irSonal Bureau of Standards

| rary, E-01 Admin. Bldg.

NBS TECHNICAL NOTE

436

Studies of Calibration Procedures

For Load Cells and Proving Rings

As Weighing Devices

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U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

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UNITED STATES DEPARTMENT OF COMMERCE

C. R. Smith, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

NBS TECHNICAL NOTE 436

ISSUED JANUARY 1969

Studies of Calibration Procedures for

Load Cells and Proving Rings as Weighing Devices

Gordon B. Anderson

Physical Measurements Section

Calibration Laboratory

White Sands Missile Range, New Mexico 88070

and

Robert C. Raybold

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

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For sale by the Superintendent of Documents, Government Printing Office

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STUDIES OF CALIBRATION PROCEDURES

FOR

LOAD CELLS AND PROVING RINGS AS WEIGHING DEVICES

BY

GORDON B. ANDERSON

Physical Measurements Section

Calibration Laboratory

White Sands Missile Range, New Mexico 88070

AND

ROBERT C. RAYBOLD

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

ABSTRACT

Elastic devices such as load cells and proving

rings, when used with comparison measurement

techniques, yield uncertainties orders of magnitude

smaller than generally accepted. Their use, in direct

reading application, is affected by numerous characteristics of materials, as well as the techniques of

application and interpretation of data. This paper is

intended to present progress made in the evaluation of

calibration techniques, to the end that such transducers may be used with a predictable uncertainty in

direct reading applications. Attempts are being made

to formulate calibration procedures which are consistent with application procedures. The confusion existing in the derivation and application of practical

force units is considered sufficient justification for

a brief discussion of forces derived from mass standards and gravitational acceleration.

Key words: Calibration, force, weighing, load cells,

proving rings, transducers, uncertainty.
INTRODUCTION

A basic precept in metrology is to strive for comparison or difference

measurement. By these techniques, maximum integrity is maintained by the

use of relatively simple measurement techniques. These techniques have

withstood the test of time, and when applied to elastic weighing devices,

the results have been illuminating and gratifying.

Load cells, as a general class of instruments, suffer from numerous

and serious limitations, unless the measurement is designed so as to minimize their limitations and maximize such advantages as a simplicity of

construction, installation and repeatability of electrical and mechanical

response characteristics.

The precision capabilities of quality load cells, when used for

comparison measurements, have been adequately established. For several

years the White Sands Missile Range (WSMR) Calibration Laboratory has given

field support to various projects in the determination of missile weignt

and center of gravity. Project requirements for mass determinations with

uncertainties (systematic error plus three times the standard deviation of

random errors) on the order of 0.05% were met satisfactorily under field

conditions by the use of substitution techniques. The WSMR Calibration

Laboratory in its early days, was part of an instrumentation group, and the use of these techniques was a natural extension of the electrical measurement techniques in daily use. As early as 1958, these techniques were being applied to the design of fixtures for center of gravity

determinations. [1]*. Data presented at the 1964 Large Mass Symposium,

held at the National Bureau of Standards (NBS) , indicated that standard

deviations on the order of 5 ppm are practically obtainable with "off-theshelf" hardware. Subsequently, measurements performed at various other

installations indicate that such standard deviations are practically

obtainable under seemingly impossible environmental conditions, when due care is given to the measurement process.

As a result of knowledge and experience gained from these tests, the

WSMR Calibration Laboratory specification for the "second generation" mass comparator was prepared. The availability of large masses of known accu- racy is rather limited, and NBS was requested to perform the acceptance

tests. The results substantiate the ability of load cells to perform as comparators with standard deviations approaching 1 ppm.

Serious reflection on measurement data obtained immediately raised the

age old question, "How good is this device when used as a direct reading

instrument?". Current production systems claimed "direct reading

accuracies" approaching 0.02%. When given serious thought, such performance could impugn the capabilities of force standards in current use. [2].

Thus, to make use of the direct reading capabilities of current production

load cells, it was thought that a calibration procedure should be developed

which would take all possible advantage of design and mimimize the effects

generally accepted as limitations. It was originally planned to present in one paper a summary of calibration data, the result of evaluation of

characteristics such as loading history, loading rate, creep, hysteresis,

temperature coefficient, temperature gradient, linearity, repeatability,

sensitivity, effect of tare, etc. It soon became apparent that this was a chore of more than considerable magnitude. The decision was made, as time

and material resources permit, to make use of routine calibration data, to

accumulate calibration history, to establish long term stability by study

*The numbers in brackets refer to similarly-numbered references at the end

of this paper.

2
of accumulated data, to verify the validity of the electrical measurements,

to establish uniform methods for treatment of the data, and to study

temperature and pressure effects.

Such an effort seems to be a hopeless task for even the most simple

mechanism, on close examination, becomes a complexity. A load cell, basically, is a simple mechanism, but when one attempts to explain its behavior

in detail it is immediately obvious that many processes are involved, some

of which are at best little understood, more usually misunderstood. To

identify, control and measure each of these would require a tremendously

large and complex research and development effort. Even if such efforts

ware fruitful, there is no assurance that knowledge gained would increase

our ability to measure with these devices. No matter how much valid theory

and associated measure are incorporated into the design, the problem always

remains of determining the constant of the instrument. This is the essence

of the calibration process.

Thus, we feel that a study of the theory of design of transducers

would be of doubtful value. This is better left to the purists. We need

to develop better measurement techniques and to determine how this device

as a system responds to a given set of conditions, so that a meaningful

calibration is produced. The fact that man, after more than 100 years

study, has been unable to explain the behavior of common engineering

materials is not sufficient justification to ignore their capabilities for

practical application. This is not to say that the purist is without a rightful place in instrument technology, but only to say that we should not

subsititue his hoped for creation of an idealized instrument for our efforts to improve utilization of the tools he has already provided us.

To study force transducers for direct reading application, four major

requirements were considered.

a. A precision loading machine with considerable versatility, to enable

us to study the effects of various loading schedules, loading rates,

tare loads, etc.

b. Flexural isolation, to minimize the effects of non-axial loading, and

to provide the ability to "make fixed" or make repeatable any

misalignment present.

c. Transducer instrumentation with sufficient stability, resolution and

linearity to study transducer response without constantly making

"instrument" corrections.

d. Uniformity in the treatment of data.

Industry has developed, and we have acquired equipment to satisfy the

requirements of a, b, and c. Data reduction procedures are formulated and

being updated constantly.

The dead weight loading machines are designed so that load increments

of less than 0.5% of capacity are available. Weights may be applied in any

order, and at a number of different controlled loading rates. The loading

may proceed from one mode to the other (tension or compression) without

disturbing the alignment of the load cell. Tare weight in compression is

essentially zero, while the tare weight in tension is kept below 0.3% at

1000 pounds. By means of the mass comparator, the machine is verified in

its normal operating configuration. Standard weights of known differences

are incorporated into the machine, so that all forces generated are directly compared, removing any uncertainty due to position in the machine.
All calibrations are performed using flexural insolation so that, as far as

is practical, no transverse loading exists. The instrumentation used is of

ratio, or millivolt per volt (mV/V) type. The standard deviation of these

indicators (available competitively) is on the order of 10 ppm.

The verification of the read-outs themselves has pointed out the need

for better electrical calibration techniques. One result has been the

procurement of a network on which any selected ratio is verifiable v/ithin an uncertainty (three times standard deviation for random error plus

systematic error) of 50 ppm and stability is such that the ratio remains

constant within 20 ppm for any one year period. Investigation is

continuing to improve our ability to precisely establish ratios, and such a network appears to have good application in the transfer of ratios among

laboratories. Another side issue evolving from these tests is the use of

mV/V indicators and the mass comparator for intercomparing standard

resistors. First efforts appear to have promise, and standard deviation of

a few parts in 10 7 seem practical.

GRAVITY AND FORCE

Gravitation is generally described as being the mutual action between

masses, by virtue of which every mass tends towards every other mass with a force (F) varying directly as the product of the two masses (mj m 2

) , and

inversely as the square of the distance (d) between their centers of mass. That is:

F a

F =

where k is a constant of proportionality. For a given pair of masses, this

is usually written as: Gm m,

"d 2 F = " ~l ~2

where G is the Universal Gravitation Constant. This is an observable

relationship and the value of G can be determined experimentally. The latest determination, by Heyl [3, 4], yields the value 6.670 x 10"^ 1 Nm 2 /kg 2

. 1 The extremely small magnitude of G indicates that small forces exist between bodies on the earth's surface. However, a fairly large force exists

between the earth and a body near the earth's surface, due to the magnitude

of the earth's mass (m ) . In describing this force, equation 3 is usually

written as: Gm m

F = -ZSZ

*e

where Re is the radius of the eartn.

This force produces an acceleration E (due to aravity) that is

F Gm.

E = - = -Cx

m— R^

e In the International System of Units (SI) , this acceleration has units of

E

_ (Nm 2 kg~ 2

) (kg) . . *

jj-j *- = m/s<

1. Newtons (N), meter (m) , kilogram (kg)

4
wnere s is seconds. Tnerefore, to describe the force of attraction between

the earth and a mass subjected to the earth's gravitational field, equation

4 may be written as

F = k (mE)

Based on the assumption that the earth is a non-rotating sphere of uniform

density, substitution of numerical values for m , G and R will yield a value for the acceleration of

5.975 x 10 21*kg x 6.670 x 10~ 11 Nm2 kg- 2 (6.371 x 10 6 m) 2 Em 9.819 N/kg

For gross calculation, such a procedure is sufficient. However, this

value differs considerably from the value usually associated with local

gravity (g_) due to the fact that tne earth is not symetrical, homogeneous,

or non-rotating. The effect of the centrifugal force due to the earth's

rotation is approximately 0.034 m/s 2 (sea level, zero latitude) and due to

the difference in polar and equatorial radii is approximately m/s 2

. Nonspherical distribution of the earth's mass accounts for approximately half

of this amount so that the total variation in g_ ^s approximately 0.05 m/s 2

. This method of computing local acceleration due to gravity should not be

used in precise force measurements.

Values of £ calculated by the above procedure differ from the values

obtained by the International Gravity Formula (HEISKANEN, 1938)

.

Corrections normally applied to the latter are:

a. Free air correction (inverse square law)

b. Bouguer Correction (to free air correction)

c. Topographic Correction, (non-uniformity of terrain)

Observed values of g_ differ from both of the above, and additionally

are usually corrected to sea level values by applying a and b above.

Generally, there are differences between theoretical values obtained by the

International Gravity Formula and those obtained from reduced observations.

These differences are called free air anomalies and are usually charted as shown in Fig. 1. For practical applications to physical problems, the user

should know which value he is using (theoretical or observed) , and what

corrections are pertinent to his use.

BY applying all known corrections and using refinements to Rater's

pendulum, the 1906 measurement at Potsdam yielded the value of 9.81274 m/s 2 for the acceleration due to gravity at that station. By observing changes

in period, pendulums were used to transfer this value to other stations

throughout the world. A base station for the United States was established

in Washington, D. C. in 1891 by the United States Coast and Geodetic Survey

which serves as the base for all U. S. Pendulum stations.

FORCE UNITS

When dealing with bodies of finite mass, having velocities which are small as compared to the velocity of light, the concept of force implies an agent or a property capable of producing a change in momentum. When force

is thus defined, then force is a derived quantity and is the product of a
mass and acceleration (a) . The product (ma) is taken as a measure of the

force and when we write F = k (ma) , k is an arbitrary constant which

defines the size of the particuTar force unit used, different choices of k

giving different sizes of force units. A simple choice would be k = 1, so that unit acceleration times unit mass produces unit force.

In tne International System of Units, the name of the force unit is

the newton. One newton will accelerate a one kilogram mass one foot per

second per second.

In the English System of Units, the name of the force unit is the

poundal (pdl) . One poundal will accelerate a one pound mass one foot per

second per second.

The newton and the poundal are usually referred to as "absolute" force

units. Unlike the kilogram force and the pound force (as generally used,

where one uses force equals mass) tiieir effect on an object is independent

of position in the universe. Absolute force units always have the physical

dimensions of (Mass x Length) /Time 2 symbolically F = MLT"" 2

. The practical engineering system of units, for very practical reasons,

equates force and mass, and force is reported in mass units. For

structural engineering work this is a convenience. Although dimensionally

unsatisfactory, there is no serious error because a design factor ranging

from two to ten is immediately applied as a safety factor. In this system

of units, force is taken to be numerically equal to mass (F = m) , the implication oeing that a force of one pound will accelerate a one pound mass

g ft/s 2 (where £ is local gravity) . This is a convenient system of units

because weight is obtained directly in mass units, that is, x force units

will accelerate y mass units x/y acceleration units. However, when the

unit of force is the pound and the unit of mass is the pound, k cannot be

equal to 1. If a force is to accelerate a one pound mass g_ ft/s 2

, then it

is obvious that the units are numerically in the ratio:

poundal

pound (force)

or, 1 pound (force) = £ poundals. The pound force is g_ times larger than

the poundal, and this requires the product (ma) to be multiplied by the

factor l/g_. (Some texts introduce a mass unit", the slug, which is numerically £ pounds mass. Tne results, however, are the same.)

As our technology advanced, the need for the precise comparison of

force measurements increased. The variation in the observed value of £

over tne earth's surface created confusion as there was no common reference

of acceleration. In 1901 the International Conference of Weights and

Measures defined the standard value of £ as being 9.80665 m/s2 approximately

32.1739 ft/s 2

. (Tne 1958 definition of the inch makes this value approximately 32.17404 ft/s 2 ). Also in the past years, since engineering applications of force measurements did not require that consideration be given to

variations in the acceleration due to gravity, buoyant forces were of no consequence. However in aero-space applications the relationship of force

and mass becomes critical and demands more exacting measurements; so to

more precisely describe the relations among force, mass and acceleration,

Newton's Second Law for a static case is written as

F = k (m pv)a (1)

where
F is force m is mass

pv is a correction for buoyancy

a is acceleration

k is a dimensionless constant, its numerical value being dependent on the choice of units for F, m, and a.

In the International System of Units (SI) , the unit of force is the

newton and equation (1) is written as:

F = k (m - pv)a (2)

where m is mass in kilograms; p is the density of the air in kilograms per

cubic meter; v is the volume of the mass in cubic meters; a is the acceleration to which the mass is subjected, in meters per second per second;

and k = 1.

In the British Engineering System of Units, the unit of force is the

pound force (lbf) and equation 1 is written as:

F = k (m - pv)a (3)

where m is mass in pounds (lb) ; p is the density of air in pounds per cubic

foot; v is the volume of the mass standard in cubic feet; a is the acceleration to which the mass is subjected, in feet per second per second, and

k = 1/32.17404.

The acceleration in the above equation when due to the earth's

gravitational field is usually determined by comparison measurements, and

tne reported value is based on the Potsdam system. It is generally agreed

that the Potsdam value of 9.81274 m/s 2 is high by about 0.00013 m/s 2

. [5]

Tne policy of the NBS is to use the International System of Units

"except when their use would obviously impair communications or reduce the

usefulness of a report to the primary recipients". The choice of units, as discussed above, should be left to each laboratory as its particular needs

require; however, for the purpose of intercomparisons among laboratories,

the use of the International Units is recommended.

To clarify the concepts discussed above, it may be well to discuss in

detail a typical calibration of an elastic device, such as a high quality

spring scale. For convenience, suppose a mass of 1 kg whose volume is

computed to be 120 cm 3

, is supported in air of density 1.0 x 10~ 3 g/cm 3 and

tne acceleration due to gravity is taken as 9.79108 m/s 2

. The derived force would be, from equation (2):

F = k (m pv)a « 1(1.000000 - 1.0 x 10" 6 x 120) (9.79108) « (0.99988) (9.79108) m/s 2 « 9.78991 newtons
The pointer should now be made to coincide with 9.78991 on the scale,

and the adjusting screw sealed. The scale will now correctly read force,

irrespective of location, as long as the constant of the instrument does

not change.

Suppose that the 1 kg mass were replaced by an object of unknown mass

and that the scale now indicates 9.63025 N, or 9.63025 = (ma) - (pv a)

The indicated force is seen to be the sum of two forces, one due to (ma)

acting downward and one due to (pv a) acting upward.

Now, the user must know what measurement he is trying to make. The

instrument has properly indicated the net downward force. This is the

usual commercial connotation of weighing. If the user wishes to identify

the mass of the unknown object, whose volume is computed to be 240 cm 3

, equation (2) can be written as:

ma = F + (pv) a ma « 9.63025 + (pv) a

or E4$T§t kg + 240 x 10

" 6

^(0.983574 + 0.000240) = .983814 kg

Now suppose that this same object and the scale were transferred to a location where the air density is 1.15 x 10~ 3 g/cm 3 and the acceleration

due to gravity is reckoned at 9.80320 m/s 2

. As before, one would write:

F = k (m - pV) a « (0.983814 - 1.15 x 10~ 6 x 240 )( 9. 80320) « 9.641820 newtons

It is clearly seen that this mass of 0.983814 kg produces a different

force when subjected to a different acceleration.

Again, if the mass were not known, since the resulting force has been

measured, the mass is computed as before:

F = k(m - pv) a or 9.641820 = ma - pv a ma = 9.641820 + 0.000276a m = 9-641820 + 0.000276

9.80320 « 0.983538 + 0.000276 « 0.983814 kg
Finally, suppose that this force indicator were now transported to a location where the air density is 1.15 x 10 -3 g/cm 3

, and the acceleration

due to gravity is 9.80370 m/s , an object of unknown mass, whose volume is

60 cm 3

, is supported as in the previous example and causes the scale to

indicate 8.32720 newtons . Then as before:

F = k (m - pv) a

or 8.32720 « (m pv) a The situation is identical to the one in the previous example; this

object weighs 8.32720 newtons. The mass of the unknown is computed as before; that is

= 8.32720 + L 15 6Q x 1Q

-6 - 9.80320 ~ 0.849436 + 0.000069 = 0.849506 kg

The past practice of the National Bureau of Standards has been to

issue calibration reports relating instrument readings to applied mass, the

derived force beina the product of mass standards and the acceleration due

to gravity at the I ndustrial Building at NBS Washington, D. C.

The results were not stated as pounds force, and it was tacitly

assumed that the user was aware of this fact. As an example, when a 10,000

pound mass was applied as load, some users concluded that the derived force

was 10,000 pounds, when actually the derived force was approximately 9993

pounds force. Failure to properly account for this difference admitted a systematic error of approximately 0.07% 2 into all measurements so referenced.

Systems of units and units of measure are a convenience to the user,

and we find no fault with any system when properly used. Due to custom and

convenience, the pound force remains as the practical unit of force. The

above procedures are applicable, however, regardless of the unit of measure

and if these procedures are used, we will have a common basis upon which to

discuss basic concepts, and the calibration of force measuring instruments.

The procedure adopted by the WSMR Calibration Laboratory is to report

the transducer's indicated output in dial divisions or mV/V per pound of

applied force, the force derived being k (m - pv)a. This is reported in ST and English units, as per equation (3).

CALIBRATION PHILOSOPHY

There are numerous instances of similarity of behavior among

distinctly different classes of instruments. The similarity between the

load cell and the D'Arsonval Movement, dating from 1882, is an example. A

list of all factors affecting performance would be lengthy and also of

doubtful value to the calibration. The effect of many of these factors can

be minimized by good design, but they are not calibrated directly. They

are indicators [6] of performance, and the calibration of the instrument

2. 0.06% gravity correction plus 0.01% buoyancy correction
will include their effect, under the conditions existing at that time. By

observance of good principle in design, craftmanship in construction, and care in use, such an instrument may be made direct reading to perhaps 0.05%

in static applications, and perhaps 2% in dynamic applications. 3 To obtain

this uncertainty, it is not necessary (or possible) to identify and calibrate separately each of the indicants. What is required is a calibration

which will reveal the operation of the instrument under a particular set of

conditions. To take maximum advantage of the capabilities of the instrument, the user should be assured that the calibration process is consistent

with the requirements of his particular application. As an example, the

usual D'Arsonval movement responds to the average value of a rectified sine

wave. Most users want an indication of the root mean squared value, so the

instrument maker scribes the scale accordingly. Now the user need not

worry as to why the meter will properly indicate the root mean squared

value, although an understandina of why may save some embarrassment, but it

is not required for the instrument to operate properly. As the waveform

departs from a sinusoid, the indication will also depart from the calibration, and unless a proper instrument constant is determined, the user will

again be subject to embarrassment. However, the instrument can be

calibrated for this condition of use, but not until the user communicates

with the calibrator.

The same situation exists in the application and calibration of a load

cell. The user must have knowledge of its behavior under a particular set

of conditions. General performance criteria may be established for load

cells as a class of instruments and as a means of standardization. This,

of course, is an economic consideration and one of ever increasing

importance. The aero-space industry is of such diversity that it is altogether proper that the formulation and promulgation of standardized

design and performance criteria be the responsibility of an organization

such as the Instrument Society of America (ISA). Recommended Practice

Guide for Specifications and Tests for Strain Gage Force Transducers for

Aero-Space Testing (RP 37.8) of sub-committee 8A of I SA is representative

of this, and the calibration data contained in the present report is submitted in the light of specific measurement requirements, rather than

attempting to cover a multitude of requirements. I t is submitted with the

hope that it may augment the RP 37.8 in the Formulation of Performance

Requirements (Sec 4), Acceptance Tests and Calibrations (Sec 5), and

Qualification Tests (Sec 6).

As has been previously stated, the effects of hysteresis and metal

creep are generally believed to be the major factors controlling load cell

performance. This may well be true, but the usual measurement process

would be hard put to separate these effects, and could probably not

separate tne two together from the effects of creep (or relaxation) in the

bond, creep in the gage, temperature compensation of the gage, modulus

compensation of the column, and various thermal, mechanical, electrical, or other effects which lack identification. Fortunately, it is not required

that we have knowledge of other than the magnitude of the combined effects,

under a given set of conditions, to produce a meaningful calibration.

Figure 2 represents data recently obtained with a load cell which has

been in service for over twelve years. At the time of purchase, typical

specifications were for linearity and hysteresis not to exceed 0.1% of full

scale. No indication of repeatability or long term stability was given by

the seller and usually there was no such requirement stated by the user.

3. It is interesting to note the superior performance of the same instrument when used in a comparison measurement.

10
Probably the most valuable calibration data obtainable would be

similar to that shown in Ficrure 2. The graph shows the loading cycle and

the output of the transducer.

After repeated application of the load prior to the recording of the

data, the load cell appears to take a set somewhat similar to the behavior

of a single crystal that is stressed beyond the proportional limit. The

fact that the change in output as a function of time may be either positive

or negative is not surprising. The change, as pointed out previously, does

not stem from any one known cause, but is further evidence of a composite

of complexities. The concept of a negative creep in metals is contrary to

observed fact. Possible causes are overshoot in the load, overshoot in the

instrumentation, thermal effects in crage and modulus compensation, or relaxation in the bond.

These data were obtained with a mV recorder at the galvanometer

terminals of a mV/V indicator. The load cell was of 2 mV/V output and 60 00

lbf capacity. The recorder sensitivity was adjusted to be 1 inch

deflection for 3 oz at 6000 lbf or approximately 1/30,000.

Data displayed in this manner readily give an indication of the number

of cycles, under a specified set of conditions, required to obtain a given

precision. Also, such a display gives an indication of the time required

for stability of output at zero and at load, and time required for the span

to stabilize with a particular loadinq history. [7]

.

I t must be emphasized that such data does not necessarily represent

any particular group or class of load cells, but is representative of one

load cell, with some particular history, and then only under a particular

set of conditions of excitation voltage, loading rate, temperature, etc.

This is believed to be representative of what can be determined for any

load cell, if one is willing to take the necessary care in calibration.

What remains to be done is for the user to design his application

procedures in such a manner that a meaningful calibration can be

accomplished

.

11
PRELIMINARY CALIBRATION STUDIES

Since January 1965, WSMR Calibration Laboratory has selected data from

75 calibrations of 21 transducers, 17 of which were calibrated both in

tension and compression. Each load cell was calibrated at 11 load points,

some with 10 and others with 5 observations at a given load. (An

observation is defined as a complete load cycle from zero to load back to zero load) . From the analysis of these data the following conclusions are

drawn:

A. Exercise of the load cell (on the order of 10 times) at 110%

capacity, will establish a stable loop and indicate performance

hysteresis.

B. Tiie first two observations generally show a significantly large

variation and are not included in the computations of the calibration report.

C. After the deletion of the first two observations, four or more

observations are needed to indicate the variability of the

measurement.

This preliminary study also included a 10,000 lbf proving ring and an electronic readout that was calibrated in compression by NBS on October 29,

19 59 and subsequently three times by WSMR Calibration Laboratory. The

calibration data, after adjustment of NBS data for the 0.07% systematic

error, are shown in Table 1. The largest change in calibration was approximately 0.06% of full scale or 6 lbf. An interesting fact is that

the uncertainty of a calibration point based on the random errors of a single calibration was about 0.012% of full scale or 1.2 lbf. The tabular

data shown in Table 1 are the average of repeated observations in dial

divisions adjusted both for instrument (zero) drift and temperature cor- rections as given by the manufacturer.

REPORT OF CALIBRATION

After the loading cycle is established, the transducer is flexed by 10

times to 110% of range. I nformation is recorded for 6 observations at a load point in the following order:

a. The instrument reading at zero load (indicator zero is offset

upscale to be able to observe zero drift)

.

b. The instrument reading at load.

c. Ambient temperature and pressure.

d. The instrument reading at zero load.

Corrected dial divisions are computed from the following equation:

Y -v _ Z

* + Z

1+l

where

12
Yj

j is corrected loaded reading

Xt , is observed loaded reading

Zj is zero reading before load

Z1+1 is zero reading after load

i is the observation number

i is the load point number

The first page of the report of calibration, as shown in Table 2, is

the general calibration information, such as manufacturers serial number,

bridge impedance, bridge voltage, time cycle, loading rate, the corrected

dial divisions and temperature during the observation.

In computing the applied pounds force (lbf) the following equations

and conditions are used at WSMR Calibration laboratory:

Fj = k(m 3 - pVj )a

where

Fj is pounds force at load j

k is 1/32.17404 m

j

is mass of load j in pounds

p is average density at WSMR 0.06 lb/ft 3

Vj is volume of nij [m^ times 0.002 ft 3 /lb]

and a is acceleration due to gravity at WSMR Calibration Laboratory

[32.12296 ft/s 2

]

.

The data were analyzed by the method of least squares with the

following functional form:

d = aF

e e where

d^ is the corrected dial divisions for the e observation

e

a is the least squares coefficient

F is the force in pounds at a given observation e where e is a number representing the order in which the data were taken.

The deviations of the least squares fit and the observed data are plotted in Figure 3. This procedure is used to analyze the departure of

the transducer's output from linearity.

Tables 3 and 4 are the final report of calibration and explanation of

the use of the calibration data. The reported dial divisions are derived

from the average of the last four (or more) readings at a given load point.

The pooled standard deviation is computed from the deviations about this

average.

13
At the present time the data are not adjusted for temperature or pressure effects on the transducer. I t is recognized that corrections for

variabilities from these sources may be necessary to correlate results obtained in an environment substantially different from that of the calibration facility.

Plots such as shown in Figure 3 are used to find patterns in the

deviations and may also be used to determine functional relationships which

better describe the output of the load cell being calibrated. Preliminary

studies indicate that a second degree equation of the following form will

generally describe the output of a transducer within the precision of the

measurement process.

de = aF

e + B p|

where a and 3 are the coefficients determined by least squares. An

alternate method of fitting the data would be to use a straight line plus a function of the deviations from a straight line.

Such computations are tedious when done by hand methods. But these

procedures are straightforward by machine methods. All computations in

this study were done using Omnitab [8]

.

Data reduction procedures are being constantly updated, and a general

purpose computer program is available to those interested.

THE FUTURE

Progress made in the development of a calibration procedure for load

cells which are to be used in missile weighing applications has been

reported herein. Much remains to be done, such as:

a. Comparison of loading schedules.

b. Response to various loading rates.

c. Effects of change of mode.

d. Effects of temperature.

e. Effects of temperature differential.

f. Effects of pressure. ,

g. Prediction of long term stability.

Equipment is now under procurement which will provide controlled

changes in temperature and pressure, so that we will obtain temperature and

pressure sensitivity data.

For field weighing applications, special jigs have been procured which

will allow for flexing of the load cells, the load being controlled by

hydraulic means. I t is hoped that time permits an evaluation of these jigs

in the near future. The advantages of such techniques in aero-space

testing are obvious. In this study we have purposely avoided the quasidynamic and dynamic applications, not because they are less important, but

because of the greater complexity of equipment and techniques required to

produce a meaningful calibration.

14
ACKNOWLEDGMENT

Acknowledgment is made to Paul E. Pontius and Joseph M. Cameron of the

National Bureau of Standards and to Glenn C. Wright and James A. Harmon of

the White Sands Missile Range Calibration Laboratory for their many helpful

discussions and suggestions.

REFERENCES

1. Donald M. Button, Gilmore Industries, "A Method of Design for a Center of Gravity Determination System". (Unpublished Report)

2. R. J. Carleton, "Precision High Capacity Force Standards", ISA

Preprint No. 36, New York, 19 60.

3. Paul R. Heyl, "A Redetermination of the Constant of Gravitation",

Journal of Research, National Bureau of Standards, Vol. 5, 1930, pp

1243-1290.

4. Paul R. Heyl and Peter Chrzanowski, "A New Determination of the

Constant of Gravitation", Journal of Research, National Bureau of

Standards, Vol. 29, 1942, pp 1-31.

5. X enneth I . Daugherty, J. Donald Define, Geophysical Studies

Section, Geo-Sciences Branch, Aeronautical Chart and I nformation

Center, "Comparison of Methods for Determining the Earth's Normal

External Gravitational Field", presented at the XIII General

Assembly of the I nternational Union of Geodesy and Geophysics,

Berkeley, California, August 1963.

6. Russell L. Ackoff, "Scientific Method, Optimizing Applied Research

Decisions", John Wiley & Sons, Inc., New York, 1962.

7. Hilding E. Aimer, "Elastic Devices as Mass Comparators", National

Bureau of Standards, (Unpublished).

8. J. Hilsenrath, G. G. Ziegler, C. G. Messina, P. J. Walsh and R. J.

Herbold, "OMMTAB", NBS Handbook 101, U. S. Government Printing

Office, Washington, D. C.

15
Figure I. Gravity Anomalies, W. S. M. R

.

16
O h17
AilDVdVD 03I,VH dO £NH0H3d

18
TABLE 1

CALIBRATION OF A PROVING RING IN COMPRESSION

Dial Divisions

Load (lbf) 10-29-59 1-21-65 3-15-65 4-27-65

998.29 74.81 74.80 74.91 74.86

1996.58 149.86 149.81 149.90 149.93

2994.88 225.23 225.01 225.30 225.32

3993.17 300.85 300.57 300.90 300.91

4991.46 376.65 376.38 376.72 376.82

5989.75 452.76 452.49 452.87 452.97

6988.05 529.17 529.16 529.17 529.35

7986.34 605.78 605.82 605.88 605.98

8984.63 682.70 682.79 682.90 683.05

9982.92 759.91 759.96 760.17 760.36

10981.22 - 837.81 837.89

19
Nomenclature : Load Cell Mfgr : S/N: Model: 10K

Mode: Tension Interval: on 2 Min. - off 2 Min.

Tare Weight :33. 12 lb Loading Rate:6 in/min.

Bridge Impedence :120 ohms Bridge Voltage: 10V

Calibrated f or :WSMR Calibration Laboratory Date 4-26-65

Load 1 Load 2 Load 3

Reading

123

4

56

1

23

4

5

6

D.D. Temp. D.D. Temp D.D. Temp

3002.3 71.2 7009.7 71.8 11031.8 72.3

3003.9 71.3 7012.3 71.8 11031.3 72.3

3004.0 71.4 7012.5 71.9 11030.9 72.3

3003.8 71.4 7011.9 72.0 11031.3 72.4

3003.0 71.4 7012.3 72.0 11031.4 72.5

3003.0 71.6 7012.2 72.2 11031.8 72.6

Load 4 Load 5 Load 6

15044.7 72.3 19055.8 73.0 23084.8 73.4

15042.1 72.3 19054.5 73.0 23083.6 73.4

15042.0 72.3 19054.3 73.1 23084.0 73.4

15042.5 72.4 19056.2 73.1 23083.1 73.4

15042.4 72.4 19054.6 73.2 23082.3 73.5

15042.0 72.6 19055.1 73.2 23082.9 73.5

Load 7 Load 8 Load 9

27102.7 73.6 31131.7 74.0 35159.3 74.4

27102.1 73.7 31132.0 74.0 35158.2 74.4

27101.9 73.7 31132.6 74.1 35157.4 74.4

27102.1 73.8 31132.1 74.1 35154.6 74.4

27102.0 73.8 31131.7 74.2 35155.5 74.4

27099.9 73.9 31131.0 74.3 35156.8 74.6

Load 10 Load 11

39188.0 71.1 43233.4 71.7

39189.3 71.2 43232.7 71.8

39188.4 71.2 43231.5 71.8

39187.0 71.3 43232.1 71.9

39188.5 71.4 43229.9 71.9

39189.9 71.4 43232.3 72.0

The report of calibration is based on the last four observations.

Table 2 REPORT OF CALIBRATION

20
Report of Calibration

Load Cell

S/N 10K

Mass (lb) lbf D.D.

750 748.72 3003.5

1750 1747.02 7012.2

2750 2745.30 11036.3

3750 3743.60 15042.2

4750 4741.50 19055.0

5750 5745.17 23083.0

6750 6738,48 27101.4

7750 7736.77 31131.8

8750 8735,07 35156.0

9750 9733.35 39300.3

10750 10731.64 43231.4

English Units F = k (jn - pu)a

where

lbf/D.D,

0.2493

0.2492

0.2487

0.2488

0.2488

0.2486

0.2486

0.2485

0.2484

0.2476

0.2482

F is force in pounds force (lbf)

m is mass in pounds

p is air density in pounds per cubic foot

V_ is volume in cubic feet

a. is acceleration in ft/sec/sec (a at place of use)

k = 1/32.17404

To obtain force in pounds force, multiply pounds force /D.D. from

table (interpolating as necessary) and multiply by D.D. observed.

To obtain mass in pounds, multiply lbf/D„D„ from table (interpolating as necessary) times DD observed and multiply by the ratio of

32.17404 to acceleration at place of use. Compute pu and add to mass

as computed above.

3 sigma (lbf) =0.5

Three sigma is an estimate of the overall uncertainty of a point

using three standard deviations based on 33 degrees of freedom as a limit to the effect of random errors of measurement, the magnitude of

systematic errors from known sources are negligible.

Table 3 REPORT OF CALIBRATION (ENGLISH SYSTEM)

21
Report of Calibration

Load Cell S/N 10K

Mass [kg] N D.D.

340.19 3330.5 3003.5

793.79 7771.1 7012.2

1247.38 12211.7 11036.2

1700.97 16652.3 15042.2

2154.56 21093.0 19055.0

2608.16 25533.6 23083-0

3061.75 29974.2 27101.4

3515.34 34414.9 31131.8

3968.93 38855.5 35156.0

4422.53 43296.1 39300.3

4876.12 47736.7 43231.4

SI Units F = k_0n- pv)a

where

F is force in newtons (N)

m is mass in kilograms

p is air density in kilograms per cubic meter

v is volume in cubic meters

a is acceleration in m/sec/sec (a at place of use)

k = 1

N/D.D.

1.10886

1.10823

1.10652

1.10704

1.10695

1.10616

1.10600

1.10546

1.10523

1.10167

1.10421

To obtain force in newtons, multiply N/D.D. from table (interpolating

as necessary) and multiply by D.D. observed.

To obtain mass in kilograms, multiply N/D.D. from table (interpolating

as necessary) times D.D. observed and multiply times the acceleration

at place of use. Compute pv and add to mass as computed above.

3 sigma (N) = 2.2

Three sigma is an estimate of the overall uncertainty of a point

using three standard deviations based on 33 degrees of freedom as a limit

to the effect of random errors of measurement, the magnitude of

systematic errors from known sources are negligible.

Table 4 REPORT OF CALIBRATION (SI)

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