Dynamic Testing of Machines and Structures

8/9/2019 Dynamic Testing of Machines and Structures

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DYNAMIC TESTING OFDYNAMIC TESTING OF

MACHINES ANDMACHINES ANDSTRUCTURESSTRUCTURES


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The determination of deformation of theThe determination of deformation of the

machines or structures at a criticalmachines or structures at a critical

frequency is calledfrequency is called dynamic testing ofd

ynamic testing of

machinesmachines..

The following two approaches can be usedThe following two approaches can be used

for this purpose:-for this purpose:- By using operational deflection shape(OD!By using operational deflection shape(OD!

measurements.measurements.

By using model testing.By using model testing.


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"n"n ODS methodODS method# the forced dynamic deflection shape# the forced dynamic deflection shape

is measured under steady state i.e.# operatingis measured under steady state i.e.# operatingfrequency of the system.frequency of the system.

$or the measurement# an accelerometer is placed at$or the measurement# an accelerometer is placed atsome point on the structure%machine as a reference#some point on the structure%machine as a reference#

and another mo&ing accelerometer is placed at se&eraland another mo&ing accelerometer is placed at se&eralother points# and in different directions.other points# and in different directions.

Then the magnitude and phase difference between theThen the magnitude and phase difference between themo&ing and reference accelerometers at all the pointsmo&ing and reference accelerometers at all the points

under steady-state operation of the system areunder steady-state operation of the system aremeasured. 'et we can find absolutely how themeasured. 'et we can find absolutely how the&arious parts of the machine mo&e relati&e to one&arious parts of the machine mo&e relati&e to oneanother by plotting these measured &alues.another by plotting these measured &alues.


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The operational deflection shape measured is &alid onlyThe operational deflection shape measured is &alid onlyfor the particular force%frequency associated with thefor the particular force%frequency associated with theoperating conditions and we cannot get the informationoperating conditions and we cannot get the informationabout deflections under other forces%frequency.about deflections under other forces%frequency.

"n"n modal testingmodal testing# natural frequencies# damping ratios# natural frequencies# damping ratiosand mode shapes are determined through &ibrationand mode shapes are determined through &ibrationtesting. )odal testing is study of the dynamic propertiestesting. )odal testing is study of the dynamic properties

of an elastic structure by identifying its modes ofof an elastic structure by identifying its modes of&ibration. "n addition# it has a characteristic mode shape&ibration. "n addition# it has a characteristic mode shapewhich defines the resonance spatially o&er the entirewhich defines the resonance spatially o&er the entirestructure.structure.

Once the dynamic properties of an elastic structure ha&eOnce the dynamic properties of an elastic structure ha&ebeen characteri*ed# the beha&ior of the structure in itsbeen characteri*ed# the beha&ior of the structure in itsoperating en&ironment can br predicted and therefore#operating en&ironment can br predicted and therefore#controlled and optimi*ed.controlled and optimi*ed.


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Operational deflection shapeO

perational deflection shape

ODS!

ODS! +n OD can be defined as any forced motion of two or more+n OD can be defined as any forced motion of two or more

points on a structure.points on a structure.

pecifying the motion of two or more points defines a shape.pecifying the motion of two or more points defines a shape.

OD depends on the forces or loads applied to a structure.OD depends on the forces or loads applied to a structure.They will change if the load changes.They will change if the load changes.

To understand any structural &ibration problems# theTo understand any structural &ibration problems# the

resonance of a structure need to be identified. This is done byresonance of a structure need to be identified. This is done by

defining its modes of &ibration.defining its modes of &ibration. ,ach mode is defined by a natural modal frequency# modal,ach mode is defined by a natural modal frequency# modal

damping and a mode shape.damping and a mode shape.


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Time domain ODTime domain OD andomandom

"mpulsi&e"mpulsi&e inusoidalinusoidal

+mbient+mbient

$requency domain OD$requency domain OD inear spectra ($$Ts!inear spectra ($$Ts!

+uto power spectra(+/s!+uto power spectra(+/s!

0ross power spectra(1/s!0ross power spectra(1/s!

$requency response functions($$s!$requency response functions($$s!

OD $sOD $s


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teady state operation is achie&ed when theteady state operation is achie&ed when theauto power spectrum(+/! of a responseauto power spectrum(+/! of a response

signal does not change o&er time or fromsignal does not change o&er time or frommeasurement to measurementmeasurement to measurement


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Frequency domain ODS,Frequency domain ODS, inear spectruminear spectrum:-frequency domain function is the:-frequency domain function is the

$$T of a sampled time domain function. /hase is$$T of a sampled time domain function. /hase ispreser&ed in the linear spectrum# so in order to obtainpreser&ed in the linear spectrum# so in order to obtainoperating deflection shapes from a set of linearoperating deflection shapes from a set of linearspectra# either the measurement process must bespectra# either the measurement process must berepeatable or the time domain signals must berepeatable or the time domain signals must besimultaneously sampled.simultaneously sampled.

+uto power spectrum (+/!+utopower spectrum (+/!:-the +/ is deri&ed by:-the +/ is deri&ed byta2ing the $$T of a sampled time domain function andta2ing the $$T of a sampled time domain function andmultiplying the resulting linear spectrum by themultiplying the resulting linear spectrum by thecomple con3ugate of the linear spectrum at eachcomple con3ugate of the linear spectrum at eachfrequency.frequency.

$$s$$s:-The $$ is a 4-channel measurement#:-The $$ is a 4-channel measurement#in&ol&ing a response and an ecitation signal. "t canin&ol&ing a response and an ecitation signal. "t canbe estimated in se&eral ways# depending on whetherbe estimated in se&eral ways# depending on whetherthe ecitation or the response has more noise.the ecitation or the response has more noise.


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The most common calculations in&ol&e di&iding anThe most common calculations in&ol&e di&iding an

estimate of the cross power systems (1/! between theestimate of the cross power systems (1/! between the

response and ecitation of the auto power spectrumresponse and ecitation of the auto power spectrum(+/! of the ecitation# at each frequency. +&eraging(+/! of the ecitation# at each frequency. +&eraging

together of se&eral 1/5s and +/5s is commonly donetogether of se&eral 1/5s and +/5s is commonly done

to reduce noise in these estimates.to reduce noise in these estimates.

The operating deflection shapes deri&ed from a set ofThe operating deflection shapes deri&ed from a set of

$$5s will contain both the magnitude and phase$$5s will contain both the magnitude and phasedeformation.deformation.

$$5s cannot be measured on operating machinery or$$5s cannot be measured on operating machinery or

equipment when internally generated forces# acousticequipment when internally generated forces# acoustic

ecitation and other forms of ecitation are eitherecitation and other forms of ecitation are eitherunmeasured or immeasurable. On the other hand#ODunmeasured or immeasurable. On the other hand#OD

can always be measured no matter what forces arecan always be measured no matter what forces are

causing the &ibration.causing the &ibration.


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TransmissibilityTransmissibilityTransmissibility measurements are madeTransmissibility measurements are made

when the ecitation force cannot bewhen the ecitation force cannot be

measured.measured.

Transmissibility is a 4-channelTransmissibility is a 4-channel

measurement li2e the $$. "t is measuredmeasurement li2e the $$. "t is measuredthe same way as the $$# but thethe same way as the $$# but the

response time is di&ided by a referenceresponse time is di&ided by a reference

signal instead of an ecitation force.signal instead of an ecitation force.

The OD obtained from a set ofThe OD obtained from a set of

transmissibility will also contain correcttransmissibility will also contain correct

magnitude and phase angle.magnitude and phase angle.


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OD $$:-OD $$:- +n OD $$ is a different 4-channel+n OD $$ is a different 4-channel

measurement that can also be used when ecitationmeasurement that can also be used when ecitation

forces cannot be measured.forces cannot be measured.

The ad&antage of OD $$ o&er theThe ad&antage of OD $$ o&er the

transmissibility is that the OD $$ has pea2stransmissibility is that the OD $$ has pea2s

at resonance# thus ma2ing it easy for locatingat resonance# thus ma2ing it easy for locating

resonance.resonance.


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)OD, 6+/,)OD, 6+/, ,perimental modal parameters are obtained from measured,perimental modal parameters are obtained from measured

OD5s. )odal parameters are obtained by post processing aOD5s. )odal parameters are obtained by post processing aset of OD data. +T or near the resonance pea2# theset of OD data. +T or near the resonance pea2# theresonance is dominated by a mode. Therefore# the OD isresonance is dominated by a mode. Therefore# the OD isapproimately equal to the mode shape. The conceptapproimately equal to the mode shape. The conceptbecomes clearer when sine wa&e ecitation is considered.becomes clearer when sine wa&e ecitation is considered.6owe&er# the OD that is measured also depends on whether6owe&er# the OD that is measured also depends on whetheror not a resonance is ecited. "n order to ecite resonance#or not a resonance is ecited. "n order to ecite resonance#the following two conditions must be met:the following two conditions must be met:

The ecitation frequency must be close to the resonanceThe ecitation frequency must be close to the resonancefrequency. +ll single frequency sine wa&e model testing isfrequency. +ll single frequency sine wa&e model testing isbased upon achie&ing the two conditions abo&e and also abased upon achie&ing the two conditions abo&e and also athird condition.third condition.

+t a resonant frequency# if the OD is dominated by one+t a resonant frequency# if the OD is dominated by onemode# then the OD will closely approimate the modemode# then the OD will closely approimate the modeshape.shape.

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Dynamic Testing of Machines and Structures