a primary deadweight tester
TRANSCRIPT
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 1/11
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
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
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 2/11
Volume 08 , Number 2, March-April 2 0 0 3
Journal of Research of th e National Institute of Standards an d Technology
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
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 3/11
Volume 08 , Number 2, March-April 2 0 0 3
Journal of Research of th e National Institute of Standards an d Technology
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
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 4/11
Volume 08 , Number 2, March-April 2 0 0 3
Journal of Research of th e National Institute of Standards an d Technology
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
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 5/11
Volume 08 , Number 2, March-April 2 0 0 3
Journal of Research of th e National Institute of Standards an d Technology
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 straight- ness 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 r^iz = 0,6) is th e piston radius at th e base of th e
piston.
1 39
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 6/11
Volume 08 , Number 2, March-April 2 0 0 3
Journal of Research of th e National Institute of Standards an d Technology
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
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 7/11
Volume 08 , Number 2, March-April 2 0 0 3
Journal of Research of th e National Institute of Standards an d Technology
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=^oj['-;(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
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 8/11
Volume 08 , Number 2, March-April 2 0 0 3
Journal of Research of th e National Institute of Standards an d Technology
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
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 9/11
Volume 08 , Number 2, March-April 2 0 0 3
Journal of Research of th e National Institute of Standards an d Technology
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 hp^i^ 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
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 10/11
Volume 08 , Number 2, March-April 2 0 0 3
Journal of Research of th e National Institute of Standards an d Technology
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
7/28/2019 A Primary DeadWeight Tester
http://slidepdf.com/reader/full/a-primary-deadweight-tester 11/11
Volume 08 , Number 2, March-April 2 0 0 3
Journal of Research of th e National Institute of Standards an d Technology
[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