Volume 106, Number 1, January–February 2001

Journal of Research of the National Institute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 106, 25–46 (2001)]

The Kilogram and Measurements

of Mass and Force

Volume 106 Number 1 January–February 2001

Z. J. Jabbour and S. L. Yaniv

National Institute of Standards and

Technology,

Gaithersburg, MD 20899-0001

zeina.jabbour@nist.gov

This paper describes the facilities, measurement capabilities, and ongoing research

activities in the areas of mass and force

at the National Institute of Standards and

Technology (NIST). The first section of the

paper is devoted to mass metrology and

starts with a brief historical perspective

on the developments that led to the

current definition of the kilogram. An

overview of mass measurement

procedures is given with a brief discussion

of current research on alternative materials for mass standards and surface profiles

of the U.S. national prototype kilograms.

A brief outlook into the future possible

redefinition of the unit of mass based on

fundamental principles is included. The

second part of this paper focuses on the

unit of force and describes the realization

of the unit, measurement procedures,

uncertainty in the realized force, facilities,

and current efforts aimed at the

realization of small forces.

Key words: force; kilogram; mass; uncertainty.

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

1. The Kilogram and Mass Measurements

1.1 The Unit of Mass

From the early history of humankind to modern times,

mass measurements have formed the corner stone for

trade and commerce. The use of weights and balances as

tools to perform mass measurements for trade dates

back thousands of years and is most likely associated

with the early civilizations of the Nile Valley and the

Middle East. Since those times, mass standards and the

technology of balances and mass measurements have

greatly evolved to meet the growing and changing needs

of society. The activities of everyday life have always

been affected either directly or indirectly by mass

measurements. Whenever one buys groceries, takes

medication, designs a bridge, space shuttle, or airplane,

trades goods—whether grains, gold, or gemstones—

mass plays a crucial and vital role. In addition to the

direct impact on trade and commerce, mass measurements impact the scientific community as well as a

broad range of manufacturing industries including

aerospace, aircraft, automotive, chemical, semiconductor, materials, nuclear, pharmaceutical, construction,

and instrument manufacturing. To ensure equity and

equivalence in trade and manufacturing at the national

and international levels, uniform standards are needed.

While mass standards have been in existence for thousands of years and some countries had rather controlled

policies on weights, uniformity was not guaranteed

across boundaries and sometimes not even within the

boundaries of one country. In the United States, the unit

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Journal of Research of the National Institute of Standards and Technology

of mass was the avoirdupois pound, and many standards

were brought over from England to the colonies to serve

as standards for trade. However, this did not form a

robust system and non-uniformity remained a major

issue. The United States government formally recognized this need and empowered Congress to “fix the

standards of weights and measures” in the Constitution

of the United States. Many attempts at adopting a

uniform system of weights were made. It wasn’t

until 1875 that the United States along with 16 other

countries signed the Meter Convention that established

the foundations of the International System of Units (SI)

that would finally provide the long sought after uniformity in the standards of weights and measures. A

detailed account of the history of weights and measures

in the United States can be found in Ref. [1].

The foundation of the SI lies with the 1791 decision

of the French National Assembly to adopt a uniform

system based entirely on the unit of length, the meter,

defined at the time as being equal to one ten-millionth

of the length of the quadrant of the earth meridian. The

unit of mass would be the mass of a cubic decimeter of

water at 4 C, the temperature of maximum density.

Based on these definitions, a prototype meter and kilogram were manufactured and deposited in the Archives

of the French Republic in 1799 forming the basis of the

presently adopted SI. The prototype kilogram became

known as the Kilogram of the Archives. In 1875, the

Meter Convention founded the “Comite ́ International

des Poids et Mesures” (CIPM), which took the responsibility of manufacturing replicas of the meter and kilogram prototypes, and the “Bureau International des

Poids et Mesures” (BIPM) whose function would be to

serve as the custodian of the prototypes, carry out future

international comparisons, and serve as the center for

disseminating the metric system. In 1878, three 1 kg

cylinders, KI, KII, and KIII, made of 90 % platinum—

10 % iridium alloy were ordered from Johnson Matthey

in England; they were delivered in 1879. They were

polished, adjusted, and compared with the Kilogram of

the Archives by four observers in 1880 at the Observatory of Paris. The mass of KIII was found to be the

closest to that of the Kilogram of the Archives. KIII was

placed in a safe at the BIPM in 1882, was chosen by the

CIPM to be the International Prototype Kilogram, and

was ratified as such by the 1st “Conference Generale

des Poids et Mesures” (CGPM) in 1889. In 1901, the

3rd CGPM in Paris established the definition of the unit

of mass: “The Kilogram is the unit of mass; it is equal

to the mass of the International Prototype of the Kilogram.” The International Prototype Kilogram is often

referred to as “IPK” and is frequently designated with

the Gothic letter K. In 1884, 40 replicas of the kilogram

were delivered from Johnson Matthey; they were compared to the mass of the IPK in 1888. In 1889, 34 of

these replicas were distributed to the signatories of the

Meter Convention who requested them. Calibration

certificates accompanied the replicas with mass values

based on comparisons with the IPK. These replicas

were in turn used by the different countries as national

standards. At that time, the United States was allocated

two Pt-Ir prototype kilograms, K20 and K4. K20 arrived

in the United States in 1890 and was designated as the

primary national standard of mass. K4 arrived later that

same year and was assigned as a check standard to

monitor the constancy of K20. Over a century later,

K20 and K4 still hold their respective positions. The six

remaining replicas were kept at the BIPM to serve as

check standards for IPK. In addition to the original 40

copies, more replicas were constructed to serve the

growing needs of the international community. In 1996,

the U.S. acquired a new prototype kilogram, K79.

Since its foundation in 1875 and until 1973, the BIPM

used two equal-arm mechanical balances: the Bunge

balance that was in service between 1879 and 1951 and

the Rueprecht balance that served the BIPM’s needs

from 1878 until 1974 [2]. In 1970, the National Bureau

of Standards (NBS), predecessor to NIST, donated a

1 kg balance, known as NBS-2, to the BIPM. NBS-2

was designed and developed at NIST to allow for the

simultaneous measurement of six 1 kg standards. The

unique constant-load, double-knife-edge design allowed

metrologists to achieve state-of-the-art resolution and

repeatability [3]. NBS-2 was used for the calibration of

1 kg standards at the BIPM between 1973 and 1992,

replacing the Rueprecht balance that was nearing 100

years of age. Currently the BIPM uses state-of-the-art

balances that are either commercially available or developed at the BIPM.

The unit of mass is only available at the BIPM. Therefore, the prototypes serving as national standards of

mass must be returned periodically to the BIPM for

calibration either on an individual basis, which could

be done anytime, or as part of a simultaneous recalibration of all the prototypes known as “periodic verification.” Since the existence of the prototypes there has

been only three such periodic verifications. The latest

one, the third periodic verification, took place between

1988 and 1992. For it, the IPK was used with the NBS-2

balance. The results of the third periodic verification

demonstrated a long-term instability of the unit of mass

on the order of approximately 30 g/kg over the last

century [4]; this instability is attributed to surface

effects that are not yet fully understood. Mass standards,

including IPK and its replicas, are stored in ambient air;

therefore, their surfaces are subject to the adsorption or

absorption of atmospheric contamination resulting in a

gain in mass over time; they also may lose mass from

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usage. The BIPM has developed a recommended

method [5] for cleaning platinum-iridium (Pt-Ir) prototypes to remove surface contaminants and restore the

artifact to its original state. In 1989, the CIPM interpreted the 1901 definition of the kilogram [6]. The interpretation, which does not imply a redefinition of the

kilogram, refers to the kilogram as being equal to the

mass of the IPK just after cleaning and washing using

the BIPM method.

In 2001, the kilogram remains as the only SI base unit

defined by an artifact and thus is constantly in danger of

being damaged or destroyed. In addition, the definition

of the kilogram makes no provision for either the artifact

surface parameters or for any environmental storing

conditions. Environmental effects combined with wear

and other material and surface properties constitute the

most probable reason for the observed instability in

mass over time. The instability in the definition of the

kilogram propagates to other SI base units that are tied

to the kilogram such as the ampere, mole, and candela.

It also propagates to derived quantities such as density,

force, and pressure. Therefore, the impact of the

instability in the unit of mass spans a broad range

of applications in the scientific and engineering

sectors.

While comparisons of nearly identical 1 kg mass

standards can be performed with a relative precision of

10–10 with commercially available balances and with

10–12 with special balances, it is clear that the limitation

in the field of mass metrology lies within the artifact

definition itself. Therefore, the ultimate need for mass

metrology is to redefine the unit of mass in terms of a

fundamental constant of nature. At the same time, it is

also crucial to pursue more stable and ideal artifacts and

transfer standards, as this will be, at least for the foreseeable future, the only practical dissemination tool.

1.2 Mass Measurement

1.2.1 Cleaning and Handling of Mass Standards

Mass standards are typically stored and used in

ambient air; therefore, they accumulate contaminants

and must be cleaned occasionally to restore them to their

original mass values. Cleaning policies and protocols

depend on the artifact material and can vary greatly

among laboratories.

The internationally accepted cleaning method of the

platinum-iridium prototypes is known as “the BIPM

cleaning method” and it is described in Ref. [5]. This

method was developed at the BIPM between 1939

and 1946; it evolved from years of experimentation on

cleaning methods that included using a variety of

solvents. The currently used BIPM method consists of

rubbing the artifact with chamois cloth that has been

soaked in a mixture of equal proportions of ether and

alcohol. Since the ether and alcohol mixture leaves a

residue, the artifact is then cleaned in a jet of steam from

doubly distilled water. Results show that this procedure

is effective in removing contamination from the surface

[4]. It is worth noting that this method relies on the

human touch and therefore can be highly irreproducible.

NIST follows this protocol to clean the national

standards of mass K20, K4, and K79 when necessary.

All other NIST mass standards and those submitted for

calibration are generally made of stainless steel and are

subjected to different cleaning procedures, depending

on their size and construction, as described below.

Mass standards made of one-piece construction in the

range of 1 g to 1 kg are cleaned by washing the artifacts

with condensing alcohol vapor, usually referred to as

“vapor degreasing.” Following washing, the artifacts are

allowed to dry and any droplets on the surface are gently

patted dry.

Mass standards larger than 1 kg and all weights of

two-piece construction are cleaned by wiping with

lint-free cheesecloth moistened with alcohol.

Fractional weights (1 mg to 500 mg) are cleaned by

soaking them in alcohol followed by gently patting them

dry.

When mass standards are contaminated with oily

residues, they are cleaned with acetone followed by

alcohol using lint-free cheesecloth. Typically, unless

specified otherwise by the customers, all mass standards

are cleaned before calibration.

After cleaning, weights are allowed to stabilize for a

period of 7 to 10 days before calibration. The stabilization period is determined based on the results of characterization of the stability of mass standards by monitoring the mass of a selected set of weights after cleaning

[7]. Before calibration, weights are stored inside or near

the balance, under cover, for a period of at least 24 hours

to reach thermal equilibrium with the surrounding

temperature. Weights larger than 10 kg require a longer

thermal stabilization period depending on their size.

The handling of mass standards requires special

precautions. Care must always be taken to minimize the

risks of dropping and therefore damaging the surface of

the artifacts. In order to minimize contamination, mass

standards must always be kept in a relatively dust free

environment with appropriate air filtration. When not in

use, mass standards must be kept under a glass bell jar

or other appropriate cover. In addition, mass standards

must never be handled with bare hands. Usually special

handling devices such as tweezers are used to avoid

direct contact. If handling by hand is required, gloves

must be worn. Gloves must be chosen to be powder free

and such that their use doesn’t result in contamination of

the artifact. In addition to contamination, handling by

direct contact with the human body results in change in

temperature that will later require additional thermal

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stabilization time. If handling devices are used, the part

that comes in contact with the mass standards must be

clean, non-abrasive, and non-magnetic. Before calibration, dust particles that could have accumulated on the

surface of the artifacts can be removed by either blowing air using a bulb type rubber syringe or by lightly

brushing with a clean brush.

1.2.2 Density Determination

High precision mass measurements require applying

an air buoyancy correction that in turn requires the

knowledge of the air density as well as the volumes or

densities of the artifacts.

The air density is computed using the internationally

accepted equation for the determination of the density

of moist air [8] from the measurement of the CO2 conconcentration, temperature, barometric pressure, and

relative humidity. All the environmental transducers are

regularly calibrated by the appropriate groups at NIST

and are traceable to the national standards of temperature, pressure, and humidity. The standard uncertainty

in the air density is 0.000 17 kg/m3 based upon standard

uncertainties of the measured temperature, barometric

pressure, and relative humidity of 5 mK, 10 Pa, and

0.5 %, respectively.

Mass standards typically have rounded edges, knobs,

and recessed bottoms, therefore determining the volume

by geometric means is neither very accurate nor practical. Volumes (or densities) are measured using an

immersed balance and hydrostatic weighing systems.

Since both systems require immersion of the weights in

a fluid, all standards must be of a one-piece construction

to avoid introducing fluid into any cavities in the

weights.

The immersed balance procedure developed at NIST

by Davis and Schoonover [9] uses the novel idea of

immersing a modified electronic balance in a bath of

fluorocarbon fluid. Volumes of mass standards in

the range from 100 g to 1 kg are measured by comparison to volume standards, of the same nominal value,

determined to a higher precision by the hydrostatic technique described below. Check standards

are incorporated in the measurements to monitor the

accuracy of the process. The relative combined standard

uncertainty in the density using this procedure

is 0.004 %. Artifacts of other denominations between

100 g and 1 kg, and special requests requiring higher

precision, are performed using hydrostatic weighing

techniques.

The hydrostatic weighing procedure uses silicon

as density reference standards [10]. The use of solid

objects as reference standards for density measurements

was first developed at NIST in 1974 [11]; this method

eliminated the use of water as a density reference

standard and is currently used in most laboratories

where high-precision density measurements are required. The hydrostatic weighing system currently in use

is essentially the same system developed at NIST in

1974 for the measurement of silicon density standards

with an electronic top-loading balance replacing the

mechanical balance. A fluorocarbon fluid is used for

most of the measurements while water is occasionally

used. Check standards are incorporated in the measurements to monitor the accuracy of the process. Mass

determinations in air and in the fluid are done against

NIST mass standards to eliminate errors due to nonlinearity of the balance. The density of the silicon

reference standards used is known with a relative

standard uncertainty of 7.510–7 from hydrostatic

weighing by comparison against stainless steel spheres

whose volumes were measured using laser interferometry [1]. The relative combined standard uncertainty

in the density using the hydrostatic system is 0.001 %.

Typically for large weights (above 1 kg), the density

of a sample of the same material is measured. The

sample should preferably be from the same bar and cut

from a location as close to the weight as possible to

minimize any effects due to nonhomogeneity of the

material.

For weights smaller than 100 g and for all weights

made of two-piece construction, either the manufacturer’s stated density or the density supplied by the

customer is used.

A new, fully automated hydrostatic density measuring system based on silicon spheres as reference

standards is currently being developed. A new system

for measuring the density of artifacts in the range from

2 kg to 10 kg is also under development. Both systems

are expected to be in operation by 2002.

1.3 Dissemination of the Unit of Mass

While the unit of mass is defined at the one kilogram

level, the mass scale must be realized over a range broad

enough to be of practical use in commerce and manufacturing. The first stage in the realization of the mass

scale is to disseminate the unit from the International

Prototype Kilogram to the national standard followed by

a transfer to a set of working standards at the one kilogram level. This is followed by dissemination to multiples and submultiples of the kilogram covering the range

from 1 mg to 27 200 kg. The traceability from the International Prototype Kilogram to the multiples and submultiples of the kilogram is shown in Fig. 1. The procedures involved are discussed in the following sections.

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1.3.1 Dissemination From the International

Prototype Kilogram to the National

Standards

The link between the SI unit of mass and the U.S.

national standard of mass is maintained through periodic

calibrations of the national standard at the BIPM. The

U.S. national standard of mass, K20, was calibrated at

the BIPM six times during its lifetime, the latest calibration being in 1999 when it was calibrated against the

BIPM working standards using a commercial electronic

balance. K4, the U.S. check standard, was calibrated

at the BIPM three times. Table 1 shows the dates of

calibration along with the masses reported on the

calibration certificates of the U.S. prototypes from the

BIPM. The combined standard uncertainty (coverage

factor k = 1) ranged from 2 g to 4 g. The densities

of the prototype kilograms K20 and K4 have been measured at the BIPM using hydrostatic weighing techniques with water as a reference standard; the measured

values are 21 539.14 kg/m3 and 21 531.77 kg/m3

,

respectively with a relative standard uncertainty

estimated at 0.003 %[13].

The masses reported in Table 1 are obtained after

cleaning and washing of the prototypes using the BIPM

method. When the prototype kilograms are not cleaned,

a correction to the “after cleaning” mass is applied. This

correction is based on a model developed by the BIPM.

Based on this model, a platinum-iridium kilogram gains

1.11 g per month for the first 3 months after cleaning.

The rate of change of mass then decreases to approximately 1 g per year [4].

1.3.2 Dissemination to the Stainless Steel

Secondary Standards

The U.S. unit of mass is traceable to the IPK through

the primary national standard of mass, K20. The mass

unit is first transferred from K20 to a set of secondary

stainless steel (SS) kilogram standards manufactured

from nonmagnetic SS alloys with nominal density of

8000 kg/m3

, polished surfaces, and chamfered edges.

Prior to the mass calibration, the densities are determined using the hydrostatic weighing method with

silicon reference standards, as described above.

Fig. 1. Traceability of mass measurements to the SI unit of mass.

Table 1. Year of calibration and masses reported by BIPM for the

U.S. prototypes

Year K20 K4

1889 1 kg – 0.039 mg 1 kg – 0.075 mg

1937 1 kg – 0.021 mg

1948 1 kg – 0.019 mg

1984 1 kg – 0.022 mg 1 kg – 0.106 mg

1992 1 kg – 0.021 mg

1999 1 kg – 0.039 mg 1 kg – 0.116 mg

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The standards are cleaned after the density measurements by vapor degreasing and are allowed to stabilize

before calibration as outlined earlier. Subsequent cleaning is performed only if a weight has been subject to

unusual contamination. A commercially available and

fully automated electronic 1 kg mass comparator with a

resolution of 1 g is used. This comparator is equipped

with a weight-handling mechanism that allows for the

simultaneous measurement of four mass standards of

equal nominal mass, which in this case is 1 kg. Figure 2

shows K20, K4, and two stainless steel kilogram

standards inside the balance during calibration. K20 and

K4 are cylindrical weights while the knob weights are

the stainless steel secondary standards. Since a balance

is essentially a force transducer that measures the net

vertical forces acting on an object, the balance reading

reflects the difference between the gravitational and

buoyant forces; if the balance is calibrated and the

sensitivity is measured [14], the balance reading allows

for the determination of the mass value. Typically, mass

measurements are performed by comparison weighing

involving a reference R and an unknown X:

mR – aVR = CR (1)

mX – aVX = CX (2)

where mR and mx, VR and Vx, CR and Cx denote the mass,

volume, and balance reading for the reference R and

the unknown X, respectively while a refers to the air

density during the measurement.

Comparing the above two equations by taking the

difference allows for the determination of the value of

the unknown:

mX = mR – a(VR – VX)–C (3)

where C = CR–CX, and the assumption was made that

the air density a does not change during this comparison. Equation (3) represents the simplest and most

fundamental mass measurement process. It is evident

from Eq. (3) that the air buoyancy correction is proportional to the difference in volumes between the reference and the unknown. Therefore, the comparison of

two artifacts of different volumes such as a 1 kg weight

made of Pt-Ir and a 1 kg weight made of stainless steel

Fig. 2. The national standard of mass K20, K4, and secondary

stainless steel standards inside the balance during measurement.

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results in a buoyancy correction of 94.2 mg assuming an

air density of 1.2 kg/m3, a volume of 125 cm3 for a

stainless steel kilogram, and a volume of 46.5 cm3 for

a Pt-Ir kilogram. In order to minimize any effect of

balance nonlinearity, small weights with total mass of

approximately 94 mg are added to the stainless steel

kilograms. The stainless steel kilograms are calibrated in

pairs, denoted X1 and X2, against the national standard

K20 while K4 acts as a check standard. The small added

masses to X1 and X2 are represented by z1 and z2,

respectively. Difference measurements Yi are obtained

with all possible combinations between all four

standards; this results in six differences:

The (+) and (–) signs in the above matrix indicate the

order in the difference measurement: (+) and (–) for

observation Y1 indicates a measurement of the difference between K20 and K4 where K20 is measured first.

Therefore, the above matrix translates into the following

equations after taking into account the buoyancy correction:

Such a series of difference measurements is known as

a weighing design. This particular weighing design is

referred to as a 4-1 design indicating that it involves four

weights of equal nominal mass. Fixing the value of one

of the standards allows one to solve this system of equations using the method of the least squares [15]. In this

case, the mass of K20 is known from the calibration at

the BIPM and is therefore used as the restraint:

mK20 = R . (7)

These weighing designs have been developed at NIST

by Cameron et al. in 1979. A full description can be

found in Ref. [15]. Such measurements allow one to

determine the masses of the unknown standards X1 and

X2 as well as K4 from linear combinations of the mass

differences Y1, ........ ,Y6 and the value of the restraint as

described in Ref. [15] after correcting each mass difference for the buoyancy correction associated with the

standards involved [16].

Since the mass of K4 is known from a calibration at

the BIPM, the determination of its mass here serves as

a check of the accuracy of the process as discussed

below.

The difference in the geometry between the Pt-Ir and

stainless steel standards results in a difference in the

relative locations of the center of mass. This results in a

change in the measured mass that is proportional to the

gravitational gradient over the range between the locations of the two centers of gravity. The gravitational

correction is given by:

1 kg 1

g

g

h (h) (8)

where h represents the distance between the centers of

mass of the two artifacts being compared, g is the acceleration of free fall, and g

h is the gravitational field

gradient. In order to quantify this correction, the gravitational gradients as well as the absolute acceleration of

free fall at the location where the mass calibrations are

performed were measured by the National Geodetic

Survey to be [(3.3510–6

)(0.0610–6)] s–2 and

(9.800 998 610–7

) m/s2, respectively. For h = 1 cm,

which is typical, the gravitational correction is 3 g.

The combined standard uncertainty in the mass of a

secondary stainless steel kilogram is computed from the

basic equation for mass determination [Eq. (3)] based

on the ISO Guide for the Expression of Uncertainty

in Measurement [17], resulting in the following

contributions:

a) Air density: the uncertainty component due to air

density is proportional to the difference in volume

between the two standards being compared. It is

evident here that the dominant component is due to

the large difference in volume 80 cm3

) between the

Pt-Ir and secondary SS kilograms. This uncertainty

component is uair = 13.3 g for an uncertainty in the

air density of 0.000 17 kg/m3

.

b) Balance: the uncertainties due to repeatability and

reproducibility are computed in accordance with

the model developed by C. M. Croarkin using the

procedures outlined in Ref. [18]. In this case,

ubalance = 2.3 g.

c) Reference, K20: this component is taken from the

calibration certificate of K20 supplied by the

BIPM; ureference = 4 g based on the 1999 calibration

certificate.

Observation (1) (2) (3) (4)

K20 K4 X1+z1 X2+z2

Y1 + –

Y2 + –

Y3 + –

Y4 + –

Y5 + –

Y6 + –

(mK20 – a1VK20) – (mK4 – a1VK4) = Y1 (1)

(mK20 – a2VK20) – (mX1 – a2VX1 + mz1 – a2Vz1) = Y2 (2)

(mK20 – a3VK20) – (mX2 – a3VX2 + mz2 – a3Vz2) = Y3 (3)

(mK4 – a4VK4) – (mX1 – a4VX1 + mz1 – a4Vz1) = Y4 (4)

(mK4 – a5VK4) – (mX2 – a5VX2 + mz2 – a5Vz2) = Y5 (5)

(mX1 – a6VX1 + mz1 – a6Vz1) – (mX2 – a6VX2 + mz2 – a6Vz2) = Y6 (6)

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d) Added masses: uncertainty in the small masses

added to the stainless steel kilograms to compensate

for the large difference due to the buoyancy correction. The uncertainty in the 94 mg as obtained from

previous calibration against NIST standards is given

by uadd-mass = 0.1 g.

e) Volume of standards: this component of the uncertainty, uvolumes, is due to the uncertainty in the volumes of the reference K20 and the unknown weights,

X1 or X2. This uncertainty component is negligible

when the air densities at the time of calibration and

the time of use of the standards are comparable [19].

f) Other less significant uncertainty components not

included in the above list are: utemperature, due to possible errors in the temperature volume expansion

coefficients and ugravity, from the gravitational corrections.

The combined standard uncertainty is given by

U=u 2

air+u 2balance+u 2reference+u 2add-mass+u 2volumes+u 2temperature+u 2gravity. (9)

When all the uncertainties mentioned above are included, the combined standard uncertainty of the mass

of a secondary stainless steel standard kilogram is found

to be 14 g (coverage factor k = 1).

The secondary standards are used as reference

standards in the calibration of the working standards at

the 1 kg level. The calibration procedure is similar and

uses the same automated comparator. However, since

the secondary and working standards have similar

volumes, the buoyancy correction is very small. Therefore, the need for added masses is eliminated and the

uncertainty in the buoyancy correction is minimized.

The major contributions to the uncertainty become

the uncertainty in the reference standard used,

ureference = 14 g and the combined repeatability and

reproducibility of the balance, ubalance = 2.3 g. The

combined standard uncertainty in the 1 kg working

standard is therefore computed to be 14.2 g.

1.3.3 Dissemination to Multiples and Submultiples

of the Kilogram

Two sets of stainless steel working standards at the

kilogram level are used to disseminate the unit of mass

to multiples and submultiples of the kilogram. These

standards have similar properties as the secondary

standards. At NIST, mass measurements traceable to the

national standard of mass are regularly performed in the

range from 1 mg to 27 200 kg. Typically, weights

come in sets consisting of weights of various denominations. For example, a 1 g to 1 kg set consists of the

following weights: 1 kg, 500 g, two 200 g, 100 g, 50 g,

two 20 g, 10 g, 5 g, two 2 g, and 1 g. Weighing designs

were developed to allow one to transfer the unit of mass

from the kilogram to other denominations while optimizing the number of measurements and the statistical

uncertainty. The protocol used for the calibration of

such a weight set is illustrated in Fig. 3. Starting with the

first series, four weights of nominal mass of 1 kg are

used: (1) 1 kg NIST reference standard, (2) 1 kg check

standard, (3) 1 kg unknown, (4) a 1 kg unknown sum

denoted by 1 kg consisting of a combination of 500 g,

two 200 g, and 100 g. Six observations are made using

the following difference measurements:

In this case, the restraint is on the reference 1 kg

weight in position (1).

The second series consists of difference measurements among 6 weights: (1) 500 g, (2) 200 g, (3) 200 g,

(4) 100 g, (5) 100 g, and (6) 100 g consisting of a

combination of 50 g, two 20 g, and 10 g. In this case, the

restraint is placed on the sum of the weights in positions

(1) to (4); this summation is known from series 1;

weight (5) serves as a check standard while (6) serves as

the restraint for the subsequent series. In this case the

following difference measurements are performed:

A complete description of the weighing designs for

the calibration of mass standards can be found in Ref.

[15]. NIST check standards are incorporated into each

Observation (1) (2) (3) (4)

1 kg 1 kg 1 kg 1 kg

Y1 + –

Y2 + –

Y3 + –

Y4 + –

Y5 + –

Y6 + –

Restraint +

Observation (1) (2) (3) (4) (5) (6)

500 g 200 g 200 g 100 g 100 g 100 g

Y1 + –– –– +

Y2 + –– – + –

Y3 + – – + – –

Y4 + – –– –

Y5 + – –– –

Y6 + – + –

Y7 + – – +

Y8 + – + –

Restraint + + + +

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series of measurements, and a NIST reference standard

is only used at the starting series; the tie to the subsequent series is provided by the measurement of the

unknowns as determined from the previous series.

Similar procedures are used for calibration of the

multiples of the kilogram. The observations are corrected for air buoyancy as well as temperature before

the masses are calculated using the least squares

method [15].

Since most mass standards in use are made of stainless steel of similar density to that of the NIST working

and check standards, the uncertainty in the buoyancy

correction is negligible. Therefore the major contributions to the uncertainty are (1) the uncertainty in the

reference standard and (2) the combined repeatability

and reproducibility of the balance. Uncertainties due to

the volumes of the unknowns cannot be included due to

the correlation between the measurements at the time of

calibration and at the future time of use of the standard

[19]; this component can be added later by the customer

based on the value for the air density at the time of

calibration of the weight at NIST and at time of use by

the customer. Figure 4 shows the combined standard

uncertainties and relative combined standard uncertainties plotted against mass values in the most commonly

used range from 1 mg to 5000 kg. The “V-shaped”

curve is a characteristic of a mass calibration uncertainty curve since the smallest uncertainty is at the 1 kg

level where the unit is defined and the uncertainty

increases as the unit is disseminated to multiples and

submultiples of the kilogram. The curve representing

the estimated industrial needs is derived from the

tightest requirements in legal metrology and contacts

with customers.

Fig. 3. A schematic description of the weighing designs used in the dissemination to submultiples of the

kilogram.

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1.4 Statistical Process Control

Statistical process control procedures are incorporated into the measurements to monitor the precision

and accuracy of the calibration process and form the

basis of the measurement assurance program for mass

calibrations. Measurement assurance programs have

been pioneered at NIST since the 1960s [20] with some

concepts, such as check standards, dating back to the

earlier days of NBS in 1926 [21]. Such procedures have

been applied to mass calibrations since 1979 [15]. Only

a brief summary is given below.

For each measurement series, the standard deviation

of the least-squares fit to the data is calculated

and compared to the accepted standard deviation of the

balance using F-test statistics [15]. The accepted

standard deviation of a balance is the pooled standard

deviation based on a very large number of measurements collected over a long period of time. By monitoring the scatter of the data obtained in the weighing

design measurements, the F-test monitors the precision

of the measurement process. The validity of the F-test

relies on the assumption that the scatter of the data

is typical of the scatter obtained from previous measurements using the same balance. Control charts are

maintained for all the balances used in the calibration

services. For each series of measurements, the standard

deviation is calculated and compared to the accepted

value that is normally obtained from a pooled standard

deviation of multiple measurements. Such control charts

monitor the performance of the balance; for example, a

continuously increasing standard deviation indicates a

possible degradation of the balance.

Check standards are mass standards with known or

“accepted” mass values. Check standards are incorporated into weighing designs; they are treated as unknowns and their masses are measured and compared to

accepted values using T-test statistics. Monitoring the

measured mass of an artifact of known mass monitors

the accuracy of the measurement process. The validity

of the T-test is based on the assumption that the mass of

the check standard does not change from its accepted

value.

Accepted values for the standard deviations of the

balances and the check standards are obtained from

yearly updates of control charts. More frequent updates

are performed if judged necessary from any unusual

results. A control chart for a particular check standard

consists of the measured values as a function of time

with a computed accepted value and statistical control

limits. Control charts monitor the stability and/or drift

of mass standards as well as abrupt changes that would

indicate possible damage. Such control charts are

maintained for check standards covering the full mass

scale covered by the calibration services.

Fig. 4. Standard uncertainty of mass calibrations at NIST. Also plotted on this graph is the estimated industry

requirement in mass metrology.

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1.5 Facilities

Electronic mass comparators, fully and partially

automated, are used for calibrations in the range from

1 mg to 10 kg, while mechanical balances are used to

cover the range between 10 kg and 27 200 kg. Partial

automation refers to the automation of the data collection from the comparators and from the transducers

monitoring the environment, as well as the automatic

analysis of the collected data; full automation also

includes the remote operation of the comparators [22].

The environmental conditions in the calibration laboratories are such that the relative humidity is set between

40 % and 50 %with variations of no more than 5 % per

24 h and the temperature is set between 20 C and 22 C

with maximum variations of 0.5 C over a period of

12 h. Electrostatic filters are used to insure proper

cleanliness with 97 % filtration efficiency.

A special area is dedicated to the calibration of large

weights between 30 kg and 27 200 kg using mechanical

balances. The temperature is maintained between 21 C

and 23 C with maximum variations of 1.5 C per 12 h.

This special area was designed to allow for the receiving, handling, and shipping of large weights and lacks

any humidity control.

A clean room facility with tight environmental

control houses a state-of-the-art, fully automated and

remotely operated 1 kg, 100 g, and 10 kg comparators.

The environmental conditions are such that temperature

is controlled to within 0.1 C at a temperature between

20 C and 22 C and the temperature gradients are less

than 0.1 C over an elevation of 1 m. The relative humidity is controlled to within 2 % at a relative humidity

between 45 % and 50 %. Cleanliness of class 1000 is

accomplished with a HEPA filtration system with

99.99 % efficiency for particles of size 0.5 m or

larger.

NIST also maintains facilities for hydrostatic [10,11]

and immersed [9] solid density measurements and for

the characterization of the magnetic properties of mass

standards [23].

1.6 Alternative Materials for Mass Standards

Efforts are currently underway to develop and

manufacture alternative mass standards to minimize the

uncertainty due to the buoyancy correction, the major

contribution to the uncertainty. Two of the methods for

minimizing this uncertainty are to minimize the difference in volume between the mass standard and unknown

or perform measurements in vacuum. Since the behavior

of mass standards under vacuum is not yet fully

understood and is not practical as a dissemination

method, methods to minimize the difference in volume

have been investigated. This requires using a material

whose density is close to that of platinum-iridium.

Tungsten with a density of 19 300 kg/m3 satisfies this

criteria and reduces the uncertainty associated with the

air buoyancy correction to 1 g. At the time of publication of this paper, the possibility of machining a

surface of tungsten to an average surface roughness of

100 nm using chemo-mechanical polishing techniques

have been demonstrated [24]. Stability tests of such

artifacts is planned for the near future.

1.7 Characterization of the Surfaces of Mass

Standards

In an effort to understand the stability of mass

standards, we have characterized the surface roughness

and profiles of our national prototype kilograms K4 and

K79 using noncontact surface profiling and optical

microscopy techniques. K4 and K79 are representatives

of the two existing types of surface finish for primary

platinum-iridium kilograms. K4 is one of the first

40 replicas made; it was hand polished. K79 is representative of the newer family of Pt-Ir kilograms manufactured at the BIPM turned using a diamond tool. A

summary of the results is provided here. For a more

detailed account of the work, see Ref. [25].

1.7.1 K4

K4 is one of two mass standards originally allocated

to the United States. The second mass standard, K20, is

the national standard of mass in the United States. Both

K4 and K20 belong to the original group of 40 prototype kilograms. All 40 kilograms were manufactured

from the same alloy and by the same process. It is

believed that the surface of K4 is representative of the

surfaces of the original national mass standards.

The machining lines on K4 are visible to the naked

eye. In addition, a few scratches are notably present on

the flat and cylindrical surfaces and have been historically reported [19]. Optical microscope profiles reveal,

in addition to the machining lines and numerous random

scratches, wear lines due to usage on balance pans for a

period spanning over more than a century. These lines

can be seen in Fig. 5 as short line-segments perpendicular to the machining lines. Using a white-light

scanning interferometer, we have measured average

roughness values, Ra, ranging from 63 nm to 84 nm at

different locations on the flat surfaces of K4 excluding

the center. The repeatability in a single measurement

location of the average roughness is 1 nm. A detailed

mapping of the surface of K4 can be found in Ref. [25].

It is worth noting that in spite of the peculiar surface

texture that K4 exhibits, its mass, relative to IPK, has

only changed by 41 g between calibrations at the

BIPM in 1889 and 1999. We are currently in the process

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of reexamining the surface of K4 after cleaning at the

BIPM with the hope of shedding some light on the

effects of cleaning on surface characteristics and possibly finding at least a qualitative correlation between

changes in surface characteristics and changes in mass

for platinum-iridium standards.

1.7.2 K79

K79 was acquired by NIST in 1996. It was manufactured at the BIPM in 1986 by turning with a diamond

tool. To the naked eye, the surface of K79 looks very

specular in comparison with K4. When K79 was placed

under the microscope, the improved surface quality was

obvious, yet, some peculiarities were found.

The surface roughness was measured with a phasemeasuring microinterferometer. The average roughness,

Ra, ranged from 10 nm to 15 nm at different locations on

the flat surfaces of K79 with repeatability of 1 nm for

a single measurement location.

In addition, the optical microscopy profiles show

evidence of increasing grain size with increasing

distance from the center, as shown in Fig. 6. The

origin of this nonuniformity in grain size is still under

investigation and is most likely attributed to the interaction between the platinum-iridium artifact and

the diamond tool or to Pt-Ir material properties.

Only a few wear marks were observed compared to the

surface of K4.

While it is commonly believed that the prototype

kilograms with improved surface properties obtained

from diamond turning are more stable than the ones

hand polished, long-term history is not yet available to

support this hypothesis.

1.8 Current Efforts for an Alternative Definition of

the Unit of Mass

Efforts to replace the artifact kilogram definition with

one based on an invariant of nature have been ongoing

for years and have been a challenge to the scientific

community. These efforts are based on two approaches:

mechanical electrical measurements, and atom

counting.

The mechanical electrical measurement approach,

which uses what has become known as a “moving-coil

watt balance,” is described in detail in this issue by

Elmquist et al [26]. The main concept is to compare a

power measured mechanically in terms of the kilogram,

meter, and second to the same power measured

electrically using the Josephson and quantum Hall

effects. This links the kilogram to one of nature’s time

invariants, the Planck constant h. One can thus consider

defining the kilogram in such a way as to fix the

value of h and to use a watt balance to implement the

definition and to directly calibrate standards of mass.

The atom counting approach aims at relating the

mass of an atom to the kilogram. Within this framework, two paths can be taken:

a) Count the number of atoms in a macroscopic object

of known mass. This is the basis of the “silicon”

project [27]. The main concept is to relate the mass

and volume of a 1 kg single crystal sphere of

silicon, lattice spacing of a unit cell of the silicon

crystal, mean molar mass of the silicon atoms in the

sphere, number of atoms in a unit cell, and the

Avogadro constant. This approach determines

the Avogadro constant and hence the mass of the

carbon 12 atom in kilograms.

Fig. 5. Optical microscopy profile of the bottom surface of K4 near

the edge revealing machining lines and wear marks.

Fig. 6. Optical microscopy profile of K79 at the center showing the

non-uniform grain size distribution.

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b) Buildup a macroscopic object atom by atom while

counting the number of atoms as they accumulate.

In one approach currently being pursued, gold ions

from an ion beam are deposited on a target [28].

When the total current is measured in terms of the

Josephson and quantum Hall effects, and the target

is weighed, the result is a value of the Avogadro

constant and again the mass of the carbon 12 atom

in kilograms.

None of these approaches has been able to rival the

present artifact definition yet. However, competing with

the present definition requires achieving a minimum

level of precision on the order of 110–8

.

1.9 Conclusions

The instability and the continuous risks associated

with the artifact definition have far reaching consequences. Any change in the kilogram directly affects

other related base units, fundamental constants, and

derived units such as density, force, and pressure. While

the ultimate goal remains to replace the artifact definition with an invariant definition, a goal that is hopefully

no longer far out of reach, artifact metrology remains an

integral part of mass metrology. Understanding the

stability of the artifact definition will, for the near

future, remain a crucial factor since no matter how the

unit will be realized in the future, the dissemination

system will most likely rely on artifacts.

2. Force Metrology

2.1 The Unit of Force

The General Conference on Weights and Measures (CGPM) ruled in 1901 that force is derived from

the basic units of mass, length, and time. In 1960, the

11th CGPM adopted the newton as the unit of force

in the International System of Units (SI), where one

newton is the force required to accelerate a mass of one

kilogram to one m/s2

, expressed in terms of SI base units

as kg 	 m 	 s–2

. At a given location, the force exerted by

an object on its supporting structure can be computed

from the mass of the object and the free fall acceleration

of gravity provided that there are no other vertical forces

acting on the object.

Although force is a derived unit, it is of such importance that almost all of the national measurement

institutes (NMIs) of the countries participating in the

Treaty of the Meter maintain facilities for its realization

and dissemination. Indeed, accurate force measurements

are required in almost all industries. For example, such

measurements are critical when testing mechanical

structures such as bridges, buildings, aircraft, and

medical prosthetics. Force measurements are required

to calibrate the testing machines used to evaluate the

strength of materials, to assure quality control in

production lines, to measure the thrust of engines,

and to certify load cells used in weighing systems.

2.2 Force Realization at NIST

Over the range of 44 N to 4.448 MN, NIST realizes

discrete static forces by suspending weights of known

mass in a known gravity field. In addition, a hydraulic

machine capable of generating forces up to 53 MN is

available for calibrating large capacity force transducers

through comparison with secondary force transfer

standards maintained by NIST.

2.2.1 The NIST Deadweight Machines

To cover the range of 44 N to 4.448 MN, NIST developed six deadweight machines in which discrete forces

are generated by deadweights. The characteristics of

these deadweight machines are given in Table 2. The

traceability of the primary force standards at NIST to

the fundamental SI units is shown in Fig.7.

The deadweights of all NIST deadweight machines

are made of stainless steel. This material was chosen

because of its well-known long-term stability.

Moreover, the working mass standards used in the NIST

Mass Laboratories to calibrate deadweights are also

made of stainless steel. Therefore, the transfer errors

associated with air buoyancy adjustments are minimized. The particular alloy used for each deadweight

machine is listed in Table 2. The design principle

involved in the three smallest and the larger NIST

deadweight machines are shown in Figs. 8 and 9,

respectively.

With the exception of the 27 kN (6.1 klbf) machine,

the NIST deadweight machines are fully automated.

Further, except for the 27 kN and the 4.448 MN

machines, all are equipped with environmental chambers to allow for the characterization of load cells as a

function of temperature in a range of –10 C to 40 C.

Today all NIST deadweight machines are able to apply

forces in ascending and descending fashion. Originally,

actuation of the deadweights of the 113 kN and 2.2 kN

deadweight machines was such that the weight frame

needed to be unloaded from the device under test, permitting only return-to-zero loading sequences [29].

During the automation of the force laboratory in 1989,

this limitation was overcome by installing pneumatically

operated stabilizing mechanisms on these two machines, enabling their deadweights to be changed while

the frame is loaded without incurring either excessive

wear on the deadweight seats or swinging of the weight

frame. These mechanisms retract from the weight frame

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shafts after each deadweight change. Ascending and

descending force sequences can now be applied in these

machines. The automation of the NIST deadweight

machines has been fully described in Ref. [30].

Table 2. Characteristics of the six NIST deadweight machines

Capacity,

kN 2.2 27 113 498 1334 4448

(klbf) (0.505) (6.1) (25.3) (112) (300) (1000)

Min. load,

kN 0.044 0.44 0.89 13 44 222

(klbf) (0.01) (0.1) (0.2) (3) (10) (50)

Min. increment

kN 0.022 0.22 0.44 4.4 44 222

(klbf) (0.005) (0.05) (0.1) (1) (10) (50)

Compression setup space:

Vertical (m) 0.25 0.61 0.76 1.02 1.65 1.98

Horizontal (m) 0.29 0.47 0.50 0.71 0.91 0.86

Tension setup space:

Vertical (m) 0.56 0.76 0.91 2.16 2.49 4.45

Horizontal (m) 0.29 0.64 0.66 0.71 0.91 1.17

Alloy of weights

AISI series 302 302 302 410 410 410

Density of weights at 20 C

kg/m3 7890 7890 7890 7720 7720 7720

2.2 kN (505 lbf) Deadweight Machine

Air-powered cylinders manipulate lifting bars that

allow the individual deadweights to be applied or

removed from the main shaft of the machine at any time

during the measurement.

Fig. 7. Traceability of NIST primary force standards to fundamental units.

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Fig. 8. Design principles of the 2.2 kN, 27 kN, and 113 kN deadweight machines.

Fig. 9. Design principles of the 498 kN, 1334 kN, and the 4448 kN deadweight machines.

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27 kN (6.1 klbf) Deadweight Machine

Hydraulic cylinders raise and lower the deadweights

individually onto the main shaft, usually only while the

machine is in the unloaded position. When the required

deadweight complement is selected, the main shaft

is positioned to allow force application to the unit-undertest. Limited ascending and descending loading is possible in this machine under special circumstances.

A unique feature of this deadweight machine is that

nominal metric forces can be applied by activating an

auxiliary deadweight set. This deadweight machine is

operated manually.

113 kN (25.3 klbf) Deadweight Machine

Each deadweight is positioned by a pair of hydraulic

cylinders. These cylinders allow application or removal

of the deadweight to the main shaft at any time. A

manually placed set of auxiliary metric conversion

deadweights is available for this machine, which produces nominal forces in 4.903 kN increments up to

107.873 kN. These conversion deadweights are used

only in nonautomated measurements.

498 kN (112 klbf) Deadweight Machine

Calibration forces are generated in this machine by

serially applying deadweights from two different stacks.

The minimum force is 13.3 kN (3000 lbf) which consists of the calibrated frame and main shaft of the

machine and is always included as the first applied force.

All other applied forces must be added to this minimum.

The main stack consists of ten 44.4 kN (10 000 lbf)

deadweights. The second stack consists of nine 4.44 kN

(1000 lbf) deadweights. The deadweights are removed

or added to the minimum 13.3 kN (3000 lbf) frame in

increments of 4.44 kN (1 000 lbf). An examination of

the available deadweight combinations reveals that in

some cases it is necessary to unload part of the small

stack in order to reach a particular ascending force

without first overshooting it.

1.33 MN (300 000 lbf) Deadweight Machine

All deadweights in this machine are applied sequentially with no further individual manipulation possible.

The deadweights are of three different sizes. There are

thirteen 44 kN (10 klbf) deadweights, four 89 kN

(20 klbf) deadweights and three 133 kN (30 klbf) deadweights. This arrangement allows the sequential calibration in ten equally spaced increments of nominal 444 kN

(100 klbf), 890 kN (200 klbf), and 1.33 MN (300 klbf)

force transducers.

4.45 MN (1 000 000 lbf) Deadweight Machine

This deadweight machine simply applies twenty

222 kN (50 000 lbf) forces sequentially. The main lifting frame raises hydraulically to pick up additional

deadweights in the stack. This machine has been fully

automated.

2.2.2 Weight Adjustment

When the force laboratory was built in 1965 the force

measurement unit in English speaking countries was the

pound force (lbf). Accordingly, in 1965, a decision was

made to adjust the mass of the weights of the deadweight machines to exert nominal pound forces; the

standard pound force being defined as the force acting

on a one-pound mass in a gravitational field for which

the acceleration of free fall is 9.80665 m/s2

. The actual

mass required to produce a nominal force was computed

from the following equation:

F = mg

9.80665 m/s2 1–

a

w

, (9)

where F is the generated standard pound force, m is the

mass of the weight in lb, g is the local acceleration of

free fall at the elevation of the center of gravity of the

weight in m/s2

, a is the air density, and w is the density

of the weight material. The uncertainties in the determination of m, a, and g are the principal sources of uncertainty in the realized force.

The mass of each weight of the NIST deadweight

machines was determined in the Mass Laboratories of

the National Bureau of Standards (NBS), the predecessor of NIST. These calibrations were performed in 1965

prior to the assembly of the deadweights in the

machines. Over the years some of the deadweights were

recalibrated in the Mass Laboratories.

The 498 kN deadweight machine was partially disassembled in 1971, and again in 1979 and in 1989, with

most of its deadweights removed and recalibrated each

time. Any changes in the mass of the deadweights of the

small and large weight stacks were well within the

assigned uncertainties. The 2.2 kN deadweight machine

was completely refurbished in 1996, and all of its deadweights were removed and recalibrated at that time; the

changes in the mass of the weights were again well

within the stated uncertainties. The results of the recalibration of the weights indicate that, as expected, the

alloys used in both the smaller and larger NIST deadweight machines are very stable over time.

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For each of the larger machines, the value of g was

estimated at the approximate center of gravity of the

major components and at the center of gravity of the

deadweight stacks. The gravity reference is located on

the concrete slab in Room 129 of the first floor of

Building 202 at the NIST site in Gaithersburg, MD,

where the deadweight machines are located. A second

site located in the basement of the same room, approximately 9 m laterally and 2.2 m below the first site, was

chosen to establish a permanent reference point for

absolute determination of the acceleration of free fall by

gravity meter measurements. The assigned value of g at

this location is (9.801018510–6

) m/s2, this value is

based upon an absolute determination conducted by

Tate in 1965. All other gravity values are based upon a

gravity gradient of –0.000003 m/s2 per meter elevation

[31]. Subsequent gravity surveys conducted at several

locations within the force laboratory by the National

Oceanic and Atmospheric Administration confirmed

the results obtained in 1965, and tied the measured

values to the National gravity base.

During a year, the air density at the Gaithersburg site

may vary over a range of 1.145 kg/m3 to 1.226 kg/m3

.

In 1965, when the facility was built, a decision was

made to use an average yearly value of air density equal

to 1.185 kg/m3

.

2.2.3 Uncertainty in the Forces Realized by

Deadweights

The relative combined standard uncertainties of the

forces realized by the deadweight machines over the

range of 44 N to 4.448 MN incorporate the uncertainties associated with the determination of the mass of the

deadweights, the acceleration due to gravity, and the air

density as follows:

(a) The relative standard uncertainty in the determination of the mass of the deadweights, uwa <0.0003 %.

(b) The maximum uncertainty caused by the use of an

average air density. This is the largest systematic

uncertainty in the applied force and is equal to

0.0005 %. The estimated relative standard uncertainty, assuming a rectangular probability distribution, is uwb  0.0003 %.

(c) The relative standard uncertainty associated with

the variation in the acceleration of free fall with

height, assuming a rectangular probability distribution, is uwc 
0.0001 %.

The combined standard uncertainty in the force realized by deadweight application is computed as

uw = u 2

wa+u 2wb+u 2wc . (10)

using the values listed in (a), (b), and (c) above yields a

combined relative standard uncertainty in the realized

force uw = 0.0005 % [32].

2.3 Comparison Force Calibration

Above 4.448 MN, NIST provides compression calibrations up to 53 MN by comparison with NIST transfer

standard strain gage load cells using a 53 MN capacity

universal testing machine shown schematically in Fig.

10 [33]. For this purpose, NIST maintains a set of three

4.448 MN NIST transfer standards, each calibrated in

the 4.448 MN deadweight machine, and a set of four

13 MN transfer standards each calibrated by comparison with three 4.448 MN transfer standards. In the

range of 4.5 MN to 13 MN, three 4.448 MN transfer

standards loaded in parallel are used, as shown in Fig.

11. The resulting standard uncertainty, computed by

combining in quadrature the uncertainties contributed

by each of the three transfer standards, is estimated at

1.7 kN, constant over the interval. Thus, the relative

standard uncertainty ranges from 0.038 % at 4.5 MN to

Fig. 10. Schematic diagram of the universal testing machine used to

perform compression calibrations in the range of 4.5 MN to 53 MN.

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0.013 % at 13 MN. From 13 MN to 40 MN, three

13 MN transfer standards are used. The resulting standard uncertainty is estimated at 5 kN, constant over the

interval, with relative standard uncertainties ranging

from 0.038 % at 13 MN to 0.013 % at 40 MN. From

40 MN to 53 MN, four 13 MN transfer standards are

used resulting in an estimated standard uncertainty of

5.9 kN, and a relative standard uncertainty ranging from

0.015 % at 40 MN to 0.011 % at 53 MN.

The standard uncertainty, in both absolute and relative

terms, in the forces realized at NIST over the entire

range of 44 N to 53 MN is shown in Fig. 12.

2.4 Instrumentation

2.4.1 Deadweight Machine Control

Instrumentation

As mentioned previously, except for the 27 kN deadweight machine, all NIST deadweight machines have

been instrumented for automated control. With the exception of the mounting and positioning of the force

sensor into the deadweight machine, all machine operations can be done under computer control. Details of the

automation have been described elsewhere [30]. A force

measurement system has two components: a sensing

component normally called a transducer, and an indicating component, called an indicator. For example, if the

transducer is a proving ring, the transducer’s response,

that is the change in diameter as the ring distorts under

an applied force, is indicated by a vibrating reed and a

spherical button mounted on the end of a micrometer.

For strain gage load cells, the change in strain along the

surface of the sensing element is indicated by a change

in the output signal relative to the voltage applied to the

load cell bridge. Only the reading of load cell indicators

has been automated. Accordingly, measurements on

proving rings are performed manually while measurements of most load cells are performed automatically.

The benefits derived from the automation implemented in the Force Laboratories are numerous. They

include the ability to perform measurements with

complex loading sequences, precise control of the

loading time intervals, and more consistent indicator

readings. In addition, evaluations of prototype load cells

involve the determination of the effects of environmental factors on load cell characteristics. For some of these

tests positioning of the load cell in the deadweight

machine is required only once, at the beginning of a test.

The associated equipment required for these environmental tests has also been automated. Thus, the thermal

bath units used to heat and cool the environmental

chamber, and the sensors used to monitor conditions

within the chamber, including the temperature of the

load cell, are also under computer control. These tests,

which typically take several days, can thus be conducted

around the clock without any manual intervention.

2.4.2 Voltage Ratio Instrumentation

The force applied to a load cell produces a change in

the resistive unbalance in the load cell strain gage

bridge. For most load cell measurements performed at

NIST, this resistive bridge unbalance is measured with a

calibrated NIST voltage-ratio indicating system. The

NIST indicating system supplies direct current excitation

to the load cell, through the use of a specially built

power supply which applies DC voltages to the load cell

excitation input leads of 5 V relative to the load cell

ground wire, yielding a 10 V difference between the

leads. This excitation voltage is stable to within 5 mV

over a time period of 15 s. The power supply was designed to switch internally the wires going to the load

cell terminals by means of a computer command, thus

reversing the polarity of the excitation signal to the load

cell. This action makes it possible to cancel out small

thermal biases in the strain-gage bridge and connecting

wires, as well as any zero offsets in the rest of the

Fig. 11. Set up for the comparison calibration of a 13 MN force

transducer.

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indicating system. The switching is not done if the load

cell is not designed to accommodate reversed polarity

excitation. The excitation voltage and the load cell output voltage are sampled simultaneously by an 8.5 digit

computing voltmeter operating in the voltage-ratio

mode; the voltmeter calculates the corresponding

voltage ratio internally and returns that value in digital

form to the computer. The voltmeter is read several

times, with the excitation voltage polarity reversed

between readings; the final voltage ratio is taken as the

average of the voltage ratios measured at each polarity.

The sampling time at each polarity, and the delay after

switching polarity before resuming the sampling, are

specified by the operator through the computer control/

acquisition program. A typical time for one complete

voltage ratio reading is 10 s. This time can be shortened

or lengthened as appropriate for the measurement being

conducted. Calibration of the voltmeters in the voltageratio mode is done by providing calibrated DC voltage

signals simultaneously to both inputs, with the DC

calibrated signals derived from a 10 V Josephson

junction reference voltage array maintained by the

Electricity Division of the NIST Electronics and

Electrical Engineering Laboratory. The NIST Electricity Division calibrates the Force Laboratories voltmeters each year. In the Force Laboratories the calibration of all voltmeters is maintained by monthly

comparison with the voltmeter most recently calibrated

by the Electricity Division. This is accomplished

through the use of two devices: a precision voltage

reference divider having a 100:1 ratio and a load cell

simulator that is stable to within 5 nV/V over a 24 h

time interval.

2.4.3 Uncertainty in Voltage Ratio Measurement

The standard uncertainty associated with the digital

voltmeters used in the NIST Force Laboratories for

voltage-ratio measurement arises from the following:

(a) The uncertainty in calibration of the voltage-ratio of

the voltmeters as determined by the NIST Electricity Division using a Josephson junction voltage

array as a primary standard; the relative standard

uncertainty in the voltage ratio over the range from

1 mV/V to 10 mV/V is

uva 
 0.0002 %.

(b) Differences between voltmeter calibrations performed by the NIST Electricity Division and comparisons to a 10 mV/V reference ratio obtained

with a precision reference divider used in the Force

Laboratories to track the voltmeter drift. The

estimated relative standard uncertainty of these

differences is uvb  0.0003 %.

Fig. 12. Standard uncertainty in the forces realized at NIST.

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(c) The repeatability in measurements for each

voltmeter (made at one-month intervals) of the

10 mV/V response relative to the precision reference divider; the relative standard uncertainty for

an individual voltmeter is uvc = 0.0003 % of the

reference ratio.

(d) The non-linearity in the voltage-ratio measurement

response of the voltmeters in the range of 1 mV/V

to 10 mV/V; the estimated relative standard uncertainty based on Electricity Division data is

uvd  0.0001 % of the reference ratio.

The combined standard uncertainty in the voltageratio instrument is given by:

uv = u 2

va+u 2vb+u 2vc+u 2vd . (11)

Inserting the values given above yields a relative

standard uncertainty for the voltage ratio of about

0.0005 %.

2.5 Procedures

The forces realized at NIST are disseminated to

industry, government, and the research community

through the force calibration services that NIST

provides. The objective in calibrating a force sensor is to

determine the functional relationship between the

applied load and the sensor response. In the Force Laboratory, this is accomplished by applying a series of

well-known forces to the sensor and observing its response on a readout instrument. Many force sensors can

be calibrated in both tension and compression modes

with the responses expected to be somewhat different in

each mode. Due to hysteresis effects, the response may

also depend on whether the loads are applied in ascending or descending order. Accordingly, for any one

sensor, there may be several distinct calibration curves.

Force calibrations at NIST are usually performed

according to the procedures specified by the American

Society for Testing and Materials (ASTM) Standard

Practice E74 [34]. A minimum of 30 forces are applied

during the course of each calibration. These forces are

applied in two or more calibration runs with typically

three positions of the sensor in the deadweight machine

to minimize the machine-sensor interactions [35-36].

The applied forces are selected at approximately every

10 % increment over of the entire calibration range.

Upon request, a device may be calibrated by modified

procedures tailored to meet particular end uses. For

example, additional loads may be added, and the loading

sequence may include both ascending and descending

loads to thoroughly characterize the hysteresis of the

force transducer. To obtain the actual response of the

transducer, the indicator reading observed during a

force application is corrected for the reading observed

without any force application. The calibration curve is

derived by fitting a polynomial to the data using the

method of least squares. The calibration curve is of the

form:

D=A0 +  Ai Fi , (12)

where D is the response, F is the applied force, Ai are the

coefficients yielded by the least-squares fit and the

summation is usually carried to an order of two or three.

ASTM E 74-95 [34] specifies a standard deviation

that is calculated from the differences between the values observed during the course of calibration and the

corresponding values computed from the calibration

curve. This standard deviation is given by:

s =  d2

j

(n–m)

, (13)

where s is the standard deviation, the dj are the differences between the measured and calculated deflections,

n is the number of measured deflections, and m is the

number of degrees of freedom in the polynomial, which

is the degree of the polynomial plus one. This standard

deviation is one of the terms used in estimating the

combined uncertainty as reported in the NIST calibration reports where it is denoted as ur. The uncertainties

contained in ur are ordinarily much greater than the

uncertainty in the applied load. The two major sources

of systematic errors are mechanical misalignment and

load-time effects [35,36]. Complex mechanical interactions between the force sensor and the deadweight

machine can cause bending, shear, and torsional loads to

act in combination with the precisely known vertical

force. In addition, the transducer response is also dependent upon the load history. A detailed statistical analysis

that yields separate estimates of uncertainty arising

from various possible sources of error can be found in

Ref. [37].

The combined standard uncertainty stated in NIST

force calibration reports is computed using the following equation:

Uc = u 2

w+u 2v+u 2r . (14)

where Uc is the combined standard uncertainty as

defined in Ref. [17], uw is the standard uncertainty of the

applied deadweight, uv is the standard uncertainty of the

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calibration of the voltage-ratio measurement instrumentation, and ur is the standard deviation calculated accordingly to ASTM E 74-95. It should be noted that the term

uv applies only in calibrations involving voltage-ratio

measurements performed using the NIST voltmeters.

In addition to performing calibrations, the Force

Laboratory performs pattern evaluation tests of load

cells used in weighing systems, which provide the basis

for the classification by weights and measures officials

of load cell families used in weighing systems. These

tests are performed in accordance with the specifications of the National Conference of Weights and

Measures Publication 14 [38], and a similar international standard, OIML R60 [39], adopted by the

International Organization of Legal Metrology. While

there are some differences between the national and

international standards, they are minimal. Both procedures prescribe deadweight loading tests of prototype

load cells for the linearity, hysteresis, repeatability, and

creep over a temperature range of –10 C to 40 C. In

addition, both require that canister load cells be tested

for atmospheric pressure sensitivity over a range of

95 kPa to 105 kPa.

2.6 Current Force Metrology Research

Two main efforts are now underway at NIST in the

area of force metrology. They include:

a) The development of a research laboratory for the

realization, measurement and repeatable dissemination of very small forces (in the micro- and

nano-newton range) to address the emergent force

measurement needs of a growing class of nanotechnologies, including atomic microscopes,

nanoindentors, and micro-electromechanical

systems (MEMS); and

b) The development of a testing facility to assess the

susceptibility of digital load cells to electromagnetic radiation.

Acknowledgments

The authors gratefully acknowledge the dedication of

T. Bartel, K. Chesnutwood, W. Crupe, S. Ho, J. Keller,

L. Martinez, and R. Seifarth in providing measurement

services of the highest quality to the U.S. Government

and industry. Z. J. J. gratefully acknowledges V. Lee for

the automation of the balances and M. C. Croarkin of

the Statistical Engineering Division of the NIST Information Technology Laboratory for her invaluable contributions to the development and implementation of

statistical process control procedures.

3. References

[1] L. V. Judson, Weights and measures standards of the United

States, a brief history, NBS Spec. Pub. 447 (1963) updated

(1976).

[2] H. P. Chester and P. Vigoureux, eds, The International Bureau of

Weights and Measures 1875-1975, NBS Spec. Pub. 420 (1975).

[3] H. E. Almer, National Bureau of Standards kilogram balance

NBS no. 2, J. Res. Natl. Bur. Stand. (U.S) 76C, 1-10 (1972).

[4] Girard G., The third periodic verification of national prototypes

of the kilogram (1988-1992), Metrologia 31, 317-336 (1994).

[5] Girard G., The washing and cleaning of kilogram prototypes at

the BIPM, BIPM (1990).

[6] BIPM, Proc.-Verb. Com. Int. Poids Mesures 57, 15-17 (1989).

[7] Z. J. Jabbour, Effects of cleaning on mass standards, manuscript

in preparation.

[8] R. S. Davis, Equation for the determination of the density of

moist air (1981/91), Metrologia 29, 67-70 (1992).

[9] R. M. Schoonover and R. S. Davis, Quick and accurate density

determination of laboratory weights, Proc. 8th conf. IMEKO

Tech. Comm. TC3 (1980).

[10] H. A. Bowman and R. M. Schoonover, Procedure for high-precision density determinations by hydrostatic weighing, J. Res.

Natl. Bur. Stand. (U.S.) 71C (3), 179-198 (1967).

[11] H. A. Bowman, R. M. Schoonover, C. L. Carroll, The utilization

of solid objects as reference standards in density measurements,

Metrologia 10, 117-121 (1974).

[12] R. D. Deslattes, Proceedings of course LXVIII Metrology and

Fundamental Constants, Summer School of Physics—Enrico

Fermi, Varenna Italy (1976), Soc. Italiana di Fisica, Bologna,

38-113 (1980).

[13] R. S. Davis, Private Communication.

[14] R. S. Davis, Note on the choice of a sensitivity weight in precision weighing, J. Res. Natl. Bur. Stand. (U.S.) 92 (3), 239-242

(1987).

[15] J. M. Cameron, M. C. Croarkin, and R. C. Raybold, Designs for

the calibration of standards of mass, NBS Tech. Note 952 (1977).

[16] R. N. Varner, R. C. Raybold, National Bureau of Standards mass

calibrations andomputer software, NBS Tech. Note 1127 (1980).

[17] Guide to the expression of uncertainty in measurement, ISO

(1993).

[18] M. C. Croarkin, An extended error model for comparison

calibration, Metrologia 26, 107-113 (1989).

[19] R. S. Davis, Recalibration of the U.S. national prototype kilogram, J. Res. Natl. Bur. Stand. (U.S.) 90 (4), 263-283 (1985).

[20] P. E. Pontius, J. M. Cameron, Realistic uncertainties and the

mass measurement process, NBS Monogr. 163, (1979).

[21] A. T. Pienkowsky, Short tests for sets of laboratory weights, Sci.

papers Bur. Stand. (S-527) 21, 65-93 (1926).

[22] V. Lee, Technical Documentation for the Mass Calibration

Laboratory Balance Automation, NISTIR 6283 (1999).

[23] R. S. Davis, Determining the magnetic properties of 1 kg mass

standards, J. Res. Natl. Inst. Stand. Technol. 100 (3), 209-225

(1995).

[24] E. Paul, Private Communication.

[25] Z. J. Jabbour and C. J. Evans, Surface roughness and profiles of

platinum-iridium prototype kilograms, manuscript in preparation.

[26] R. E. Elmquist, M. E. Cage, Y. T. Tang, A. Jeffery, J. R. Kinard,

R. F. Dziuba, N. M. Oldham, and E. R. Williams, The Ampere

and Electrical Standards, J. Res. Natl. Inst. Stand. Technol. 000

(2001).

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Journal of Research of the National Institute of Standards and Technology

[27] P. Seyfried and P. Becker, The role of NA in the SI: an atomic

path to the kilogram, Metrologia 31, 167-172 (1994).

[28] M. Glaeser, Proposal for a novel method of precisely determining the atomic mass unit by the accumulation of ions, Rev. Sci.

Instrum. 62, 2493-2494 (1991).

[29] R. A. Mitchell, Force Calibration at the National Bureau of

Standards, NBS Technical Note 1227, U.S. Department of

Commerce, National Bureau of Standards, Gaithersburg, MD

(1986).

[30] K. W. Yee, Automation of Strain Gage Load Cell Force Calibrations, Proc.1992 Natl. Conf. of Stand. Lab. Workshop and

Symposium, Washington, DC (1992) pp. 387-391 .

[31] R. D. Tate, Acceleration Due to Gravity at the National Bureau

of Standards, J. Res. Natl. Bur. Stand. (U.S.) 72 (1), 1-20 (1967).

[32] T. W. Bartel, S. L. Yaniv, and R. L. Seifarth, Force Measurement

Services at NIST: Equipment, Procedures, and Uncertainty,

1997 Natl. Conf. of Stad. Lab. Workshop and Symposium (1997)

pp. 421-431

[33] A. F. Kirkstein, Universal Testing Machine of 12-Million lbf

Capacity at the national Bureau of Standards, Spec.Pub. 355

(1971).

[34] ASTM E 74-95, Standard Practice of Calibration of ForceMeasuring Instruments for Verifying the Force Indication of

Testing Machines, ASTM Annual Book of ASTM Standards,

Volume 03.01 (1996).

[35] R. A. Mitchell and P. E. Pontius, Inherent Problems in Force

Measurement, Exper. Mech. 22, 81-88 (1982).

[36] M. Peters, A. Sawla, and D. Peschel, Uncertainty in Force

Measurement, Report of the CCM Working Group Force, PTBTericht MA-17 (1990).

[37] C.P. Reeve, A Statistical Model for the Calibration of Force

Sensors, NBS Technical Note 1246, (1988).

[38] NIST handbook 44, Specifications, Tolerances, and Other

Technical Requirements for Weighing and Measuring Devices,

(1999).

[39] International Organization for Legal Metrology R60, Metrological Regulations for Load Cells, Bureau International for Legal

Metrology, Paris, France (1991).

About the authors: Zeina J. Jabbour joined the Physics

Laboratory at NIST in 1994 as a National Research

Council Postdoctoral fellow. She is currently the Leader

of the Mass and Force Group of the Manufacturing

Metrology Division in the Manufacturing Engineering

Laboratory at NIST. Simone L. Yaniv served as the

Leader of the Force Group from August 1986 through

October 2000. She served as the senior program analyst

in the Director’s Office of the Manufacturing Engineering Laboratory from 1994 to 1995, and as the Deputy

Chief of the Automated Production Technology Division,

the predecessor of the Manufacturing Metrology

Division, from 1995 to 1998. She is now retired.

46