BRUEL & KJAER 4323 User guide

Accelerometer Sets Type 4319/4323
Accelerometer Packages Type 4359/4363
The Bruel & Kjcer accelerometers have been
designed for maximum dependability and
versatility in use. A rugged waterproof con -
struction together with low sensitivity to en-
vi ron mental changes make these accelero-
meters suitable for most vibration measure-
ments both in the laboratory and under field
conditions .
BRUEL& K~.AER
NA;.RUM , DENMARK. Teleph.: 80 05 00 . Cable : BRUKJA . Telex: 5316. COPENHAGEN
88 4819 / 23 - 0300069

Accelerometer Sets
Type 4319/4323
Accelerometer Packages
Type 4359/4363
OCTOBER 1968

Contents
0. Introduction 3
1. Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Physical Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Environmental Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Shock Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Effect of Mounting Torque .......................................... 10
Long Term Stability ............................................... 10
Piezoelectric Materials
............................................ 10
Natural Resonance Frequencies .................................... 11
2. Factory Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Cable Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Voltage Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Charge Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Transverse Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Undamped Natural Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Frequency Response Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Temperature Sensitivity ............................................ 21
Calibration Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3. Mounting Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Mounting Thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Mounting of Accelerometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Mounting of Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4. Preamplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Voltage Preamplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Charge Amplifiers ................................................. 33
Bruel & Kjcer Preamplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5. Measuring Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
BrGel & Kjcer Measuring Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Preamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Integrating Networks .... .............................. . ... ...... .. 57
Amplifiers and Indicating Instruments .............................. 57
Ground Loops ...... .... .... ..... .. ..... ... ....................... 60
6. Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Portable Instrumentation ..... ... ....... .... ........................ 63
Vibration Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Vibration Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Shock Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
8. Accessories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
9. Conversion Charts, Tables etc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
10. Specifications .................................................... 77

0. Introduction
The accelerometer is an electromechanical transducer which produces at
its
output terminals an e.m.f. proportional to the acceleration to which the
transducer is subjected. The output signal can be electronically processed
and read on a
meter or some other suitable indicating device.
The Bruel & Kjrer accelerometers are small,
light and of rugged construction,
suitable
for most vibration measurements, both in the laboratory and in field
environments. Versatility in use has been a prime goal and special care has
been taken
to ensure a wide frequency range, high sensitivity and good
temperature characteristics. Furthermore, these accelerometers have low
transverse sensitivity,
negligible mounting error and low sensitivity to severe
environmental conditions, such as humidity, high temperature, corrosive
atmospheres and magnetic fields. The acoustical sensitivity and influence of
cable whip are also minimized.
The accelerometers are designed for measurements on parts subjected to
mechanical vibrations, such as machinery, vehicles, ships, aircraft, buildings
etc., and are also used as
controlling elements for vibration test purposes.
Combined with the B & K preamplifiers and frequency analyzers the frequency
spectra of the vibrations can be readily analysed.
For absolute measurements it is necessary to know the sensitivity
of the
vibration transducer employed. Each B & K accelerometer is supplied with
individual
calibration data and a frequency response curve, all taken as part
of the production test procedure. The aim has been to supply the maximum
amount
of information on the calibration sheet to ensure a completely pre-
dictable performance of the accelerometers.
The accelerometers have type numbers
4339- 4343 during the production and
calibration stages. When they are sold they are accompained by certain
accessories, such as cables, mounting screws etc. and have the following
ordering specifications.
Accelerometer Sets Type 4319 - 4323.
Accelerometer Packages Type 4359- 4363.
Se .e chapter 10, Specifications.
3

1. Description
Construction
The Bruel & Kjrer
Accelerometers Type 4339 and 4343 are of the piezoelectric
compression type with a construction indicated schematically in Fig. 1.1. They
are made to have
exactly 10 mV/g and 10 pC/g sensitivity respectively to be
used with voltage and
charge preamplifiers with fixed gain .. The single-ended
compression build-up make them insensitive to acoustic noise, and by means
of a specially constructed cable connection the influence of cable whip is
reduced to a minimum.
P!882:1i':8:8:&!m~!l:B:B:IL--Housing
~;:;j~~)f--spring
/H----Mass
Piezoelectric discs
-iiiililiiiFii~;__--
L;..:..:..:...;.:.;...:..I...IIt----eoutput terminals
Base
L-------~ ~·~~~~~
Fig. 1.1. Schematic drawing of a piezoelectric accelerometer.
The transducing element consists of two piezoelectric*) discs on which is
resting a heavy mass. The mass is preloaded by a
stiff spring and the whole
assembly is mounted in a metal housing with a
thick base. When the accelero-
meter is subjected to vibration, the mass will exert a variable force on the
piezoelectric discs. This force is exactly proportional to the acceleration of
the mass. Due to the piezoelectric effect a variable potential will be developed
across the two discs , which is proportional to the force and therefore to the
acceleration of the mass. For frequencies much lower than the resonance
frequency
of the mass and the stiffness of the whole accelerometer system
the acceleration of the mass will be virtually the same as the acceleration
of the whole transducer , and the potential produced will therefore be pro-
portional to the acceleration to which the transducer is subjected. This
potential can be picked up from the output terminals of the accelerometer and
used
for determination of the vibration amplitude, waveform and frequency.
*) Lead Zirconium Titanate.
4

It has been the aim with these accelerometers to make a versatile transducer
which can successfully meet the requirements
of the majority of research
scientists and vibration engineers. High precision and stability have been
coupled with a universal applicability which makes the accelerometers suit-
able for all but the most specialized applications.
The
accelerometer housing is of an all welded stainless steel construction
which makes it absolutely waterproof. The special ceramic input socket
ensures complete sealing even after several times
of temperature cycling up
to 250° C.
UI 021
Fig. 1. 2. Physical dimensions of the Accelerometers Types 4339 and 4334.
Physical Dimensions
It is generally true that an accelerometer should be as light as possible in
order not to influence the vibration of the specimen on which it is mounted.
For measurements on heavy machinery etc.
this causes no problem but for
lighter structures, such as for example a thin metal plate, the transducer
weight is important.
The resonance frequency of a vibrating single degree
of freedom system is
fo = J__ Vk
2 :rr mo
where mo is the effective lumped mass and k is the lumped stiffness restrain-
ing the mass.
It is easily seen that adding another mass, e.g. an accelerometer , will result
in a change in resonance frequency according to the formula
+= Vm1 : omo
where f1 is the new resonance frequency and m1is the added mass.
Thus any mass added to a vibrating structure will influence the vibration to
some extent, but provided
the added mass is small the influence is often
negligible. A 10% increase in mass will reduce the resonance frequency by
about
5%.
The sensitivity of a piezoelectric accelerometer is directly proportional to
the mass acting on
the piezoelectric disc. This limits the extent to which
5

the accelerometer weight may be reduced without loosing too much of the
sensitivity. For many applications it is also important that any strain developed
in the material on which the accelerometer is fixed is not transmitted to the
piezoelectric element as this would show up in the output signal, indicating
an acceleration which actually is not present. It is therefore necessary to
make the accelerometer base thick, in order to isolate the piezoelectric disc
from such strain. The requirements of high sensitivity, low strain sensitivity
and good high frequency response are in
conflict with requirements for small
physicaf dimensions and weight, so that for general purpose accelerometers
some useful
compromise must be found.
The B &K Accelerometers Types
4339 and 4343 have a base made of stainless
steel (AISI 303) and a total
weight of 16 grammes (0.57 oz.). The physical
dimensions are given in Fig. 1.2.
Environmental Sensitivity
Accelerometers are often used to measure vibration in the field or on
specimens subjected
to severe environmental tests. It is therefore important
that their sensitivity to environmental changes is as small as possible. The
factors that may influence accelerometers performance are primarily tem-
perature, humidity and rapidly varying ambient pressure (Sound). The
temperature
effect is to reduce the voltage sensitivity of the accelerometer
at
higher temperature, but if the accelerometer has undergone a suitable
temperature cycling process in the production stages, the sensitivity will
revert to its normal value when the temperature is brought back to normal
again. Beyond a certain temperature (the Curie point)
the piezoelectric
element is permanently damaged.
The BrOel & Kjrer accelerometers Type 4339-4343 are designed to be used
for
temperatures up to 260° C (500° F) without cooling. The sensitivity will be
slightly reduced at the higher temperatures, but the necessary heat cycling
process has been carried out, so that no permanent change will take place.
It should be noted that great care has been taken to use materials which will
withstand high temperatures. The thermal coefficient of expansion of in-
sulating material and metal parts are carefully matched in
order to maintain
humidity sealing.
The accelerometers are
brought up to 250° C and left to cool down to about
50° C several times during production and calibration until performance is
stable.
Tests have also been conducted in order to find the influence of low tem-
peratures on
accelerometer performance. The voltage sensitivity increases
steadily down to some
-100°C and then levels out, while the capacity under-
goes a gradual decrease with decreasing temperature. The charge sensitivity
is
practically constant.
Typical performance characteristics are given in Fig. 1.3 for the temperature
range -100 to + 260° C (-150 to + 500° F).
6

-100
dB
6
4
-3
-4
-5
-6
Voltage Sensitivity
300 •c
Temperature
2U~22
Fig. 1.3. Typical performance characteristics for the accelerometers in the
temperature range -100 to + 260° C.
Cooling
When the accelerometers are fixed on surfaces with temperatures exceeding
250° C it is possible to reduce the temperature of the accelerometer base by
inserting a
cooling plate between the base and the measuring surface.
When a
mica washer such as the one included in the Accelerometer Kits
4319/4323 is used between the mounting surface and the cooling plate, ex-
perience has shown that temperatures up to 350-400° C may be measured
on the mounting surface with less than 250° C in
the accelerometer base.
A stream
of air passing over the cooling plate considerably aids the cooling
process. The set-up shown in Fig. 1.4 has been tested in the laboratory.
In this set-up the mounting surface was heated to 450° C while less than
200° C were measured in the acce ,lerometer base.
For high temperature measurements one should always employ Teflon cable,
B & K part No. AO 0038. The cable delivered with the accelerometer, B & K
No. AO 0037 is based on Polyethylene and PVC which will not withstand
more than 100°
C. Also for low temperature measurements, from -40° C
downwards, the Teflon cable should be employed.
Aluminium
~ Screen
Air~-~
77/;~))~;;T/??T//J?
266122
Fig. 1.4. Forced air cooling of an accelerometer.
7

Vacuum Test
The B & K accelerometers Type 4339-4343 are sealed
and tested under water
in an evacuated jar for leaks. This eliminates the risk of inferior performance
in
moist atmospheres or environmental test chambers where heavy con-
densation may take place.
A photograph of the test set-up is shown in Fig. 1.5. The smallest leaks show
up immediately as
bubbles rising to the surface.
Fig. 1.
5. Vacuum test set-up.
When the accelerometers are used for measurements in liquids or in very
moist environments it is necessary to seal the cable entry, as shown in
Fig. 1.6.
Sealant
m»"»»»>'~m
26572(/
Fig. 1.6. Sealing of cable entry.
A good sealant for the cable entry is for example Dow Corning Silastic
RTV 731 (room temperature vulcanizing silicon rubber) or General Electric
equivalent. These sealants show excellent performance
for a wide tempera-
ture range·, (- 100 to + 500° F) .
8

Acoustical Sensitivity
Effects due to acoustical excitation are unavoidable with piezoelectric
accelerometers, but may be reduced by careful design. The B &K accelero-
meters are
of a rigid, mechanically isolated construction and pressure vari-
ations in the
air will have little effect on the force exerted on the piezo-
electric element. One may generally assume that the vibrations induced in
the vibrating specimen will give rise to a much higher acceleration signal
than the
direct acoustical excitation of the accelerometer itself. In cases
where very
low accelerations are to be measured in an intense acoustic field,
however,
care must be exercised in order to obtain correct results. Typical
acoustic sensitivity for the accelerometers has been measured and found to
be less than 0.1 flV /flbar, i.e. less than 0.2 flV for 74 dB sound pressure level.
At 140 dB sound pressure level the output is less than 100 flV.
Magnetic Sensitivity
The magnetic sensitivity has been found to be less than 0.5 flV /Gauss for the
least favorable orientation
of the accelerometer in the magnetic field.
Polarity
The polarity of the accelerometers is such that an acceleration directed from
the mounting surface into
the body of the accelerometer results in a positive
e.m.f. on
the centre conductor of the output terminals.
Volts
±1
±2
±3
±4 ±5 ±6
±7 ±8
±9
±10 g X 1000
Fig. 1.7. Part of shock test machine and typical output versus shock
amplitude plot.
9

Shock Perlormance
Accelerometers will often withstand higher shock in one direction than the
other
while not exceeding the maximum limit of the accelerometer. The mass
is pressed against the ceramic with a certain force and this force determines
the upper limit to which the accelerometer output will increase linearly with
increased
shock amplitude in the negative direction. In the case of 4339 / 4343,
however, the mass-spring system is designed very carefully to avoid this affect.
The curves given in Fig. 1.7 apply
to shocks in both positive and negative
directions.
Effect of Mounting Torque
The
effect of mounting torque is less than 1 % change in sensitivity up to
5000 Hz for 6- 60 kgcm (5 to 50 lb-in) mounting torque.
Long Term Stability
A prime goal during design and manufacture has been to achieve maximum
stability under severe environmental conditions. However, when an accelero-
meter is used for measurement under severe conditions of shock and heat,
one should not rely on
this as a primary standard. It would be advisable to
recalibrate such an accelerometer at relatively short intervals of time.
However, a calibration vs. time history is closely followed
for a number of
representative units taken from
production lots and they show less than 2 %
change per year.
Piezoelectric Materials
The
quality of piezoelectric accelerometers depends largely upon the per-
formance
of the material used for the sensing elements. Monocrystalline
materials such as quartz and Rochelle salt, have been used in the past, but
are now superseded by polycrystalline,
artificially polarized ceramics like
barium titanate, lead zirconium titanate, lead metaniobate
or similar materials.
Large variations in
electrical and mechanical properties are obtained by small
changes in composition, and most manufacturers are continuously investigat-
ing and improving
their compositions in order to make them more suitable
for
their particular purposes.
The most important
factors for general purpose accelerometers are Curie
point, sensitivity, temperature stability, capacity, resistance and time stability.
Unfortunately some
of these are conflicting, high sensitivity for example, has
often to be sacrified for good time or temperature stability.
In the table below are given some properties of commonly used ceramics as
given by their manufacturers. The Curie point is the temperature at which the
ceramic changes its crystal structure and looses its polarization, the piezo-
electric constant indicates the sensitivity, and the dielectric constant indicates
the
capacity for a given shape and size. Trade names are used as the true
composition of the ceramic is usually not disclosed by the manufacturer.
10

Manufacturer and
Curiepoint
Piezoelectric Dielectric
Trade Name oc
Constant Constant
10-12 Coui./Newt.
(Rei. Perm.}
Clevite
I
Ceramic "B"
115 149 1300
Clevite
PZT4
325 285 1475
Quartz & Silice
p 1-60
351
400 1500
Plessey 120 83 1000
Casonic Grade 3
Quartz 300
I
2 4
B & K (1966} 350 300 1500
Natural Resonance Frequencies
The natural resonance frequency of an accelerometer is not fixed. It depends
not only upon the mass and stiffness of the accelerometer but also upon the
mass (and stiffness) of the object on which it is mounted.
Some confusion persists as to what is the natural frequency and different
definitions are seen.
The situation is best illustrated with a drawing. Fig. 1.8a shows a schematic
drawing of an accelerometer which consists of several masses and springs
connected in series. These springs are representations of the contact stiffness
between the various parts of the accelerometer.
This mechanical system can be further simplified into that of Fig. 1.8b. Here
M is the seismic mass resting on the piezoelectric element, B is the mass of
the accelerometer base and housing. K is the equivalent stiffness of the
system between M and B. The natural frequency of such a system is equal to
fo = fMV1 + ~
where fM is the natural resonance frequency of the mass M upon the spring
of stiffness K.
Now two resonance frequencies are easily thought of:
1. The free hanging resonance frequency , i.e. the resonance frequency obtain-
ed with the system freely suspended in air.
This resonance frequency is entirely dependent upon the ratio of M and B,
and it is seen that making the base B very light the resonance frequency
may be very high. This resonance frequency is therefore of no practical
11

Seismic mass
Contact stiffness
Piezoelectric disc
Conta· ct stiffness
Piezoelectric disc
Contact
stiffness
Mass of base
a)
M
K= Equivalent
stiffness
b)
266o20
Fig. 1.8 a. Schematic drawing of accelerometer as a dynamic system.
b.
Simplified system.
value, in fact the higher it is compared with the mounted resonance fre-
quency defined below the poorer is the mechanical construction of the
transducer. (A thin base may cause bending of the piezoelectric due to
strain from the mechanical part on which the vibration is measured).
2. The
mounted resonance frequency with the accelerometer firmly fixed to
a
structure of infinite stiffness and mass.
This results in a value
for B of infinity and the resonance frequency is
equal to fM which is the natural resonance frequency of the mass M on the
spring
of stiffness K.
This resonance frequency is of great practical value as it is approximately
the one obtained when the
accelerometer is mounted on a structure which
is heavy compared with the accelerometer mass.
Unfortunately
it is difficult to measure the mounted resonance frequency as
defined above, since an infinitely heavy mass is hard to bring into motion.
A
compromise has therefore to be made and there are standards which define
the mounted resonance as
that obtained with the accelerometer mounted
on a one inch cube of steel (Bruel & Kjcer use a steel block of weight 180
gram). Such a block is easily set into controlled motion at frequencies up to
some 50 kHz.
12

B
B=base+180 grams
/j
~// ~ / /M /#)1
266ol9
Fig. 1.9. Possible configurations for definitions of natural resonance frequency.
This mounted resonance may be used directly as a basis for vibration meas-
urements as long as
the accelerometer seismic mass is much smaller than
the mass
of the calibration mounting block. The natural frequency obtained
is
practically identical with the mounted resonance frequency on an infinite
mass.
However, when the
accelerometer mass is large the natural frequency obtained
will be too high, thus if B = 5 M we obtain
i.e. a value which is
10% high.
For the Bruel & Kjrer accelerometers the ratio of weights of the seismic mass
to the weight of the base is about 1 : 1 and therefore the free hanging re-
sonance
will be about 1.5 times the mounted resonance and the resonance
obtained on the 180 grams
block of steel is 2-4% higher than that which
would be obtained on an infinite mass.
A small difference in resonance frequency is obtained by considering the
damping present in the accelerometer. Thus undamped natural frequency is
defined as
the frequency at which the difference between the motion of the
mass and base lags
the motion of the base by a phase angle of 90°, whereas
damped natural frequency is the frequency of decaying oscillations after an
initial excitation. The difference is negligible for high Q piezoelectric accelero-
meters such as the ones manufactured by Bruel & Kjrer.
The undamped natural frequency given on the B &K accelerometer calibration
charts is the free hanging undamped natural frequency.
13

2. Factory Calibration
Each individual accelerometer has before leaving the factory undergone a
very thorough ageing, testing and
calibration procedure to ensure the user of
a high quality product. A typical calibration chart as supplied with the
accelerometers is shown in Fig. 2.1.
=...,a-tr:a. +
......... ~~g{!!~( ~~~
--:::-..::-- .e ... t.f?. ._ .. ··'- -~ .. •c
O... ..... tl •.... !:'.<?. '!f. ... , :
................. .... !:~:!':f? •.. .V/t "
-.. ....... ....... r/..:t. fii~~C~~
~,.....,.. ...... ...t:t:l. /1. .... ,
__ .___ ..... ... .(.:!?. . ...
F-~~ · Z=_a
~:~===-=~~~
....._.. .w- ... ,....._. ____
...- .
o... t::?::~:. ~ll ................. ~~ .........
Cable Capacitance
Bra.I&ICJ~r
~ .... ~-::=..~..... o o o o o a o o o o o o a o o o o o o o o o coo o o o coo
-- o.c .............. : __ ... ._ __ _
'=-=----- . ·~ -
I ~ +a
! -- --
:-
-, A :5
- -~~§.~~
--
=.,~g:=-
:"'- - ... --
Fig. 2.1. A typical calibration chart.
The capacitance of the accelerometers are given including the capacitance
of the ordinary B & K connecting cable, so that when other cables are used,
the
change in cable capacitance must be taken into account , as this deter-
mines the effective sensitivity of the accelerometer. To find the capacitance
of the accelerometer alone, deduct the cable capacitance given on the
calibration chart. The standard length of cable included is 1.2 m (4 ft).
The
capacitance of the 1.2 m cable is around 105 pF (micromicrofarad) but the
individual value is given on the calibration chart.
Voltage Sensitivity
The voltage sensitivity of the accelerometers with connecting cable is deter-
mined at a frequency of 50 Hz and at room temperature (appr. 20° C).
Fig. 2.2
shows the instrumentation employed.
The
accelerometers are calibrated at 50 Hz, the frequency being controlled
by a crystal controlled 100 Hz frequency standard, which gives a frequency
accuracy better than ± 0.01 %.
14

Accelerometer
Preamplifiers
Type
2623
Steel Springs
Reference Voltage
50 Hz 5V
100Hz
50 Hz Variable V
Frequency Analyzer
Type
2107
Stroboscope
and
50 Hz
Generator
100Hz
Standard
Frequency
Fig. 2.2. Set-up used for calibration of absolute sensitivity of the accelero-
meters.
The shaker providing the mechanical excitation is mounted on a large con-
crete block which is supported by steel springs, giving the whole assembly
a natural resonance frequency of about 1 Hz. This ensures isolation from
background vibration .
The
calibration of all units is achieved by comparison between a standard
accelerometer and the unknown in a back to back mounting as shown in
Fig. 2.2. The standard is
frequently checked with a microscope observing the
displacement directly, with an accuracy of ± 1 %.
The distortion in actual vibration units is kept below 2 °/o and max. influence
on peak to peak amplitude below 0.5 %.
The output from the accelerometer is measured with a B & K Frequency
Analyzer set to 50 Hz and calibrated with a reference voltage of exactly the
same
frequency as the signal to the shaker, giving a total voltage measuring
accuracy of ± 0.15 %.
The total accuracy on the sensitivity calibration of the accelerometers is thus
better than ± 2 %.
The calibration vs. time history is closely followed for a number of re-
presentative
units taken from production and they show less than 2% change
per year.
Note that the
calibration is valid for the accelerometer with its individual
connecting cable, and remember to take any change of cable capacitance
into account when different cables are employed.
15

Also the input capacity of the preamplifier must be taken into account. The
influence
of this capacity in the calibration set-up is eliminated with a sub-
stitution measurement. In practice the capacity will be less than 10 pF using
a normal B & K amplifier and plug such as B & K Cathode Follower Type
2615, Source Follower 2616 or 4 pF in the case of Preamplifier 2623.
Note also the units employed in
the calibration. The sensitivity is given in
mV/g = mVR Ms/ gRMs = mVP ••k/ gP. ak · If, for example, the sensitivity is required in
mVRM s/ gP ••k the sensitivity given should be multiplied by 0.707.
Charge Sensitivity
The calibration of the accelerometer charge sensitivity is achieved with the
same set-up as described in the previous section. The voltage preamplifier
(2623) is replaced by the charge amplifier (2624), see Fig. 2.2, and the
accuracy
of the calibration is the same as before. The charge sensitivity is
expressed in
pico-coulumb /g and is independent of the capacitive loading on
the accelerometer.
Capacitance
The capacitance of the accelerometer is given including the cable capacitance
as specified on the calibration sheet. Accelerometer capacitance comes into
the question when
the low frequency cut-off of the measuring system is com-
puted, as
it determines the effect of loading on the accelerometer.
The capacitance is calculated from the voltage sensitivity and the charge
sensitivity. The relationship is given by:
S charge = S voltage (Ca + Cc)
C. + Cc = S
charge
S voltege
where c. = accelerometer capacitance and Cc = cable capacitance.
Transverse Sensitivity
Transverse sensitivity is the maximum sensitivity to a transverse acceleration
expressed in percent
of the reference sensitivity in the intended measuring
direction.
The transverse sensitivity
of the accelerometers is primarily due to irregular-
ities in
the ceramics, and limitations in the mechanical coupling between
ceramic and metal parts. Careful mechanical machining helps
to minimize
transverse sensitivity.
Transverse sensitivity can be regarded as a result of the axis of the accelero-
meter making a small angle with the
direction of the maximum sensitivity as
shown in Fig. 2.3.
Imagining the accelerometer placed in a rectangular coordinate system, as
shown, the vector representing the maximum sensitivity can be resolved into
16

Main axis
sensitivity
100%
\
\
\
\ Minimum
, sensitivity
in this
direction
Fig. 2.3. Graphical illustration of transverse sensitivity.
two components: the main axis sensitivity which is the one called voltage or
charge sensitivity on the calibration chart, and the transverse sensitivity
given on the calibration chart as a percentage of
the main axis sensitivity.
The voltage obtained from
an accelerometer is a product of the acceleration
vector and the component of the sensitivity in the same direction, so that
in a certain transverse direction, at
right angles to both the main axis and
the max. transverse sensitivity axis the accelerometer output will be minimum.
In order to maintain a low transverse sensitivity the user should always mount
the accelerometer on a flat, clean surface and keep
the accelerometer mount-
ing surface free from burrs and scratches. Also he should avoid very large
shocks in the transverse direction, such as might be caused by dropping
the accelerometer on the floor, and large temperature shocks.
If the accelerometer is properly handled and mounted, the transverse sensitiv-
ity will normally be below
10% up to 5000 Hz. Above 5000 Hz it is very diffi-
cult to establish useful test facilities for transverse measurements. The type
of mounting
of the accelerometer will, however, undoubtedly set a limit at
a frequency somewhat lower than that
for operation in the main direction.
Fig. 2.4 is a typical frequency response
for transverse sensitivity at frequencies
up to 5000
Hz.
The transverse sensitivity of the accelerometers is specified as being less than
3% of the main axis sensitivity. However, the individual maximum transverse
sensitivity is given on
the calibration chart, and in addition the direction of
17

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Transverse
1000
10000
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Fig. 2.4. Frequency response curve for transverse sensitivity of an accelero-
meter .
-
Fig. 2.5. Part of the arrangement for obtaining transverse sensitivity.
minimum transverse sensitivity is marked with a red dot on the side of the
accelerometer.
In the factory calibration the transverse sensitivity is measured at approx-
imately 30 Hz on a rotating table whose motion sideways is more than 100
times larger than the motion in the vertical direction. See Fig. 2.5.
18