windows-1256 measuring vibration

8/9/2019 Windows-1256 Measuring Vibration

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Introduction

This booklet answers some of the basic questions asked

by the newcomer to vibration measurement. It gives abrief explanation to the following:

See Page

Why do we measure vibration? 2 & 3

Where does it come from? 3

What is vibration? 4

How to quantify the vibration level 5

The vibration parameters, Acceleration,

Velocity and Displacement 6

Measurement Units 6

Which parameter to measure 7

The piezoelectric accelerometer 8

Practical accelerometer designs 9

Accelerometer types 10

Accelerometer characteristics 11

Accelerometer frequency range 12

Avoiding errors due to accelerometer resonance 13Choosing a mounting position for the

accelerometer 14

How to mount the accelerometer 15 & 16

Environmental Influences General 17

Environmental Influences Temperature 18

See Page

Environmental Influences Cable Noise 19

Other Environmental Influences 20 & 21

Accelerometer calibration 22

A simple calibrator 23

Force and impedance measurements 24

Logarithmic scales and decibels 25

Why use an accelerometer preamplifier? 26

The vibration meter 27

What is frequency analysis? 28

Constant bandwidth or constant percentagebandwidth frequency analysis 29

Filter bandwidth considerations 30

Defining the filter bandwidth 31

Measuring instrumentation 32Recording results 33

Using vibration measurements 34

Vibration as a machine condition indicator 35

Vibration trouble shooting charts 36 & 37

Vibration and the human body 38

Revision September 1982

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Background

Since man began to build machines for industrial use,

and especially since motors have been used to powerthem, problems of vibration reduction and isolation haveengaged engineers.

Gradually, as vibration isolation and reduction tech-niques have become an integral part of machine design,the need for accurate measurement and analysis of me-

chanical vibration has grown. This need was largely sa-tisfied, for the slow and robust machines of yesteryear,by the experienced ear and touch of the plant engineer,or by simple optical instruments measuring vibratory dis-placement.

Over the last 15 or 20 years a whole new technology ofvibration measurement has been developed which is suit-

able for investigating modern highly stressed, high speedmachinery. Using piezoelectric accelerometers to convertvibratory motion into an electrical signal, the process of

measurement and analysis is ably performed by the vers-atile abilities of electronics.

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Where does it come from?

In practice it is very difficult to avoid vibration. It usually

occurs because of the dynamic effects of manufacturingtolerances, clearances, rolling and rubbing contact be-tween machine parts and out-of-balance forces in rotat-ing and reciprocating members. Often, small insignifi-cant vibrations can excite the resonant frequencies ofsome other structural parts and be amplified into majorvibration and noise sources.

Sometimes though, mechanical vibration performs a use-ful job. For example, we generate vibration intentionallyin component feeders, concrete compactors, ultrasoniccleaning baths, rock drills and pile drivers. Vibration test-ing machines are used extensively to impart a controlledlevel of vibration energy to products and sub-assemblieswhere it is required to examine their physical or func-

tional response and ascertain their resistability to vibra-tion environments.

A fundamental requirement in all vibration work,whether it is in the design of machines which utilize itsenergies or in the creation and maintenance of smoothlyrunning mechanical products, is the ability to obtain anaccurate description of the vibration by measurementand analysis.

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What is Vibration?

A body is said to vibrate when it describes an oscillating

motion about a reference position. The number of timesa complete motion cycle takes place during the period ofone second is called the Frequency and is measured inhertz (Hz).

The motion can consists of a single component occuringat a single frequency, as with a tuning fork, or of severalcomponents occuring at different frequencies simultane-

ously, as for example, with the piston motion of an inter-nal combusion engine.

Vibration signals in practice usually consist of very manyfrequencies occuring simultaneously so that we cannotimmediately see just by looking at the amplitude-time

pattern, how many components there are, and at whatfrequencies they occur.

These components can be revealed by plotting vibrationamplitude against frequency. The breaking down of vibra-tion signals into individual frequency components iscalled frequency analysis, a technique which may be con-sidered the cornerstone of diagnostic vibration measure-

ments. The graph showing the vibration level as a func-tion of frequency is called a frequency spectrogram.

When frequency analyzing machine vibrations we nor-mally find a number of prominent periodic frequencycomponents which are directly related to the fundamen-

tal movements of various parts of the machine. With fre-quency analysis we are therefore able to track down thesource of undesirable vibration.

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Quantifying the Vibration LevelThe vibration amplitude, which is the characteristic

which describes the severity of the vibration, can be qu-antified in several ways. On the diagram, the relation-ship between the peak-to-peak level, the peak level, theaverage level and the RMS level of a sinewave is shown.

The peak-to-peak value is valuable in that it indicates the

maximum excursion of the wave, a useful quantity

where, for example, the vibratory displacement of a ma-chine part is critical for maximum stress or mechanical

clearance considerations.

The peak value is particularly valuable for indicating the

level of short duration shocks etc. But, as can be seen fromthe drawing, peak values only indicate what maximum levelhas occurred, no account is taken of the time history of the

wave.

The rectified average value, on the other hand, does take

the time history of the wave into account, but is consid-ered of limited practical interest because it has no directrelationship with any useful physical quantity.

The RMS value is the most relevant measure of ampli-

tude because it both takes the time history of the waveinto account and gives an amplitude value which is di-rectly related to the energy content, and therefore thedestructive abilities of the vibration.

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The Vibration Parameters, Acceleration, Velocity and Displacement.

Measuring Units

When we looked at the vibrating tuning fork we consid-ered the amplitude of the wave as the physical displace-ment of the fork ends to either side of the rest position.In addition to Displacement we can also describe themovement of the fork leg in terms of its velocity and itsacceleration. The form and period of the vibration remainthe same whether it is the displacement, velocity or ac-

celeration that is being considered. The main differenceis that there is a phase difference between the ampli-

tude-time curves of the three parameters as shown inthe drawing.

For sinusoidal signals, displacement, velocity and acceler-ation amplitudes are related mathematically by a func-tion of frequency and time, this is shown graphically in

the diagram. If phase is neglected, as is always the casewhen making time-average measurements, then the ve-

locity level can be obtained by dividing the accelerationsignal by a factor proportional to frequency, and the dis-placement can be obtained by dividing the acceleration

signal by a factor proportional to the square of fre-quency. This division is performed by electronic integra-

tors in the measuring instrumentation.The vibration parameters are almost universally mea-sured in metric units in accordance with ISO require-

ments, these are shown in the table. The gravitationalconstant "g" is still widely used for acceleration levels al-

though it is outside the ISO system of coherent units.Fortunately a factor of almost 10 (9,81) relates the two

units so that mental conversion within 2% is a simplematter.

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The Piezoelectric AccelerometerThe transducer which, nowadays, is more-or-less univer-sally used for vibration measurements is the piezoelec-

tric accelerometer. It exhibits better all-round characteris-tics than any other type of vibration transducer. It hasvery wide frequency and dynamic ranges with good line-arity throughout the ranges. It is relatively robust and re-liable so that its characteristics remain stable over a longperiod of time.

Additionally, the piezoelectric accelerometer is self-gene-rating, so that it doesn't need a power supply. There areno moving parts to wear out, and finally, its accelerationproportional output can be integrated to give velocity anddisplacement proportional signals.

The heart of a piezoelectric accelerometer is the slice ofpiezoelectric material, usually an artificially polarized fer-

roelectric ceramic, which exhibits the unique piezoelec-tric effect. When it is mechanically stressed, either intension, compression or shear, it generates an electricalcharge across its pole faces which is proportional to theapplied force.

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Practical Accelerometer DesignsIn practical accelerometer designs, the piezoelectric ele-

ment is arranged so that when the assembly is vibratedthe mass applies a force to the piezoelectric elementwhich is proportional to the vibratory acceleration. This

can be seen from the law, Force = Mass x Acceleration.

For frequencies lying well under the resonant frequency

of the complete spring-mass system, the acceleration ofthe mass will be the same as the acceleration of the

base, and the output signal magnitude will therefore beproportional to the acceleration to which the pick-up issubjected.

Two configurations are in common use:

The Compression Type where the mass exerts a com-pressive force on the piezoelectric element and

The Shear Type where the mass exerts a shear force on

the piezoelectric element.

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Accelerometer TypesMost manufacturers have a wide range of accelerometers,at first sight may be too many to make the choice easy. A

small group of "general purpose" types will satisfy mostneeds. These are available with either top or side mountedconnectors and have sensitivities in the range 1 to 10 mVor pC per m/s

2. The Brel & Kjr Uni-Gain types have

their sensitivity normalized to a convenient "round figure"such as 1 or 10 pC/ms

-2to simplify calibration of the

measuring system.

The remaining accelerometers have their characteristicsslanted towards a particular application. For example,small size acclerometers that are intended for high level orhigh frequency measurements and for use on delicatestructures, panels, etc. and which weigh only 0,5 to 2grammes.

Other special purpose types are optimized for: simulta-neous measurement in three mutually perpendicularplanes; high temperatures; very low vibration levels; highlevel shocks; calibration of other accelerometers by com-parison; and for permanent monitoring on industrialmachines.

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Accelerometer Characteristics (Sensitivity, Mass and Dynamic Range)

The sensitivity is the first characteristic normally consid-

ered. Ideally we would like a high output level, but here

we have to compromise because high sensitivity nor-mally entails a relatively big piezoelectric assembly andconsequently a relatively large, heavy unit.

In normal circumstances the sensitivity is not a criticalproblem as modern preamplifiers are designed to acceptthese low level signals.

The mass of the accelerometers becomes importantwhen measuring on light test objects. Additional masscan significantly alter the vibration levels and frequen-cies at the measuring point.

As a general rule, the accelerometer mass should be nomore than one tenth of the dynamic mass of the vibrat-

ing part onto which it is mounted.

When it is wished to measure abnormally low or high ac-celeration levels, the dynamic range of the accelerome-ter should be considered. The lower limit shown on thedrawing is not normally determined directly by the accel-erometer, but by electrical noise from connecting cablesand amplifier circuitry. This limit is normally as low as

one hundredth of a m/s2

with general purpose instru-ments.

The upper limit is determined by the accelerometer'sstructural strength. A typical general purpose acceler-ometer is linear up to 50000 to 100 000 m/s

2, that is

well into the range of mechanical shocks. An acceler-ometer especially designed for the measurement of me-

chanical shocks may be linear up to 1000km/s2(100000 g). 11


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Accelerometer Frequency Range ConsiderationsMechanical systems tend to have much of their vibrationenergy contained in the relatively narrow frequency

range between 10 Hz to 1000 Hz but measurements areoften made up to say 10 kHz because there are often in-teresting vibration components at these higher frequen-

cies. We must ensure, therefore, when selecting an ac-celerometer, that the frequency range of the accelerome-ter can cover the range of interest.

The frequency range over which the accelerometer gives

a true output is limited at the low frequency end in prac-tice, by two factors. The first is the low frequency cut-offof the amplifier which follows it. This is not normally aproblem as the limit is usually well below one Hz. The

second is the effect of ambient temperature fluctuations,to which the accelerometer is sensitive. With modern

shear type accelerometers this effect is minimal, allow-

ing measurements down to below 1 Hz for normal envir-onments.

The upper limit is determined by the resonant frequencyof the mass-spring system of the accelerometer itself.

As a rule of thumb, if we set the upper frequency limitto one-third of the accelerometer's resonance frequency,

we know that vibration components measured at the up-per frequency limit will be in error by no more than+ 12%.

With small accelerometers where the mass is small, theresonant frequency can be as high as 180kHz, but forthe somewhat larger, higher output, general purpose ac-celerometers, resonant frequencies of 20 to 30kHz are

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Avoiding Errors due to Accelerometer Resonance As the accelerometer will typically have an increase insensitivity at the high frequency end due to its reson-

ance, its output will not give a true representation of thevibration at the measuring point at these high frequen-cies.

When frequency analyzing a vibration signal, one mayeasily recognize that a high frequency peak is due to the

accelerometer resonance, and therefore ignore it. But ifan overall wideband reading is taken which includes theaccelerometer resonance it will give a totally inaccurate

result if, at the same time, the vibration to be measuredalso has components in the region around the resonantfrequency.

This problem is overcome by choosing an accelerometerwith as wide a frequency range as possible and by using

a low-pass filter, which is normally included in vibrationmeters and preamplifiers, to cut away the undesired sig-

nal caused by the accelerometer resonance.

Where measurements are confined to low frequencies.high frequency vibration and accelerometer resonance ef-fects can be removed with mechanical filters. They con-sist of a resilient medium, typically rubber, bonded be-

tween two mounting discs, which is mounted betweenthe accelerometer and the mounting surface. They willtypically reduce the upper frequency limit to between

0,5 kHz to 5 kHz.

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Choosing a Mounting Position for the AccelerometerThe accelerometer should be mounted so that the de-sired measuring direction coincides with its main sensi-tivity axis. Accelerometers are also slightly sensitive to vi-brations in the transverse direction, but this can nor-mally be ignored as the transverse sensitivity is typicallyless than 1% of the main axis sensitivity.

The reason for measuring vibration on the object will us-ually dictate the position of the measuring point. Takethe bearing housing in the drawing as an example. Here,

acceleration measurements are being used to monitorthe running condition of the shaft and bearing. The accel-erometer should be positioned to maintain a direct pathfor the vibration from the bearing.

Accelerometer "A" thus detects the vibration signal fromthe bearing predominant over vibrations from other partsof the machine, but accelerometer "B" detects the bear-ing vibration, probably modified by transmission througha joint, mixed with signals from other parts of the ma-chine. Likewise, accelerometer "C" is positioned in amore direct path than accelerometer "D".

The question also arises in which direction shouldone measure on the machine element in question? It isimpossible to state a general rule, but as an example, for

the bearing shown, one could gain valuable informationfor monitoring purposes by measuring both in the axial

direction and one of the radial directions, usually theone expected to have the lowest stiffness.

The response of mechanical objects to forced vibrations

is a complex phenomenon, so that one can expect, espe-cially at high frequencies, to measure significantly differ-

ent vibration levels and frequency spectra, even on adja-cent measuring points on the same machine element.14


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Mounting the AccelerometerThe method of mounting the accelerometer to the mea-

suring point is one of the most critical factors in obtain-ing accurate results from practical vibration measure-ments. Sloppy mounting results in a reduction in themounted resonant frequency, which can severely limitthe useful frequency range of the accelerometer. The

ideal mounting is by a threaded stud onto a flat, smoothsurface as shown in the drawing. A thin layer of grease

applied to the mounting surface before tightening downthe accelerometer will usually improve the mounting stiff-ness. The tapped hole in the machine part should be suf-

ficiently deep so that the stud is not forced into the baseof the accelerometer. The upper drawing shows a typicalresponse curve of a general purpose accelerometer

mounted with a fixing stud on a flat surface. The reso-nant frequency attained is almost as high as the 32kHz

mounted resonant frequency attained under calibrationwhere the mounting surface is dead flat and smooth.

A commonly used alternative mounting method is theuse of a thin layer of bees-wax for sticking the acceler-

ometer into place. As can be seen from the responsecurve, the resonant frequency is only slightly reduced (to29kHz). Because bees-wax becomes soft at higher tem-

peratures, the method is restricted to about 40C. Withclean surfaces, bees-wax fixing is usable up to accelera-

tion levels of about 100 m/s2

.

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Mounting the AccelerometerWhere permanent measuring points are to be esta-blished on a machine and it is not wished to drill and tapfixing holes, cementing studs can be used. They are att-ached to the measuring point by means of a hard glue.Epoxy and cyanoacrylate types are recommended as softglues can considerably reduce the usable frequencyrange of the accelerometer.

A mica washer and isolated stud are used where the

body of the accelerometer should be electrically isolatedfrom the measuring object. This is normally to preventground loops, but more about that under "EnvironmentalInfluences". A thin slice should be peeled from the thickmica washer supplied. This fixing method also givesgood results, the resonance frequency of the test acceler-ometer only being reduced to about 28 kHz.

A permanent magnet is a simple attachment methodwhere the measuring point is a flat magnetic surface. Italso electrically isolates the accelerometer. This methodreduced the resonant frequency of the test accelerome-ter to about 7 kHz and consequently cannot be used formeasurements much above 2kHz. The holding force ofthe magnet is sufficient for vibration levels up to 1000to 2000 m/s

2depending on the size of the accelerome-

ter.

A hand-held probe with the accelerometer mounted ontop is very convenient for quick-look survey work, but

can give gross measuring errors because of the low over-all stiffness. Repeatable results cannot be expected. A

low-pass filter should be used to limit the measuring

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Environmental Influences Temperature

Typical general purpose accelerometers can tolerate tem-peratures up to 250C. At higher temperatures the pie-zoelectric ceramic will begin to depolarize so that thesensitivity will be permanently altered. Such an acceler-ometer may still be used after recalibration if the depola-rization is not too severe. For temperatures up to 400C,accelerometers with a special piezoelectric ceramic areavailable.

All piezoelectric materials are temperature dependent sothat any change in the ambient temperature will resultin a change in the sensitivity of the accelerometer. Forthis reason all B & K accelerometers are delivered with asensitivity versus temperature calibration curve so thatmeasured levels can be corrected for the change in accel-erometer sensitivity when measuring at temperatures sig-nificantly higher or lower than 20C.

Piezoelectric accelerometers also exhibit a varying outputwhen subjected to small temperature fluctuations, calledtemperature transients, in the measuring environment.This is normally only a problem where very low level orlow frequency vibrations are being measured. Modernshear type accelerometers have a very low sensitivity totemperature transients.

When accelerometers are to be fixed to surfaces withhigher temperatures than 250C, a heat sink and micawasher can be inserted between the base and the mea-suring surface. With surface temperatures of 350 to400C, the accelerometer base can be held below250C by this method. A stream of cooling air can pro-

vide additional assistance.

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Environmental Influences Cable Noise

Since piezoelectric accelerometers have a high output im-

pedance, problems can sometimes arise with noise sig-nals induced in the connecting cable. These distur-bances can result from ground loops, triboelectric noise

or electromagnetic noise.

Ground Loop currents sometimes flow in the shield ofaccelerometer cables because the accelerometer and

measuring equipment are earthed separately. The

ground loop is broken by electrically isolating the acceler-ometer base from the mounting surface by means of anisolating stud and mica washer as already mentioned.

Tribo-electric Noise is often induced into the acceler-

ometer cable by mechanical motion of the cable itself. Itoriginates from local capacity and charge changes due to

dynamic bending, compression and tension of the layers

making up the cable. This problem is avoided by using aproper graphited accelerometer cable and taping or glu-ing it down as close to the accelerometer as possible.

Electromagnetic Noise is often induced in the acceler-

ometer cable when it lies in the vicinity of running ma-chinery. Double shielded cable helps in this respect, butin severe cases a balanced accelerometer and differen-tial preamplifier should be used.

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Other Environmental InfluencesBase Strains: When an accelerometer is mounted on a

surface that is undergoing strain variations, an outputwill be generated as a result of the strain being transmit-ted to the sensing element. Accelerometers are designedwith thick, stiff bases to minimize this effect: DeltaSheartypes have a particularly low base strain sensitiv-ity because the sensing element is mounted on a centrepost rather than directly to the accelerometer base.

Nuclear Radiation: Most B & K accelerometers can beused under gamma radiation doses of 10k Rad/h up toaccumulated doses of 2 M Rad without significantchange in characteristics. Certain accelerometers can beused in heavy radiation with accumulated doses in ex-cess of 100 M Rad.

Magnetic Fields: The magnetic sensitivity of piezoelec-

tric accelerometers is very low, normally less than 0,01to 0,25 m/s

2per k Gauss in the least favourable orienta-

tion of the accelerometer in the magnetic field.

Humidity: B & K accelerometers are sealed, either by

epoxy bonding or welding to ensure reliable operation inhumid environments. For short duration use in liquids,or where heavy condensation is likely, Teflon sealed ac-

celerometer cables are recommended. The accelerome-ter connector should also be sealed with an acid freeroom temperature vulcanizing silicon rubber or mastic.

Industrial accelerometers with integral cables should beused for permanent use in humid or wet areas.

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Other Environmental InfluencesCorrosive Substances: The materials used in the con-

struction of all Brel & Kjr accelerometers have a high

resistance to most of the corrosive agents encountered

in industry.

Acoustic Noise: The noise levels present in machinery

are normally not sufficiently high to cause any signifi-

cant error in vibration measurements. Normally, the

acoustically induced vibration in the structure on whichthe accelerometer is mounted is far greater than the air-

borne excitation.

Transverse Vibrations: Piezoelectric accelerometers are

sensitive to vibrations acting in directions other than

coinciding with their main axis. In the transverse plane,

perpendicular to the main axis, the sensitivity is less

than 3 to 4% of the main axis sensitivity (typically < 1%). As the transverse resonant frequency normally lies at

about 1/3 of the main axis resonant frequency, it should

be considered where high levels of transverse vibration

are present.

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Accelerometer CalibrationEach Brel & Kjr accelerometer is supplied individually

calibrated from the factory and is accompanied by a com-prehensive calibration chart. Where accelerometers arestored and operated within their specified environmentallimits, i. e. are not subjected to excessive shocks, temper-atures, radiation doses etc. there will be a minimalchange in characteristics over a long time period. Testshave shown that characteristics change less than 2%,even over periods of several years.

However, in normal use, accelerometers are often subjected to quite violent treatment which can result in asignificant change in characteristics and sometimes evenpermanent damage. When dropped onto a concrete floorfrom hand height an accelerometer can be subjected to ashock of many thousands of g. It is wise therefore tomake a periodic check of the sensitivity calibration. Thisis normally sufficient to confirm that the accelerometer

is not damaged.

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A Simple CalibratorThe most convenient means of performing a periodic cali-bration check is by using a B & K battery-poweredcalibrated vibration source. This has a small built-in

shaker table which can be adjusted to vibrate at pre-cisely 10 m/s

2.

The sensitivity calibration of an accelerometer is checkedby fastening it to the shaker table and noting its output

when vibrated at 10m/s

2

. Alternatively an accelerome-ter can be reserved for use as a reference. This ismounted on the shaker table with the accelerometer to

be calibrated. The ratio of their respective outputs whenvibrated will be proportional to their sensitivities, and asthe sensitivity of the reference accelerometer is known.

the unknown accelerometer's sensitivity can be accu-rately determined.

An equally useful application for the portable calibratoris the checking of a complete measuring or analyzing se-tup before the measurements are made. The measuring

accelerometer is simply transferred from the measuringobject to the calibrator and vibrated at a level of

10 m/s2. The meter readout can be checked and if a le-

vel or tape recorder is being used, the 10 m/s2

calibra-tion level can be recorded for future reference.

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Force and Impedance

MeasurementsForce transducers are used in mechanical-dynamicsmeasurements together with accelerometers to deter-mine the dynamic forces in a structure and the resultingvibratory motions. The parameters together describe themechanical impedance of the structure.

The force transducer also uses a piezoelectric element,

which when compressed gives an electrical output pro-portional to the force transmitted through it. The forcesignals can be processed and measured with exactly thesame instrumentation used with accelerometers.

For point impedance measurements on very light struc-tures, the accelerometer and force transducer can becombined into a single unit called an impedance head.

Most impedance measurements, however, are per-formed using a separate accelerometer and force trans-ducer.

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Logarithmic Scales and DecibelsWe often plot frequency on a logarithmic scale. This hasthe effect of expanding the lower frequencies and com-

pressing the higher frequencies on the chart, thus givingthe same percentage resolution over the whole width ofthe chart and keeping its size down to reasonable propor-tions.

Logarithmic scales are also used to plot vibration ampli-tudes; this enables the decibel scale to be used as a helpin comparing levels. The decibel (dB) is the ratio of one

level with respect to a reference level, and therefore hasno dimensions. But in order to quote absolute vibrationlevels, the reference level must be stated.

For example, we can say that one vibration level is10 dB greater than another level without any further ex-planation, but if we wish to say that a vibration level is

85 dB we have to refer it to a reference level. We shouldsay therefore, that the vibratory velocity is 85 dB ref.10-

9m/s. (See chart below).

As yet, standard dB reference levels are not commonlyused in vibration measurement. The reference levels rec-ommended by standardisation for vibration work are

shown in the table.

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Why use an Accelerometer

Preamplifier?Direct loading of a piezoelectric accelerometer's output,

even by relatively high impedance loads, can greatly re-duce the accelerometer's sensitivity as well as limit itsfrequency response. To minimise these effects the accel-

erometer output signal is fed through a preamplifierwhich converts to a much lower impedance, suitable forconnection to the relatively low input impedance of mea-suring and analyzing instrumentation (1).

With measuring amplifiers, analyzers, and voltmeters aseparate accelerometer preamplifier is used while vibra-tion meters intended for use with piezoelectric acceler-ometers normally have the preamplifier built-in.

In addition to the function of impedance conversion,most preamplifiers offer additional facilities for condition-

ing the signal. For example (2) A calibrated variable gainfacility to amplify the signal to a suitable level for inputto, for example a tape recorder; (3) A secondary gain ad- justment to "normalize" awkward" transducer sensitivi-ties; (4) Integrators to convert the acceleration propor-

tional output from accelerometers to either velocity ordisplacement signals; (5) Various filters to limit the up-per and lower frequency response to avoid interferencefrom electrical noise, or signals outside the linear por-tion of the accelerometer frequency range; (6) Other facil-ities, such as overload indicator, reference oscillator,and battery condition indicator are also often included.

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The Vibration Meter

The block diagram shows how a typical modern vibrationmeter is built-up. The accelerometer is connected to acharge amplifier input stage with an input impedance of

several G so that a separate preamplifier is not neces-sary. With a charge amplifier input, long input cablesfrom the accelerometer, (up to several hundred meters),

can be used without any appreciable loss in sensitivity.

An integrator stage allows velocity and diplacement par-ameters, as well as acceleration, to be measured.

The high-pass and low-pass filters can be adjusted so asto limit the frequency range of the instrument to therange of interest only, thus reducing the possibility of in-terference from high and low frequency noise. Afterproper amplification the signal is rectified to a DC signal

suitable for displaying on a meter or chart recorder. Thedetector can either average the RMS level of the signalor register the peak to peak level, and if required can re-tain the maximum value occurring. This is a particularlyuseful feature for measuring mechanical shocks and

short duration (transient) vibrations.

After passing through a linear to logarithmic converter

the signal is displayed on a logarithmic meter scalecovering two decades.

An external bandpass filter can be connected to the vibra-tion meter so that frequency analysis can be performed.Output sockets are provided so that the rectified and un-rectified vibration signal can be fed to an oscilloscope,tape recorder, or level recorder.

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What is Frequency Analysis?The vibration meter will give us a single vibration level

measured over a wide frequency band. In order to revealthe individual frequency components making up the wide-

band signal we perform a frequency analysis.

For this purpose we use a filter which only passes thoseparts of the vibration signal which are contained in a nar-

row frequency band. The pass band of the filter is movedsequentially over the whole frequency range of interest

so that we obtain a separate vibration level reading foreach band.

The filter can consist of a number of individual, conti-

guous, fixed-frequency filters which are frequencyscanned sequentially by switching,

or alternatively, continuous coverage of the frequencyrange can be achieved with a single tunable filter.

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Constant Bandwidth or

Constant Percentage Bandwidth

Frequency Analysis?There are two basic types of filter used for the frequencyanalysis of vibration signals. The constant bandwidthtype filter, where the filter is a constant absolute band-width, for example 3 Hz, 10 Hz etc. and the constant per-

centage bandwidth filter where the filter bandwidth is a

constant percentage of the tuned centre frequency, forexample 3%, 10% etc. The two drawings show graphi-cally the difference in these two filter types as a function

of frequency. Note that the constant percentage band-width filter appears to maintain a constant bandwidth,

this is because it is plotted on a logarithmic frequencyscale which is ideal where a wide frequency range is tobe covered. On the other hand, if we show the two typesof filter on a linear frequency scale, it is the constant

bandwidth filter which shows constant resolution. Theconstant percentage bandwidth filter plotted on a linearfrequency scale shows an increasing bandwidth with in-creasing frequency which is not really practical.

There is no concise answer to the question of whichtype of frequency analysis to use. Constant percentagebandwidth analysis tends to match the natural responseof mechanical systems to forced vibrations, and allows awide frequency range to be plotted on a compact chart.It is subsequently the analysis method which is mostgenerally used in vibration measurements.

Constant bandwidth analysis gives better frequency reso-lution at high frequencies and when plotted on a linear

frequency scale is particularly valuable for sorting outharmonic patterns etc. 29


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Filter Bandwidth ConsiderationsThe selectivity of the filter, that is the narrowness of the

passband, governs the resolution of the frequency analy-sis obtained. Vibration spectra from a gearbox are shown

in the drawing to the right. The upper spectrum was re-corded using a 23% constant percentage bandwidth fil-ter, while the lower spectrum, of the same signal, was

recorded using a 3% bandwidth filter. It can be seen thatby using a narrower bandwidth filter more detail is ob-tained so that individual peaks in the vibration spectrumcan be isolated.

The disadvantage with narrow bandwidth analysis is thatthe time required to obtain a particular accuracy getsconsiderably longer as the filter bandwidth gets nar-rower.

Because of the long time needed to cover a wide fre-quency range with narrow bandwidth analyzers a prelimi-

nary analysis is often made with a wide filter bandwidthin order to reveal particularly interesting parts of the fre-quency spectrum. The analyzer is then switched to a nar-row bandwidth to make a detailed analysis of the part ofinterest. At higher frequencies a constant bandwidth an-alyzer switched to. for example, 3 Hz bandwidth enables

extremely detailed analysis to be performed.

To sum up. the best selection of bandwidth and analysismethod is in most cases that which gives adequate reso-lution over the whole frequency range and which allowsthe analysis to be carried out. in the shortest time.

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Defining the Filter Bandwidth An ideal filter would pass all frequency components oc-

curing within its bandwidth and reject completely all oth-ers. In practice, electronic filters have sloping skirts so

they do not completely eliminate frequency componentslying outside their specified bandwidth. This promotesthe important question, how do we specify the filterbandwidth?

Two methods of measuring the filter bandwidth are com-

monly used. The most often used, defines the bandwidthas the width of the ideal straight sided filter whichpasses the same amount of power from a white noisesource as the filter described. The second definition isthe width of the filter characteristic where the filter at-tenuation is 3 dB lower than the normal transmission le-vel. Only filters with a relatively poor selectivity will havea 3 dB bandwidth substantially different from the effec-tive noise bandwidth.

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Measuring Instrumentation A portable, general purpose vibration meter as describedon p. 27 will usually be the most convenient measuringinstrument to use but vibration measurements can alsobe made in the field with a suitable B & K sound level

meter. The microphone is substituted by an integratoradaptor and accelerometer to enable the meter to mea-sure the RMS level of acceleration, velocity and displace-

ment. However these meters do not have the conveni-ence of a charge amplifier input and need to be cali-

brated separately for each measuring parameter. Batteryoperated filters can be added to enable octave, third-oc-tave, and narrow bandwidth analysis to be performed.

Mains-operated laboratory oriented instrumentation of-fers greater versatility, especially in the detailed analysis

and data reduction spheres. A basic measuring chainwould consist of accelerometer, preamplifier, and a mea-

suring amplifier, possibly with an external filter. Themeasuring amplifier and filter are often combined intoone instrument which is called a Frequency Analyzer orSpectrometer.

The ultimate in operating convenience and analysisspeed is obtained with a real-time analyzer, where atarge number of parallel frequency bands are evaluatedalmost instantaneously and shown on a continuously up-dated display screen. Real-time analyzers are usuallyequipped with a digital output and remote control facili-ties so that they can be connected to a tape punch, com-puter etc., to make fully automatic analysis systems.

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Vibration as a Machine Condition IndicatorMachines seldom break down without warning, thesigns of impending failure are usually present long be-

fore breakdown makes the machine unusable. Machinetroubles are almost always characterised by an increasein vibration level which can be measured on some exter-nal surface of the machine and thus act as an indicator.

The bathtub curve shown is a typical plot of vibration le-vel against time that demonstrates this effect. With nor-

mal preventive maintenance, repairs are carried out at

fixed intervals based on minimum life expectancy forwearing parts. By delaying repair until vibration levels in-dicate the need, but before breakdown, unnecessarystrip-down (which often promotes further faults) and de-lays in production are avoided.

This "on condition" maintenance of machinery hasproven to give appreciable economic advantage by increa-

sing the mean time between shutdown while still preven-ting the surprise and damaging effects of catastrophic fai-

lure during service. These techniques are now widelyused especially in the continuous process industries.

The vibration level which may be allowed before under-taking a repair is best determined through experience. Atpresent, general opinion suggests that the "action level"

should be set at two to three times (6 to 10 dB above)the vibration level considered normal.

We have already seen that with frequency analysis of vi-bration signals we are able to locate the source of manyof the frequency components present. The frequency

spectrum of a machine in a normal running condition

can therefore be used as a reference "signature" forthat machine. Subsequent analyses can be compared to

this reference so that not only the need for action is indi-cated but also the source of the fault is diagnosed.

The diagnostic chart on the following two pages will help

isolate the cause of excess vibration when the offendingfrequencies can be discovered through frequency analy-

sis.

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Vibration Trouble Shooting Chart (A)

Nature of Fault Frequency of Dominant

Vibration (Hz=rpm/60)

Direction Remarks

Rotating Members

out of Balance

1 x rpm Radial A common cause of excess vibration in machinery

Misalignment &

Bent Shaft

Usually 1 x rpm

Often 2 x rpm

Sometimes 3 & 4 x rpm

Radial

&

Axial

A common fault

Damaged Rolling

Element Bearings

(Ball, Roller

,

etc.)

Impact rates for

the individual

bearing components*

Also vibrations athigh frequencies

(2 to 60kHz) often

related to radial

resonances in

bearings

Radial

&

Axial

Uneven vibration levels, often with shocks.

*Impact-Rates:

Journal Bearings

Loose in Housings

Sub-harmonics of

shaft rpm, exactly

1/2 or 1/3 x rpm

Primarily

Radial

Looseness may only develop at operating speed and

temperature (eg. turbomachines).

Oil Film Whirl or

Whip in Journal

Bearings

Slightly less than

half shaft speed

(42% to 48%)

Primarily

Radial

Applicable to high-speed (eg. turbo) machines.

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Vib ti T bl Sh ti Ch t (B)


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Vibration Trouble Shooting Chart (B)Nature of Fault Frequency of Dominant

Vibration (Hz = rpm/60)Direction Remarks

Hysteresis Whirl Shaft critical speed PrimarilyRadial

Vibrations excited when passing through critical shaftspeed are maintained at higher shaft speeds. Can sometimesbe cured by checking tightness of rotor components

Damaged or worn

gears

Tooth meshing

frequencies (shaft rpmx number of teeth)and harmonics

Radial

&Axial

Sidebands around tooth meshing frequencies indicate

modulation (eg. eccentricity) at frequency correspondingto sideband spacings. Normally only detectable withvery narrow-band analysis.

MechanicalLooseness

2 x rpm Also sub- and inter-harmonics as for loosejournal bearings

Faulty Belt Drive 1, 2. 3 & 4 x rpmof belt

Radial

UnbalancedReciprocatingForcesand Couples

1 x rpm and/ormultiples for higherorder unbalance

PrimarilyRadial

IncreasedTurbulence

Blade & Vanepassing frequenciesand harmonics

Radial&

Axial

Increasing levels indicate increasing turbulence.

ElectricallyInduced Vibrations

1 x rpm or 1 or 2times sychronous

frequency

Radial&

Axial

Should disappear when turning off the power.

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Vib ti d th H B d


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Vibration and the Human BodyIt has long been recognized that the effects of direct vi-bration on the human body can be serious. Workers can

be affected by blurred vision, loss of balance, loss of con-centration etc. In some cases, certain frequencies and le-

vels of vibration can permanently damage internal bodyorgans.

Researchers have been compiling data over the last 30years on the physiological effects of vibrating, hand-heldpower tools. The "white finger" syndrome is well known

among forest workers handling chain saws. A gradual de-generation of the vascular and nervous tissue takes

place so that the worker loses manipulative ability andfeeling in the hands.

Standards are at present under preparation which willrecommend maximum allowable vibration spectra at thehandles of hand-held power tools.

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Vibration and the Human BodyThe first published international recommendation con-cerned with vibration and the human body is ISO 2631 1978 which sets out limitation curves for exposure

times from 1 minute to 12 hours over the frequencyrange in which the human body has been found to bemost sensitive, namely 1 Hz to 80 Hz. The recommenda-tions cover cases where the human body as a whole issubjected to vibration in three supporting surfaces,namely the feet of a standing person, the buttocks of a

seated person and the supporting area of a lying person.Three severity criteria are quoted: 1) A boundary of re-duced comfort, applicable to fields such as passengertransportation etc. 2) A boundary for fatigue-decreasedefficiency, that will be relevant to vehicle drivers and ma-chine operators, and 3) The exposure limit boundary,which indicates danger to health.

It is interesting to note that in the longitudinal direction,that is feet to head, the human body is most sensitive tovibration in the frequency range 4 to 8 Hz. While in thetransverse direction, the body is most sensitive to vibra-tion in the frequency range 1 to 2 Hz.

A battery-operated vibration meter dedicated to the meas-

urement of vibratory motion with respect to its ability tocause discomfort or damage to the human body is nowavailable.

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We hope this booklet has served as an informative introduction to

the measurement of vibration and will continue to serve as a

handy reference guide. If you have other questions about measure-ment techniques or instrumentation, contact your local Brel &

Kjr representative, or write directly to :

Brel & Kjr

2850 Nrum

Denmark

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windows-1256 measuring vibration

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