Piezoelectric Accelerometers and Vibration Preamplifier

8/20/2019 Piezoelectric Accelerometers and Vibration Preamplifier

1/160


2/160

PIEZOELECTRIC

CCELEROMETER

AilD

VIBRATION

REAMPLFIER

HAl{DBOOK

by

Mark Senldge, BSc

and

Torben

R. Llcht, MSc

Revislon

November1987

hn6

m Dmmd: K

LaM &Sen IS.

Ox-zmctdruo


3/160

CONTENTS

1. V|BRAT|ONTEASUREMENT ............

................

1.1.TNTRODUCTTON

... . . . . . . . . . . . . . . . . . . .

1.2.WHY MEASURE IBRATTON? . . . . . . . . . . . . . . . . . . . . .

1.3.WHAT S V|BRAT|ON?.. . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

1.4.V|BRAT|ON ARAMETERS............ ..............

1.5.THE

QUANTIFICATIONF VIBRATION EVELS ............

Linear amplitude

and

frequency

cales

...........................

Logarithmicamplitudeand frequencyscales .................

1.6.ANALYSISOF VIBRATIONMEASUREMENTS ..............

1

2. THE PIEZOELECTRICACCELEROiIETER

2.1. NTRODUCTION . . . . . . . . . . . . . . . . . . . . .

t2

2.2.OPERATTONF AN ACCELEROMETER .......................

3

Analytical

reatmentol accelerometer peration ...............................4

2.3.FREQUENCY ANGE ........;................

. . . . . . . . . . . . . . . . . . . . .8

Upper frequency imit ..........

9

Lower

frequency

imit ..........

0

2.4.PIEZOELECTRIC ATERTALS ...................

0

2.5.PRACTICAL

CCELEROMETER ESIGNS ....................

2

Line-drive ccelerometers

Other designs .................. ............................

5

2.6.ACCELEROMETER

ENSITIVITY .............5

Chargeand voltage sensitivity ..................

6

Uni-Gainosensitlvity ............8

Linearityand

dynamlc

range .......... ..........

8

Transverse

sensltlvlty ..........

9

2.7.PHASE

RESPONSE

..............

0

2.8.TRANSTENT

ESPONSE .............. .............

3

Leakageeffects ....................3

Ringing

. . . . . . . . . . . . . . . . . . . . .

5

12

Zero shift .........

7


4/160

3.

VIBRATION REAMPLTFTERS

.. . . . . . . . .

. . . . . . . . . . . . . . .8

3.1.

PREAMPLTFTER

ESTGN ND OPERATTON... . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . .

9

3.2.CHARGEAMPLIFIERS . . . . . , . . .

9

Chargesensit iv i ty

. . . . . . . . . . . . . . . . .

0

Lower LimitingFrequency ................. ....... 4

Capacitive oadingof input by accelerometer

ables

.......................

8

Chargeattenuation

......,.......9

Nolse n chargeampli f iers

. . . . . . . . . . . . . . . . . . . . . . . .

0

3.3.VOLTAGE REAMPLTFTERS............

........... 4

Voltagesensitivity

................

5

Lower Limiting

Frequency

................. .......

56

Noise n voltage

preamplif iers

..................

7

3.4.PREAMPLIFIER UTPUTCABLES ...........

7

3.5.

L|NE-DRTVE

YSTEMS

... . . . . . . . . . . . . . .

. . . . . . . . . . . . .

8

Br0el

&Kjer

line-drive

accelerometer nd line-drivesupply ...........

1

BrUel

Kjer

line-driveamplif ier

and

line-drive

supply .....................1

3.6.COMPARISON F THE SENSITIVITY

F

DIFFERENT

VIBRATION REAMPLIFIER

YSTEMSTO

EXTERNAL O|SE

SOURCES . . . . . . . . . . . . . . . . . . .1

Groundedaccelerometer nd charge

preamplif ier

................... ' ........

+

Grounded

accelerometer

with

charge

preamplif ier

(" f loat ing"

nput) . . . . . . . . . .

. . . . . . . . . 5

Brriel&Kjar l ine-driveamplif ierand

power

supply

(grounded nput) .......... ......... 6

BrUel

Kjar

line-driveamplif ierand

power

supply

(" f loat ing"

nput) . . . . . . . . . .

. . . . . . . . .

8

Line-drive system based

on

constant

current

power

supply

. . . . . . . . . . . . . . . . . .

. . . . . . 0

Balancedaccelerometer nd differential harge

ampli f ier . . . . . . . . . .

9

fnsufatedmounting

of the

accelerometer

...........-.........1

3.7.SPECTAL REAMPLTFTEREATURES.. . . . . . . . . . . . . . . . . . . . . . . . . .1

fntegrationNetworks ...........2

Fi l ters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

Overload ndicator ...............8

ReferenceOscillator ...-........8

PowerSuppl ies . . . . . . . . . . . . . . . . . . . . .8

ACCELEROMETER ERFORMANCEN PRACTTCE ...............................9

4.1. NTRODUCTTON ... . . . . . . . . . . . . . . . . .9

4.2.ENVTRONMENTALFFECTS

.....................0

Temperature ange ........... ...........................

0

Temperatureransients .......

2


5/160

Acoustic

sensitivity

.. '.. ' ........4

Base

strains

. . . . . . . . . . . . ' . . . " . . . . . . . ' .

5

Humidity

.'......-. 5

Magnetic

sensitivity

.............

6

Radiat ion

. ' . . . ' . . . 6

4.3.MASS LOADINGEFFECTSOF ACCELEROMETERS........................6

4.4.MOUNTTNG

HE ACCELEROMETER

... . . . . . . .

. . . . . . . . . . . . . . . . . . .8

Vibration est

surface

inish

requirements

.........

........ ' .

9

Mount ing

ocat ion

.. . . . . ' . . ' . . . . . . .

9

Determination

of the

frequency

response

of accelerometers

using different

mounting

echniques

..'.. ' .90

Stud

mount inS

.. . . . . . . . . . . . . . . . .

. . . . . . . ' . . ' . . . . . . . . . . . . . . . '

0

Wax mount inS

.. . . . . . . . . . . . . . . .

. . . . . . . ' . . . ' . . . . ' . . ' . . " . . ' .

3

Magnetic

mounting

.'.. '..........5

Self-adhesive

mounting

discs

...........

....... ' 7

Adhesives

..... '..

8

Probes

.. . . . . . . . . . .

02

4.5.MECHANICAL

ILTERS

.. . . . . . . . . . . . . . . .

. . . . . . . . . .

05

Description

.... 105

Operation

..... '106

4.6.ACCELEROMETER

ABLES

.. . . . . . . . . . . . . . . . . .

07

4.7.GROUNDTNG

RECAUTIONS

.. . . . . . . . . . . . . . . . .

09

ACCELEROMETER ALIBRATION ND TESTING ................................11

5'1 ' NTRoDUcr loN

"""""""""

111

Why

calibrate

an accelerometer?

....... ' .-

13

5.2.

THE HIERARCHY

F CALIBRATION

TANDARDS

.. . . . . . . . . . . . . . . . . . . . . . . .

14

The

general

hierarchy

.'.....

114

The

hierarchy

t B&K

.. . . . . . . . . . . . . . . . .

. ' . . ' . . . . . . .15

The accuracy

ol calibration

echniques

...............

......

118

5.3.

CALTBRATION

ETHODS

... . . . . . . . . . . .

. . . . . . . . . 19

Laser Interferometery .'......119

Other absolute

methods

'.......... ' ....... ' ......

21

Comparison

calibration

by

the

"back-to-back"

method

..".

121

FFT-based

back-to-back

calibration

'-..-

123

The

use

of calibrated

vibration exciters

for sensitivity

hecking

.".. 124

5.4.

MEASUREMENT

F OTHER

ACCELEROMETER

ARAMETERS

.

125

Transverse

ensitivity

.'.."..

125

Frequency esponse .... '...... 26

Undamped

natural

requency

...... '......... ' .

28

Capacitance

.........-..........."..

29


6/160

6.

5.5.

DETERMINATIONF THE EFFECTS F

THE ENVIRONMENT

oN THE ACCELEROMETER PECTETCATTONS

.........

29

Temperature

ransientsensitivity

...........29

Temperature ensitivity

.....

129

Base strain sensitivity

.......

30

Acoust icsensit iv i ty . . . . . . . . . . . .30

Magneticsensitivity

...........

31

Temperatureimits

. . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . .31

Shock imits

. . . . . . . . . . . . . . . . . . . . . . . . .32

5.6.FACTORY

ESTINGOF ACCELEROMETER ABLES

.....................

32

5.7.CALTBRATTON

QUTPMENT.. . . . . . . . . . .

. . . . . . . . 33

Calibration

System

Type

9559

................33

Individual alibrationequipment

............33

5.8.STANDARDS

ELATING O THE CALIBRATION

oF ACCELEROMETERS .. . . . . . . . . . . . . . . . . . . . . . . . .34

APPENDTCES.. . . . . . . . . . . . . . .

. . . . . . . . . . . .37

APPENDIX . Conversion harts

. . . . . . . . . . . . . . . . . . .

38

APPENDIX .

Vibrationnomogram

...............

41

APPENDIX

C. Vibrationstandards

.................42

APPENDfX . BrUel&Kjer

Vibrat ionLiterature

. . . . . . . . . . . . . . . . .42

APPENDIX

.

Summary

f Bruel&Kjer

Preampli f iers. . . . . . . . . . . . . . . . . . . . . . . . . . .

44

APPENDIX . Summaryof BrUel Kjar instruments

with built- in

preamplif iers

......146

APPENDIXG. BrUel&Kjar

accelerometer

requencyand dynamic

range charts

......148

APPENDIX . Summary

of BrUel Kjar accelerometers

. . . . . . . . . . . . . . . . . . . . . . ,50


7/160


8/160

SYMBOL

NOTATION

Accelerometer lectrical

Quantities

Va

=

Open circuit

accelerometer

voltage

Qu

=

charge

generated

by

pi -

ezoelectricelements

ca

=

Capacitance

ot accelerom-

eter

Ra

=

Resistanceof accelerome-

ter

So,

=

Chargesensitivityof accel-

erometer

Sn

=

Voltage

sensitivityof accel-

erometer

loaded)

S,,o

=

Voltage

sensitivityof accel-

erometer

open

circuit)

Ch

=

Capacitance o the housing

of a balanced

accelerome-

ter

from

the output

pins

Cable Electrical

Quantities

C"

=

Capacitance

of

cable

R"

=

Series

reslstance

of cable

Rb

=

Resistance

between centre

conductor and screen

C"

=

Capacitance between

screen

and inner

conductors

In balanced accelerometer

cable

Cd

=

Capacitance of dielectric

in

balanced accelerometer

cable

en

=

Triboelectriccharge noise

Preamplifier

Electrlcal

Quantities

Re

=

Preamplifier Input resls-

tance

Ca

=

Preamplifier input capaci-

tance

Ct

=

Feedbackcapacitance

R'

=

Feedback esistance

A

=

Gainof operational mpli f i -

er

Vi

=

Preamplifier nput voltage

vo

=

Preamplifier

output

voltage

4

=

Feedback mpedance

Zt

=

Total impedance of accel-

erometer, able

and

pream-

pl i f ier

nput

li

=

Current

from

C,

l" = Current through feedback

capacitor

vc

=

Voltage across

feedback

capacitor

Ct

=

Total capacitanceof accel-

erometer, able and

pream-

pl i f ier

nput

Rt

=

Total resistance

of acceler-

ometer, cable and

pream-

pl i f ier

nput

Rloat

=

Resistance of

"floating"

stage of

preamplifier

CMRR

=

Common Mode Rejection

Ratio

of

"floating"

opera-

tional amplifier

en

=

Noise voltage

i"

=

Noise

current

Ro

=

Output

resistance

ol

line-

drive ampli l ier


9/160

1. VIBRATIONMEASUREMENT

1.1. NTRODUCTIOI{

Recent

years

have

seen the

rise of vibration

problems

associated

with

struc-

tures which

are

more delicate and intricate, and

machineswhich are faster and

more

complex.

The

problems

have been coupled

with

demands

for lower

running costs and increased efficiency. Concern

has also arisen about the

effects of noise and

vibration

on

people

and on the working lifetime of manu-

factured items. Consequently, here has been a

requirement for a

greater

understandingof the causes of

vibration

and

the

dynamic

response of struc-

tures to

vibratory forces. To

gain

such an understandingan

accurate, reliable

and versati le vibration transducer

is required. In addition, advanced measure-

ment

and analysis equipment

is often used. However, both the

versatility and

capability

of such

equipment would be wasted

without

an

accurate vibration

signal from a reliable vibration transducer.

The

piezoelectric

accelerometer

s the optimum choice ol vibration transduc-

er. The extensive

range

of

high

performance

measuring equipment

now

avail-

able

can

fully utilize the very wide frequency

range

and

dynamic range offered

by this type of vibration transducer.

This handbook is

intended

primarily

as a

practical guide

to

making

accurate

vibration measurementswith Br0el& Kjer

piezoelectric

accelerometers.

1.2.

WHY MEASURE VIBRATION?

Vibration is measured or many different

reasons. n

general

all uncontrolled

vibration is an undesirable

phenomenon

which

gives

rise to noise, causes

mechanical

stress and

is a

possible

cause of structural

ailure. Four broad areas

of vibration measurementcan be defined:

1. Vibration Testing. As part of a generalenvironmental est program or as a

part

of engineering

design, vibration testing

performs

the vital role ol

finding out how well a component can endure

the vibration environments

which it

is likely

to encounter

in a real-life situation.


10/160

l)urlng a vibration

est,

a structure

an

aircraft component

or

example)

s

subjected

o high vibration

evels

with a vibration

exciter.

Thevibration

evel

ls held

constant n

defined requency

egions

and the frequency

s

swept.

This s

achievedwith a vibration

exciter

controller

and a feedback

acceler-

ometerwhich

provides

data

concerning he

acceleration

o which

he struc-

ture s subjected.With the additionof a second accelerometer ttached o

the

structure, requency

esponse nformation

s obtained.

Fig. 1.1.

Vibration

testing

of an insulator

used

in the construction

of a

high

voltage

electricity

pylon

2


11/160

2. Machine

Health Monitor ing and

Fault

Diagnosis

In i ts simplest orm an

overall

measurement

f vibration

level on

a machine

is used to

give

a

warningof

impending

problems.

However,

more

informat ion

an be

ob-

tainedby

frequency nalysis.

his echnique

nvolvesmeasuring

he charac-

teristic

requency

pectrumof the

vibrationof

a machine

n

good

condition

and monitor ingany changesof the spectralcomponents singvibrat ion

measurements ver

a

period

ol

time. Such

changesare

normally

ndications

of impending

roblems.

Faultdiagnosis

an also

be

performed

using

vibra-

tion

measurements.

Fig. 1.2. Vibration

measurements

are used

in a machine-health

monitoring and

fault diagnosis

program


12/160

ln Industry

ibration

measurements

lso form

the

basis or

correcting

shaft

unbalance

n rotating

machines.

Unbalance

s a

cause

of high vibration

levels

which

often lead

to fatigue

and

bearing

ailures.

3. Structural

Analysis.

This

is a

powerful

experimental

method

or

determin-

ing the dynamic behaviourof a structureusing vibrationmeasurements.

Using

a force transducer

and an

accelerometer,

he excitation

signal and

vibration

esponse

of a

structureare

measured

imultaneously

sing

a dual

channel analyzer.

High

speed

computation,

performed

within

the analyzer

and

often in

conjunction

with

a desk-top

computer,

provides

essential

information

or the

designverif ication

and modification

of structures

ary-

ing in

size from

small

turbine

blades o large

bridges.

Fig.

1.3. The

structural analysis

of a train

carriage

using vibration measure-

ments

4


13/160

4. Human

VabrationMeasurement.This area concerns

he

measurement

f

the

vibration ransmitted o humanbeings.

Thesevibrationscan,

or

exam-

ple,

originate from

passenger

vehicles and hand-held

power

tools. The

measured

vibration evels

are

then related o

human comfort and

health

criteria

by International tandards.

Fig. 1.4. Measuring

the vibration

levels transmitted

from the

handle ot a chain

saw

using an accelerometer

and a

vibration

meter

1.3.WHAT

IS VIBRATION?

Vibration

is a dynamic

phenomenon

observed as a

to-and-fro

motion about

an equilibriumposition.Vibration is caused by the transfer or storage of

qnergy

within structures,

resulting

rom the action

of one or mbre

forces.

Vibration

is

often a by-product

of an

otherwise useful

operation and

is very diflicult

to

avoid.


14/160

Vlbretlons

can be observed in

the tirne domain,

i.e.

the change in the ampli-

tudc of the

vibration with t ime

("time

history"). Vlbration

time

histories

can

fall

Into one

of several classes as defined by their'mathematical form or by the

rtatlstlcal

properties

of the motions

they contain.

Vibrations

can also be looked

at

fn the

frequency

domain where the vibration is

described

by its frequency

Bpectrum,The two domains are related mathematicallyvia the Fourier Trans-

/orm.

Consult

he

Br0el

&

Kjer

book

"Frequency

Analysis" which deals with this

toplc.

Unlike other

vibration

transducers,

piezoelectric

accelerometersare used to

measure arl types of vibrations regard lessof the nature

of

the vibration in the

time domain

or the frequency

domain, as

long

as the accelerometer has the

correct frequency and dynamic ranges. Because

of the

wide frequency

and

dynamic

ranges

of

piezoelectric

accelerometers t is always

possible

to find a

particular ype for any vibration measurement. t is only the analysis echniques

which must

change according to the type of vibration.

1.4. VIBRATIONPARAI'ETERS

The

piezoelectric

accelerometer

measures

acceleration and

this

signal can

be

electronically ntegrated once to

provide

the velocity

signal and a second

time to

provide

the displacement signal. This is an attractive feature

of

piezo-

electric accelerometers.

Fig. 1.5

shows the effect of

integrating

the acceleration of an

electric

drill.

The vibration is displayed in the lrequency

domain.

The integrator

acts as a

low-pass

filter

and attenuates the high frequency components

present

before

the

integration.

Using an

integration network

effectively

"throws

away" infor-

mation about the vibration. Obviously

his

is

only acceptable

f

the lost informa-

tion

is not required

for the

purpose

of the measurement.

Acceleration should always be used if there is no reason for an integration.

For example, an obvious reason for measuring velocity is to obtain the actual

vibration

velocity

magnitude. t'is also often desirable to minimize

he dynamic

range requirementsof

the

measuring

nstruments n the vibration measurement

set-up and

hence

ncrease he signal-to-noise atio of the measurement.This is

achieved by

using the

parameter

which

gives

the flattest frequency spectrum

(see

Fig.1.5(b)).

Only frequency

analysis can

reveal

the

frequency

composition

of a

vibration

signal. For broad-band

(wide

frequency content) measurements

on

rotating machlnes

he

velocity

parameter

s

found to be the best in 70o/o

t

al l

cases, acceleration

n

30% and displacement s hardly ever used. Displacement

parameters are sometimes used for measurements of low frequency and large

displacementvibrations often

encounteredon

structures

such as ships, build-

ings and bridges.

6


15/160

a)

--L

o tr tr tr u o tr tr tr

o D o tr o o o o o o

o o tr o tr o o o tr

o o o o o D

q

o o o

p

o-o

Q

o-EItr tr tr

R.ciitir:-aa

I m-|ffi Lim

FG:-l

6Jr

fr. sd.-Norm l-6dr

t4t

EF:-O.3-ff

rru.r &Kid

,mm qu ?q l - : :q

q

' -@

rm

m

&

nPMrrm m

m

tutr iplyF4

bl.by- l

ooEotr

oo t rot ro t r t r t rD

oD oDtrEl t ro t ro o

oot r t ro o

.:-i-6-u

fr.

W:-Nomal-mds

PF SFd:-o3-mn

1ffi l rmmRilr l@s@

c)

.-L tr tr tr tr tr tr tr tr tr o

o E tr o o o o o tr o

o o tr tr o tr tr o tr

o tr o o o tr tr o.tr

-D

D-o

Q

o o tr o o

- -hdilL:--AC

Loo-|ffi

unFra:-1.6J2

fr. sod:-Nmal-d. Fq. -Sp.d:-0,3-m

rdaKi.r

,m@E l?q

- - :4

-qa

Em

lm 3m @

Bilrrm m

m

Fig. 1.5.

Frequency analysis of

the vibration ot

an electric drill

using the three

different

measurement

parameters-acceleration,

velocity and displace-

ment

When complex

signals such

as shocks and

impulses are

measured

ntegra-

tion

networks should

notbe used because

hey introduce

phase

errors

resulting

in ser ious amplitude

measurement

errors.

1.5. THE

OUANTIFICATION

OF

VIBRATION

LEVELS

There are several ways of quantifying the vibration amplitude of a signal in

the time domain.

The actual

measurementunits

(for

example,

n/s2,

m/s2,

g

etc)

may differ although

the descriptors described

in this section are

widely used.


16/160


17/160

5.

Crest Factor:

Defines he

ratio of the

peak

value of

a signal o the RMS

value.

From he definit ion

of RMS

above, he crest

factor

for the sine wave

in Fig. 1.6 s

2.

As the vibration

becomes

more mpulsive,

r more

random,

the crest

factor increases.

This simple

relationship

s easily calculated

with

a simple

vibration

meter equipped

with

RMS

and

peak

facilit i€s.When

makingwide-bandmeasurements n a machine'sbearinghouslng,an in-

crease

in a single

vibration component

caused

by a

faulty bearlng

may be

undetectable

n the

RMS measurement,

ut might be

indicatedby

an

in-

crease

in the crest

factor. Hence

by monitoring

the

growth

of the crest

factor, it is

possible

to

predict

a

breakdown

or element

fault.

Another example

of the utility

of crest

factors can be

found

in

structural

testing techniques.

The crest

factor of

the input signal

to the structure

can

reveal

mportant information

about

the excitation.

lf the crest

factor is

very

high, as can be the case with hammer excitation, the structure may be

driven

into non-lineardynamic

behaviour.

A

high crest factor

also indicates

that

the input

may not contain

sufficient energy

to obtain

a

good

signal-to-

noise ratio.

On the other

hand, a high crest

factor

is an indication

that the

input

has a wide

frequency

range.

1.5.1. inear

Amplitude and

Frequency Scales

Linear amplitude and

frequency scales

are used

in vibration

measurements

when a

high

resolution s needed.

A linear frequency

scale

helps to separate

closely

spaced

frequency components.

The

linear lrequency scale

gives

the

lurther

advantage

that equally

spaced

harmonic components

of a

vibration

signal

are

easily recognized.

1.5.2.

ogarithmic

Amplitude and

Frequency Scales

Piezoelectric

accelerometers

are capable

of accurate

vibration

measure-

mentsover extremelywide dynamic and frequencyranges.Therefore, o obtain

convenient

nterpretation of

results the following

are often

required:

1.

An amplitude scale

which

can accomodate

vibration amplitudes

from the

lowest

detectable

amplitudes

up to shock

amplitudes,

and

which can also

simplify he comparison

of

vibration amplitudes.

2.

A

frequencyscale with

the same

percentage

esolutionover the

whole

width

of the

recordingchart.

The two objectives

can be achieved

using

the followihg:


18/160


19/160

1.6.ANALYSISOF

VIBRATION

MEASUREIIENTS

The amount of

information hat can be obtained

from tradltlonal

tlme domain

analysis

s limited

althoughmodern

time

domain

analysis

echnlquesare be-

coming

more

powerful.

However,

wlth the addition of

frequency analysls

equip-

ment, such as analogue and digital frequency analyzers,very useful addltlonal

information

is obtained.

No in-depth coverage of

instruments ol thls

nature ls

given

in this

handbook.The Br0el&Kiar

books

"MechanicalVlbratlon and

Shock

Measurements'

and

"Frequency Analysis" should be

referred to

for I

solid theoretical

background

in frequency analysis,

while the

main and short

cataloguesshould

be consulted

or

details

of the range of

instrumentsavallable

from

Br0el& Kjar.

The complexity

of the measuring

nstrumentationand

the analysis

of results

may

vary widely. But

in

every

case the vibratlon

transducer s

the most critical

link in

the

measurement

hain, for without an accuratevibration signal the

results

of further analysis

will

not be reliable.

The most reliable,

versatile and accurate

vibration transducer

is the

piezo-

electric

accelerometer.


20/160

2. THE PIEZOELECTRIC

CCELEROMETER

2.1.

NTRODUCTION

The aim of this chapter

is to

give

a basic,

and often theoretical

nsight nto the

operation and the

characteristicsof the

piezoelectric

accelerometer.

Due to

the

nature

of

its operation he

performance

of

the vibration

preamplifier

will need to

be

included to a small extent.

However for a complete

description

of the

operation

and characteristics

of

preamplifiers,

Chapter 3

"Vibration

Preampliti-

ers" should be consulted.

A summary of

the complete

Br0el

&

Kjer range

of

accelerometers

an be found

in Appendix H.

The

piezoelectric

accelerometer

is widely accepted

as the best

available

transducer for the absolute

measurementof

vibration.

This is

a

direct result of

these

properties:

1. Usable over very wide frequency ranges.

2.

Excellent inearity over a

very wide dynamic

range.

3.

Accelerationsignal can

be electronically

ntegrated o

provide

velocity and

displacement

data.

4. Vibration measurements

are

possible

in

a

wide range of environmental

conditions

while stil l

maintaining xcellentaccuracy.

5.

Self-generatingso

no external

power

supply is required.

6. No moving parts hence extremelydurable.

7. Extremely compact

plus

a

high

sensitivity

to mass

ratio.

In order to appreciate

hese advantages

t is worth examining

he character-

istics of a

few

other

types of

vibration transducer and

vibration measurement

devices.

1. Prorimity

probe.

A

device

measuring only

relative

vibration

displacement.

It has a response o

static displacements

and also a

low electrical imped-

ance output. However, the device is not self-generatingand the high fre-

quency performance

is

poor.

In addition the

vibrating surface

must be

electrically conductive.

12


21/160

2. Capacitive

probe.

A small,

non-contact,

ibrationdisplacementransducer

with a high sensitivity

nd a wide frequency

ange.

The

disadvantages

re,

however, that

the vibrating surface

must be electrically

conductive, the

probe's

dynamic range

is very limited and

it is diff icult o callbrate.

Position

potentiometer.

A low cost,

low impedance device

capable ol

measuring static displacements. However, the dynamic and lrequency

rangesare

imitedand the device

only has a short

working

ifetimeand low

resolution.

Piezoresistive transducer.

A vibration acceleration

transducer

which

is

capable of

measuring static accelerations.

The

measuring frequency

and

dynamic

ranges can be

wide. The

limited

shock

handlingcapacity

means

that this type of transducer

is easily

damaged. Viscous damping

is often

used to

protect

the transducer against

shocks.

However, this

leads to a

reduction n the operating temperaturerange and alters the phase charac-

teristics.

Moving coil.

A

self-generating

ow

impedancevibration

velocity ransducer.

It is severely

imited in i ts

frequency range and dynamic

range,

s

suscepti-

ble to

magnetic fields and is affected

by its orientation.

2.2.

OPERATION

OF

AN ACCELEROMETER

Fig.2.1 llustrates simplif ied

model of a BrUel Kjer

DeltaShear@

cceler-

ometer showing

only the mechanical

parts.

The active elements

of the acceler-

ometer

are the

piezoelectric

elements.

These

act as

springs connecting

the

Fig.2.1. Schematic of a

Brhel&Kjar Delta Shear@

piezoelectric

accelerometer

13

5.


22/160

barc ol the accelerometer

o the seismic

masses

via the rigid

triangular

centre

po t.

When

the accelerometer

s vibrated

a force,

equal to the

product

of the

tccoleratlon

of a seismic mass

and its mass,

acts on each

piezoelectric

ele-

ment. The

piezoelectric

elements

produce

a charge

proportional

to

the applied

lorce. The seismic

masses

are constant

and consequently

he elements

pro-

duce a charge which

is

proportional

to

the acceleration

of the seismic masses.

As the seismic massesacceleratewith the same magnitudeand phase as the

accelerometer

base over

a wide frequency

range,

he output of

the accelerome-

ter is

proportional

o the acceleration

ol the base and hence

o the acceleration

of the

surtace onto which

the

accelerometer s mounted.

The

above model can

be

simplified as shown in

Fi9.2.2.

2.2.1.

Analylical

Treatment

of

Accelerometer

Operation

Fig.2.2

shows

a

simplified model ol

the accelerometer

described in

the last

section

and referenced

o

an inertial system. The

two masses

are unsupported

and connected

by

an

ideal

spring. Damping s neglected

n

this model because

BrUel

& Kjer

accelerometers

have very low

damping

factors.

Fiq.2.2.

Simplitied model

of an

accelerometer

total

seismic

mass

mass

of the

accelerometer

ase

displacement f the seismicmass

displacement

f the accelerometer

ase

m8

lfl6

xs

X6

)q

xb

14


23/160

l-

-

distance

between

he seismic

mass and

the bese

when

the

accelerometer

s

at rest

in the

inertial

system

11

-

equivalent

stiffness

of the

piezoelectric

elements

F"

=

harmonic

excitation

force

Fo

=

amplitude

of excitation

force

(t

=

excitation

frequency

(radls)

=

hrf

o)n

=

natural

resonance

requency

ol the

accelerometer

radls)

o)m

=

mounted

resonance

frequency

of the

accelerometer

(radls)

f.

=

mounted

resonance

requency

of

the accelerometer

Hz)

f

-

excitation

frequency

(Hz)

The

following

expressions

describe

the

forces

present

in the

model

F

=

k(X"

-xo-L)

(spr ing

orce)

moxo = F * Fe(force on base)

D"f,"

=

-

F

(force

on seismic

masses)

The equation

of

motion

for

the

model can

be

lound

*"-xo

+-ry=-

ry.

x"-xo-q-+

(1)

ms

fi|6

lL

m6

or

1tt

=

-k-+Fssin@t

lfl6

Where

1

=

1*1

It

ms ft16

or

-

=

lll"lf,O

' ms+mb

p

is often

referred o

as the

"reduced

mass" and

r

is the

relatlve

displace-

ment

ol the

seismic

mass

o the

base

15


24/160

f

=

Xs-Xb-L

When he accelerometer

s in a free hanging

osition

and s not beingexcited

by external orces

(Fr=

0) the equationof

motion for its free vibration reduces

to

1ri

=

-kr

Thissimpledifferentialequationcan be solvedby assuming hat the displace-

ment of ms relative to rno varies harmonicallywith an amplitude R. In other

words

r

=

Fsin

cof

-pRaz

sin

ot

=

-

kB

sin orf

and therefore the

resonance frequency

of the accelerometer,


25/160

The resonance requency

when mounted will change

if

the structure is not

infinitely igid or

if

the accelerometer

mounting echnique

ntroduces

n addi-

tional

compliancebetween he base and

the

structure.

The resonancewill split

up in two and the

lowest resonance requency

will

be

lower than the mounted

resonance requency.This is examined

n

Chapter

4.

The forced vibration of the accelerometer

must now be examlned.

The

applied

orce

on the accelerometer

must be

included n

the

analysisalongwlth

the

natural resonance requency,crrn,

reviously

defined.

The equation of

motion

for the model

(1

now

becomes

i

+

on2

a

-J-9- sin crrt

=

0

mb

and assumingagain that the

displacements f the masses

vary sinusoidally

then

-c,r2Bsin@f

@n2Rsint , , l f

Fo

sin


26/160

thc natural

esonance

requency

f the

accelerometer. onsequently

he force

on the

plezoelectric

lements nd

the electrical

gutput rom the accelerometer

alao

ncrease.

s

the

piezoelectric

lements

used

n Bruel& Kjer

accelerome-

tere

exhibit

constant

orce sensitivity

he

increase

n electricaloutput

ol an

accelerometerear ts resonancerequencys attributable ntirely o the natu-

ral

resonance f

the accelerometer.

he ypicalshape

of a

frequency esponse

curve

of an accelerometer

see

Fig.

2.3)and amplitude

measurement rrors

are

related

o this

equation.

This is covered

n section

2.3.

The ree

hanging

natural esonance

requency

f the accelerometer

epends

heavilyon

the

ratio of the total

seismic

mass to the

mass of the

rest of

the

transducer

ut

primarily

o that

of the base.

As a

general

ule he

total seismic

mass of

an accelerometer

s approximately

he sameas

the mass

of the base

and this

gives

the

relationship

mounted resonance

requency

free

hanging

resonance

requency

2.3.Frequency

Range

The relativechange

n electrical

output

from an accelerometei

s shown

n

Fig.2.3.

A frequency

esponse

curve of this

kind shows

he variation

n the

accelerometer's

lectrical

utput

when t

is

excited

by a constant

ibration evel

over

a

wide frequency

ange.

To obtain such

a frequency

esponse

urve the

accelerometers mountedonto a 1809 exciterhead.Hence he approximation

1

u2

o

@

o

o

6

o

t

usetul

Frequency

anges

10% imlt = 0,3 f-

3 dB limlt

-

0,5

l.

Maln

Axls Chatgs

or

Voltage Sensltlvlty

1

Prooortion of Mounted R$mme Frequency m

18

Fiq.2.3.

Relative sensitivity

of an

accelerometer

vs' frequency


27/160

to

the

mounted

resonance

requency

of the accelerometer

an

be found.

This

frequency

esponse

curve

s related

o equation

4)

n the

lasl

sectlon.

However,

lhe

mounted

resonance

requency

can

now be

directly substltuted

nto

(4)

to

obtain

A=i1 i t (s)

r- ls l-

\

c,t-

/

Equation

(5)

can

be used

to calculate

he deviation

between

he measured

and

the actual

vibration

at any

requency

and

to define useful

requency

anges.

2.3.1.Upper

Frequency

Limit

Fig.2.3

shows

that lhe

mounted

resonance

frequency

determines

he fre-

quency

range

over which

the

accelerometer

can

be used

while a constant

electrical

output

for

a constant

vibration

input

is still

maintained.

The

higher the

mounted

resonance

requency, he

wider the

operating

fre-

quency

ange.

However,

n order

to

have a

higher mounted

esonance

requen-

cy it

is necessary

o have

either stiffer

piezoelectric

elementsor

a lower

total

seismic

mass.

The stiffness

ol

the

piezoelectric

elements

s

generally

constant

so a

lower seismic

mass

is required.

Such a lower

mass

would

however exert

less force on the piezoelectricelement and the accelerometerwould conse-

quently

be

less sensitive.

Thereforeaccelerometers

possessing

very high

fre-

quency

performance

are less

sensitive.

conversely,

high sensitivityaccelerom-

eters do

not

have very

high frequency

measurement

apability.

several

useful requency

anges can

be defined

rom the

frequency

esponse

curve

of an

accelerometer.

They are:

5olo

Frequency

Limit

is the frequency

at

which there

s a 5%

deviation

between

the measuredand the actualvibration evel appliedto the base of the acceler-

ometer.

The maximum

vibration

frequency

which can

be measured

with this

accuracy

s approximately

one

fifth

(0,22)

of the

mountedresonance

requency

of the

accelerometer.

10% Frequency

Limit is the

frequency

at which

there

is a

10% deviation

between

he measured

and the

actual

vibration

evel applied

to the

base

of the

accelerometer.

he

maximum

vibration frequency

which can

be measured

with

this accuracy

is

approximately

one third

(0,30)

imes

the mounted

resonance

frequency

of the

accelerometer.

3dB

Frequency

Limit

is the

frequency

at

which there

is a 3dB

difference

between

he

measured

and the actual

vibration

evel

applied

to the base

of the

19


28/160

accelerometer.

he maximum

vibration requencywhichcan be measuredwith

this accuracy

is approximately one half

(0,54)

imes the mounted resonance

frequencyof the accelerometer.

2.3.2.Lower Frequency Limit

Piezolelectricaccelerometers are

not

capable

of

a

true DC response. The

piezoefectric

elementswill only

produce

a charge when acted upon by dynamic

forces.

The

actual

ow frequency imit is

determined

by the

preamplilier

o which

the accelerometer

s

connected as

it is

the

preamplifier

which

determines

he

rate

at

which the charge leaks away from the accelerometer.Measurementsof

vibrations at

frequencies

down to 0,003

Hz

arc

possible

with BrUel

&

Kjar accel-

erometers and

preamplifiers.

Applications equiring a low frequency imit in the order of fractionsof a hertz

are

very rare

and consequently

he lack of a true DC response is seldom a

drawback.

Chapter3,

"Vibration

Preamplif iers", houldbe consulted

or

a description f

the

low frequency

performance

of

preamplifiers.

Environmental ffects associ-

ated with

low frequencymeasurements

are covered

n Chapter 4

"Accelerome-

ter

Performance n Practice".

2.4. P'EZOELECTRIC MATERIALS

A

piezoelectric

material is

one

which

develops

an electrical charge when

subjected to a force. Materials

which

exhibit this

property

are intrinsic

piezo-

electric

monocrystals

such

as

quartz

and Rochellesalt, and artificially

polarized

ferroelectric ceramics which are mixtures of different

compounds

such

as

barium titanate, lead z irconate and

lead metaniobate.

The processby which the ceramics are polarized s analogous o the process

by

which

a

piece

of soft

iron

can be

magnetised by a magnetic field . A

high

voltage surge is applied across two ends of the

material. The

domains

within

the molecular structure of the material become aligned

in

such a

way

that

an

external force causes deformations of the domains and

charges of opposite

polarity

to form on opposite ends of the material.

Fig.2.4.

shows a s implified

illustrationof this effect. When a

piezoelectric

accelerometer

s vibrated forces

proportional

o the applied acceleration act on the

piezoelectric

elements and

the

charge

generated

by them is

picked

up by the contact.

lt is

the extremely

linear relationshipbetween he applied

force

and the developedcharge,

over a

very wide

dynamic

and frequency range, which results

n

the excellent charac-

teristics of the

piezoelectric

accelerometer.

The

sensitivity of a

piezoelectric

material is

given

in

pC/N.

20


29/160


30/160

Ferroelectric

eramics may

be

produced

in

any desired

shape and their

composltlon

may

be varied o

give

them special.properties

or different

appli-

catlons,

With

piezoelectric

monocrystall ine

materials

such

as

quartz

his is not

th€ case

as their

composit ion s f ixed

and their

shape s restricted

y the size

of

crystal

from which

they

are cut. Because

of this accelerometers

which

use

monocrystall inelements enerally avea lowersensit ivity nd nternal apaci-

tance than those with ferroelectr ic

eramic

elements.

Piezoelectricmaterials

used in

Br0el&Kjar

accelerometers

re designated

P223, P227, PZ

45 and PZ 100.These

have

the following

properties:

1. PZ 23

belongs o the lead

titanate, ead

zirconate amily

of ferroelectric

ceramics

and is artificially

polarized.

t may

be used at

temperaturesup

to

250'C

(482"F).

Due o its high

sensit ivity

approx.

00

pClN)

and

other

good

all round

properties

t is

used in most Brtiel

&Kjer accelerometers.

2. PZ27 is

an artif icially

olarized

ead zirconate

itanate

elementvery

similar

lo P723. lt

is suitable or

use

in

miniature

accelerometers.

3. PZ 45 is

a specially ormulated

artif icially

polarized

erroelectric

ceramic

which has

a

particularly

flat

temperature response

and may

be used

at

temperatures

f

up

to 400'C

(752F\.

lt is

used n Br0el

&Kjer differential,

high temperature

and high shock

accelerometers.

4. PZ 100 s

a carefully

selected and

prepared

quartz

crystal. t may

be used

at

temperatures

up to 250'C

(482'F)

and has

excellent stabil ity

with low

temperature ransient sensit ivity. t is used in the BrUel Kjer Standard

Relerence Accelerometer

Type 8305

and in the force

transducers.

The

type of the

piezoelectric

element

used in any

particular

BrUel& Kjer

accelerometer

can be found in

the accelerometer

Product Data.

2.5.PRACTICAL

ACCELEROMETER

ESIGNS

Three

different mechanical

constructions

are used in the

design ol

BrUel Kjar accelerometers. he f irst two designs, Planar Shear and Delta

Shearo are

shown n Fig.2.5. A

Compression

Design

(see

Fig.2.6) s

also in

use. Due to its superior

performance

he Delta Shear@

esign is used in nearly

all BrUel&Kj@r

ccelerometers.

1.

Delta Shear@

Derign. Three

piezoelectric

elements and three masses

are

arranged n

a triangular

configuration around

a triangular centre

post.

They

are held in

place

using

a

high

tensile clamping ring. No

adhesivesor

bolts

are required

to hold

the assembly

together and this

ensures optimum

performance

and reliability.

The ring

prestresses

he

piezoelectric

elements

to give a high degree of linearity. The

charge

is

collected between

the

housing

and the clampingring.

22


31/160

P

M

R

B

P

M

R

B

Planar

Shear

Delta

Shear@

2.

Fiq.2.5.

Planar Shear

and Delta Shear@ esigns.

M=Seismic Mass,P=Piezoe-

lectric Element, R=Clamping Ring and B:Base

The

Delta

Shear@

esign

gives

a high sensitivity-to-mass

atio

compared o

other designs

and has a

relatively

high resonance frequency and

high

isolation rom

base strains

and temperature ransients .

The

excellentoverall

characteristics f

this

design

make t ideal or both

general

purpose

accel-

erometers

and more specialized ypes.

Planar

Shear.

In

this

design

the

piezoelectric

element undergoesshear

deformation s in the DeltaShear@ esign.Two rectangular l icesof piezo-

electric

material

are arranged on each side of a

rectangular

centre

post.

Two masses

are

formed

as

shown in Fig.2.5 and

held

in

position

using a

high

tensilestrength

clamping ing

performing

he sam e functionas in the

Delta

Shear@ esign.

The

base and

piezoelectric

elements are effectively

isolated rom

eachother hus

giving

excellent

mmunity

o basebendingand

temperature luctuations.

Centre

Mounted

Compression

Design. This traditional, imple construc-

tion

gives

a

moderately high

sensitivity-to-mass

atio. The

piezoelectric

element-mass-spring ystem is mounted on a cylindrical centre post at-

tached to the base of the accelerometer.

However,

because he

base and

centre

post

effectively act as a spring

in

parallel

with

the

piezoelectric

elements,any dynamic changes

n

the base such as bending or thermal

expansions can cause stresses

in the

piezoelectric

elements and

hence

erroneous

outputs.

Even

though

BrUel&

Kjer employ

very

thick bases to

minimize these effects

in

compressiondesigns, bending and stretching

forces

can still be transmitted o the

piezoelectric

elements.This will result

in

an erroneous

non-vibration elated

output at the

frequency

of the

vibra-

tion. In the previoussection it was seen that temperature luctuationscan

also

produce

charge

n

the

piezoelectrics

which are

picked

up

in

Compres-

sion

Designs.

3.

23


32/160

s

M

P

B

Centre

Mounted

Compression

Fig. 2.6.

Traditional

Compression

Design.

M=Seismic

Mass,

p=piezoelectric

Element,

B=Base,

and S=Spring

For

the reasons

mentioned

above BrUel

& Kjer

only

produce

compression

design

accelerometers

or high

level measurements

i.e.

shock

measure-

ments)

where

the erroneous

output is

small

comparedwith

the vibration

signal.

A compression

design

is also

used for the

Standard

Reference

Accelerometer

hich

s used

n the controlled

environment

f accelerometer

calibration.

Here he

additionof

a beryllium

disc strengthens

he base

and

minimizes

he

effect of

base bending.

This accelerometer

s

inversely

mounted n

order to measure

more

accurately

he vibration

at the

base of

the accelerometerwhich is mountedonto it.

2.5,1.Line-drive

Accelerometers

These

accelerometers

ontain

a built-in

preamplifier.

line-drive

accelerom-

eter s

shown n Fig.2.7

Theaccelerometer

art

of this

design s identical

o the

Delta

Shear@

onstruction

mentioned

above. The

electronic

part

utilizes

hick

film micro-circuitry

echniques

o

produce

a

preamplifier

with excellent

perfor-

mance

characteristics.

hapter3 includesa descriptionof the operationof the

preamplilier

section.

Line-drive

accelerometers

equire

an external

power

supply

or their

opera-

tion. The

built-in

preamplifier

s

supplied

by a constant oltage

and

he vibration

signal s transmitted

back

o the

externalsupply

unit n the form

of the modulat-

ed

power

supply

current.This

system s

also described

n Chapter

3.

Built-in

preamplifiers

do however

ntroduce

emperature

and shock limita-

tions.To

overcome

his Briiel&

Kjer also

produce

a

separate ine-drive

pream-

plifier for use with accelerometers.

24


33/160

Fig.2.7. A Briiel &Kjer line-drive accelerometer with its housing removed to

reveal the built-in electronics

2.5.2.Other designs

Other designs of accelerometerexist, based

around

the

compression and

shear deformation

principles.

Br0el&Kjer only use the designs mentioned

above as

these,

and in

particular

the Delta Shear@design,

give

the most

uncompromising

erformance

vailable. he ollowing

eneral

designs

may

stil l

be

found

elsewhere;

Annular Shear Designs where the

piezoelectric

elements and

masses

are

formed into rings and simply

glued

ogether.

lsolaled

Shear

(Bolted

Shear) s similar o the

planar

sheardesignexcept he

piezoelectricelements are secured using a bolt.

2.6.ACCELEROMETER ENSITIVITY

So far it has

been seen that an accelerometer

s

a self-generatingdevice

whose electrical output is

proportional

to the applied acceleration. n order to

assess the accelerometer's role as a measurementdevice, the relationship

between

ts input

(acceleration)

nd output

(charge

or

voltage)

s

now

examined

in more detail.

25


34/160

2.t.1.

Gharge

and

Voltage Sensitivity

The

plezoelectric

accelerometer

can be

regarded as either

a charge source

or a

voltage source.

The

piezoelectric

elementacts

as a capacitor

C, in

parallel

wlth

a very

high internal

eakage

resistance,8* which,

for

practical purposes,

can be ignored. t may be treated either as an ideal chargesource,Oa n parallel

with C, and the cable

capacitance

Cc or as

voltage source

V" in series

with C,

and

loaded by C", as shown

in Fig.

2.8. The equivalent

circuits

for both models

are shown

in Fig.2.8. Both

models can be

used independently

ccording

o

which model

yields

the easiest calculations.

Fig. 2.8. Equivalent electrical

circuits

for

piezoelectric

accelerometer

and

con-

nection cable

The choice

of accelerometer

preamplifier

depends

on whether

we want

to

detect charge

or voltage

as the electrical

output

from the accelerometer.

The charge

sensitivity,

So",of

a

piezoelectric

accelerometer

s calibrated

in

terms of charge (measured n pC) per unit of acceleration:

.q =

PC-POnus-POpeat

-qa

ms-2

tnS-2nus

llls-2peax

Likewise,

he voltage ensitivity

an

be expressed

n terms

of voltage

per

unit

of acceleration:

=

tV

=

iY u -

=

ms-2

tns-2nus

mVpear

q

Ca+C"

Voltage

Equivalent

"=v'

unlt ot acceleietion

26

src

fis-2o""*


35/160

It

can be

seen rom

the simplified

diagrams

hat

the voltage

produced

by the

accelerometer

s

divided

between

he

accelerometer

apacitance

and

the

cable

capacitance.

Hence

a change

in

the cable

capacitance,

caused

elther

by

a

different

ype

of cable

and/or

a change n

the

cable ength,

wlll

cause

a

change

in the voltage

sensitivity.

A

sensitivity

ecalibration

will

ther€fore

be requlred.

This s a major disadvantage f using voltagepreamplification

nd ls examlned

in

greater

detail in chapter

3. charge

amplifiers

are

used nearly

all the

flme

nowadays.

At low

and medium

requencies,

within

the

useful

operating requency

ange

of an

accelerometer,

he voltage

sensitivity

s

independent

of

frequency.

Thls

afso

appf es

to the

charge

sensitivity

of

accelerometers

sing

pz

45

and

pz

1oo

piezoefectric

materials,

but not

to those

using

pZ23

and

pz27

piezoelectric

malerials.

nstead,

his

piezoelectric

material

has

been

designed

so that

both

the charge sensitivity and capacitancedecrease by approximalely2,So/o er

decade

ncrease

n frequency.

The

effect of

this decrease

s

to

partially

offset

the output

rise

at resonance.

Therefore,

he maximum

deviation

between

he

measured

and

actual

accelerations

over

the useful

operating

requency

range

of accelerometers

mployingPZ

23 with

medium

o high

resonance

requencies

is

only

+

1voot the

acceleration

applied

to the

base of

the accelerometer,

s

indicated

n

Fig.2.9.

Fig.

2.9.

charge

and voltage

sensitivity

versus

frequency

for

an

accelerometer

using

PZ 23

piezoelectric

material

50

%

40

=

o

o

o

o

6

o

CE

UsofulFrequency

Range

_

0,3

tn

- ChargeSensitivity Deviation < r 5%

- --

Voltsge Sensitivity

Deviarion

<

+

1096

Slope

2,5%/

Frequency

o,q)l

0,01

0,1

Proportlon

ot Mount€d

Resonanc6

Fr€quency

m


36/160

2.6.2.

Unl.Gelno

Senritivity

Almoot

every BrUel&Kjar

acceleromet€r

s ot

the Uni-Gaino

design.

This

m€ans

hat

their measured

sensitivities

have been adjusted

o

within 2o/o l

a

convenient

alue such as

1; 3,16;

10 or 31

6

po/ms-2.

With Uni-Gain@

cceler-

ometers

one

accelerometer can be replaced by another of the same type

wlthout

urther adjustment

of any instrument

etting.

Because

he

valuesabove

are

10dB apart

relative o each

other, the

calibration

of

measurement

ystems

and

set-ups

s very easy.

For example,

f

one

accelerometer

s

exchanged

or

another

of a difterent

ype, only

ixed

gain

changes

of

10dB are

requiredon

the

measurement

nstrumentation.

Uni-Gaino

sensitivities

are

achieved

n BrUel&

Kjer accelerometers

y care-

tully adjusting

he

mass of the seismic

elements.

2.6.3.

Linearity and

Dynamic

Range

Linearity

s a fundamental

equirement

of

any measuring

system.

The ouput

from

the system

must be

linearly

elated o the

input over

as wide a

frequency

and dynamic

ange as

ls required.

The excellent

inearityof

BrUel&

Kjar accel-

erometers

s il lustrated

n Fig.2.10.

Fig. 2.10.

Accelerometer

output

versus acceleration

for

piezoelectric

acceler-

ometerc demonstratlng the linearity and wide dynamic range

o

a

o

o

5

u

Lower lmit set by

noise trom

Preampllfler

+

cable

+

envlronm€nt

Upps

limit set by

AGelerometer

=

160

dB

(10E:

)

l


37/160

The

piezoelectric

accelerometer

s

an

extremely

inear devlce over a

very

wide dynamic

range because of

the linear

performance

ol the

plezoelectric

elements

over a

wide

dynamic

ange. n theory

he accelerometer

s llneardown

to zero acceleration.

Howevera

practical

ower imit

is

determlned

by the

noise

inherent n the

measurement ystem.

This noise can

have

several

sources of

origin and these are discussed n Chapters3 and 4.

When an

accelerometer

s

taken

beyond ts

maximum acceleratlon

lmlt the

performance

becomes

ncreasingly

non-linear.

At levels far in excess of

the

maximum imit

the

preloading

ing

might begin o slip down

the

piezoelectrlc

elements

and eventually hort-circuit

with

the

base, hus

rendering he acceler-

ometer useless.

n

practice

this

will never

happen unless he

accelerometer

s

subjected

o shock

levelswell outside

its specified

operating

range.

2.6.4.

Tlansverse Sensitivity

When

an accelerometer

as acceleration

appliedat

right angles o

its mount-

ing axis, here

will still be some output

rom the accelerometer.

On the acceler-

ometer

calibration

chart the transverse

sensitivity

s

quoted

as a

percentage

f

the

main axis sensitivity.

deally he

transverse

sensitivityol an accelerometer

shouldbe

zero,but

in

practice

minute

rregularities

n

the

piezoelectric

lement

and

in

metal

parts prevent

his.

At BrUel&Kjar

particular

attention s

paid

to

selection

of homogenous

piezoelectric

ceramics and

to careful

machining,

polishing nd liningup of accelerometer arts.Thuswith properhandling nd

30

dB

20

b10

io

o

o

€.0

6

{,

n

-zo

I

--

Mountod

I

Besonance

,i\

Frequoncy

Useful

FrequencyRano€

-

| /l \

fm

0,@ol 0,001

0,01

0,1 1

10

Proportlonof Mounted

R€sonance

requ€ncy

zmgn

Fig.2.11.The relative responseof an accelerometer o'main axis and trans-

verse axis

vibrations

29


38/160

mountlngon a

flat,

clean surface,

he maximum

ransverse

sensitivity

of most

Br0cl&

KJar

accelerometers

an be kept

below 4oh

ot the main

axis sensitivity

at 30

Hz

(see

Fig.2.11).

At lrequencies

ess than

one sixth

of the main

axis mounted resonance

lrequency ransversesensitivitycan be kept below 10%.At frequencies ust

over one third of

the main axis

mounted resonance

requency

t is

difficult

to

specify

exact values

of transverse

sensitivity

as transverse

resonance

oc-

curs.This

s indicated

n Fig.2.11.

As

if ustrated n

Fig.2.'12, ransverse

sensitivitycan

be regarded

as the result

of the maximum

charge

and voltage

sensitivity

axis of the

accelerometernot

being

quite

alignedwith

the mounting

axis. Because

of this

there are

directions

of

maximum

and

minimum

transverse

sensitivitywhich

are at right

angles

o

one anotherand to the mainsensitivityaxis. lt is therefore he mo(imum value

of transverse

sensitivity which

is specified

on

the accelerometer

calibration

chart. The

direction

of minimum

sensitivity

is marked

by a red

dot on the

accelerometer

ousing.

This s

a unique eature

of BrUel&

Kjer accelerometers.

It

should be noted

that the Delta

Shear@

esign, having

constant

stiffness n

all

transverse directions,

has

only one transverse

resonance.

Other

shear

designs

may have

two or more

transverse

esonances.

Axis of

-

/l

maximum


39/160

As the transverse resonance s

just

outside

the

useful operatlng frequency

range of an accelerometerand with

a

peak

amplitude

ust

below the main

axis

sensitivity, t is important

that transverse

vibrations

and shocks are kept well

below he

specified

main

axis continuous

ibration

imits.Slmllarly,

roppingor

banging accelerometers can subject them to large transverse

shocks

well

outside

practical

design limits

and

permanent

damage can be caused to the

piezoelectric

elements nside

the accelerometer.

The following

precautions

can be taken against severe ransversevlbratlons:

1. Align

the

red

dot in the directionof maximum ransverse

cceleratlon.

Fig.2.13.

Chart for determining

the accelerometer transverse

sensitivity

in

any

direction when

the maximum transverse

sensitivity

is known

s$

oo)

S-

l'r'tZVzl/-d--=:-N-A

s' zvlrtl

'?

S-,/Z/tlZ/Zj€ZalffN-"

s-

,ralralzzz

-a

S

//Z


40/160


41/160

The

sensitivity and

phase

responses

of an accelerometer are

shown in

Fig.2.14.

At frequenciesbelow

the

mounted resonance

he

phase

shift intro-

duced s insignificant.At frequencies

ery close o the resonance,

he motion

of

the seismic masses ags

that of the base

and

phase

distortion ls Introduced.

However,

with Br0el& Kjar accelerometers

mall

resonance

damplng

factors

ensure thet the frequency range over which resonanceoccurs ls relatlvely

narrow,

and therefore he accelerometermay

be operatedwell

beyond ts

rated

useful

requency

ange without

introducing

phase

distortion.

Nevertheless, t is

also necessary to consider the

phase

linearity

of the

charge or voltage

preamplifier

used, especially f integration

networks and

other filters

are

in

use. This is especially mportant

when measuring ransient

vibrations

nd mechanical hocks.

2.8.TRANSIENTRESPONSE

When

measuring ransientvibrations

and shocks

particular

attentionmust

be

paid

to the overall linearity

of the system

as

otherwise

he reproduced ran-

sientswill

be distorted.Piezoelectric

ccelerometers re extremely inear

rans-

ducers

and

wlll reproduce

a wide range

of transients without

problem.

The

accelerometer s

the least frequent

source of error when

poor

measurements

are made of transients.More

often it is the

preamplifier

and any

associated

filters and integration

networkswhich

cause the

problem.

However,

o ensure

the accuracy ol the measurement t is necessary o consider the following

transient

phenomena.

2.8.1.Leakage Effects

In Fig.2.15,

a distortionhas

taken

place

n the waveformof

a

quasi-static

acceleration

ulse,

such as might

be encountered

uring a

rocket

aunchor in a

fast

elevator.The

distortion is caused

by the accelerometerand

preamplifier

combinationoperating n the incorrect requency ange and can be explained

as follows:

When he accelerometer

s subjected o

a

quasi-static

accelerationa

charge

is developed

on the

piezoelectric

elements.By virtue of the elements

capaci-

tance, his charge s

stored

n

the elementand

prevented

rom

"leaking away"

by the very high leakage

esistanceof the

accelerometer.

However,

due

to the

finite eakage

ime constantof the

accelerometer nd the input mpedance

and

lower limiting frequency

setting on the

preamplifier,

some charge eaks

away

and this resulls n

a negative

slope

waveform

as seen

between

points

A and B.

When he acceleration tops, he charge changesa correspondingamountand

drops below

the

zero

level to

point

C

before rising back up to

the zero level

33


42/160

6

o

o

o

e

Fig. 2.15. The

distortion

ot a waveform

of a

quasi-static

acceleration

input

caused by

"leakage"

associated with

the accelerometer

and

pream-

plifier

again

at

point

D. The rate

of exponential

hange

betweenA and

B and between

C and D is

the same

and is

determinedby the

time constant

set by the

accelerometer nd preamplifier.

This

effect causeserrors in

the measurement

f the

peak

amplitude

of the

acceleration

nd is caused

by the

accelerometer

eing used with

the wrong

Lower Limiting Frequency

n the

preamplifier.

Measurement

rrors

of

peak

amplitudedue

to

leakage

may

be kept to within

5% by

ensuring hat

the

-3dB

Lower

LimitingFrequency

f the

preamplifier

s less

than 0,008/T,

whereT is

the

period

of a square waye

ransient.

For measurements

n half-sine

ran-

sients he Lower

LimitingFrequency

must

be less

than 0,05/T.

The frequencybandwidthof the entire measurement ystem required o

measure

uch ransients

with

specifiedaccuracies

an

be

found rom

Fig.2.16

whichalso ncludes

he

upper requency equirement

ecause

ransient ignals

have

higher frequency

componentswhich

must also

be reproducedwithout

distortion.

The

distortlon

of the waveform

of transients,

and in

particularquasi-static

vibrations,

caused by

using the accelerometer

with

the

incorrect

requency

range

can appear

simllar o

the distortion

produced

by

other

phenomena

uch

as zero

shift

(see

sectlon2.8.3).

t must be

understood

hat the causes,

and

hencesolutions,of the problemsare different.

34


43/160

Frequ€ncy R6ponse

should be

flat witr|in th6e limib

0.1

5

- '- '0.1

0.2

0.5 1 2

5

10

20 50 rm zfi

Puls Duration

{ms}

6ffio/l

Fig.

2.16. Vibration system

-3dB

lower and

upper limiting

frequencies required

for acceleration measurements

of

pulses

of duration

T keeping ampli-

tude

measurement errors

less than 5 and 10%

respectively

2.8.2.

Ringing"

This term

is

used

to describe the distortion

produced

by an accelerometer

which is being used o

measure ransientvibrations

outside ts useful

requency

range.

An

example

of the

resultingdistortedsignal

s

shown

n Fig.2.17.

The

resonanceol the

accelerometer

s

excited

with high frequency

vibration com-

ponents

and

this should be avoided.A first

warning

of

ringing

might be

given

by

an overload

indication on the

preamplifier.

"Ringing" causeserrors

in

the

measurementol

peak

vibration amplitude.

For

5%

peak

measurementerror the accelerometer

mounted resonance requency

should not be

less than'10/T

where T is the length of the transient

n seconds.

35


44/160

Fig.

2.17. Waveform

distortion

due to

"ringing"

The accelerometer

esonance

an be damped

o

reduce he ringing and

make

optimum use of the measurement ystemdynamic range and bandwidth.This

may be achieved

using a mechanical

ilter

for mounting

he accelerometer

see

section

4.5)

or

by applying

he accelerometer

ignal

to a

preamplifier

ncorpo-

rating a

Iow-pass

ilter. In the latter case

the

filter must

have a high frequency

attenuation

slope of

12dBloctave

and a

-3dB

upper

limiting frequency

f,

corresponding

o approximately

half the accelerometer

mounted

resonance

trequency

^(i.e.

f,

=

0,5

f.).This

gives

he system

esponse hown

n Fig.

2.18'

enabf

ng a half-sine

wave transient

of duration

f

=

1 |

f^ to

be

measured

with

less than 10% amplitude

error.

Fig.

2.18. Low

pass

filter or

preamplifier

response

required to damp

mounted

resonance

lrequency f. of accelerometer

lor

measurement

of half

sine

type shock

pulses

of duratlon

T=1/f^ seconds

with

less than

10%

amplltude

error

36

, /

, \

\ .

Filter

R6ponse

-\

Uppcr Limiting

Frequency

fu

=

0,5

f-----lr

\

\

. \

Acoeleromet€r

respons with

Filter

Attenuatlon

Slope

=

12 dB/Octave

0,1

0,2 0,5

1

Proportlon

of Mounted

Reeonenc€

requency .


45/160

2.8.3.

Zero

Shilt

Consider

the

accelerometer

output signals n

Fig.2.19 resulilng

rom two

identical half

sine

pulses.

In both

cases distortion

of the waveform

has

been

introduced

by the accelerometer.

The measurement

dynamic levels

were very

close to the maximum acceleration imit of the accelerometer.

Fig.

2.19. Accelerometer

and

preamplifier

output

resulting

from a hatf-sine

pulse

of such

a

high

level

that

"zero

shift"

has been

introduced

lf the

piezoelectric

elementsare not

considered

o be

perfectly

elastic

materi-

als, then when

the force

on the

element is

suddenly decreased

the molecular

domains may not

all return

to the state

they were

in before

the shear force

was

applied.

Therefore,

when

the force is removed

the elements

stilt

produce

a

charge

which slowly

decays with

time as

the

preamplifier

output returns

o zero

at a rate determined

by its

Lower Limiting

Frequency.

This

phenomenon

occurs

randomly

and with random

sign.

The

time taken for

the zero

shift to disappear

may

be a factor

of 1000 imes

longer than the length of the original pulse. Therefore, large errors result

if

integration

networks

are

used.

A mechanical

ilter

can

often

guard

against zero shift

effects.

REMEMBER: ero

shift,

"Leakage"

and "Ringing"

are only

problems

when

the

accelerometer s

used outside

its useful

Piezoelectric Accelerometers and Vibration Preamplifier

Documents