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CHAPTER 18

CALIBRATION OF PICKUPS

M. Roman Serbyn

Jeffrey Dosch

INTRODUCTION

This chapter describes various methods of calibrating shock and vibration transduc-

ers, commonly called vibration pickups. The objective of calibrating a transducer is

to determine its sensitivity or calibration factor, as defined below. The chapter is

divided into three major parts which discuss comparison methods of calibration,

absolute methods of calibration, and calibration methods which employ high accel-

eration and shock. Field calibration techniques are described in Chap. 15.

PICKUP SENSITIVITY, CALIBRATION FACTOR,

AND FREQUENCY RESPONSE

As defined in Chap. 12, the sensitivity of a vibration pickup is the ratio of electrical

output to mechanical input applied along a specified axis. 1–3 The sensitivity of all

pickups is a function of frequency, containing both amplitude and phase informa-

tion, as illustrated in Fig. 18.1, and therefore is usually a complex quantity. If the sen-

sitivity is practically independent of frequency over a range of frequencies, the value

of its magnitude is referred to as the calibration factor for that range, but it is speci-

fied at a discrete frequency. The phase component of the sensitivity function likewise

has a constant value in that range of frequencies, usually equal to zero or 180°, but it

may also be proportional to frequency, as explained in Chap. 12.

The frequency response of a pickup is shown by plotting the magnitude and phase

components of its sensitivity versus frequency. This information is usually presented

relative to the value of sensitivity at a reference frequency within the flat range. A

preferred frequency, internationally accepted, is 160 Hz.

Displacements are usually expressed as single-amplitude (peak) or double-

amplitude (peak-to-peak) values, while velocities are usually expressed as peak,

root-mean-square (rms), or average values. Acceleration and force generally are

expressed as peak or rms values. The electrical output of the vibration pickup may

be expressed as peak, rms, or average value. The sensitivity magnitude or calibration

factor are commonly stated in similarly expressed values, i.e., the numerator and

18.1

18.2

CHAPTER EIGHTEEN

0 °

PHASE RESPONSE

–30 °

–60 °

–90 °

AMPLITUDE (SENSITIVITY)

RESPONSE

–120 °

–10

–150 °

–20

–180

0.05

–30

0.1 0.2 0.3 0.4 0.5

PROPORTION OF MOUNTED RESONANCE FREQUENCY f m

1.5

FIGURE 18.1 Pickup amplitude and phase response as functions of frequency. ( After M. Ser-

ridge and T.R. Licht. 4 )

denominator are both peak or both rms values. Examples of typical sensitivity spec-

ifications for an accelerometer: 2 pC per m/sec 2 , 10 millivolts/m/sec 2 , 5 milliV/ g

(where C is the symbol for coulomb, V is the symbol for volt, and g is the accelera-

tion of gravity). For some special applications it may be desirable to express the sen-

sitivity in mixed values, such as rms voltage per peak acceleration.

CALIBRATION TRACEABILITY

In calibrating an instrument, one measures the instrument’s error relative to a refer-

ence which is traceable to the national standard of a country. A calibration is said to be

traceable 5 to a national or international standard if it can be related to the standard

through an unbroken chain of comparisons—all having stated uncertainties. In the

U.S.A., for example, national vibration standards are maintained at the National Insti-

tute of Standards and Technology in Gaithersburg, Maryland. A number of other

national metrology laboratories having known capabilities for maintaining national

vibration standards are listed in Table 18.1. Countries whose national laboratories do

not provide a national vibration standard may belong to a regional international asso-

ciation, such as NORAMET (North American Metrology Cooperation), EUROMET

(European Metrology Cooperation), or OIML (Organization for Legal Metrology)

that can assist transducer manufacturers in setting up steps necessary for establishing

traceability to a national standard.

Vendors of transducers must be able to show that calibrations of their instru-

ments are traceable to a national standard by means of calibration reports stating

the value(s) of sensitivity, measurement uncertainty, environmental conditions, and

18.3

CALIBRATION OF PICKUPS

TABLE 18.1 National Standards Laboratories Responsible for the Calibration

of Vibration Pickups

Institution

Laboratory

Location

Country

CSIRO

Natl. Measurement Laboratory

Lindfield

Australia

INMETRO

Laboratório de Vibrações

Rio de Janeiro

Brazil

NRC-CNRC

Inst. Natl. Meas. Stds.

Ottawa

Canada

NIM

Vibrations Laboratory

Beijing

China

CMU

Primary Stds. of Kinematics

Prague

Czech Repub.

B&K

Danish Prim. Lab. for Acoustics

Naerum

Denmark

BNM

CEA/CESTA

Belin-Beliet

France

PTB

Fachlabor. Beschleunigung

Braunschweig

Germany

IMGC

Sezione Meccanica

Torino

Italy

NRLM

Mechanical Metrology Dept.

Tsukuba

Japan

KSRI

Division of Appl. Metrology

Daedeog Danji

Rep. of Korea

NMC

SIRIM

Berhad

Malaysia

CENAM

Div. Acustica y Vibraciones

Queretaro

Mexico

DSIR

Measurement Stds. Laboratory

Lower Hutt

New Zealand

VNIIM

Mendeleyev Inst. for Metrology

St. Petersburg

Russia

ITRI

Center for Measurement Stds.

Hsinchu

Taiwan

NIST

Manufacturing Metrology Div.

Gaithersburg

U.S.A.

identification of the standard(s) used in the calibration procedure. Depending on

the application, there may be one or more links to the national standard.

Primary and Secondary Standards. Primary standards, 6,7 maintained at national

metrology institutes, are derived from absolute measurements 8 of the transducer’s

sensitivity, measured in terms of seven basic units. For example, the absolute meas-

urement of “speed” must be made in terms of measurements of distance or distance

and time, not by a speedometer. Thus the word absolute implies nothing about preci-

sion or accuracy. An example of a laboratory setup for the calibration of primary-

standard accelerometers, derived from absolute measurements, is shown in Fig.

18.2. 9

A vibration exciter generates sinusoidal motion which is measured by a

ACCELEROMETER

STANDARD

AIRBORNE

ACCELERATION EXCITER

INTERFEROMETER

LASER

SIGNAL-

PROCESSING

SYSTEM

LIGHT

DETECTOR

DUMMY

MASS

INDICATING

INSTRUMENT

(STANDARD)

FIGURE 18.2 Primary (absolute) calibration of an accelerometer standard using laser interferom-

etry. ( After von Martens. 9 )

18.4

CHAPTER EIGHTEEN

Michelson interferometer (described later in this chapter). The vibration is applied

to the base of the standard accelerometer whose output is measured. A dummy

mass, mounted on its top surface, simulates the conditions when this standard

accelerometer is used to calibrate a secondary standard 10 accelerometer by the com-

parison method described in the next section. Secondary standards (also referred to

as transfer standards or working standards ) are maintained at various government

laboratories and industrial laboratories. A secondary standard accelerometer may be

calibrated either from absolute measurements or from a comparison with a primary

standard accelerometer. Such secondary standards are usually used for purposes of

comparisons of calibrations between laboratories or for checking production and

field units.

COMPARISON METHODS OF CALIBRATION

A rapid and convenient method of measuring the sensitivity of a vibration pickup to

be tested is by direct comparison of the pickup’s electrical output with that of a sec-

ond pickup (used as a “reference” standard) that has been calibrated by one of the

methods described in this chapter. A comparison method is used in most shock and

vibration laboratories, which periodically send their standards to a primary stan-

dards laboratory for recalibration. This procedure should be followed on a yearly

basis in order to establish a history of the accuracy and quality of its reference stan-

dard pickup.

In this method of calibration the two

pickups usually are mounted back-to-

back on a vibration exciter as shown in

Fig. 18.3. It is essential to ensure that

each pickup experiences the same

motion. Any angular rotation of the

table should be small to avoid any dif-

ference in excitation between the two

pickup locations. The error due to rota-

tion may be reduced by carefully locat-

ing the pickups firmly on opposite faces

with the center-of-gravity of the pickups

located at the center of the table. Rela-

tive differences in pickup excitation may

be observed by reversing the pickup

locations and observing if the voltage

ratio is the same for both positions.

Calibration by the comparison method is limited to the range of frequencies and

amplitudes for which the reference standard pickup has been previously calibrated.

If both pickups are linear, the sensitivity of the test pickup can be calculated in both

magnitude and phase from

FIGURE 18.3 Comparison method of calibra-

tion: Pickup 2 is calibrated against Pickup 1 (the

reference standard). The two pickups may be ex-

cited by any of the means described in this chap-

ter. ( After ANSI Standard S2.2-1959, R 1997. 1 )

e t

e r

S t =

S r

(18.1)

where

S t = sensitivity of test pickup

S r = sensitivity of reference standard pickup

e t = output voltage from test pickup

e r = output voltage from reference standard pickup

18.5

CALIBRATION OF PICKUPS

Several calibration methods described below are variations on the implementation

of Eq. (18.1); they differ mainly in the manner of vibration excitation.

USING THE COMPARISON METHOD

A simple and convenient way of performing a comparison calibration is to fix the

test pickup and reference standard pickup so they experience identical motion, as in

Fig. 18.3. Then, set the frequency of the vibration exciter at a desired value, adjust the

amplitude of vibration of the vibration exciter to a desired value, and then compare

the electrical outputs of the pickups. Often, instead of making a comparison at a

fixed frequency, a graphical plot of the sensitivity versus frequency is obtained by

incorporating a swept-frequency signal generator in the calibration system.

RANDOM-EXCITATION-TRANSFER-FUNCTION METHOD

The use of random-vibration-excitation and transfer-function analysis techniques

can provide quick and accurate comparison calibrations. 11 The reference standard

pickup and the test pickup are mounted back-to-back on a suitable vibration exciter.

Their outputs are usually fed into a spectrum analyzer through a pair of low-pass

(antialiasing) filters. The bandwidth of the random signal which drives the exciter is

determined by settings of the analyzer.

This method provides a nearly continuous calibration over a desired frequency

spectrum, with the resulting sensitivity function having both amplitude and phase

information. Since purely sinusoidal motion is not a requirement as in the other cal-

ibration methods, this lessens the requirements for the power amplifier and exciter

to maintain low values of harmonic distortion. A very useful measure of process

quality is obtained by computing the input-output coherence function, which

requires knowledge of the input and output power spectra, the cross-power spec-

trum, and the transfer function.

CALIBRATION BY ABSOLUTE METHODS

RECIPROCITY METHOD

The reciprocity calibration method is an absolute means for calibrating vibration

exciters that have a velocity coil or reference accelerometer. This method relates the

pickup sensitivity to measurements of voltage ratio, resistance, frequency, and mass.

For this method to be applicable, it is necessary that the vibration exciter system be

linear (e.g., that the displacement, velocity, acceleration, and current in the driver

coil each increase linearly with force and driver-coil voltage). The reciprocity

method is used chiefly with electrodynamic exciters 12

but also with piezoelectric

vibration exciters. 13

The reciprocity method generally is applied only under controlled laboratory

conditions. Many precautions must be taken, and the process is usually time-

consuming. Several variations of the basic approach have been developed at

national standards laboratories. 14,15 The method described here has been used at the

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