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PUBLICATIONS

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QC1oS°?k7koifk''?^?:'P^'°" °' NBS call UOIOO .U5752 N0.1232 1987 V198 C.I NBS-P

NBS TECHNICAL NOTE 1

U.S. DEPARTMENT OF COMMERGE/National Bureau of Standards

QC

100

.U5753

#1232

1987

C. 2

A Description of NBS

Calibration Services

in l\/[echanical

Vibration and Shocic

D. C. Robinson, M. R. Serbyn, and B. F. Payne
m he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

ff Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety.

The Bureau's technical work is performed by the National Measurement Laboratory, the National

Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Institute for Materials

Science and Engineering

.

The National Measurement Laboratory

Provides the national system of physical and chemical measurement;

coordinates the system with measurement systems of other nations and

furnishes essential services leading to accurate and uniform physical and

chemical measurement throughout the Nation's scientific community, in- dustry, and commerce; provides advisory and research services to other Government agencies; conducts physical and chemical research; develops,

produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

• Basic Standards^

• Radiation Research

• Chemical Physics

• Analytical Chemistry

The National Engineering Laboratory

Provides technology and technical services to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement

capabilities; provides engineering measurement traceability services; develops

test methods and proposes engineering standards and code changes; develops

and proposes new engineering practices; and develops and improves

mechanisms to transfer results of its research to the ultimate user. The

Laboratory consists of the following centers:

• Applied Mathematics

• Electronics and Electrical Engineering^

• Manufacturing Engineering

• Building Technology

• Fire Research

• Chemical Engineering^

The Institute for Computer Sciences and Technology

Conducts research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and economy in Government

operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing

the Federal Information Processing Standards Program, developing Federal ADP standards guidelines, and managing Federal participation in ADP

voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and provides the technical foundation for computer-related policies of the Federal Government. The Institute consists of the following centers:

• Programming Science and

Technology

• Computer Systems

Engineering

The Institute for Materials Science and Engineering

Conducts research and provides measurements, data, standards, reference

materials, quantitative understanding and other technical information fundamental to the processing, structure, properties and performance of materials; addresses the scientific basis for new advanced materials technologies; plans

research around cross-country scientific themes such as nondestructive

evaluation and phase diagram development; oversees Bureau-wide technical programs in nuclear reactor radiation research and nondestructive evaluation; and broadly disseminates generic technical information resulting from

its programs. The Institute consists of the following Divisions:

Ceramics

Fracture and Deformation

Polymers

Metallurgy

Reactor Radiation

'Headquariers and Laboratories a( Gaithcrsburg, MD, unless otherwise noted; mailing address Gaithersburg. MD 20899. ^Some divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithersburg, MD.
NBS

RESEARCH

INFORMATION CENTER Ai3sc

NBS TECHNICAL NOTE 1232 ^^^^

A Description of NBS Calibration /^«^

Services in Mechanical Vibration and

''^ Shock

D.C. Robinson

M.R. Serbyn

B.F. Payne

Acoustic Measurements Group

Automated Production Technology Division

National Bureau of Standards

Gaithersburg, MD 20899

February 1987

U.S. Department of Commerce

Malcolm Baldrige, Secretary

National Bureau of Standards

Ernest Ambler, Director
National Bureau of Standards Technical Note 1 232

Natl. Bur. Stand. (U.S.), Tech. Note 1232, 26 pages (Feb. 1987)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1987

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington DC 20402
Table of Contents

1. INTRODUCTION

2. COMPARISON CALIBRATION OF ACCELEROMETERS

2.1 Description of Service

2.2 Low-Frequency Range

2.2.1 General Characteristics of Exciters

2.2.2 Calibration Procedures

2.3 Mid-Frequency Range

2.3.1 General Characteristics of Exciters

2.2.3 Automated Comparison Calibration

2.4 High-Frequency Range

2.4.1 General Characteristics of Exciters

2.4.2 Automated Comparison Calibration

25 Special Test of Shock Transducers

3. ABSOLUTE CALIBRATION OF REFERENCE EXCITERS AND

ACCELEROMETERS

3.1 Absolute versus Comparison Calibration Service

3.2 Ronchi Rulings Methods

3.3 Fringe-Counting Interferometer

3.4 Reciprocity Calibration

3.5 Automated Fringe-Disappearance Interferometer

3.6 Laser Interferometer using the J - Null Method

3.7 Folded-Beam Interferometer

4. REFERENCES

III

1. INTRODUCTION

There are two principal categories of measurement used in the calibration of

accelerometers and reference exciters at the National Bureau of Standards:

comparison and absolute. When the calibration factor is obtained directly from

a measurement of quantities which form the base units of a system of units,

the calibration is called absolute [1]. The comparison method involves

simultaneous measurement of the outputs of the transducer under test and a reference transducer of known and stable characteristics, with both devices

subject to the same excitation. The comparison method has been implemented

by constructing a vibration exciter with a built-in or attached transducer and a space for mounting an accelerometer to be tested. A test accelerometer can be

readily calibrated by direct comparison of its voltage to that of a standard.

The comparison method is very simple and relatively inexpensive, compared to

the absolute methods of calibration, which can be very time consuming. This

survey document describes the methods of calibrating vibration pickups by

comparison with NBS standards, including a special shock calibration service,

and absolute methods used primarily in the calibration of the reference

standards.

A summary is given of the various calibration procedures, beginning with the

comparison calibration procedures using electrodynamic, air-bearing, and

piezoelectric exciters which cover the low, mid, and high-frequency ranges,

respectively. A shock calibration service which employs analog-to-digital

converters and fast Fourier transform analysis to calibrate a test accelerometer

in terms of a reference accelerometer is then described. The last section

describes the absolute calibration procedures which are primarily used to

calibrate the reference exciters and accelerometers.

2. COMPARISON CALIBRATION OF ACCELEROMETERS

2.1 Description of Service

Once the standard accelerometer has been calibrated by one of the absolute

methods described later, smoothing is performed on the experimental data.

The resulting frequency response function is the sensitivity of the standard. A

test accelerometer is readily calibrated by mounting it on the exciter and

obtaining the voltage ratio of the test and standard accelerometers. The

sensitivity of the test accelerometer is given by

^test

^test ~

^standard (v

Estandard
where:

^test ~ voltage output of the test accelerometer

^standard ^ voltage output of the Standard accelerometer, and

^standard ~ sensitivity of the standard accelerometer.

Comparison calibrations of accelerometers and other vibration pickups are performed routinely in a permanent facility. Both the single-ended and the

back-to-back type transfer standards are accepted. The measurements are performed under the environmental conditions recommended by the pertinent

ISO standard [2], namely at a temperature of 23 ± 3° C and a relative

humidity of 50 ± 20 percent. The test procedures are automated and

computer controlled.

The pickups are normally calibrated at discrete frequencies in the range 10- 10,000 Hz, and the normal test accelerations are 2, 5, and 10 g, where g is the

standard acceleration of free fall, equal to 9.80665 m/s/s. The measurand is the

sensitivity, whose magnitude is also called calibration factor, of the vibration

pickup. It is defined as the ratio of an electrical output quantity to a mechanical input quantity. For example, the calibration of an accelerometer

may be reported as charge sensitivity in pC per g for the pickup alone or as voltage sensitivity in mV per g for the pickup-amplifier combination. (For

non-American users the preferred units would be pC per m/s/s .) Because

sensitivity is a ratio of two phasor quantities, it contains a phase component in

addition to the magnitude. Phase calibration is also provided, upon request,

and is expressed in degrees.

The NBS standards to which comparison is made are carefully maintained and

periodically recalibrated by absolute methods. Transfer of accuracy is assured

by established measurement procedures which are automated and computercontrolled. The uncertainty of a comparison calibration varies from ± 1

percent to ± 3 percent, depending on the frequency range and the particular

test requested [3]. This information is provided to the user as part of the

calibration report. User requirements which do not fall into the categories

listed in Ref. 3 can usually be met by a special test performed at cost by

prearrangement. A summary of the calibration methods is shown in Table 1.

The exciters used for the comparison method are calibrated by an absolute

method based on optical interferometry or the reciprocity principle (or both).

The reference transducer is usually an accelerometer, although it can be a coil

moving in a magnetic field. Since no single vibration exciter or calibration

procedure is adequate for the frequency range of 2 to 15,000 Hz, several

options for presenting the particular material of this Section exist. We have

chosen to do it on the basis of frequency range.
Table 1 - Methods Used to Calibrate Accelerometers

Range Estimated

Uncertainty*

(%)

Calibrator Acceleration

(g)

Frequency

(Hz)

Method

Low- 0.2-2.5 2-4 ± 2 Comparison to reference Frequency 5-100 ± 1

standard calibrated by

Exciter an optical ruling (2-10

Hz) or laser interferometer fringe counting

(2-lOOHz) method.

Air- 2-10 <50 ± 2 Comparison to reference Bearing 50-2,000 ± 1

standard calibrated by

Exciter 2,500-3,000 ± 2 reciprocity (lOHz-lOkHz)

3,500-10,000 ± 3 and checked by interfero- metric methods.

PiezoElectric

2-100 3,000-10,000

11,000-15,000

± 2

± 3

Comparison to reference standard calibrated bv Exciter

Shock

Exciter

50-5,000 10-10,000 ± 5

a laser fringe-dis- appearance interfero- meter.

"Back-to-back" comparison to a standard cali- brated using continous sinewave excitation. Shock pulses are "halfsine" having pulses widths from 40-0.2 ms.

*The uncertainty is a statement of possible random and systematic errors from

all known sources expressed as a root mean square value.
2.2 Low-Frequency Range

2.2.1 General Characteristics of Exciters

An electrodynamic vibration exciter has been developed to calibrate

accelerometers at low frequencies down to 2 Hz. This work has provided the

National Bureau of Standards with the capability of covering a frequency

range of 2 to 100 Hz. The maximum acceleration amplitude is 2.5 g peak or as limited by a displacement of approximately 4.5 cm double amplitude. The

attainable amplitude and accuracy of accelerometer calibration on this exciter

is limited by transducer size, weight, geometry, and vibration sensitivity.

Examples of the types of pickups which can be calibrated are servo or force

balance, piezoelectric, piezoresistive, and strain gage accelerometers.

The low-frequency vibration exciter. Type

LF-1, is shown in Fig. 1. It is a variant of

the Dimoff Type 200 exciter [4,5], designed

for the frequency range 1-100 Hz; in fact,

many of the components are identical.

Full documentation of this exciter is found in Ref. 6. The motion of such an

exciter must have very low waveform

distortion and minimal components of

motion in all directions other than axial.

In addition, the attainable amplitude must

be large enough to produce an

accelerometer signal that can be accurately

measured. The reference accelerometer

system consists of a servo accelerometer

and amplifier. Absolute calibration of the

reference standard is discussed in a later

section on the procedures for absolute

calibration of the reference exciters. M

I

2.2.2 Calibration Procedure

FIGURE 1. LOW FREQUENCY AIR

BEARING SHAKER LF-1

The calibration procedure is based on Eq. (1), with the standard consisting of a stable servo accelerometer mounted inside the moving element of the exciter.

The chief difficulty in this type of calibration lies in the measurement of the

voltage output at low frequencies. The need of the measurement to encompass

at least several vibration cycles raises the requirement of stationarity of the

signal, while the reduced response of the sensor increases the signal-to-noise

ratio. In order to minimize errors, two approaches to measuring voltage have
been used: a true-rms differential voltmeter and an ac-to-dc converter followed

by a dc-to-frequency converter. A fast-response, low-frequency sampling

voltmeter, developed at NBS, will soon be tested in this application.

The estimated uncertainty in the measured values of the sensitivity factors for

accelerometers calibrated on the low-frequency exciter, by comparison to the

internal reference standard, does not exceed ± 1 percent from 100 to 5 Hz and

± 2 percent below 5 Hz. This estimated uncertainty is for an accelerometer

having a sensitivity of approximately IV ^

per g. It is also assumed that the

accelerometer is suitable for use as a laboratory standard, i.e., it has a high

signal-to-noise ratio, miminimal sensitivity

to case strain, minimal thermal sensitivity

shift, etc. Increases in estimated

uncertainity must be made on an

individual basis for accelerometers which

do not possess the above characteristics.

2.3 Mid-Frequency Range

2.3.1 General Characteristics of Exciters

The Dimoff air-bearing Type 200 exciter is shown in Fig. 2 and its general

characteristics are described in Ref. 4. FIGURE 2. DIMOFF AIR

BEARING SHAKER TYPE 200

The accelerometer to be calibrated is attached to the calibrator table, and the

reference accelerometer is inside the moving element. The armature and the

table are as rigid as practical to minimize table bending and to maximize the

frequency of the first axial resonance. Air bearings are used to assure low

distortion and low transverse motion. Sinusoidal motion is obtained when a sinusoidal current is passed through the drive coil. The present range of

calibration is 10 to 10,000 Hz for comparison calibration using these exciters.

The use of reciprocity calibrated standards for performing routine comparison

calibrations is discussed in Ref. 5. Transverse motions of the mounting table

for these exciters have been measured using two accelerometers mounted with

their principal axes mutually perpendicular to the direction of motion. These

and other determinations provide assurance that the transverse acceleration is no greater than 1.5 percent of axial acceleration [7]. Further details of the

Dimoff Type 200 exciters which are used in most comparison accelerometer

calibrations at NBS are given in Ref. 5.
VIDEO

DISPLAY

MASS

STORAGE

PRINTER

PLOTTER

REMOTE DISPLAY

RS 232

•STANDARD'

"TEST"

PROGRAMMABLE

SWITCH

DESKTOP

COMPUTER

SIGNAL

GENERATOR

SHAKER

SCOPE

DIGITAL

VOLTMETER

POWER

AMPLIFIER

FIGURE 3. COMPONENTS OF AUTOMATED COMPARISON SYSTEM

23.2 Automated Comparison Calibration

Figure 3 shows a diagram of the components used in the automated calibration

system. Most accelerometer calibrations at NBS are performed by the

comparison method using the Dimoff Type 200 exciters. The various methods

of absolute calibration of these exciters and their built-in accelerometers are described in Sec. 3. The measurement procedure for the automated calibration

system, which applies to both the mid-frequency and high-frequency ranges, can

best be explained by reference to the functional diagram of Fig. 3 [5]. The

output voltage from a low-distortion programmable signal generator is amplified by a power amplifier and energizes the exciter at a given test frequency and acceleration. The digital voltmeter (DVM) is programmed to

read first the voltage output of the standard accelerometer in the exciter

(E standard ) ^^^ then the voltage output of the test accelerometer (E ^^^^

). The

DVM samples the voltages and they are stored in the computer memory.

Typically 25 voltage readings are stored in a sample. These voltages are then

averaged and the standard deviation, normally less than 0.1 percent, is computed. The DVM is programmed so that samples which may be affected

by spurious signals are discarded. Upon the completion of the data sampling,

the sensitivity of the test accelerometer is calculated from Eq. (1). The

sensitivity for this test frequency is stored in computer memory and

calibrations at the remaining test frequencies and accelerations are performed

in the same manner.
Usually accelerometers are submitted for calibration with an accompanying

charge amplifier which converts the charge output of the accelerometer to an

ac voltage that can be readily measured on a digital voltmeter. Some users prefer to obtain a calibration of the pickup alone in terms of the charge per

unit acceleration (pC per g). The procedure in this case is to use a NBS

charge amplifier of known charge gain and to calibrate this amplifier and

accelerometer system in the usual manner. The final step is to divide the

resulting calibration factors by the charge gain of the NBS amplifier and thus

obtain the required charge sensitivity. The procedure for measuring the charge

gain of the charge amplifier is given in Ref. 5.

The last stage of the calibration process consists of data reduction and

reporting, which are also done by the computer. The data collected in the

computer memory consist of: (1) test frequency, (2) voltage output from the

NBS standard, (3) voltage output from the test accelerometer. Two exciters are

used, and each accelerometer is calibrated twice on each exciter, for a total of

four sets of calibration data. The computer program averages the four sets and rounds the average sensitivity to reflect the accuracy of the calibration in

the number of digits reported. At the present time, the automated calibration

data are given in NBS Reports of Calibration over a frequency range of 10 Hz

to 10,000 Hz. The automated comparison system is used also for double-ended,

or "piggy-back" accelerometers over this frequency range. A calibrated standard

accelerometer is mounted on top of the piggy-back accelerometer to be

calibrated, and a comparison calibration is performed on the piggy-back

accelerometer. Additional information on the test report and the assessment of

uncertainty and quality control are given in Ref. 5.

2.4 High-Frequency Range

2.4.1 General Characteristics of Exciters

Most methods for the accurate calibration of vibration pickups require

sinusoidal motion with low distortion along a single axis over a wide range of

frequencies. The air-bearing exciters described above satisfy these requirements

extremely well at frequencies up to several kilohertz. At higher frequencies,

when transverse motion of the moving element becomes objectionable,

piezoelectric exciters can be used to generate uniaxial motion over a wide

frequency range. A stagger-tuning method has been developed for building

such exciters which have low waveform distortion, minimal errors due to

transverse motion, and a relatively good approximation to flat frequency

response over a wide range [8]. The NBS piezoelectric exciters can be used

over a frequency range from 3,000 Hz to 30,000 Hz, but comparison calibrations are routinely requested only over the range from 3,000 to 15,000 Hz. A

simplified representation of a piezoelectric exciter is shown in Fig. 4. The

table material must be sufficiently stiff that the mechanical impedance of that

portion of the surface affected by the pickup attachment at any given

frequency will be much greater than the impedance of the pickup attachment.
The base must also have a sufficiently high mechanical impedance so that the

behavior of the piezoelectric exciter does not vary unduly with different

supporting structures. The dimensions of the base transverse to the long axis

1.5 INCH

0.04 INCH BUTYL RUBBER

0.03 INCH BUTYL RUBBER

TABLE

BR5E

2 INCH

1 INCH HLUMINH

2 INCH RLUMINR

1 3/4 INCH RLUMINR

5/8 INCH RLUMINR

1 INCH RLUMINR

PIEZOELECTRIC DISKS

0.3 INCH, ERCH

2 INCH TUNGSTEN CRRBIDE

FIGURE 4. PIEZOELECTRIC VIBRATION EXCITER

must be small relative to the wave length of sound in the material in order to

reduce transverse motion, but sufficiently large to provide adequate flexural

rigidity. Further details of the piezoelectric exciter characteristics are given in

Ref. 8.

2.4.2 Automated Comparison Calibration

The measurement procedure for the automated calibration system is the same

as for the mid-frequency method previously described, except for the exciters.

Most comparison calibrations are performed on the Dimoff vibration exciters,

which have a usable frequency range of 10 Hz to 10,000 Hz. There is gradually

increasing magnitude of transverse vibration at the higher frequencies, which

accounts for reduced accuracy in that frequency range. To some users this 1 percent increase in uncertainty is unacceptable. Others require a calibration at frequencies beyond 10 kHz. In those cases a piezoelectric exciter is used with

a standard accelerometer that has been calibrated interferometrically. This

approach to maintaining a 2 percent uncertainty up to 10,000 Hz has been used

at NBS since 1981 [9]. If the accelerometer to be calibrated is of the
single-ended type, the standard must be of the back-to-back type, and vice

versa. The rest of the measurement system and procedure remain unchanged

[10, 11].

2.5 Special Test of Shock Transducers

A new shock accelerometer measurement service is being offered by the

National Bureau of Standards. A computer-controlled waveform analysis and

signal processing device, employing Fast Fourier Transform techniques to

transform time-domain data into frequency-domain data, is used to determine

the frequency- dependent sensitivity in both magnitude and phase of an

accelerometer. The time-domain comparison also yields the values of peak

acceleration as well as the velocity obtained by integrating the

acceleration-versus-time curve. Comparison shock calibrations, in the frequency

domain, greatly simplify the measurements necessary to perform calibrations

throughout an acceleration range from 50 to 5,000 g. Generally, this is accomplished with the use of "half-sine" pulses having pulse widths from about

40 ms to 02 ms.

The laboratory equipment consists of four main items: a mechanical shockgenerating machine, two accelerometers, a data capture and analysis system, and

a computer for data storage and manipulation. These items provide a means

for transient-data generation, data collection and reduction, and calibration of

the test accelerometers versus a reference standard.

The reference system consists of a piezoelectric accelerometer and a matched

solid-state charge amplifier. Because the accelerometer is of the "piggy-back"

configuration, other test accelerometers can be directly mounted to its top.

This permits calibration by the "back-to-back" comparison method, where the

electrical outputs of the reference accelerometer and test accelerometer are compared. The accuracy of this method is directly dependent on the accuracy

of the calibrated reference.

Table 2 - Test Accelerations and Pulse Widths for

Special Shock Calibration Service

Nominal Peak Acceleration Average Pulse Width

(g) (ms)

50 6

100 4

500 2

1000 1

2000 OS

5000 03
The nominal peak accelerations (± 10 percent) and corresponding pulse widths

of this measurement service are given in Table 2. The reference accelerometer

is linear to within 0.5% over the range of acceleration amplitudes given in the

table.

3. ABSOLUTE CALIBRATION OF REFERENCE EXCITERS AND

ACCELEROMETERS

3.1 Absolute versus Comparison Calibration Service

The approach to vibration calibration at NBS can be summarized as follows.

A high-quality exciter with a very stable internal accelerometer is designed and

constructed. These standards are calibrated by absolute methods, and a smooth

curve is fitted to the experimental data. These results, appropriately weighted

and plotted as a function of frequency, yield the calibration factors for the

NBS standards.

Considerable effort has been devoted to obtaining the best possible calibration

for the standard exciters and accelerometers since most calibrations issued by

NBS will be based on these standards. A long history of performance has been

maintained on the NBS standards to provide enough data for good statistical

analyses. The error associated with transferring a calibration from an NBS

standard to a test accelerometer is thereby minimized. The calibration of the

standards is periodically checked, using absolute methods. The inherent

stability of these standards, together with the use of a controlled environment

in which they are stored and used, give added confidence in the uncertainty

statements for each test. Consequently, a calibration by comparison is not to

be considered inferior to an absolute calibration: as has already been suggested,

the distinction between the two is not on the basis of accuracy.

If absolute methods were used on each customer accelerometer tested, the cost

would be unjustifiably high for most users. Thus, the comparison method,

which is simple and relatively inexpensive, is requested almost exclusively. The

absolute methods are normally reserved for the calibration of NBS standards.

In the mid-frequency range, a method based on the reciprocity principle has

established itself alongside several interferometric methods; for measurements at low or high frequencies, interferometric techniques are more reliable.

The absolute methods described below are neither competing nor equivalent

but, rather, complementary. Their ranges of applicability and special features

will be pointed out. In general, it should be noted that, with the exception of

the Ronchi-grid and reciprocity methods, they are adaptations of the Michelson

interferometer to particular dynamic problems.

10
3.2 Ronchi Rulings Method

Two methods for calibrating electrodynamic low-frequency vibration exciters are the optical ruling and interferometric fringe counting methods. The first

method, which is no longer used routinely, makes use of two optical rulings

(Ronchi grids) to measure the amplitude of vibrational displacement.

STATIONARY RONCHI

RULING

PINHOLE

PHOTOMULTIPLIER

FIGURE 5. RONCHI RULING CALIBRATION SYSTEM

A diagram of this calibration system is given in Fig. 5. The two Ronchi

rulings are mounted so that the ruled lines and the ruled surfaces are parallel.

The exciter vibrates the moving ruling with respect to the stationary ruling,

causing the intensity of the laser beam entering the photomultiplier tube to be

modulated. For each displacement equal to the width of the line-pair, an

electrical pulse is generated by the photomultiplier. (A line pair is one

transparent line and one opaque line on a Ronchi ruling.) The number of

pulses per vibration cycle is directly proportional to the displacement

amplitude. Assuming sinusoidal motion, the acceleration, a, is calculated from

a = (2-17 if d - tt2 f2v /n (2)

where d = displacement amplitude,

f = frequency of vibration,

V = number of pulses per vibration cycle, and

n = number of line pairs per unit length on the Ronchi rulings.

The uncertainty associated with this method was determined as follows. Before

being mounted inside the moving element of the exciter, the reference standard

(servo accelerometer) was calibrated several times. Static calibration was

11
performed on a tilt table [12]. The uncertainty of the static value of the

sensitivity was ± 0.1 percent. The reference standard was also checked against

another NBS vibration standard, described in Section 2.3.1, from 10 to 50 Hz.

The agreement was within 2 percent.

3.3 Fringe-Counting Interferometer

A diagram of the interferometric fringe counting calibration system is given in

Fig. 6. The He-Ne laser light has a wavelength of 632.8 nm. The configuration

is basically a Michelson interferometer using a corner cube retro-reflector

mounted on the exciter. The photo-diode generates an electrical pulse for each

\I2 displacement and the counter records one fringe count. The number of

pulses per vibration cycle is directly proportional to the displacement

amplitude.

PHOTODIODE

AMPLIFIER /--v.•^, ^ K—I V / LASER \ ^==^^-J2__» NT

BEAM SPLITTER

CORNER

CUBE REFLECTOR PO'

MIRROR

DRIVE COIL

FUSE

DC POWER

AMPLIFIER

COUNTER

REFERENCE

STANDARD OUTPUT

AMPLIFIER

oscillatorI

WAVE ANALYZER

oscilloscope

voltage

measuring

systems

FIGURE 6. FRINGE COUNTING INTERFEROMETER

The acceleration is calculated from

12
a = (277 if d = \v 7t2 f2/2 (3)

where \ = wavelength of the laser light, in meters,

V = number of pulses per vibration cycle, and the other symbols have the

previously-defined meanings.

A discussion of estimated errors in the fringe-counting laser interferometer

method is given in Ref. 6. Typically, the root-mean-square error for this

method is ± 0.5 percent.

3.4 Reciprocity Calibration

The reciprocity calibration method is used to calibrate vibration exciters

equipped with a velocity coil or an accelerometer. This method is based on

measurements of voltage ratio, resistance, frequency, and mass.

The Bouche-Levy reciprocity calibration method consists of two experiments: (1)

measurement of transfer admittance between the driving coil and the reference

accelerometer, and (2) measurement of the voltage ratio of the reference

accelerometer and the open-circuited driving coil of the vibration exciter when

the latter is driven mechanically by an external shaker [13-17].

In both voltage-ratio and transfer-admittance measurements, the static value of

the vertical position of the coil in the gap of the magnet is critical because of

the limited distance over which the magnetic field is uniform. It is important

to keep this position constant throughout the calibration procedure. For this

reason, an optical detector and position control are incorporated into the

calibration system. A control unit is attached to a dc motor which controls

the vertical position of the moving element. Once a position is selected, the

control unit will keep this position constant. This greatly improves

repeatability of data and provides for ease of operation.

POWER

HMPLIFIER \

"N MflTCHINC inPEOHNCE

I /X /

DRIVER COIL^

c

_ 2

>

FUNCTION

CENERHTOR

PRECISION ^ RESISTOR N ///

^ — ACCELEROMETER FIGURE 7. CONNECTIONS FOR TRANSFER-ADMITTANCE

IN THE RECIPROCITY EXPERIMENTS

13
The first experiment consists of measuring the electrical transfer admittance

using the circuit of Fig. 7. The relationship defining this transfer admittance is Y = I/E,2 (4)

where

Y = transfer admittance

E^2 = voltage generated in the standard accelerometer and amplifier,

I = current in the driver coil, and the bold letters denote phasor (complex)

quantities.

The current is determined by measuring the voltage drop across a standard

resistor. The phase, (|>y , of Y is measured with a phase meter having an

uncertainty of ± 0.1 deg or better.

Transfer admittance measurements are made with a series of masses attached,

one at a time, to the table of the exciter. Also, a zero-load transfer

admittance measurement is made before and after attaching each mass. This

zero-load measurement is denoted by Y^ . Using the measured values of Y,

and Yq , graphs of the real and imaginary values of the ratio

T, = M, / (Y-YJ (5)

are plotted versus M^ for each frequency, where M^ are the values of mass

attached to the table. The zero intercepts, Jj and J^. , of the resulting

nominally straight lines and their slopes, Q and Q^. , are computed by a weighted least-squares method [16]. The values of Y^, used in the calculations are obtained by averaging the values of the Y^ measurements before and after

each measurement of Y using different masses. These computed values are used

in determining the sensitivity of the standard.

STflNDRRD ACCELEROMETER

DRIVER COIL M

^?rzr—,

FIGURE 8. CONNECTIONS FOR VOLTAGE-RATIO MEASUREMENT

IN THE RECIPROCITY EXPERIMENTS

The electrical connections for the second experiment are shown in Fig. 8. The

ratio of two voltages is measured while the exciter is driven with an external

14
exciter. The voltage ratio is given by

R = Ei4 / E,; (6)

where E^^ = voltage generated in the standard accelerometer and amplifier,

and

^15 ~ open-circuit voltage in the driving coil.

After R , Jj. , Jj , Q^ and Q. have been determined for a number of

frequencies, f, the sensitivity of the exciter is calculated using the relationships

(given in Refs. 13-15):

where j = the unit imaginary vector,

J = Jr + JJi . Q = Q, + jQi , and

M = J (Y-YJ / (1- Q(Y-YJ ) The sensitivity of the exciter is, therefore, determined from the measured

quantities Q, J, T, f, and the masses M^^ which are attached to the exciter table.

The sensitivity as computed from eq. (7) has the units of V per m/s/s if the

values of the measurands are in the SI system. If the masses M^^ are not in

kilograms, appropriate conversion factors must be applied to the quantities J, Q,

and M. A commonly used engineering formula [17], with the mass expressed

in pounds and the sensitivity in mV per g, is S = 2635 (RJ/ jf)

1/2

, (8)

which assumes that MQ/J « 1, a condition usually satisfied in practice. The

use of a computer greatly facilitates the application of the reciprocity

calibration process. A desktop computer programmed in BASIC performs the

necessary calculations and controls the acquisition of data [15].

Originally stainless steel masses were used, but they limited the usable

frequency range to about 5 kHz by resonating at relatively low frequencies.

To extend the frequency range, a new set of masses was fabricated of tungsten

carbide. The values range from 93 grams to 185 grams; the effects of lower

mass values are difficult to resolve. The calibration factors for a 20-gram mass

are computed by interpolating between the zero-load and 93-gram-load

sensitivities. The surfaces of the masses which attach to the exciter table were

ground and lapped flat across their surfaces to within one wave-length of

visible light. The surfaces of the exciter tables are also lapped flat. With

these changes, reciprocity data can be obtained from 10 Hz to 10 kHz.

15
Reference 4 discusses the error analysis for a reciprocity calibration of an

air-bearing exciter with a ceramic-moving element. It is unrealistic to assume

that all of the errors listed there are correlated, and the square root of the

sum of the squares is considered to be a more valid estimate of uncertainty.

It is ± 0.85 percent.

The frequency range where the reciprocity method has been found to be most

accurate is from 100 to 1000 Hz. Below 100 Hz, difficulties in suspension of the

moving element in electrodynamic exciters cause cross-axis motion to be

difficult to control; in this range, the fringe-counting method has proven to be

less vulnerable to the problem. Above 1000 to 2000 Hz (depending on the

exciter) harmonic distortion increases slightly on most exciters, thereby

decreasing the accuracy somewhat. Above 1000 to 2000 Hz, the fringedisappearance method and the use of piezoelectric exciters have proven to be

the most accurate, apparently due to lower distortion in motion generated by

the piezoelectric exciters in this frequency range.

OSCILLATOR

SHRKER

MIRRORS/

SHAKER 3- :-^-

AMPLIFIER

FREQUENCY

SYNTHESIZER

be:rm_

splitter

LASER

DETECTOR D C VOLTMETER

A C VOLTMETER

COMPUTER

FIGURE 9. OPTICAL MEASUREMENT SYSTEM FOR

121 nm DISPLACEMENT

3.5 Automated Fringe-Disappearance Interferometer

A two-beam Michelson Interferometer has been adapted to measure the

magnitude and phase of the sensitivity characterizing a vibration pickup and

the system is fully automated with the use of a desktop computer. It was

designed to operate in the frequency range 1 to 20 kHz, depending on the

vibration exciter used. The measurement system is shown schematically in Fig.

9. If the difference of the interferometer optical path length, 2\ = 2(Lj -L2 ),

16
is modulated by periodically vibrating one of its mirrors, both the amplitude

and the phase of this modulation are encoded in the intensity of the light

impinging on the photodetector.

The sensitivity of a pickup is defined as the ratio of its electrical output to

the mechanical input. In the case of an accelerometer excited by sinusoidal

displacement, the magnitude of the sensitivity S is given by

S = V2 E / (2 77 f)2 d, (9)

where f is the frequency, d is the peak value of the vibratory displacement,

and E is the rms value of the accelerometer output.

Because the value of d in Eq. (9) is determined by the wavelength of the light

used, the method is described as absolute, although, in a strict sense, this

designation applies only to the displacement measurement.

The basis for the measurement is the following equation for the time-averaged

output, I, of the photodetector [18]:

1= A +B cos(47tA / X )J^(4iT d/X ), (10)

where J^^ is the Bessel function of the first kind of order zero, and A, B are system constants. A low-frequency (0.1 - 0.5 Hz) sinusoidal or triangular sweep

is applied to the piezoelectric drive of the "fixed" mirror to cause periodic

changes in A . These changes produce a slowly varying component in the

photodetector output which can be followed by a dc voltmeter. To extract the

displacement amplitude d from the Bessel function J^^ (4tt d/X ), the computer

records

M = max(r) - min(r) (11)

as a function of E when A is varied.

On substituting the expression for d from Eq. (9) into Eq. (10),

47T V2_E

~x" '(o2 S'

M = 2BJo ( i?-

y--(~f- ) . (12)

Since we are ultimately interested in the root of J^ (4TTd/X), the Bessel function

is replaced by the first two terms of its Taylor expansion about the root,

resulting in a linear relationship between M and E. The E-intercept, therefore,

becomes

EIm=o = 2.40482 A S/ (4tt V2) (13)

17
from which S can be calculated. When the vibration exciter is set precisely at

121.10-nm peak displacement and the acceleration is expressed as a multiple of

the standard acceleration of free fall, g = 9.80665 m/s/s , the working formula

for sensitivity becomes

S = (2.9008/ P ) El^^o mV per g, (14)

where E is the rms value of the accelerometer output in millivolts, and f is the vibration frequency in kilohertz.

Details of the measurement of the magnitude of S are given in Ref. 18. That

paper also discusses measurement of the phase of S, whose implementation,

however, has not yet reached the state of completion sufficient for

documentation in this Technical Note.

The first performance test of the measurement system consisted of ascertaining

the response of the system components to changes in critical parameter values.

It was found that the smallest measurable changes in displacement magnitude

was less than 0.1 percent, corresponding to about 0.1 nm. Reference 17 describes

a computer-controlled displacement interferometer used to evaluate the

performance of piezoelectric exciter designs. Six reflecting mirrors are mounted around the perimeter of the top surface of the exciter, with the

center section reserved for transducer mounting. By measuring the sensitivity

of the transducer mounted at the center with reference to the 121.1 nm

displacement of each mirror, one can effectively map the motion of the surface

of the exciter. The data for the sensitivity values for the six positions for a stagger-tuned exciter described in Ref. 8 have shown a maximum spread of less

than 2 percent for any frequency tested.

The noise floor for the very-low-frequency diagnostic signals sampled with the

dc voltmeter is about 1 mV. This permits a 60-dB dynamic range in M = 2BJ^^

(4tt d/\ ). In terms of displacement this means that only the band 121.0 to 121.2

nm is below the noise floor. The sensitivities obtained for a test accelerometer

by this method agree with those obtained by reciprocity to within 1 percent

over the frequency range 3 - 10 kHz. The frequency range is determined

primarily by the characteristics of the vibration exciter. The range of

calibration is about 1 to 10 kHz for the routine test range and extends to 30

kHz for special tests. Although the results have been highly repeatable, at the

present time only a 2 percent accuracy is claimed for the magnitude [10].

3.6 Laser Interferometer Using the J^ -Null Method

This method, although mathematically similar to fringe disappearance, relies on

finding the nulls in the fundamental (ac) component of the signal from the

photodetector. The instrumentation is, therefore, quite different, except for the

interferometer. Environmental restrictions are more severe.

18
The interferometer apparatus is mounted on a granite isolation platform with

air springs as isolators. This isolation from floor movement is required to

provide the necessary stability in the photodetector signals. Air currents in the

room can cause some problems by moving the interferometer components and

changing the refractive index of the air. A shield around the beamsplitter and

mirrors helps stabilize the interferometer. An active method of stabilization

has also been successfully tested [20].

A He-Ne laser is used in this interferometer. The fixed mirror, fabricated of

fused silica, is mounted in a holder with micrometer adjustments for rotation

and tilt. The fused silica beamsplitter is in a similar mount. The

beat-frequency oscillator of a wave analyzer serves as signal source to drive the

exciter and also to filter the photodetector signal. The configuration is shown

in Fig. 10.

To make amplitude measurements, the following procedure is followed. Before

energizing the exciter, the interferometer must be aligned by use of the

micrometer adjustments on the beam splitter and fixed-mirror mounts. After

energizing the exciter, the translation stage of the photodetector is adjusted for

maximum voltage on the analyzer meter. To achieve maximum signal-to-noise

ratio, small adjustments in the position and orientation of the photodetector

assembly are required.

riXED MIRROR

BEHM SPLITTER

] -''k 1 LASER

EXCITER ~~1

T

HCCELEROMETER [QDETECTOR

H C VOLTMETER <3

POWER AMPLIFIER

INPUT BEAT FREQUENCY OSCILLATOR

RESTORED OUTPUT

WAVE ANALYZER

SCOPE

FIGURE 10. OPTICAL MEASUREMENT SYSTEM

FOR 193 nm DISPLACEMENT

The filtered signal from the photodetector will go through nulls as the

vibration amplitude is increased. The amplitude of the photocurrent follows

the form [21]:

Ij = 2BJi (4 TT d/\ ), (15)

19
where Jj is the first-order Bessel function of the first kind, and the other

symbols have the previously defined meanings.

At discrete amplitudes of vibration, corresponding to nulls of the \ Bessel

function, the acceierometer output is measured by a digital voltmeter. The

sensitivity is then calculated according to Eq. (9) above. The null points may

be established by the wave analyzer, and are usually at least 60 dB below the

maximum photodetector output signal. With the He-Ne light source, the first

null occurs at d=192.96 nm. Since the filtered output of the photodetector is a replica of the vibrational displacement, a phase calibration of the pick-up can

readily be obtained with this set-up [22].

3.7 Folded-Beam Interferometer

The folded-beam interferometer is very similar to the Michelson

interferometers described in the previous sections. Its purpose is to increase

the resolution of the displacement measurement. For example, if the

information-carrying beam of a fringe-counting interferometer is made to

undergo seven folds, the double- amplitude displacement necessary for a dark-bright fringe change at the photodetector is only one-seventh of the

normal X/4. The artifice of beam folding is not limited to any particular

method of processing the information. It has also been applied to the method

of Section 3.6 to maintain a more uniform test acceleration over a broad range

of frequencies.

EXCITERfc::^

I

TRHNSLHTION

STRGE

POWER AMPLIFIER

TRHNSLHTION

STHGE

INPUT BEHT FREQUENCY OSCILLATOR RESTORED

OUTPUT

WHVE HNHLYZER

PHOTODETECTOR

SCOPE

FIGURE 11. FOLDED BEAM INTERFEROMETER

A folded-beam configuration is shown in Fig. 11. The light from the laser source is split into two beams: a reference beam and a beam impinging on the

20
mirror attached to the moving element of the vibration exciter. The latter

beam then undergoes multiple reflections between this mirror and an adjustable

one in front of the moving element. The number of such reflections (folds)

depends on the distance and angle between the mirrors. The emerging beam

then enters a second beam splitter where it recombines with the reference

beam. The angle between the normal to the exciter top and the incident light

beam must be small to minimize the error in the amplitude measurement. The

error will be proportional to (1-cos 9 ), where 6 is the angle between the

incident light and the normal. The apparatus is mounted on a granite

isolation platform with air springs as isolators. This isolation from floor

movement is required to improve the signal-to-noise ratio of the photodetector

output.

4. References

1. IEEE Standard Dictionary of Electrical and Electronic Terms, p.l (IEEE,

Inc. New York 1977).

2. ISO/DIS 5347 Methods of Calibration of Vibration and Shock Pickups,

distr. by American National Standards Institute, New York, (International

Organization for Standardization, 1985).

3. National Bureau of Standards Calibration Service Users Guide,Nat. Bur.

Stand. (U.S.), Spec. Publ. 250 (1986).

4. T. Dimoff and B. Payne, "Development and Calibration of NBS Vibration

Shaker AF V," NBS Report 9670, January 1968.

5. B. F. Payne, and M. R. Serbyn, "Calibration of Accelerometers by

Comparison with NBS Standards," NBS Technical Note (in preparation).

6. R. S. Koyanagi, "Development of a Low-Frequency Vibration Calibration

System," Experimental Mechanics, 15, 443-448 (1975).

7. T. Dimoff, "Electrodynamic Vibration Standard with Ceramic Moving

Element,"!. Acoust. Soc. Amer. 40, 671 (1966).

8. E. Jones, W. B. Yelon, and S. E. Edelman, "Piezoelectric Shakers for

Wide-Frequency Calibration of Vibration Pickups," J. Acoust. Soc. Amer.

45, 1556-1559 (1969).

9. B. F. Payne, "Absolute Calibration of Back-to-Back Accelerometers," Proc.

ISA 27th Intlnstrumentation Symposium, Indianapolis, Ind. April 26-30,

1981.

10. B. F. Payne, "The Back-to-Back Accelerometer as a High Frequency

21
Vibration Standard," Proc. ISA 31st Int. Instrumentation Symposium, San

Diego, CA, May 6-9, 1985.

11. B. F. Payne, "The Application of Back-to-Back Accelerometers to

Precision Vibration Measurements," J. Research NBS 88, 171-174, (1983).

12. American National Standard, "Methods for the Calibration of Shock and

Vibration Pickups," S2.2-1959 (R1976), (American National Standards

Institute, New York, NY).

13. S. Levy and R. R. Bouche, "Calibration of Vibration Pickups by the

Reciprocity Method," J. Research NBS 57, 227-243 (1956) RP2714.

14. R. R. Bouche and L. C. Ensor, "Use of Reciprocity Calibrated

Accelerometer Standards for Performing Routine Laboratory Comparison

Calibrations, "Shock and Vibration Bull., 34, Part 4, pp. 21-29, February

1965.

15. B. F. Payne, "Absolute Calibration of Vibration Generators with Timesharing Computer as Integral Part of System,"Shock and Vibration Bull.,

36, Part 6, pp. 183-184, February 1967.

16. R. R. Bouche, Development of Standards for the Measurement of

Vibratory Motion, Ph.D. Thesis, Department of Mechanical Engineering,

University of Maryland, 1959.

17. R. R. Bouche, Calibration of Shock and Vibration Measuring Transducers

(The Shock and Vibration Information Center, Washington, DC 1979).

18. B. F. Payne, and M. R. Serbyn, "An Automated System for the Absolute

Measurement of Pickup Sensitivity," Nat. Conf. of Standards Laboratories

1983 Workshop and Symposium, Boulder, CO, July 18-21, 1983.

19. B. F. Payne, "Automation of Vibration Testing at the National Bureau of

Standards,"Proc. lES 30th Annual Technical Meeting, Orlando, FL, May

1-3, 1984 (lES, Mt. Prospect, IL).

20. M. R. Serbyn, and W. B. Penzes, "A Real-Time Active Vibration

Controller,"ISA Transactions, 21, 55-59 (1982).

21. V. A. Schmidt; S. Edelman, E. R. Smith, and E. Jones, "Optical

Calibration of Vibration Pickups at Small Amplitudes," J. Acoust. Soc.

Amer., 33, 748-751, (1961).

22. M. R. Serbyn and F. A. Andrews, "Measurement of the Phase of

Vibrational Displacement by a Laser Interferometer," J. Acoust. Soc.

Amer., 46, 2-5 (1969).

22
NBS»n4A (REV. 2-80) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

iNlBS/TN-1232

2. Performing Organ. Report No, 3. Publication Date

Feb. 1987

4. TITLE AND SUBTITLE

A Description of NBS Calibration Services in Mechanical Vibration and Shock

5. AUTHOR(S)

D. C. Robinson, M. R. Serbyn, B. F. Payne

6. PERFORMING ORGANIZATION (/fjo/nt or other thon NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

«U(9WNS;r»]i:^Z)XOLXXK3CMX

Gaithersburg, MO 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State, ZIP)

Same as item 6.

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual sumnf)ary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Accurate calibration of accelerometers requires that accurate measurement techniques

be developed and maintained. Calibrations of vibration exciters and pickups are performed by comparison with the response characteristics of NBS standard accelerometer^

or by absolute methods. This paper gives a summary of the various calibration procedures used in the calibration of accelerometers and reference exciters. The

frequency ranges, vibration levels and accuracy statements for standardized tests

designed to meet a variety of user needs are listed.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Absolute calibration; accelerometers; calibration services; comparison calibration; fre

quency ranges; interferometer; reciprocity method; reference exciter; shock calibration

standard accelerometer; vibration measurements

13. AVAILABILITY

KX] Unlimited

I I For Official Distribution. Do Not Release to NTIS

y^ Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

[^31 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

26

15. Price

^U.S. GOVERNMENT PRINTING OFFICE: 1987 — 181-076/60030 USCOMM-DC 6043-P80

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