) Chap. V.

[16] re d Long, Private Communication.

[17] . L. M. Poiseuille (1840) .

[18] . P. Landau an d E. M. Lifshitz, Fluid Mechanics, Vol. 6, New

York, Pergamon (1959).

[19] F Molinar an d M. Vitasso, High Temp. High Pres. , 59

(1976).

[20] . F. Dolinskii, Loskutov, Polukhin, Measurement Techniques

15 , . 80 Translated ro m zmeritel 'naya Tekhnika , -8

(1972) .

1 44





[21] . H. Meyers an d R. S. Jessup, J. Res. Natl. Bur. Stand. U.S.)

6,(1931).

[22]

.

W.

Schmidt,

S.

A.

Tison,

nd

C.

D.

Ehrlich,

Metrologia

36 , 565-570 (1999).

[23] . F. Berg an d S. A. Tison, AICheE J. 47 (2), 26 3 - 270 (2001) .

[24] . R. Reitz nd F. . Milford, Foundations of Electromagnetic

Theory, 2 nd Ed., Addison-Wesley Publishing Co mp a ny (1967).

About the authors: r. amlesh Jain s he Head of

th e orce nd Hardness tandards roup t he National Physical Laboratory— India and was a guest

researcher at NIST. Walter J . Bowers is a researcher in

th e Pressure and acuum Group with NIST. ames .

Schmidt s esearcher t NIST formerly n he Pressure and Vacuum Group and presently in th e Fluid Sciences Group. he National Institutes of Standards

and echnology s n gency f he echnology

Administration, .S. Department ofCommerce.

145

Documents

A Primary DeadWeight Tester