Vibration Control Book 07

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Vibration Measurement & Controlby Brian McLauchlan


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B. McLauchlan TAFE SI 2006

Authors Note: These notes are provided for student use in NationalModule EA 7766L The notes are not to be reproduced in any formwithout the authors written permission.

While every attempt has been made to ensure accuracy of thematerials in these notes, the author accepts no responsiblity for anyliability or loss in respect to the application of the informationpresented.

Brian S. McLauchlan 1990 - 2007

TAFE Mechanical Engineering

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TABLE OF SYMBOLS

.......................... ..density, kg/m3

f........................... ..frequency, Hz

ff.............................forcing frequency, Hz

fn............................natural frequency, Hz

k.............................spring constant, N/m

m............................mass, kg

............................angular frequency, rad/sec

x.............................displacement in meters

X ............................displacement in meters at time t

v.............................velocity in m/sec

a.............................acceleration in m/sec2

y.............................position in meters


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Table of Contents

Vibration - Concepts................................................................ 4

Vibration - Measurement........................................................ 13

Instrumentation For Vibration Measurement ............................. 27

Vibration Isolation................................................................. 43

Vibration - Human Effects ...................................................... 60

Balancing Of Machinery.......................................................... 67

Balancing Of Machinery.......................................................... 67

Vibration Specification ........................................................... 74

Appendix ............................................................................. 78

Vibration Exercises................................................................ 79

Glossary Of Vibration Terms ................................................... 84


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Vibration - Concepts

1.1 Introduction

Many machines and processes in engineering generate vibration .

In a few cases this vibration is intentional as in vibrating sortingscreens, ultrasonic cleaners and earth compaction machines .Mostly though, the vibration is an undesireable effect.The vibration generated can cause a number of effects that aretroublesome . The most serious are related to fatigue and injury tohumans exposed either to the vibration directly or the effects ofnoise caused by the vibration . Vibration may also contribute toexcessive wear, fatigue failure and other premature failure ofmachine components.

Many vibration problems are due to inadequate engineering designof a product, or the use of a machine in a manner that has notconsidered the possible effect of vibration.

In this course we will investigate the basics of vibration with theintent of being able to measure and assess problem areas . Thereare many very complex vibration problems that requiresophisticated computer modelling to solve. It is often the casehowever that awareness at the design stage will eliminate or reducethe vibration to a level that is acceptable, using relatively simple

methods.

1.2 Simple Harmonic Oscillation

The simple model of a spring and a mass may be used toinvestigate the basic ideas of vibration . In this model a spring ofspring constant k, suspends a mass m . Spring constant ismeasured in Newtons / meter (N/m) . Mass is of course, inkilograms.

Figure one shows this model with a spring constant of 400 N/mand a mass of 4 kg . If the mass is displaced down, then released,the mass will oscillate at a frequency that is independant of theamount of initial displacement. This frequency is called theNATURAL FREQUENCY.

The equation that determines the natural frequency of this systeminvolves both the spring constant and the mass. As the springconstant is increased, so the natural frequency increases.


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m

k

Figure 1.1 - Vibrating Spring/Mass System

The effect of the increased mass is to decrease the naturalfrequency so that the form of the relationship is:

fnk

m=

1

2

Our system in figure one thus has a natural frequency of 1.6 Hz.Note that the angular frequency, , is related to the frequency f by

the factor 2 , so that this equation can be written as:

=m

f 2= so

If our simple system is set in motion we may measure thedisplacement over a period of time. We will find that thedisplacement repeats after a time called the PERIOD, which is theinverse of frequency . In the case of our example in figure one, thefrequency is 1.6 Hz and so the period is 0.625 seconds.

The fact that the vibration repeats is described by the termPERIODIC and the motion of one period is called a CYCLE. If weplot the cycle of displacement over the time of one period we willfind that the result is a curve like that in figure 2. This is a curvethat is able to be described by the familiar sine function.

x = A sin ( t )


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where the magnitude x goes from a maximum value of A to aminimum of - A over a cycle related to an angular function andthe time t . Where the object moves in this manner it is known asSIMPLE HARMONIC MOTION.

Vibrat

ion

time

Figure 1.2 Displacement / Time For A Periodic Vibration

For displacement the sine function can be written as:

X = A sin ( t )

where

X - displacement from rest position, m at time t.A - peak displacement, m. - angular frequency, rad/sec

t - time, seconds.

1.3 Displacement - Velocity - Acceleration

In most considerations of vibration problems we will deal with oneof three possible parameters for vibration measurement. The firstwe have described above. The other two are velocity andacceleration. To understand the relationship of the three

parameters, displacement, velocity and acceleration is important toan understanding of vibration.


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Displacement - A measure of the distance a vibrating body moves.

Velocity - A measure of the speed of motion of a vibrating body.

Acceleration - A measure of the rate of change of speed (velocity) ofa vibrating body.

The equations for each can be written as shown below. ( Note: seeappendix A for details of the derivation of these equations.)

)sin( tAX =displacement

velocity)cos( tAX =

acceleration)sin(2 tAX =

For a particular vibration, the parameters in these equations, A and, are constant and common. This means that these threemeasures of vibrations are always related in a predictable way. Thisis fine but does all this mathematics mean much in a real problem?

Well, let's consider the physical significance of these equations.


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-10

-8

-6

-4

-2

0

2

4

6

8

10

Vibr

ation

time

Displacement Velocity Acceleration

Figure 1.3 Relationship Of Displacement,Velocity & Acceleration

In figure 1.3, each of the above equations has been plotted for onecycle, with the displacement as the reference for time zero. Forour vibrating spring - mass system this diagram shows that :

i.at time zero, the velocity is maximum with displacement andacceleration zero. The mass is moving past its rest point.

ii.at 1/4 cycle later the velocity has reduced to zero withdisplacement maximum and acceleration maximum in the otherdirection. The mass has stopped at the peak of a cycle.

iii.at 1/2 cycle the displacement and acceleration have againbecome zero while the velocity is a maximum. The mass is againpassing its rest point.

iv.at 3/4 cycle the displacement is at a negative maximum with

acceleration a maximum in the opposite direction. The velocity iszero.

v.the cycle is complete with displacement, velocity and accelerationat their original values.

We see from this that the mathematics describes what is happeningto the mass at any time in the cycle. We will use the variousmeasures of vibration - displacement, velocity and acceleration toassess problems of machine vibration.


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1.4 Units

Before any assessment can be made however, we must be aware ofthe units used in vibration. These are summarised in the tablebelow.

PARAMETER UNITS USED

DISPLACEMENT m , mm , um

VELOCITY m/sec , mm/sec

ACCELERATION m/sec2 , " g " ( % of 9.8m/sec2 )

Table 1.1 Units For Vibration Measurement

We will make use of these units but must first consider further theproblem of our vibrating spring mass system.

1.5 Forced Vibrations

So far we have caused the spring mass system to vibrate only at itsnatural frequency. The mass is displaced and then released causing

a series of oscillations. What happens if the system is pushed by aforce that also oscillates ?Figure 1.4 shows the system acted on by an external force causingdisplacement of the base, that has a periodic nature.

x(t)

x'(t) m

Figure 1.4 Forced Oscillations Of The Spring Mass System

We might expect some oscillation and that it will depend on the

frequency of the "EXCITING FORCE" and the natural frequency ofour spring mass system. If the differential equation for the system


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is solved and the frequency response for the system is plotted wehave a diagram like that shown in figure 1.5.

0.01

0.1

1

10

0.1 1 10

Amp lif ication

Frequency Ratio

Figure 1.5 Response Of 1 Degree Of Freedom System

Figure 1.5 calls our spring - mass system a ONE DEGREE OFFREEDOM SYSTEM because the motion of the mass is described byonly one displacement measurement. (ie displacement is along oneaxis only)

The response diagram shows some important information that shallnow be considered.First, the mass has a response which theoretically goes to infinitywhen the exciting force coincides in frequency with the natural

frequency. This response is known as RESONANCE.

In practice the response at resonance will not be infinite due tolosses in other parts of the system. However the resonantbehaviour is significant because the system responds with a greaterdisplacement than that applied!

This is clearly undesirable.

It can also be seen that below the resonance frequency, the

response climbs steadily and is always more than the applieddisplacement. Above resonance however, the response drops


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rapidly, showing less and less displacement with increases infrequency.

How can this knowledge help us ?

If the frequency of the forced vibration is always above that of theNATURAL FREQUENCY of the system, then the vibration of the massis less than the applied vibration. In fact, if the applied vibration ismore than 3 times the natural frequency, the vibration of thespring/mass is less than 10% of the input vibration. This meansthat we have ISOLATED the mass from the vibration to the extentthat only 10% of the vibration gets to the mass.

A similar situation applies if the mass in our system has the forcingfrequency applied to it directly. Consider a small diesel engine.

When operating, the rotating and reciprocating parts of the enginewill cause a vibration at the running speed of the engine. In oursimple model the engine is the mass and provides also the forcedvibration. We wish to isolate the vibration of the engine from themounting base of the engine.

If we use a spring mounting with a stiffness that ensures aNATURAL FREQUENCY of 3 times less than that of the enginerunning frequency, we will ISOLATE the mounting base of theengine from 90% of the vibration produced by the engine.

1.6 Damping

In the section above, it was observed that the vibration atresonance is limited by the system losses. The loss can becontrolled to provide a more suitable frequency reponse for thesystem. The provision of suitable energy losses in a system istermed DAMPING. Damping will have the effect shown in figure1.6.

In the figure the term DAMPING RATIO is used to express theamount of damping used. The value where damping ratio is equalto 1.0 is called CRITICAL DAMPING.


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Critical damping is defined by:

ccritical km= 2 Damping greater than critical will have a ratio greater than 1.0.

Damping less than critical, will have a ratio less than 1.0. Dampingcauses the response at natural frequency to be reduced but causesthe shape of the response curve to alter at other points. This will bediscussed in detail in section

0.01

0.10

1.00

10.00

0.1 1 10

Frequency Ratio

Ampl if ication Ratio

0

0.050.1

0.2

0.5

1.0

Damping

Ratio

1.0

0.5

0.2

0.1

0.05 0

Figure 1.6 Response to Forced Vibration (1 DOF Spring-Mass)


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Vibration - Measurement

2.1 Introduction

The vibration of machines can be considered as an oscillatorymotion of part or all of the machine. So far we have seen that asimple vibrating system, the spring/mass system, has a harmonicmotion. This motion can also be termed PERIODIC because itrepeats itself exactly over fixed time period. In this section we willconsider what other vibratory motions are possible and the basicideas for analysing these motions.

2.2 What Are We Measur ing ?

The motion of the vibrating system is measured with the unitsdescribed in a previous section (1.4). What was not specified waswhat amplitude was to be specified with these units. Figure 2.1shows a sinusoidal waveform with the possible ways of measuringamplitude.

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-8

-6

-4

-2

0

2

4

6

8

10

Vib

ration

time

RMSPeak Peak to peak

Figure 2.1 Measuring Vibration Amplitude

The equations of motion specify the PEAK amplitude (see 1.3) butwhen measuring our measuring device could be constructed tomeasure any of PEAK, PEAK to PEAK or RMS amplitude values.Many measuring systems measure RMS (Root Mean Square) valuesbecause this value is proportional to the power in the vibrations of asystem.

This means that care should be taken to establish what is being

measured by an instrument. In particular, when the procedure of


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converting between displacement, velocity and acceleration is used,the correct amplitude must be known for correct integration.

2.3 Harmonic Periodic Vibration

The vibration that has been described so far, that has a singlefrequency and is sinusoidal can also be described as harmonicperiodic vibration. Harmonic is an alternative term for sinusoidal,and periodic means repeating regularly.A sinusoid is able to be described precisely by knowing its frequencyand amplitude.

2.4 Vibration That Is Not Harmonic

Our simple spring mass system gives rise to harmonic periodic

vibrations. This is not the only possible type of vibration that wemay encounter. In fact it is probably the least likely to be found inmost engineering systems.We should first consider the possiblity of a vibration that is periodicbut not harmonic. That is, its motion is not described by a simplesinusoidal signal, but the motion may repeat itself continuously intime. Such a vibration can be termed periodic and an example isshown in figure 2.3.

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-10

-5

0

5

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

time

Ampl itude

Figure 2.3 Periodic Non Harmonic Vibration

If we wish to determine the frequency content of this signal, howcould it be done ? A mathematician called Fourier determined thatfor any complex signal, its frequency content could be found byconsidering the complex signal as the sum of a series of sine andcosine functions. In the example above, which is the acceleration of

the piston in an engine, the signal can be analysed into two sine


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signals of differing amplitude andfrequency. In this example theFourier analysis can be seen to give the wave form in figure 2.3using two harmonically related sinewaves. This is illustrated infigure 2.4.

-15

-10

-5

0

5

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

time

Amp li tude

Figure 2.4 Fourier Components Of A Signal

So far we have dealt with relatively simple types of vibration. Muchof the time, however, we will be dealing with a vibration that ismuch more irregular than those we have seen previously. Thisirregular type of vibration is termed RANDOM VIBRATION.

Random vibration is characterised by irregular motion cycles thatnever repeat themselves exactly. This means that the analysis willbe somewhat more complicated. In view of this added complexity,you may be tempted to ask, how common is this type of vibration?.

Consider the motion of any form of vehicle used for transport, suchas cars, trains or aircraft. It is rare that any of these vehicles willexperience purely periodic vibrations. In fact much design effort isexpended to avoid certain periodic vibration that may result inresonance and consequent damage due to excessive vibrationamplitude.

Vehicle Common periodic vibration

Car Suspension resonance from corrugated road surface

Aircraft Body vibration due to turbulence

Ship Roll due to sea swells

Rail wagon Yaw instability above design speed


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Much machinery vibration can occur as random vibration with addedperiodic components. It is thus a common and important type ofvibration to consider in engineering.

Random vibration may have a signal that is like that of figure 2.6.This shows the complex nature of the motion of a componentexperiencing this type of vibration.

Figure 2.6 Typical Random Vibration Signal

2.5 Analysis of Vibration Signals

Recall that a periodic harmonic signal can be completely specifiedby an amplitude and a frequency. For other signals we are alsointerested in these parameters.To help express these we use a special graph called a frequencyspectrum that plots amplitude on the vertical axis and frequency onthe horizontal axis.


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2.5.1 Spectrum Of A Periodic, Harmonic Vibration

What does the frequency spectrum of the vibration of our springmass system look like? We have only one frequency and a singleamplitude. The spectrum thus appears as a single line at the

natural frequency of the spring mass system with an amplitudedepending on the size of the motion of the mass. Figure 2.2 showsa typical spectrum for our simple spring mass system.

Frequenc

Amplitude

Figure 2.2 Frequency Spectrum Of Harmonic Vibration

If a complex periodic wave is broken up into its' Fouriercomponents, a frequency spectrum can also be constructed. If eachFourier component is a sinusoidal signal of a certain amplitude thespectrum will be a series of peaks on the spectrum. The example in

figure 2.4 is represented as a frequency spectrum in figure 2.5.

f1 f2 Fre uenc

Amplitude

Figure 2.5 Frequency Spectrum For The Signal Of Fig.2.3

In the frequency spectra shown above we have indicated anamplitude. This could be the peak amplitude of the signal or it could

be the RMS amplitude.


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Because the Fourier spectral analysis breaks a complex wave intosine or cosine components the RMS or peak amplitude can be easilyconverted from one to the other.

Amplitude

Time

Frequency

f1

f2

Figure 2.7 Creating a Frequency Spectrum

Figure 2.7 shows how the signal, which is varying in time, is brokenup into components which can be shown on the frequencysprectrum graph.

The frequency spectrum is like a cross section at a point in time ofall the components that make up the signal being studied.

How can we analyse a random vibration signal ? What do we use foramplitude ? What do we use for frequency ? It is clear that whenwe have a periodic signal, we can predict from its appearance overone cycle, the future cycles. With a random signal this is notpossible. Theoretically we have a signal that must be infinite inlength and the whole signal should be studied.


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Fortunately statistics can be used to analyse the properties of thisinfinite signal by using a sample from the signal. Like moststatistical procedures this means that the sample we take must be arepresentative sample, otherwise our analysis will be inaccurate.

For example, if I intended to use a statistical method to find themost popular food in Australia and I asked only adult males over 70in Alaska for their opinion my results would not be particularlyvaluable !

Similarly, when analysing vibration signals I must use a goodsample, usually determined by having a long enough sample whereconditions are stabilised. This means that the following will be

approximately constant:

Speed of a machine (eg velocity of a car; rpm of a motor)Loading on a machine (eg power output of an engine)Forced vibration (eg quality of a road surface that a car travels on)

Just what is a long enough sample under these conditions isdependant on the frequency content of the signal and will befurther discussed in the data analysis section, but basically requiresthat lower frequencies require longer recording times for the same

accuracy as higher frequencies. (see page 23)

2.5.2 Analysis Of Random Vibration Signals

A random vibration signal may be analysed using an amplitudeanalysis and/or a frequency analysis method. The simplest means ofassessing random vibration is to measure the RMS signal level overa period of time. This will give and idea of the average energycontent of the signal and is useful for many applications.

An analysis of the PROBABILITY of occurence of a particularamplitude value will give an asessment of what sort of vibrationlevels can be expected and how frequently a particular level willoccur. For example, a motor car travelling along a road will havesome vibration felt by the passengers continuously. Large bumpswill give larger vibration levels, but less frequently.

This type of analysis commonly results in a normal curve that ismet frequently in naturally occurring processes. Figure 2.8 shows

a Normal ( or Gaussian) curve generated by this type of analysis.


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Frequency

Mean or average

Spread

Vibration Amplitude

Figure 2.8 Normal Curve From Vibration Amplitude Analysis

Like the other signals we have dealt with, we are commonly alsointerested in the frequency content of the random vibrationsignal.Fortunately, Fourier analysis is applicable to random signalsin the same way as other data. The Fourier analysis of a randomsignal results in an infinite number of sinusoidal components ofdifferent amplitudes and frequencies. The resulting spectrum istheoretically a continuous curve rather than single line values.Figure 2.9 shows the type of curve that could result from this typeof analysis.


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Frequenc

Amplitude

Figure 2.9 Frequency Spectrum For Random Vibration

Because we cannot deal with infinite numbers of amplitudes andfrequencies, this curve is usually approximated by a series of linesrepresenting frequency values.A frequency spectrum for a random vibration is sometimes called aspectral density or power spectrum. These are all measures of thefrequency content of a random vibration signal.

2.5.3 Filtering

We have seen how to classify the time behaviour of a signal andthat it can be broken into frequency components and expressed asa frequency spectrum.The question then arises as to how are we going to achieve thefrequency analysis to get a frequency spectrum. The basic idea offrequency analysis rests on an understanding of filters. We haveheard of filters in mechanical systems. These are used to limit the

particle size passed through a fuel or lubricating system, forexample.

In a similar way electronic filters can be made which restrict thefrequencies that are allowed to pass through them. A filter may beeither a LOW PASS, HIGH PASS or BAND PASS FILTER.

The FREQUENCY RESPONSE CURVES for these types of filter areillustrated in figure 2.10. The low pass filter will allow onlyfrequencies


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up to a certain value to pass through. Any higher will be blocked.In a similar manner the high pass filter will allow only thosefrequencies above a certain level to pass through. The point wherethe frequencies will become blocked can be changed by design.

Low Pass Hi h Pass Band Pass

A

Figure 2.10 Low Pass, High Pass And Band Pass Filters

The band pass filter can be considered to be a combination of a lowpass filter and a high pass filter. This gives a filter that will passfrequencies over only a narrow range.We can make such a narrow band filter with either a fixed value ofrange or may make it a fixed width and variable frequency so wecan tune it to the band that we want.

It is this band pass filter that makes frequency analysis possible.If a complex signal is measured by a transducer, the electronicsignal representing the transducer signal may be passed through aband pass filter and the level measured. This level will be only theamplitude of the frequencies that are passed by the filter. If arange of filters are used then the whole range of frequency ofinterest can be covered in small frequency increments. The mostcommon set of band pass filters used are in octave or 1/3 octave

bands. An octave covers a frequency range such that the lowestfrequency in the range is half the value of the highest frequency inthe range.

Filters for octave bands are generally labelled by the middle orcenter frequency of the whole band. One third octave band filtersbreak each octave band range into three. Octave and 1/3 octavefilters are more commonly used for noise measurement, however1/3 octave bands are used in a number of standards, especially

those concerned with human effects of vibration.


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2.5.4 Narrow Band Analysis

To achieve the discrimination needed for vibration analysis, filterswith narrow bands are needed. This can be achieved byconstructing more filters OR by using a technique known as Fourier

Analysis.

Fourier Analysis is a mathematical technique that can determinefrequency content in as narrow bands as desired. It is usuallyachieved using electronic systems such as an FFT analyser or acomputer. (note : FFT is Fast Fourier Transform, a mathematicalsimplification to make the calculation quicker)

2.5.5 Limitations Of Frequency Analysis

The use of any filtering technique for frequency analysis mustconsider the limitations of the equipment. Any filter does not cut offcompletely those frequencies outside its bandwidth. There is also alimitation on the minimum time required for a filter to accuratelydetermine the magnitude of the filtered data. This is called theaveraging time.

Limitations Of FFT Analysis

Due to the popularity of FFT analysis it is considered essential tomention some important limitations in use of this technique.

a. averaging time - the averaging time must be carefully selectedto ensure that the amplitude is accurately measured. For manyacoustic measurements this will not be significant but the sameaveraging for lower frequency analysis, often the case for vibrationwork, may cause significant errors. The FFT process must average(sometimes called "ensemble averaging") over a number of spectra

to give accurate amplitude results. The following should beconsidered:

Number of Error Length of data recordspectra 95% c.i. for full scale frequency

100Hz 1kHz 10kHz8....... ........ 2.8dB 32 3.2 0.3216..... ........ 2.0dB 64 6.4 0.64

32..... ........ 1.46dB 128 12.8 1.2864..... ........ 1.06dB 256 25.6 2.56


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128... ........ 0.74dB 512 51.2 5.12256... ........ 0.54 dB 1024 102.4 10.24

|______________________|time in seconds

Notes: c.i. - confidence interval,this means that all data are within the error limitspecified with 95% confidence. (this means that there is a 95% probability that theerror will be no greater than that listed)

Length of data record - means how long the recording of the data must be, withoperating conditions constant, to give enough time for the analysis.

Table 2.2 Averaging Times For FFT Analysers


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Example:

This table shows that for 95% confidence that if I require theaccuracy of the data to be no worse than +/- 0.54 dB, and I set amaximum frequency of 1000 Hz on the analyser, I will require 256

averages. These 256 averages will take 102.4 seconds of data or102.4/60 = 1.7 minutes.

The table has some important consequences. The time limits oftencause problems for data recording at low frequency. For instance,ifthe analyser is now used at 100 Hz full scale setting,a recording of17 MINUTES is required for the highest accuracy!( 1024/60 = 17)

Often then, a trade off of accuracy and time recording must bemade.

b. windows - The FFT process is a mathematical simplification. Itrelies on the correct data being input to give accurate answers. Inthe FFT process a block of data is converted to digital informationand then frequency analysis is performed. The next block of data istreated similarly and then averaged with the first block.If the two blocks of data do not "fit together" like acontinuous wave,the FFT analysis process will calculate non- existing frequencies !

To overcome the problem of data blocks with "non - fitting" ends aprocess called WINDOWING is used. This process ensures that dataalways fits together. A "window" here is a mathematical weightingcurve that is used to ensure that the sampling that occurs with theFFT averaging process still has acceptable accuracy.

It uses windows called Hanning, Hamming or rectangular. TheHanning and Hamming windows are for use with continuoussignals. The rectangular window is usually only used for analysis

ofimpulsive signals.

c. Anti - aliasing There is always a problem with limiting themaximum frequency of a signal when converting from analogue todigital, as required by FFT analysers and computers. When a signalis to be digitised it is converted to a series of numbers. Eachnumber represents a sample point of the continuous wave that isthe acoustic or vibration data. If the sample points are taken too

far apart the frequency data is not able to be accurately specified.


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This is because the sample data may represent the signal frequencymeasured or multiples of that signal at higher frequency.

To prevent aliasing,the higher frequency components must beremoved by a LOW PASS FILTER. This filter is usually provided by

the manufacturers of FFT analysers but must be provided also whenusing a computer for FFT analysis. This aspect is often overlookedwhen using computer based systems and can lead to serious errors.

The frequency of sampling should then be set to be at least twicethe limiting frequency of the low pass filter.

It is preferable in fact to set the sample frequency higher forgreater confidence in the frequency data. The problem of aliasingshould not be overlooked as incorrect data analysis will result if

aliased data is used.

Like most instrumentation, it is possible to get out values fromfrequency analysers that seem reasonable but may not be accurate.Ensure that the correct procedure is used for any frequencyanalysis.

time

Sample Period

Signal constructed from samples.

time

Sample Period

Signal constructed from samples.

Figure 2.10 Sampling to Eliminate Aliasing When Digitising


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Instrumentation For Vibration Measurement

3.1 Transducers

A transducer is a device that converts a small amount of theenergy of the quantity to be measured into another form of

energy, usually electrical. This conversion is to allow for ease ofmeasurement as typically it is easier to record and analyse electricalsignals.

In vibration measurement, we may wish to measure the vibrationdisplacement, velocity or acceleration.The choice of measurementwill depend on how the data obtained from the measurement wil beused. Because of this choice we have transducers suitable formeasuring each quantity. The transducers may make use of thefollowing techniques for energy conversion:

a.piezo - electric effectb.piezo - resistive effect (silicon strain gauge)c.inductanced.capacitancee.resistancef.optical

3.1.1 Displacement Transducers

These may be either non - contact inductive or capacitance types,resistance types or may use a DIFFERENTIAL TRANSFORMER tomeasure displacement. Alternately, double integration of anaccelerometer signal may be used to provide displacement.

The non-contact types are often used to measure shaft postion inrotating machinery. They operate by sensing the change in amagnetic or electrical field between the sensor and the shaft as theshaft varies its motion relative to its bearings.

The differential transformer uses a set of three coils of wire woundon a cylinder common to all. (fig 3.1) An alternating voltage is fedto the center winding at a fixed frequency and level. A slug movesinside the cylinder and its position determines the proportion ofsignal induced in each of the other two coils.


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Input

Output

Slug

Figure 3.1 Differential Transformer Displacement Transducer

The slugs' displacement is thus able to be determined. In use, thecoils are attached to a component and the slug to another so thatthe relative displacement between the components is measured.Resistance types use an electrical POTENTIOMETER (variableresistor ) that moves in response to the displacement applied. Thepotentiometer is supplied with a steady voltage and the varyingresistance provides a varying voltage signal proportional todisplacement.The differential transformer and potentiometer types are usually

used for relatively low frequency measurement up to about 20 Hz.Displacements up to about 300 mm can be measured.

Higher frequencies are possible with the other types (up to200kHz) but often this is possible for only very smalldisplacements.

3.1.2 Velocity Transducers

Velocity measurement may make use of all the types oftransducers above, excepting the potentiometer type. In addition,the signal from an accelerometer may be integrated to givevelocity.

3.1.3 Acceleration Transducers

Probably the most common vibration measuring transducer is theaccelerometer. The measurement of acceleration can be made bymany types of transducers and the signal is able to be integrated togive either velocity or displacement signals.(Note: although theoretically possible, the differentiation of signals from

displacement to velocity etc. are usually avoided due to stability problems withelectronic differentiation)


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Piezo Electric Accelerometers

These are a very common type of accelerometer with a wide rangeof frequency small size and rugged construction. They use a mass

that is attached to a crystal of material that varies its charge inresponse to mechanical stress. (fig 3.2) If the mass is accelerated,the crystal provides a signal proportional to the acceleration.

Piezo accelerometers cover a wide range of sensitivity from about.00005 m/sec.sec (5 x 10 g) to 200, 000 m/sec.sec (20, 400g).

Electronics

Mass

Piezocrystal

BaseConnector

Figure 3.2 Basic Arrangement of a Piezoelectric Accelerometer

Piezo Resistive Accelerometers

These types of accelerometer use a silicon strain gauge. This typeof strain gauge is not the metal foil type commonly used forengineering strain measurements.

The metal foil type is more linear and much easier to handle thanthe silicon type.For permanent measurement situations however,the silicon type has the advantage of giving higher sensitivity.

These accelerometers use a mass supported on a beam which hasthe strain gauges attached.(fig.3.3) The strain in the beam isproportional to the applied force and hence the acceleration. Thesetypes can give good sensitivity and a response at zero Hertz, withgood high frequency response.


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Base

Mass

Cantilever Beam

Strain Gages

Connector

Figure 3.3 Piezoresistive Accelerometer

They are usually larger than an equivalent piezo electric type withthe exception of some special micro types designed for very highlevel acceleration measurements.

Servo Accelerometers

These types of accelerometer use a technique of measuring theforce required to restore a mass to its rest postion whenaccelerated.This force is of course, proportional to the accelerationapplied to the accelerometer.This type of accelerometer can bemade very sensitive to low acceleration levels, with a frequencyresponse from 0 to up to 500 Hz.

3.1.4 Optical Transducers

Optical transducers have not been used extensively in generalpurpose vibration measurement. Recently instruments have beenproduced that allow relatively easy use of laser interferometertechniques. Although very expensive, these methods are extremelypowerful for studying vibration of large surfaces or where a non-contact measurement is needed, such as on fast moving machinecomponents.

3.2 Selection Of A Transducer

With any vibration measurement, we must have some idea of therange of vibration amplitude and frequency that is to be measuredso that an appropriate transducer can be selected. We should notsimply select a transducer with very high amplitude and frequencyrange performance, as the sensitivity small vibration levels may notbe adequate. Frequency response data is needed to select thetransducer and may be quite different for different transducerdesigns.


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The useable part of the frequency response is on the flat or LINEARpart of the curve and if used outside this range, the results givenwill be incorrect due to change of sensitivity.

Care should also be taken not to expose very sensitive transducers

to shock as they may be damaged. This includes transport invehicles to the measurement site. The mass of the transducer isalso important.Recall that the natural frequency of a vibratingsystem is related to spring constant and mass in the system.Adding a significant mass to the system will change the systems'vibrational character. The transducer mass must thus be verysmall compared to the system.

The type of environment should also be considered when choosingthe transducer.The temperature range, moisture level, dust,

possibility of impact etc. should all be taken into account. For verydifficult environments or permanent mounting in industrialsituations, special ruggedised types of transducer are available.

3.3 Transducer Mounting

A vibration transducer will measure ALL the vibration that occurs atthe measuring point. This means that the mounting of thetransducer must not provide additional vibration to that being

measured. Mostly this means that the transducer should beconnected well to the item being measured and any brackets usedfor mounting should be very stiff.


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Piezo-electric transducer attachment (Pt 1 courtesy Bruel & Kjaer)


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Piezo-electric transducer attachment (Pt 2 courtesy Bruel & Kjaer)


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3.4 Use Of Condit ioning Ampl ifiers

Many of the transducers for vibration measuremnt require the useof a CONDITIONING AMPLIFIER.This is an electronic device that :

amplifies the small signal from the transducer to a moreuseful level and range

may provide power supply to the transducer allows the measured signal to be recorded in other

instruments. ensure that the signal from the transducer does not overload

the recording devices

A conditioning amplifier is not essential for some transducers, but

is recommended for all vibration measurement to ensure consistentresults. The conditioning amplifier is essential for piezo electrictransducers, due to the very small signal level generated by thesedevices.

Some conditioning amplifiers also contain the integration circuitsneeded to convert acceleration signals to either velocity ordisplacement. Whatever conditioning is applied it must always beremembered to isolate, electrically, the transducer from themachine being measured when mains electrical supply is used.

This is to prevent electrical noise pickup by the earth connections.(called ground loops)

Transducer

Conditioning Amplifier Meter or Other

Measuring Device

Figure 3.4 Conditioning Amplifier and Transducer


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3.5 Calibration

In any measuring system the dimensions measured must beassured to be correct. This is especially true where the system ismeasuring complex data such as random vibration, as the data is

not easily determined to be correct by inspection. Calibration is theterm given to the process of comparing the measuring system to areference standard measurement and determining thesystems'response. In vibration measuring systems, calibration isable to be carried out in the field, before measuring data, for mosttypes of transducer. In addition, regular recalibration checks oftransducers should be made by the equipment supplier or thenational standards authority. In Australia this authority is theNational Measurement Laboratory.

3.5.1 Methods Of Calibration

Calibration must use a reference source for vibration and a meansof determining the value of the reference.

a. Vibration exciters - These devices range from hand held size tovery large structural testing devices.Some devices have a fixed, stable level of vibration that is suitableas a reference for calibration without further equipment. Otherdevices require the additional use of a reference accelerometer orother transducer for determining the vibration level. The smallerdevices are suitable for smaller piezo electric transducers. Thelarger devices are only limited by the mass of the transducer andthe available force from the exciter.

CalibratorTransducer


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b. Displacement calibration - For displacement transducers the useof some length reference may be adequate for calibration. (staticonly) For example, differential transformers may be calibrated bygauge blocks or precisely machined reference gauges.

DVDT

Calibration reference length (guage blocks)

c. Static calibration with gravity - The use of servo accelerometers,piezo resistive accelerometers or other types of transducer with aresponse at zero Hz may allow the calibration to be done by tiltingin the earths' gravitational field.

AccelerometerAngle to provide desired static acceleration due to gravity

acceleration= 9.81 x sin


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d. Low frequency pendulum - A pendulum may be used to oscillatean accelerometer in the earths' gravity to give low frequencycalibration.

Pendulum

Accelerometer

e. Centrifuge - An accelerometer may be placed in a centrifuge toallow very high accelerations to be developed.

Centrifuge

Accelerometer


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Many of the calibration systems described above are not suitablefor field work. Thus reliance must be placed on the sensitivity ofthe transducer ( eg volts/g , mV/mm , mV/m/sec) and if this isthe case a calibration of the voltages in the system must be madeto give an accurate reference.

This can be done using the internal calibration on someconditioning amplifiers or a precision voltage reference source.Whenever possible, the whole vibration system should becalibrated. That is, when the transducer is recieving the calibrationlevel, the amplifier and recording devices should also be operated torecord the level right through the system. This tends to preventerrors in calculation of system performance as the data recordedcan be compared to the recorded reference signal.

3.6 System Errors

Any measurement system has an error associated with thatmeasurement. It is essential that some consideration of the levelof error of measurement be made. The frequently used estimate isthat of the method of expected error. This is a value that can beexpected for the ordinary circumstances. It is expressed as:

Error e e e e n= + + + +21

22

23

2......

the en are the errors for each part of the measurement (ie eachinstrument )

For example, consider the following system:a. transducer error +/- 1%b. conditioning amplifier error +/- 1.5%c. tape recorder error +/- 3%d. frequency analyser error +/- 0.4%

Error = + + +1 15 3 042 2 2. . 2

= +/- 3.5 %

While this may appear to be a large error, it is typical of most fieldmeasurements which are of the order of +/- 5% accuracy. Notethat this is not the worst case error which can be as much as 1 +1.5 +3 + 0.4 = +/- 5.9 % for the example above. This is theerrorthat would occur if the worst error occurred in each instrumentat the same time. This process is also only considering system


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errors, not errors of use of the equipment. Incorrect use, poorcalibration or malfunctioning equipment can give unpredictableerrors.

3.7 Measurement Of Shock

Comments about shock measurement have been left to this sectionas this area is particularly sensitive to the concern of errors andcalibration. Transducers that are to measure shock must becarefully constructed to give a sensitivity that is in the direction ofthe measurement axis and no other. For example, some typesofgeneral purpose accelerometers are adequate for generalmeasurement but under shock conditions they may exhibitsensitivity in other directions leading to false results. It ispreferable that transducers for shock measurement be calibrated at

the levels of shock to be measured. This will ensure a reasonableconfidence in the transducer performance. At the same time theconditioning amplifier should be considered as this must give arapid rise time to follow the impulse or shock data. The taperecorder or data analyser also must be "fast enough" to record thedata reliably. Test them all at calibration if possible. Calibrationcan be done using a falling pendulum which collides with a barrier.This is a specialised area and assistance should be sought toensure accurate results.

3.8 Data Recording

Vibration data may make use of the following means of datarecording:

chart recorders tape recorders continuous analysis digital recorders computers

3.8.1 Recording On Paper Chart

a.Pen Recorders these may be used to record the amplitudevariations with time so that these can be studied manuallly. Theycan't be used for signals that change much more rapidly than 200Hz. They are useful to study variation in level with time, peaklevels and decay rates in buildings.

b.Printers - some printers can make a chart like the pen recorders.More frequently they are used to give a permanent record of

vibration levels at various times during a measurement. Useful forlong term studies to give hard copy that can be plotted later.


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allows direct input to computer via a digital output port. This savesa digitising process which is otherwise needed for computer dataprocessing.

3.8.4 Digital Memory

By coding the data into digits, it may be stored in an electronicmemory of the type used in computers. Devices such as eventrecorders and some data loggers use this method. This technique isusually only used for relatively short bursts of data such asexplosions due to the limits of storage of the memory.

3.8.5 Computers

Computers have been used for many years for data analysis.Special input electronics modules have been available formultichannel measurement and analysis. In recent years, thedevelopment of high quality sound cards for PC and laptops haveprovided a relatively low cost data entry system.

3.8.6 Calibration

Recording devices must be calibrated so that the recorded valuescan be interpreted later. The most direct and simple way tocalibrate is to record the transducer calibration. This gives areference level on the recording device.

CALIBRATION is essential for confidence in measurement


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3.9 Data Analysis Instrumentation

The use of correct instrumentation for data analysis will allowthorough and meaningful results from vibration measurement. Thetypes of possible data analysis has been discussed. The type of

equipment needed to carry out these analyses will now bedescribed.

3.9.1 Vibration Meter

A very common and simple means of measuring vibration is to usea vibration meter. This type of device gives an overall reading ofthe vibration level, usually an RMS value. The vibration meter mayinclude signal conditioning and integrating sections so that anaccelerometer can be used for measuring acceleration, velocity or

displacement. This type of instrument may also include weightingcurves that may be used for the assessment of particular types ofvibration such as machinery or human comfort.

3.9.2 Weighting Curves

As with acoustic measurement, the use of weighting curves is alsocommon in vibration analysis. The weighting curve can be a filteror it can be produced by numerically adjusting frequency data thatis produced by an FFT analyser. Weighting curves are usedprimarily in vibration analysis for the assessment of human effectsof vibration. The numerical adjustment of data referred to above isusually performed on a computer.

3.9.3 Frequency Analysers

Much use is made in vibration analysis of frequency analysers.The most commonly used analyser is a constant bandwidth FFT(Fast Fourier Transform) instrument. While it is possible to utiliseconstant percentage bandwidth instruments such as one-thirdoctave analysers, as used in acoustic analysis, these instruments

generally cannot provide the detail needed at lower frequencies formachine vibration analysis.

It is essential in most measurements of vibration that the frequencycan be determined with an accuracy that can discriminate betweenthe different parts that are causing vibration and this is easilyachieved with the FFT analyser.FFT analysers are often implemented as hardware or firmware unitsbut may also be implemented as software applications in PCs orlaptops.


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Vibration Isolation

4.1 Machine Vibration

All machinery has some vibration. This fact has already been usedto advantage in machine condition monitoring. In many caseshowever we wish to either isolate the machine vibration from otherequipment or from people or isolate the equipment from vibration.As we have seen already, the vibration of a spring mass system canbe expressed in the form of a frequency response curve. (seefigure 4.1).

4.1.2 Degrees Of Freedom

The curve in figure 4.1 is the response to forced vibration of a"single degree of freedom " system. Such a system has motion thatis restricted to one direction of displacement. If the possible axes ofdisplacement are considered for three dimensions, (figure 4.2)

Figure 4.2 Position In Three Dimensions

it can be seen that for a general three dimensional position in spaceof a single rigid body, that six degrees of freedom are possible. ( iesix possible directions of displacement) The single degree offreedom system then has only one possible direction ofdisplacement which may be either a translational or rotationaldisplacement. Very few real machines are single degree of freedomsystems. Most are composed of many parts with connections of


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varying rigidity. This greatly increases the complexity of theanalysis of the machine and its' vibration.

Response to Forced Vibration

0.01

0.10

1.00

10.00

0.1 1 10

Frequency Ratio

Amplif ication Ratio

0

0.05

0.1

0.2

0.5

1.0

Damping

Ratio

1.0

0.5

0.2

0.1

0.050

Figure 4.1 Frequency Response Curve

One Degree Of Freedom System

For instance, many vehicle suspension systems are designedconsidering all the degrees of freedom possible. (eg motor cars,trains) This may require analysis of over 20 degrees of freedom !This type of analysis can only be reasonably achieved by usingcomputer programs called simulations that solve the mathematicalmodels of the system continuously in time. Fortunately, for many

purposes use of a single degree of freedom system as anAPPROXIMATION to the real system is possible. In this course we


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will only deal with single degree of freedom systems. It is essentialhowever to be aware of the limitation of this approximation whendesigning vibration isolation for machines.

4.1.3 The Response Curve And Transmissibli ty

The response curve shown in figure 4.1 has two axes. Thehorizontal axis is the ratio between the natural frequency and theapplied ( "forcing ") frequency. The vertical axis is labelledTRANSMISSIBILITY.

We have used this axis to determine either force ratio ordisplacement ratio for the vibrating systems. The termTRANSMISSIBILITY refers to the ratio of transmitted force ordisplacement to that applied to the system. (see figure 4.3)

As an example, we may consider the reduction in force to thefoundation of a machine which has isolators providing a ratio offorced to natural frequency of 4. This gives a TRANSMISSIBILITY of0.04 (vertical axis, zero damping).

This means that force caused by the vibration of the machine whenoperating (ie at the forcing frequency) will be reduced to 0.04 of theoriginal at the machine foundation or base. The transmissibility is0.04 or a (1 - 0.04) x 100 = 96% reduction in force level.

The transmissibility is a description of the quality of performance ofa vibration isolation system and may be applied as a designstandard. It may describe either force or displacement reduction ofthe system. Although we have only calculated single degree offreedom examples, transmissiblity may be applied to any system.

An alternative means of expressing this requirement is theISOLATION. The isolation value is frequently used on data sheetsfor commercial vibration control products.

Isolation is a measure of the reduction of vibration and isexpressed as a percentage. The calculation above forTransmissibility = 0.04 showed that this was a 96% reduction invibration level. The 96% is the isolation.

This leads to the relationships:

Isolation % = (1- Transmissibility) x100

Transmissibility = (1- Isolation)

(note: use the decimal form of percentage to make this formula work; eg 96% =0.96)


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m m

Input exciting force F

Force on support G

T = G/F

Input displacement Y

Displacement of Mass X

T= X/Y

figure 4.3 Showing Transmissibility for force and displacement

4.2 Static Deflection

When calculating the natural frequency of a system, the followingformula is used:

m

k=

With any system the spring constant k must be determined to suitthe above formula and the transmissiblility required.


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Consider the spring constant:

F = k x

where k = spring constant, N/mF = force , Nx = displacement , m

If a machine is lowered onto an isolation system, the springs willdeflect from their unloaded position by an amount proportional tothe mass of the machine. This is called the static deflection. If thestatic deflection is known we can calculate the spring constant. Wethus have, using the above equation;

k Fx

=

so,

kmg

xstatic=

If this information is substituted in the equation for naturalfrequency we have:

=mg

mxstatic

or

=g

x

We thus have another way of expressing the natural frequency of asystem in terms only of the static deflection. How is this useful ?For a required transmissibility, say 0.1, we can determine therequired frequency ratio to be about 3.4 (figure 4.1) By knowing theforcing frequency we determine the required natural frequency.

natural =forcing / 3.4


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We may now determine the required static deflection directly fromthe equation developed above. The suppliers of vibration isolatorsoften supply information in this form (static deflection and mass) sothat this simple relationship can be used for design.

4.3 Center Of Gravity

When machinery is being installed with vibration isolators it is oftennecessary to consider the position of the center of gravity of themachine. This is the position where all the mass of the machine canbe considered to act through a single point giving the same staticforce.

If the center of gravity is known, vibration isolators can bepositioned at equal displacements from this point to ensure equalloading. Equal loading on each isolator is preferable as this meansthat all isolators are of the same type. This prevents confusionduring maintenance and minimises spare parts stock. The center ofgravity is calculated in the conventional method of mechanics usingmoments about an arbitrary point.

It is preferable to mount the isolators vertically in the plane of thecentre of gravity. This will prevent some possible additional rockingvibration.

This arrangement is not always practicable and is usually reservedfor machines that are very large or that have a particularly difficultvibration problem. It should be seriously considered also in thecase of a machine that is very tall compared to its width.

These situations are illustrated in figure 4.3.


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a) conventional mounting

Centre of Gravity

b) mounting in plane of center of gravity

Figure 4.3 Center Of Gravity And Mounting Of Isolators

4.3.1 Location Of Isolators

We have already observed that the isolators should be mounted soas to have equal vertical static force. There are a number of otherpractical concerns regarding the positioning of isolators so that theyoperate as designed.

a)Horizontal spacing:

In figure 4.4 a) the isolators are shown positioned at equal spacingfrom the center of gravity however, the isolators are also very closetogether. This could cause problems of rocking vibration. It is thuspreferable to mount the isolators as far apart as is practicable.


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b)Lateral loading:

If the isolators are to operate as desired it must be ensured thatthe required spring constant is achieved. It is possible that thearrangement of mechanical drives or other connections to the

machine will add stiffening to the spring constant of the isolators.

Remember that a decrease in the spring constant will increase theisolation and so an increase in the spring constant will DECREASEthe isolation. Careful attention to the design will ensure that thisproblem does not arise.

Figure 4.5 a) shows examples of designs that interfere with theoperation of the isolators. Methods of improving the design areshown in figure 4.4 b).

a)close mounting (unsatisfactory)

b) far apart mounting (desirable)

Figure 4.4 Position Of Isolators


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a) external loading on isolators (unsatisfactory)

b) correct design to remove isolator side loads

Figure 4.5 Design Of Isolator Installation

c) Connection of pipes electrical etc.

In a manner similar to that described in part b), the stiffness maybe effected by pipework or other connections to a machine that isfitted with vibration isolators. Because this is not always a seriousreduction in spring constant, these items are often ignored. Theadditional problem here is that the vibration may be transmittedalong these connections, causing excessive noise and poteniallyexcessive stresses that could lead to failure of parts.

This is illustrated in figure 4.6 a) where a number of unsatisfactory

arrangements are shown. In 4.6 b) alternative arrangements areshown. Often these alternatives also provide allowance for thermalexpansion of machines and certainly will reduce the incidence offailure in connections.


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a) direct connection to machinery (unsatisfactory)

b) connections that isolate vibration

Figure 4.6 Connections To Vibrating Machines

d) Spring Constant with Multiple Isolators

In all the analysis, we have assumed a spring / mass system with aspecific spring constant but have only referred to one spring.

Most realistic isolation designs for machines require 4 or moresprings.

How do we relate the spring constant from the analysis to thepractical application?

Springs can be connected in either series or parallel as shown infigure 4.7. The same results apply to either tension or compressionsprings.


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If K = 100 N/m fo r all springs:

K total (Series) = 25 N/mK total (Parallel) = 400 N/m

K

K

K

K

KKKK

K total = K + K + K + K

K total = 1 / (1/K + 1/K + 1/K + 1/K)

Series Parallel

Springs in Series or Parallel

Figure 4.7 Spring Constant for Multiple Springs

Figure 4.7 shows that springs in series decrease the spring ratewhereas the same springs in parallel increase the spring rate(compared to the rate of a single spring)

When supporting a machine with multiple springs the spring

constant determined from the analysis must be divided by thenumber of springs that will be used for support. The new springconstant determined will be used to select the actual springs used.

For example, the required spring rate for isolation of machinevibration might be 50kN/m. If 4 springs are to be used forsupporting the machine, then each spring will require a springconstant of 50/4 =12.5 kN/m.


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4.4 Types Of Isolators

4.4.1 Materials

Many materials may be used for isolation of vibration. A list of the

common types follows:

Material Form that it is used

felt felt matfelt composites

cork cork blockscork composites

composite materials rubber with non - metallicreinforcementNeoprene and cork

rubbers natural rubbersynthetic rubbers

wire mesh

metal spring coil springleaf springs

air air bellows

Each material has an area of specific application related to the

available static deflection. This means that selection in someapplications may be limited to one type of isolator. Figure 4.8shows the typical range of application for the types of material.


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Deflection Natural Frequency Isolator

mm Hz

250

25

2.5

0.25

0.025

1.0

10

100

Air

Metal Springs

Rubbers

Cork

Figure 4.8 Areas Of Use Of Isolation Materials

4.4.2 Using Materials

FELT A matrix of textile fibres which is usually supplied in sheetform. Usually used for applications where well balanced machinesare expected to produce vibrations at acoustic frequencies. It isnecessary to use a low loading per unit area to prevent settling andloss of isolation. Often used between a concrete machine base andthe foundation or floor.

CORK A naturally occurring substance that is processed intoconvenient shapes for use. Cork may be used for high compressiveloads at low acoustic frequencies (50 - 60 Hz)

More widely used than felt as the engineering properties are morereadilly available. Able to be treated against most industrialcontamination.

RUBBERS These materials offer a wide range of mouldable shapesand properties that provide isolators for many applications. Rubbermaterials have varying resistance toindustrial contaminants and the following should be considered:

1 Temperature of operation

2 Ozone3 Sunlight


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4 Liquids eg oils

The manufacturers'data should be consulted to ensure adequate lifein the particlular environment that is to be considered.

METAL SPRINGS Used in the range 3 - 10 Hz these isolators providethe lower frequency area of isolation after the rubbers. A widerange of spring types and sizes means that a suitable design isusually able to be achieved and provide good environmentalperformance. These springs however usually have very lowdamping and generally require external damping to achieve desiredperformance.

AIR SPRINGS Used for high isolation at low frequency and in somecases where vibration amplitude is very small. The air spring

system can provide a constant hieght with varying load whilemaintaining the required isolation performance.Although more complex and costly than other systems, it is oftenthe only choice for high performance isolation.

4.5 Damping

The term damping has been mentioned previously and must beconsidered in all isolation design. Damping refers to that part of avibrating system that provides loss of vibration energy, either

intentionally or unintenionally. Damping ensures that vibrationdoes not continue indefinitely after excitation of the system occurs.Isolation materials have a degree of internal damping. Some valuesare listed in table 4.1

Material Approximate damping ratiosteel 0.005rubbers 0.05air damping 0.17felt/cork 0.06

Table 4.1 Damping Ratios Of Some Materials

The effect of damping appears in figure 4.1 as the damping ratio.This is the ratio of actual damping to critical damping (see sect. 1and 2).


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It can be seen that the isolation effect reduces as dampingincreases so why have damping ? Damping provides a limit to theoscillations at resonance. For many machines operation atresonance will not occur but may be experienced at start up orduring run down. Other machines may not be able to completely

avoid resonant operation and thus damping must keep oscillationsat an acceptable level. Damping also effects the natural frequencyof the system. The natural frequency of the system is altered by :

f fnd n= 12

wherefnd= natural frequency with damping

fn= natural frequency

= damping ratio

In many cases the effect is small, for example with rubberisolators with a damping ratio of 0.05 the change in naturalfrequency is less 0.2 %.

4.6 Real Isolation

Actual isolation may not be exactly as predicted by the one degreeof freedom model. The reductions at acoustic frequencies may beless than that in the transmissiblity graph. This comes from thesimplified mathematics used for this system. In a real system themass and stiffness of the support structure are important inachieving reasonable performance.

4.6.1 Support Structure

As a guide, the mass of the supporting structure should be at least

1000 times greater than the mass that is vibrating. Thefoundation stiffness is also of concern because it acts as anotherspring in the system. The natural frequency fn of the spring masssystem of the isolated machine should be lower than the lowestnatural frequency of the foundation structure. The naturalfrequency of the foundation should also not be an exact multiple offn. To assist in this it is better to have as low stiffness isolator aspossible when the foundation is suspected of some significantflexibility such as a suspended floor.An example of this is a machine operating at 1500 rpm could be

isolated on a basement floor of a building with 95% isolation by astatic deflection of 8.6 mm.


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For suspended floors such values as:

10 m span 10 mm static deflection12 m span 10.7 mm " "15 m span 11.2 mm " "

are recommended by a machine supplier.

4.6.2 Mounting Frame

Any frame that is used to mount a vibrating machine should bedesigned with maximum feasible stiffness to prevent amplificationof vibration.

4.6.3 Lateral Stability

When designing any vibration isolation installations it is clear that itis desireable to have a relatively large static deflection. Thisprovides minimum transmissibility. An isolator with low stiffness(ie large static deflection) may also have a low lateral stiffness.This may affect other modes of vibration but also may causeproblems with excessive motion of the isolated machine.

This type of problem is usually more significant if the machinery isin motion as in a vehicle. Acceleration or retardation of the vehiclewill mean a large longitudinal or lateral force must be transmittedby the vibration isolators. The large force and /or displacementresulting could damage the isolators or even disconnect themachine from its mountings.To overcome this motion is often limited by safety stops or resilientbumpers. This problem also often limits the practical springconstants usable and hence place a limit on the realisable maximumperformance of isolators. Thus, even though it is theoreticallypossible to achieve a reduction of 99. 99% of the vibration it maynot be practical due to the very low lateral spring constant leadingto instability.

4.7 Isolation Of Equipment From Base Vibrations

In most of the above examples we have been discussing theisolation of a vibrating machine from the structure that is carryingit. In some cases, such as the use of delicate equipment on avibrating machine, the isolation is to minimise the vibration recievedby this equipment. Even with low transmissiblity isolation,damage may occur to the sensitive equipment. This is because of

the resonant effect that we have already studied. Low level


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vibrations that are transmitted can be amplified by a resonance inthe equipment.

To avoid this problem we must know what the resonances are. Wehave seen already that most real systems are multi - degree of

freedom systems. The analysis for these systems is complex butmay often be achieved using finite element methods on a computer.

We can also experimentally study the response of the system tovibration by placing the delicate equipment on a "shaker" like thoseused for calibration but with the ability to provide a variablefrequency and level. Resonances of equipment can then beobserved by accelerometers or non-contact measurement usinglaser interferometry.

4.8 Summary of Isolator Considerations

For practical design of isolators then we should consider:

the required transmissibility

b) even spacing from the center of gravity

c) positioning in the plane of the center of gravity

d) positioning of equipment to avoid loss of isolator performance

e) minimising vibration transmission through pipes etc.

f) the type of isolator material and its environment

g) damping of the isolator and need for additional damping

h) effect of the isolator at higher frequencies

i) support stiffness and mass

j) lateral stability of the isolators


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Vibration - Human Effects

5.1 The Human Body

The human body is composed of soft tissue and a hard skeleton

with connections of firmer muscle tissue. This structure has thenbasically a rigid frame with masses hung on resilient (springy)mountings. This means that the human body can be consideredas a complex of spring mass systems that will respond to vibration.

There are two major areas of concern for the human effects ofvibration:

a.whole - body vibration (vibration applied to the entire body)b.hand - arm vibration (vibration applied in a limited area of the

hand/arm as when using vibrating tools)

5.2 Whole Body Vibration

Interest in the response of the human body to vibration began withthe transport industries. Concern with passenger comfort in railvehicles, ships, aircraft and limits for military vehicles eachgenerated research into this area.

The research has shown many similarities but, as yet little

correlation between vibration levels and injury has beenestablished. The vibration criteria are thus not as clearly defined inrequirement as for instance noise exposure. In noise exposure, wewere concerned with damage to the human ear. What are theeffects on the human body from vibration ?

5.2.1 A Body Model

The human body can be modelled as a series of spring masssystems made up of muscle and tissue as spring elements, bodyorgans as masses and connected via the skeleton.

The different spring - mass systems represent the different partsof the body, for example, the internal organs are suspended bytissues forming the spring mass system. Each system will have adifferent natural frequency. This means that certain vibrations willmake different parts oscillate.


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Figure 5.1 The Human Body as a Spring Mass System (Coerman et al)

5.3 Testing Human Vibration Sensit ivi ty

Most of the testing for human vibration sensitivity has been done bysubjecting volunteers to varying sinusoidal vibration and recordingtheir response. This method does not completely establish theresponse of the body to a complex vibration, such as multiple axisvibration, but does give an indication of trends. This means that theeffects of random vibration, for instance, will not always follow thesame sensitivity curves Recent work (1997) has begun to addressthis problem to get more accurate data..


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5.3.1 Direction Of Vibration

For whole body vibration, the vibration may enter the body while ina standing or seated position. The vibration may be horizontal,vertical or lateral. The human body has differing sensitivity in each

of these directions due to differing stiffness in each plane. Thismeans that muscle effort is required to restrain the body parts,leading to fatigue. The vibration may even interfere with theorgans' function, such as distortion of vision by vibration of the eye.Excessive levels of vibration can lead to tissue damage or illness.For example, oscillations from earth moving machinery may causespinal injury.

5.4 Vibration Criteria

Due to the differing uses for vibration criteria they been frequentlyconsidered in separate categories of comfort limits and exposurelimits.

5.4.1 Comfort L imi ts

These limits are established to provide passenger comfort in thetransport of humans. Comfort limits are usually expressed in termsof time of exposure. That is, a lesser comfort level is acceptable forshort duration trips and for longer trips lower levels of vibrationmust be provided. This is to ensure that the passenger will not beexcessively fatigued at the end of the journey. Each mode oftransport has differing vibration source mechanisms. This leads todiffering comfort criteria. For example, ships must consider verylow frequency vibration which does not occur in most other forms oftransport. Aircraft have high frequency vibrations that are moreirregular than other transport.

5.4.2 Exposure Limits

These limits have been set to indicate the maximium levels thathumans can be exposed to in industrial situations. In using theselimits, it should be noted that the fatigue level will be higher and sotask performance will reduce. If these limits are to be used, theyshould be considered as infrequent exposures as in an emergencysituation.

5.4 The ISO Standard

The vibration limits for human exposure have been expressed as an

ISO standard. This standard has been used as the basis for theAustralian Standard (AS2670) Although this standard is based on


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pure sinusoidal vibration tests on subjects, it has becomeacceptable to use this in the absence of more precise information.

It is a good guide for general industrial applications and as a startpoint for establishing special purpose vibration standards.

Weighting curves are used to give a single value measure ofcomfort levels. The Australian standard has also included the verylow frequency extension to the ISO standard that covers the motionsickness region.

Modified criteria are used as guidelines for exposure limits to protectagainst ill health or injury.

5.5 Instrumentation

Considering the frequency range of the human sensitivity to wholebody vibration, we can determine the frequency range andsensitivity of the required measuring instruments.

The standard shows that a maximum level of 1.0 g will beapplicable for most measurements. The frequency range will bebetween 50 and 100 Hz, depending on the likely vibration source

spectrum. For example, aircraft measurements will require up to100 Hz, while motor vehicle measurements will be adequatelycovered by a 50 Hz range. If motion sickness measurements are tobe made, the low frequency range, 0.1 to 1.0 Hz, must also beconsidered. For these types of measurement, the use of servoaccelerometer or piezo resistive accelerometer types is common.The piezo electric types sometimes cannot provide the lowfrequency sensitivity, unless specially selected.The measurement of vibration should be made at the point of

entry of the vibration to the human body. That is, if the subject isseated, the vibration limits apply at the seat surface not the floor

that the seat is attached to.This is because the seat itself may amplify the vibration that comesfrom the floor.The low frequency of the vibration data means that only FM tape

recorders can be used to record the information. A suitableconditioning amplifier must also be selected.

As the measured data may be either weighted or unweighted theassessment according to the standard will be in two possiblemanners:


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i. weighted data compared directly to the AS2670 curves todetermine the allowable exposure time

ii. unweighted data is first weighted in each frequency band andthen compared to the AS2670 curves.

In the first case, the RMS value from the instrumentation is directlycompared to the curves. The second case may utilise computercalculation to speed the weighting and assessment process.

Where vibration is steady, the first method may give the mostrapid result. If vibration is unsteady, for example, random vibrationin a vehicle, an averaging process may be needed to ensure thecorrect exposure is determined. This may be achieved by measuresat various levels that are typical of the environment and summing in

proportion to the time exposed at each level. This is equivalent tothe Leq method used for noise.

Alternatively, a sample may be taken over a representative periodusing an integrating process to determine the total exposure.

5.6 Hand Arm Vibration

Whole body vibration is frequently able to be maintained at orbelow fatigue levels so that significant injury is not normally of

concern. With hand arm vibration however, there is a real dangerof serious and permanent injury. Vibration at high levels applied tothe hands while using machinery or tools can cause disease of theblood vessels, joints and blood circulation system.The result is what is called "vibration white finger" or Reynauds'

disease. Circulation of the blood becomes so poor that fingers andhands may turn white and in extreme cases permanent tissuedamage or gangrene may result. The type of machinery that cancause this type of injury is that producing high levels of vibrationand which must be hand held for long periods of time. Forexample:

Chainsaws, chipping hammers, rivetting guns, power grinders,and hammer drills.

These types of machines may be found in many industries and areoften able to generate very high levels of vibration in human handsand arms.

5.7 Hand Arm Exposure Limi ts


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An ISO standard has been developed which forms the basis of theAUSTRALIAN STANDARD. The Australian Standard also includesreccommendations for medical recording of the effects of vibrationexposure to the hand arm. This is because of the relatively limitedexperience in Australia with this disease. The standard specifies the

postition for measuring vibration levels as an axis system related tothe human skeleton at the wrist.

This is to standardise the level allowed in the measured direction.The standard provides a weighting curve from which allowableexposure can be determined.


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5.8 Instrumentation

The most appropriate instrumentation for this work is an integratingvibration meter with the standard weighting curve. This allows themeasurement of vibration directly in a weighted RMS value that can

be compared to the allowab

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Vibration Control Book 07