NBSIR 77-1229

Accelerometer Calibration — A Comparison Between

CESTA and NBS

James D. Pollard

Engineering Mechanics Section

Mechanics Divijion

Institute for Basic Standards

National Bureau of Standards

Washington, D C. 20234

January 1 977

Final

U. S. DEPARTMENT OF COMMERCE

NATION/ L BUREAU OF STANDARDS

NBSIR 11-M2B

ACCELEROMETER CALIBRATION -- A COMPARISON BETWEEN

CESTA AND NBS

James D. Pollard

Engineering Mechanics Section

Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

January 1977

Final

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director
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CONTENTS

Page

1. INTRODUCTION 1

2. DESCRIPTION OF EQUIPMENT 1

3. COMPARISON TEST DESCRIPTION 2

4. INTERFEROMETER TEST DESCRIPTION 3

5. METHOD OF TEST 4

6. RESULTS OF TEST - SYSTEM 1 5

7. RESULTS OF TEST - SYSTEM 2 10

8. UNCERTAINTY OF RESULTS 15

9. CONCLUSIONS 15

10. ACKNOWLEDGEMENTS 16

11. REFERENCES 17

1
TABLES

Page

1. Results of comparison calibration of System 1. 6

2. Summary of comparative test results for System 1. 7

3. Results of interferometric measurements of System 1. 9

4. Results of comparison calibration of System 2. 11

5. Summary of comparative test results for System 2. 12

6. Results of interferometric measurements of System 2. 14

ILLUSTRATIONS

Figure 1.

Figure 2.

Page

Sensitivity of System 1. 8

Sensitivity of System 2. 13

11
ACCELEROMETER CALIBRATION —

A COMPARISON BETWEEN CESTA AND NBS

James D. Pollard

ABSTRACT

This report describes a vibration measurement interchange between a French laboratory

(CESTA) and the National Bureau of Standards

(NBS) . Methods of calibration at NBS and re- sults of the calibration of two commercially

available double ended or "piggy-back" type

accelerometers are discussed. No difficulties

were encountered in the calibration of System 1,

however, above 4000 Hz difficulties were ex- perienced in the calibration of System 2.

Key Words: Accelerometers; calibration; measurements; vibration; vibration exciters; vibration

standards

.

1. INTRODUCTION

The measurement techniques of individual laboratories charged with

the calibration of physical standards for measurement of vibration differ

considerably. This report describes a measurement interchange, involving

vibration measuring instruments, between the National Bureau of Standards

(NBS) and a French national laboratory within the Aquitaine Center for

Scientific and Technical Studies (CESTA)

.

2. DESCRIPTION OF EQUIPMENT

Two commercially available, laboratory quality accelerometers and

their associated charge amplifiers were used in these tests. These

accelerometers are used as transfer standards and are of the double-ended

or "piggy-back" type. One of the transfer accelerometers was manufactured

in the United States and the other was manufactured in Europe, In this

report these shall be referred to as System 1 and System 2, respectively.

A precision piezoelectric quartz accelerometer system was used as a reference standard. This system was periodically calibrated and maintained

as a standard by the National Bureau of Standards. Although it had been

calibrated in April 1976, it was recalibrated just prior to these tests,

and the sensitivity factors used to reduce the data were adjusted to con- sider the slight drift shown by the history of the system.
One of the transfer standards (System 1) has a 1/4-28 UNF mounting

hole at the upper end. A 1/4-28 to 10-32 adaptor stud which provided a definite thread depth for both accelerometers was used. The other transfer

standard accelerometer (System 2) had a 10-32 UNF mounting hole at the

upper end. A cable with a length of seven meters and a measured capacitance of 810.9 picofarads was furnished by CESTA and was used with the

transfer systems throughout the tests.

The electrical connections for each accelerometer were cleaned and

the connectors were securely attached. The cables were taped to the vibration generator as close to the accelerometer connections as possible

without interfering with the motion. During the entire test period, line

power was left applied to the charge amplifiers and all measuring equipment .

In all instances, the accelerometer outputs were applied to a charge

sensing amplifier. For System 1 and System 2, two separate but identical

model number charge amplifiers were used. These amplifiers were manufactured in France and their gain was nominally 1000 mV/pC. The NBS

amplifier had a gain of nominally 10 mV/pC. The frequency-gain response

of each of the test amplifiers was measured and used in the data analysis.

Problems were encountered in the gain measurements and insufficient time was available to resolve the problems and to assess the amplifier gain

measurement uncertainty.

The transfer standard accelerometers (System 1 and 2) had been calibrated by the French laboratory just prior to their arrival at NBS and

more tests were to be made upon their return to CESTA.

3. COMPARISON TEST DESCRIPTION

The CESTA transfer standard accelerometers (System 1 and 2) were calibrated by a comparison method using an NBS accelerometer as a reference

standard. The reference accelerometer was mounted on top of each of the

test accelerometers throughout the comparison calibration. The accelerometers were attached with a stud which permitted the mating surfaces to be

in direct contact with each other and were tightened with a torque of nominally 2 Nm. Two Dimoff Vibration Standards [1]* were used as vibration

exciters

.

An automated comparison calibration facility at NBS is used to calibrate accelerometers on a routine basis [2], A software program in a mini-computer controls the entire test process. The program contains

codes which are translated into frequencies and voltages by a programmable

oscillator which in turn supplies a input to a power amplifier. This then

drives the vibration exciter. At each test frequency there is a preset

acceleration level which is program controlled through a closed-loop process to insure that this level remains constant.

* Numbers in brackets correspond to references given at the end of this

report

.

2
Since the charge amplifiers used with the transfer standard accelometers had high outputs, the automated system calculated the sensitivity

factors using the relationship:

S = S R

t s where S = sensitivity of the transfer accelerometer,

t S = sensitivity of the reference accelerometer, and

s R = ratio of the transfer accelerometer voltage to the reference

accelerometer voltage,

^

_ Transfer accelerometer voltage

Reference accelerometer voltage

The system sensitivity factors are the open circuit output of the charge

amplifier in millivolts per unit acceleration in g* (mV/g) . The automated system is capable of measuring these ratios to within a few tenths

of one percent.

The waveform of each accelerometer's charge amplifier output was monitored on an oscilloscope. The waveform harmonic distortion generally

did not exceed one-percent. The transverse motion ratio, although not

monitored, is believed to be less than one percent over most of the frequency range under normal exciter load conditions. Lateral resonances at

a few narrow frequency bands may cause the transverse motion ratio to be

greater than one percent, but how much greater is not known.

4. INTERFEROMETER TEST DESCRIPTION

The normal method used to calibrate accelerometers on piezoelectric

exciters is that of a modulated photoelectric measurement of amplitude

utilizing a Flzeau interferometer and a fringe disappearance technique

[3]. The light source is a HeNe laser. A small reflector is attached to

the vibrating surface to be measured. The upper interferometer plate, a plano-convex lens, is mounted just above the plane reflector. In order

to induce a low modulating frequency of vibration in the upper plate, a small piezoelectric mass-reaction exciter is mounted on the lens support

and is driven at a frequency of about 100 Hz. A photodetector views the

center fringe and produces a signal which is applied to a narrow-band filter

which is phase locked to the 100 Hz modulating frequency.

* In this study, units of acceleration are expressed in gravitational

units of g. This was done to facilitate communication with the Intended

reader. Conversion to SI units may be accomplished by using the relationship 1 g

= 9.80665 m/s^.

3
In operation, the main exciter is first left at rest and the modulating frequency is induced in the upper plate. The amplitude of the

modulating vibration is adjusted to bring the photodetector output to

its first maximum. The mean mirror separation is then adjusted to further maximize the output. Control of the mirror separation is achieved

by superimposing a dc bias on the ac driving signal to the modulating

exciter. The main exciter on which the accelerometer is mounted is then

driven to an amplitude which causes the photodetector signal to drop to

a very distinct null (fringe disappearance). The output of the accelerometer is measured at this time to give one calibration point. Sensitivity

factors are computed from values of displacement amplitude, frequency,

and output voltage of the charge amplifier. For the system used, fringe

disappearance occurs at a double displacement amplitude of 242.2 nm

(9 . 536 y in) .

Measurements on the CESTA accelerometers were made by cementing a mirror onto the upper mating surfaces of each of the accelerometers.

Data obtained from this test cannot be compared directly to the results

from the comparison test described earlier. The "piggy-back" type accelerometers exhibit a mass-loading sensitivity, that is, their sensitivity

changes as a function of the mass, and geometry of that mass, which is

mounted on the upper surface. Normally, this "mass" is another accelerometer to be calibrated. However, in this test the "mass" is only a small

glass mirror. The mass loading effect is generally larger at frequencies

greater than 2 or 3 kHz. The values obtained from this test apply only

under the conditions of this test. No methods have yet been developed

which allow interferometric measurements to be made on double-ended,

piggy-back type accelerometers with realistic mass loading conditions.

However, it is possible to compare results obtained from two laboratories

under the same mass loading conditions (i.e., with a mirror only as the

mass). At the conclusion of the NBS testing the mirrors were left attached to the two CESTA accelerometers so they could be tested using a similar procedure at the French laboratory. Only then can any comparisons be made between the NBS and CESTA results using this type of

measurement technique.

5. METHOD OF TEST

A comparison calibration on the NBS automated system, consisted of

two runs from 10 to 10 000 Hz on one of the two NBS vibration generators.

Data was taken at 10, 15, 30, 50, and 100 Hz at 100 Hz increments between 100 and 1000 Hz and at 500 Hz increments between 1000 and 10 000

Hz. After completion of a test, the entire assembly, consisting of the

reference standard, stud and transfer standard was removed, mounted onto

the second vibration generator and tested as above. The entire test was

then repeated. This yielded four sets of data for the system. Both

systems were subjected to the same cycle of testing. Both systems were

once again tested in the same manner. At the conclusion of the comparison test program each system had been calibrated 8 times at 33 frequencies

giving a total of 264 data points per system.

4
The interferometric test consisted of four data points at each of

20 frequencies between 1000 and 10 000 Hz in 500 Hz increments. Two

different exciters were used with a repeat test on one of the exciters.

This yielded a data set of 240 measurement points.

6. RESULTS OF TEST - SYSTEM 1

Table 1 presents the data and the average for each of the data

points resulting from testing on each of the two NBS Dimoff Vibration

generators. The four data points from each generator were averaged to

yield the value of sensitivity for each of the test frequencies. The

data presented are system sensitivity factors (mV/g) . These factors were

determined by comparing the voltage output of the charge amplifier used

with the transfer standard accelerometer to the output of the reference

standard.

Table 2 presents a summary of the comparison calibration data for

System 1. The average data from the two Dimoff exciters are in column 2 and 3. Column 4 is the overall mean. Column 5 gives the factors used

to adjust the reference system sensitivity factor to account for the

calibration history of the system, and column 6 is the corrected transfer

system sensitivity factor. Column 7 is the gain of the charge amplifier

used with System 1. To present the results also in terms of the charge

sensitivity of the accelerometer, the system sensitivity was divided by

the amplifier gain. The results of this are in the last column. The

accelerometer sensitivity factor is the output of the accelerometer

in picocoulombs per unit acceleration in g (pC/g). Figure 1 is a graph

of the system sensitivity. It is believed that whipping of the cable,

which generates spurious signals due to triboelectric effect, and the

poor signal-to-noise ratio of the test charge amplifier were responsible

for the 10 and 15 hertz points showing an unexpected rise.

Table 3 presents the results of the interferometric testing. Columns 2, 3, and 4 are the average of the four data points from the three

runs. Column 5 is the overall average of all the data. Column 6 gives

the charge amplifier gain in units of millivolts per picocoulomb (mV/pC)

.

The last column is the result of dividing the system sensitivity (column

5) by the gain to give accelerometer sensitivity in units of picocoulombs

per g (pC/g)

.

A comparison of the data generated during these tests with informal

CESTA data showed that, in the frequency range of 30 to 7000 Hz (which

is the upper limit of the CESTA measurements), the NBS data generally

averaged a difference of less than one percent from the CESTA mean. The

NBS data was lower at each of the test frequencies. Above 7000 Hz, the

NBS data indicated a rise of about three percent at 10 000 Hz. The

slight variations in response between 2500 and 7000 Hz are believed to

be caused by interactions between the reference and transfer standard as an assembly.

5
Table

1.

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of

comparison

calibration

of

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Results

of

interferometric

measurements

of

System

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7. RESULTS OF TEST - SYSTEM 2

Table 4 presents the data and the average for each data point re- sulting from testing System 2 on each of the two NBS Dimoff Vibration

generators. The four data points from each generator were averaged to

yield the value of sensitivity for each of the test frequencies. The

data presented are the system sensitivity factors (mV/g). These factors

were determined by comparing the voltage output of the charge amplifier

used with the transfer standard accelerometer with the output of the

reference standard.

Table 5 presents a summary of the comparison calibration data for

System 2. The average data from the two Dimoff exciters is in column 2 and 3. Column 4 is the overall mean. Column 5 is the correction factor

used to account for the calibration history of the reference system,

and column 6 is the corrected system sensitivity factor. Column 7 is

the gain of the charge amplifier used with System 2. Again, to present

the results also in terms of the charge sensitivity of the accelerometer,

the system sensitivity was divided by the amplifier gain. The results

of this are in column 8. The accelerometer sensitivity factor is the

output of the accelerometer in picocoulombs per unit acceleration in g

(pC/g) . Figure 2 is a graph of the system sensitivity. The unexpected

rise at 10 and 15 hertz is again believed to be caused by cable motion

and the poor signal-to-noise ratio of the charge amplifier.

Table 6 presents the results of the interferometric testing. As

with System 1, column 2, 3, and 4 are the average of four data points

from the three runs. Column 5 is the overall average of all of the data.

Column 6 gives the charge amplifier gain, and the last column is the

accelerometer sensitivity.

The results of the calibration of this transfer standard at NBS

compare closely with informal CESTA data in the range of 30 to 3000 Hz.

The results from the two laboratories tend to overlap very well.

Difficulties were encountered in the calibration of System 2. Results indicated a difference, when mounted on the two NBS exciters, of

1 to 2.5 percent in the response above 4000 Hz. It had been noted during

check-in of this equipment that the upper and lower surfaces of this accelerometer were badly scarred. Time was expended in refinishing these

surfaces. An additional run on both exciters Indicated an improvement

in the response but the differences were still considerably greater than

usually expected. This can be seen by comparing these results with the

corresponding results from System 1. The data included in this report

is the data obtained after refinishlng.

10
Table

4.

Results

of

comparison

calibration

of

System

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of

interferometric

measurements

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The NBS laboratory had available another accerlerometer of this same

type. This was substituted for the CESTA System 2 accelerometer and data

taken. This second accelerometer did not exhibit any such deviation in

the response above 4000 Hz. The reason for the problem in the CESTA

accelerometer was not determined. Additional testing should be performed

at the French laboratory to determine the cause of this anomalous behavior.

8. UNCERTAINTY OF RESULTS

The calibration procedures followed at NBS will generally give

system sensitivities (mV/g) with uncertainties of not more than one percent over the frequency range of 10 to 1000 Hz and two percent from 1000

to 10 000 Hz. An additional uncertainty of about 0.25 percent would be

expected in measuring amplifier gain and converting to accelerometer

sensitivity (pC/g).

In the tests covered here, the amplifier noise level and possible

triboelectric effects due to cable whipping have introduced a significant,

but unevaluated, additional uncertainty at 10 and 15 Hz. The problem en- countered with System 2 (Section 7) also added to the uncertainty of the

results for this system above 4000 Hz. Since the effects of these problems were not determined, an estimate of uncertainty at 10 and 15 Hz and,

for System 2, at the higher frequencies cannot be given.

Examination of the results of the amplifier gain measurements has

shown them to be less consistent than expected. It is not known whether

this problem was a result of the amplifier behavior or of the gain mea- surement process. Unfortunately, the systems were not available at NBS

long enough for these factors to be resolved. As a result, the accelerometer sensitivities also contain an additional, unevaluated uncertainty,

and no value of this uncertainty can be given.

With the exceptions noted above, the usual uncertainties can be as- signed to the results of these tests.

9. CONCLUSIONS

The results should be considered valid only for the methods and hardware tested. Although there was general agreement with the limited, informal CESTA data that was available, several things do remain unexplained.

For example, the almost constant difference between the NBS measurements

and the CESTA measurements of System 1, and the problem of System 2 above

4000 Hz. In the first case, the results agree within the claims of both

laboratories and the difference may be in the measurement techniques

employed and the random and systematic errors expected. Certain interactions between the particular units tested are difficult to ascertain

and might have had an effect. Some of these might have been column reso- nances of the reference and transfer standards as a column assembly,

relative motion between the upper and lower surfaces of the transfer standard, strain sensitivity of the transfer standard, noise, etc. The problem with System 2 above 4000 Hz remains unexplained.

15
10 . ACKNOWLEDGEMENTS

The writer wishes to thank Roscoe L. Bloss, Chief, Engineering

Mechanics Section, for his assistance in the preparation of this report.

Thanks also to John D. Ramboz for his guidance and help. Oliver W.

Price is thanked for obtaining the interferometric data. A special note

of appreciation from the entire NBS team to Jean Fromentin of CESTA for

a most enlightening and free exchange of information during this visit.

16
11. REFERENCES

[1] Dimoff, T. , ''Electrodynamic Vibration Standard with a Ceramic Moving

Element", Journal of the Acoustical Society of America, Vol. 40,

No. 3, Sept. 1966, pp. 671-676.

[2] Payne, B. F., "An Automated Precision Calibration System for Accelerometers", Instrument Society of America 17th National Aerospace

Instrumentation Symposium, May 1971.

[3] Schmidt, V. A., Edelman, S., Smith, E. R. , and Pierce, E. T.

,

"Modulated Photoelectric Measurement of Vibration", Journal of the

Acoustical Society of America, Vol. 34, No. 4, April 1962, pp. 455-

458.

17
NBS-1 14A IRE V. 7-73.

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PL)IM-K ATION OR RHPORT NO.

NBSIR 77-1229

2. Gov’t Acccs.sii>n No.

3. Recipient’s Accession No.

4. TITLK AND SUBTITLK

Accelerometer Calibration —

A Comparison Between CESTA and NBS

5. Publication Date March 1977

6 . Performing Organization (iodc

7. AUTHOR(S)

James D. Pollard

8 . Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Prdject/Task/Work Unit No. 2130149

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, Stste, ZIP)

Same as No.

13. Type of Report & Period Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

This report describes a vibration measurement interchange between

a French laboratory (CESTA) and the National Bureau of Standards (NBS)

Methods of calibration at NBS and results of the calibration of two

commercially available double ended or "piggy-back” type accelerometers

are discussed. No difficulties were encountered in the calibration of

System 1, however, above 4000 Hz difficulties were experienced in the

calibration of System 2.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Accelerometers; calibration; measurements; vibration; vibration exciters;

vibration standards.

18. AVAILABILITY Unlimited

For Official Distribution. Do Not Release to NTIS

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lx Order F rom National Technical Information Servi

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