Force Torque Shaftpower Vibration

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Introduction

A force is any influence that causes an object toundero a certain chane, either concernin itsmo!ement, direction, or eometrical construction"

A force can accelerate objects by #ullin or #ushinthem" The relationshi# between force, mass, andacceleration was defined by Isaac $ewton in hissecond law of motion, which states that an object%s

force is the #roduct of its mass and acceleration"Force = Mass x Acceleration


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Methods of Force Measurement

A measure of the unnown force may be accom#lished bythe methods incor#oratin the followin' (alancin the force aainst a nown ra!itational force on a standard

mass ))) Scales & Balances.

Translatin the force to a fluid #ressure and then measurin theresultin #ressure)))" Hydraulic & Pneumatic Load Cells.

A##lyin the force to some elastic member and then measurin theresultin deflection))" Proving ring.

A##lyin the force to nown mass and then measurin the resultin

acceleration" (alancin the force aainst a manetic force de!elo#ed by interaction

of a manet and a current carryin coil"


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Pro!in -in

The #ro!in rin is a de!ice used to measure force" Itconsists of an elastic rin of nown diameter with ameasurin de!ice located in the center of the rin"

Pro!in rins come in a !ariety of si.es" They are made of a

steel alloy" Manufacturin consists of rouh machininfrom annealed forins, heat treatment, and #recisionrindin to final si.e and finish"

Pro!in rins can be desined to measure either

com#ression or tension forces" Some are desined tomeasure both" The basic o#eration of the #ro!in rin intension is the same as in com#ression"


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A #ro!in rin is a circular rin of rectanular cross section asshown in the Fi" which may be subjected to tensile orcom#ressi!e forces across its diameter"

The deflection is small and hence the usefulness of the #ro!inrin as a calibration de!ice de#ends on the accuracy with whichthis small deflection is measured"

This is done by usin a #recision micrometer shown in the

fiure" In order to obtain #recise measurements one ede of themicrometer is mounted on a !ibratin reed de!ice which is#luced to obtain a !ibratory motion"

The micrometer contact is then mo!ed forward until a

noticeable dam#in of the !ibration is obser!ed"Pro!in rins are normally used for force measurement within

the rane of /"0 1$ to /"0 M$" The maimum deflection isty#ically of the order of /2 of the outside diameter of the rin"


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3oad 4ells

3oad cells are elastic de!ices that can be used formeasurement of force throuh indirect methods i"e"use of secondary transducers"

3oad cells utili.e an elastic member as the #rimarytransducer and strain aue as secondary transducer" +hen the combination of strain aue 5 elasticmember is used for weihin it is called laod cell"

The !arious ty#es of load cells that eist includeHydraulic load cells, Pneumatic load cells andStrain gauge load cells.


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6ydraulic 3oad cells

6ydraulic load cells are force7balance de!ices, measurin weiht as a chane in #ressure of the internal fillin fluid"

In hydraulic load cell, a load or force actin on a loadin headis transferred to a #iston that in turn com#resses a fillin fluid

confined within an elastomeric dia#hram chamber" As the force increases, the #ressure of the hydraulic fluid

increases" This #ressure can be locally indicated or transmittedfor remote indication or control"

This sensor has no electric com#onents and immune totransient !oltaes so it is ideal for use in ha.ardous areas"

The ad!antaes of 6ydraulic load cells are it is e#ensi!e and !ery com#le"


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Pneumatic 3oad 4ell

Pneumatic load cells o#erate onthe force7balance #rinci#le"These de!ices use multi#ledam#ener chambers to #ro!idehiher accuracy than can ahydraulic de!ice"

Pneumatic load cells are oftenused to measure relati!ely small weihts in industries wherecleanliness and safety are of#rime concern"


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Strain aue 3oad 4ell

Basic Princile of Strain gauge load cell +hen steel cylinder is subjected to a force, it tends to chane in

dimension" 8n this cylinder, if the strain aues are bonded, the strainaue also is stretched or com#ressed, causin a chane in its lenthand diameter"

This chane in dimension of the strain aue causes its resistance tochane" This chane in resistance or out#ut !oltae of the strain aue

becomes a measure of a##lied force"

The main #arts of the strain aue load cell are as follows" They are acylinder made u# of steel on which four identical strain aue are

mounted and out of four strain aues, two of them 9-/ and -:; aremounted alon the direction of the a##lied load9!ertical aues;" Theother two strain aues 9-< and -= 6ori.ontal aues; are mountedcircumferentially at riht anles to aues -/ and -:"


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!eration of strain gauge Load cell

Case "

+hen there is no load 9force; on the steel cylinder, all the four aues willha!e the same resistance" As the terminals $ and P are at the same #otential,the wheat stone bride is balanced and hence the out#ut !oltae will be .ero"

Case #

$ow the load 9force; to be measured 9say com#ression force; is a##lied onthe steel cylinder" >ue to this, the !ertical aues -/ and -: will under ocom#ression and hence there will be a decrease in resistance"

At the same time, the hori.ontal aues -< and -= will under o tension andthere will be an increase in resistance" Thus when strained, the resistance of

the !arious aues chane"$ow the terminal $ and P will be at different #otential and the chane in

out#ut !oltae due to the a##lied load 9force; becomes a measure of thea##lied load force when calibrated"


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Force 4alculation

&a t

P vP

AE AE e e= =-

31

1 3

g a

R R S

R R e

DD= =

2 4

2 4

g t

R R S

R R e

D D= =

Where: A is the cross-sectional area

E is the modulus of elasticity

v is Poissin’s ratio of the material

S is a aue factor

g S P

AE =

g vS P

AE =

!1 "

2

g s

o

S P v V V

AE

+=

#S

#$


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Advantages of Load cell -ued and com#act construction$o mo!in #arts4an be used for static and dynamic

loadin6ihly Accurate +ide rane of measurement4an be used for static and dynamicloadin

$isadvantages of Load cellMountin is difficult4alibration is a tedious #rocedure"

Selection of load Cell(elow are some of the im#ortant#arameters that need to be considered while selectin the load cell"Si.e Accuracy +eiht rane8#eratin tem#erature>uration of measurements

Mountin8ut#ut ty#e4ost>irection of loadinTy#e of load cell


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Torque:

%orces that cause e&tended o'(ects

to rotate are associated

)ith tor*ues+ ,athematically the

tor*ue on a .article is defined as

the cross-.roduct:

Where

is the .article/s .osition

vector relative to a .ivot+

is the force actin on the

.article+

r

F


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Torque Measurement Methods

Torque may be measured by the followinmethods' ?ra!ity (alance Method

Mechanical Torsion Meter 8#tical Torsion Meter

*lectrical Torsion Meter

Strain aue Torsion Meter


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8#tical Torsion Meter

>ue to torque, an anular twist 9anular dis#lacement;occurs on the shaft between its ends" This anle of twist ismeasured by usin o#tical means where in anulardeflection of liht rays is #ro#ortional to twist and hence

the torque"The main #arts of an o#tical torsion meter as follows'

A shaft is used on which two castin M and $ are connected at a nowndistance"

A tension stri# linin the two castins"

Two mirrors which are fitted and alined on the castins"

A liht beam fallin on the mirrors, an o#tical system and a torquecalibrated scale"


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!eration of otical torsion meter

+hen the shaft is transmittin torque, a relati!e mo!ement occurs between castins M and $, and due to this, the mirrors will chane#osition 9 #artial inclination between the two mirrors; since theyare attached to the castins"

As the mirrors are constantly made to reflect a liht beam on thetorque calibrated scale, due to the chaned #osition of the mirrors,there will be an anular deflection of the liht rays which ismeasured from the calibrated scale"

This anular deflection of the liht rays is #ro#ortional to the twist

on the shaft 9relati!e mo!ement of castin M and $; and hence thetorque of the shaft"

Alications of otical torsion meter It is used in steam turbines and I"4 enines


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*lectrical Torsion meter

>ue to the a##lied torque, there is a relati!edis#lacement between the two slotted discs"

>ue to this relati!e dis#lacement of the slotted discs,

a #hase shift eists between the #ulse enerated bythe transducers"

+hen these #ulses are connected to an electronicunit, it will show a time la#se between the two

#ulses"This time la#se between the two #ulses is

#ro#ortional to the twist of the shaft and the torqueof the shaft"


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$escrition of %lectrical orsion Meter

The main #arts of anelectrical torsion meterare as follows' A shaft connected

between a dri!in enineand a dri!en load"

Two slotted discsattached on either side ofthe shaft"

Transducer 9manetic or#hoto electric ; to count#ulses from the slotteddisc"


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!eration of %lectrical orsion Meter

The teeth #roduce !oltae #ulses in the transducers"

+hen torque is not a##lied on the shaft, the teeth of the both thediscs #erfectly alin with each other and hence the !oltae #ulses#roduced in the transducers will ha!e .ero time difference"

(ut when torque is a##lied on the shaft, there is a relati!edis#lacement of the slotted discs due to twist e#erienced by theshaft and hence the teeth of both the discs will not alin witheach other and hence the !oltae #ulses #roduced in thetransducer will ha!e a time difference 9that is , time la#se;"

This time la#se between the #ulses of the two discs is#ro#ortional to the twist of the shaft and hence the torque of theshaft"

A measure of this time la#se becomes of torque when calibrated"


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Strain ?aue Torsion Meter

4onstruction' Four bonded wire strain aues are mounted on a:0@ heli with the

ais of rotation and are #laced in #airs diametrically o##osite"

+hen the aues are accurately #laced and ha!e matchedcharacteristics, the system is tem#erature com#ensated and insensiti!eto bendin and thrust or #ull effects"

Any chane in the aue circuit then results only from torsionaldeflection"

+orin'

+hen the shaft is under torsion, aues / and : will elongate as a result ofthe tensile com#onent of a #ure shear stress on one diaonal ais, while <and = will contract due to com#ressi!e com#onent on the diaonal ais"These tensile and com#ressi!e #rinci#al strains can be measured and henceshaft torque calculated"


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Ad!antaes & 3imitations

Fully tem#erature com#ensated"

?i!es the maimum sensiti!ity for a i!en torque"

Pro!ides automatic com#ensation for bendin and

aial loads"The main limitation associated is the connection of

the bride to its #ower source and dis#layarranement"

?ood results from the strain aue method area!ailable only when the shaft e#eriences sufficientstrain to #roduce a measurable out#ut sinal"


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Shaft Power Measurement 9>ynamometers;

A dynamometer is an instrument for measurinthe #ower eerted by a source or the amount of#ower consumed by a load"

The dynamometers are classified as follows' A'sortion $ynamometer( It wors on the #rinci#le that

the #ower measured is con!erted in to heat by friction or othermeans" The #ower absorbed is lost as heat and dissi#ated tosurroundins"

Mechanical (raes' #rony braes -o#e (raes"

6ydraulic or fluid friction braes

*ddy current >ynamometer"


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ransmission $ynamometer( They wor on the#rinci#le that the #ower bein transmitted either to or fromdynamometer is not absorbed or dissi#ated" Aftermeasurin the enery is con!eyed to surroundins in a

useful mechanical or electrical form" Torsion and belt dynamometer"

*#icyclic train dynamometer"

Strain aue dynamometer"

$riving $ynamometers( these instruments #ower andalso su##ly enery to o#erate the tested de!ices"

*lectrical 4radled >ynamometer


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Prony (rae >ynamometer

Two wooden blocs are mounted diametrically o##osite on a flywheelattached to the rotatin shaft whose #ower is to be measured"

8ne bloc carries a le!er arm, and an arranement is #ro!ided totihten the ro#e which is connected to the arm" The ro#e is tihtened soas to increase the frictional resistance between the blocs and the

flywheel" The torque eerted by the #rony brae is"

T B F"3

where force F is measured by conventional force measuringinstruments, like balances or load cells etc" The #ower dissi#ated in the brae is calculated by the followin equation"

where force F is in Newton's, L is the length of lever arm in meters, N

is the angular speed in re!olution #er minute, and in watts!


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+hen the brae is to be o#erated the lon end of le!er is loaded with weihts and nuts are tihtened until the enine shaft runs at constants#eed and the le!er is in hori.ontal #osition"

Cnder this condition the moment due to weiht + must balance the

moment of frictional resistance between the blocs and #ulley" +hen the dri!in torque is not uniform the dynamometer is subjected to

se!ere oscillations"

Wor0 done in one revolution

1 2or*ue 3 Anle turned in radians

1 T × 2π N-m

∴ Wor0 done .er minute 1 T ×2πN N-m

We 0no) that 'ra0e .o)er of the

enine


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The #rony brae is ine#ensi!e, but it is difficult to adjust andmaintain a s#ecific load"

Limitation ( The #rony brae is inherently unstable" Its ca#acity islimited by the followin factors"

i; >ue to wear of the wooden blocs, the coefficient of friction !aries between the blocs and the flywheel" This requires continuoustihtenin of clam#" Therefore, the system becomes unsuitable formeasurement of lare #owers es#ecially when used for lon #eriods"

ii; The use of #rony brae results in ecessi!e tem#erature rise whichresults in decrease in coefficient of friction leadin to brae failure"In order to limit the tem#erature rise, coolin is required" This isdone by runnin water into the hollow channel of the flywheel"

iii; +hen the machine torque is not constant, the measurin

arranement is subjected to oscillations" There may be chanes incoefficient of friction and hence the readin of force F may bedifficult to tae"


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-o#e brae dynamometer

It is another form of absor#tion ty#e dynamometer which is mostcommonly used for measurin the brae #ower of the enine"

It consists of one, two or more ro#es wound around the flywheel orrim of a #ulley fied riidly to the shaft of an enine" The u##er end

of the ro#es is attached to a s#rin balance while the lower end ofthe ro#es is e#t in #osition by a##lyin a dead weiht as shown inFi"

In order to #re!ent the sli##in of the ro#e o!er the flywheel, wooden blocs are #laced at inter!als around the circumference of

the flywheel" In the o#eration of the brae, the enine is made to run at a

constant s#eed" The frictional torque, due to the ro#e, must beequal to the torque bein transmitted by the enine"


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3et " # $ead load in newtons,

% # %pring balance reading in newtons,

$ # $iameter of the wheel in metres,

d # diameter of rope in metres, and

N # %peed of the engine shaft in r!p!m! ∴$et load on the brae B 9" & % N

+e now that distance mo!ed in one re!olution B D9 $( dm

∴ +or done #er re!olution B 9" ) % * +$ ( d Nm

and wor done #er minute B 9" ) % *+$ ( d N Nm

∴ (rae #ower of the enine,


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Fluid friction 96ydraulic; >ynamometer

This ty#e of dynamometer uses fluid friction rather than dryfriction for dissi#atin the in#ut enery"

)ater vortex dynamometer( It consists of a rotatin discand a stationary casin" The rotatin disc is eyed to the dri!in

shaft of the #rime mo!er and it re!ol!es inside the stationarycasin"

The casin is mounted on anti friction bearins and has a braearm and a balance system attached to it" The casin is in twohal!es, one of which is #laced on either side of the rotatin disc"

Semi elli#tical recesses in the casin match with thecorres#ondin roo!es in the rotatin disc to form chambersthrouh which a stream of water flow is maintained"


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+hile the brae is o#eratin the water follows a helical #ath in thechamber, consequently the !ortices and eddy currents are setu# in water and these tend to turn the dynamometer casin in the directionof rotation of shaft" This tendency is o##osed by the brae arm and

balance system due to which torque is measured" The control of the brain action is carried out by !aryin either the

quantity of water or its #ressure or the distance between the rotatindisc and the stationary casin"


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Advantages( In addition to brain action, the constant su##ly of

water is #ro!ides coolin effect"

6ih absor#tion ca#acity at low cost and in a small s#ace" (y #ro!idin a dash 5#ot dam#er system it is #ossible to

ha!e #rotection from huntin effects"


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*ddy 4urrent >ynamometer

It o#erates on the #rinci#le that when an isolated conductor cuts acrossmanetic flu, !oltae is induced and local currents called eddy currents flowin a short circular #ath within the conductor" These eddy current etsdissi#ated in the form of heat"

It consists of a toothed steel rotor mounted on the shaft of test enine, it

rotates inside a smooth bared cast iron stator the clearance between thestator and motor bein !ery small" The stator carries an ecitin coil which iseneri.ed by >4 su##ly from an eternal source"

The stator is cradled on antifriction bearins and is #ro!ided with a brae armto which is attached a s#rin balance or a scale #an"

+hen the dynamo is o#erated the rotor turns and chanes a constant chanein flu density an all stator #oints" 4onsequently eddy currents are induced

which o##ose the rotation of rotor"

The moment of resistance is measured by the brae arm and then torque andshaft #ower may be calculated"


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Csual #ower limitB =@@6"PCsual S#eed limitB

E@@@-PM

Advantages(

?ood control at lowers#eeds"

4om#arati!ely small si.e fora i!en ca#acity"

Suitable for hiher s#eed

rane"


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Vibration Measurement *i'ration is a mechanical #henomenon whereby oscillations occur about

an equilibrium #oint" The oscillations may be #eriodic such as the motion ofa #endulum or random such as the mo!ement of a tire on a ra!el road"

yes of vi'ration

Free vi'ration occurs when a mechanical system is set off with an initialin#ut and then allowed to !ibrate freely" *am#les of this ty#e of !ibrationare #ullin a child bac on a swin The mechanical system will then !ibrateat one or more of its natural frequency and dam# down to .ero"

Forced vi'ration is when a time7!aryin disturbance 9load, dis#lacementor !elocity; is a##lied to a mechanical system" The disturbance can be a#eriodic, steady7state in#ut, a transient in#ut, or a random in#ut" The#eriodic in#ut can be a harmonic or a non7harmonic disturbance" *am#les

of these ty#es of !ibration include a shain washin machine due to animbalance, trans#ortation !ibration 9caused by truc enine, s#rins, road,etc";"


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+hy do we want to measure !ibrationG

Seismology( Vibrations caused by earthquaes andother natural #henomena can ha!e a #rofound effecton the world"

Mac+inery( Vibrations caused by badly balancedrotatin equi#ment or friction is a waste of eneryand #otentially destructi!e"

Sound( 3are sound #ressures can be damain

and sound is often #roduced by machinery !ibrationso can re#resent a sim#ler means of measurin

!ibration of an object"


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Vibration can be indicati!e of

*cessi!e wear of bearins or shafts of rotatinequi#ment"

Imbalance of rotatin equi#ment"

*cessi!e friction"

Machine not worin at rated s#eedsHo!erworin"

*arthquae"""


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Seismic Instrument

In !ibration analysis of a mechanical system, it is required to measure thedis#lacement, !elocity and acceleration com#onents of a system"

An instrument, which is used to measure these #arameters, is referred as !ibrationmeasurin instrument or seismic instrument"

The major requirement of a seismic instrument is to indicate an out#ut, whichre#resents an in#ut such as the dis#lacement am#litude, !elocity or acceleration of

a !ibratin system as close as #ossible" mseismic mass

cdamping coefficient of seismic

unit

-stiffness of spring used in

seismic unit .absolute displacement of seismic mass

ybase e.citation +assume %/0

1#+.y displacement of seismic mass


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A ty#ical seismic instrument consists of a massconnected throuh a #arallel s#rin and dam#erarranement to housin frame"

The frame is attached to the !ibration source to bemeasured" Vibrational motion is measured as therelati!e dis#lacement between the mass and thehousin frame"

This dis#lacement is measured by an a##ro#riatetransducer, some eam#les include linear !ariabledifferential transformers 93V>T;, strain aues andPie.oelectric crystal"


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Seismic instruments are used to measure the dis#lacement, !elocity and acceleration com#onents of a !ibratory system"

(asic theory of Seismic instruments is based on forced

!ibration considerin the !ibratory system under baseecitation" A sinle Seismic instrument can be sued as !ibrometer, !elometrer and accelerometer usin suitablecalibration"

$islacement measuring instrument ,*i'rometer- It is an instrument used to measure the dis#lacement of a !ibratin

system"

Acceleration measuring instrument

,Accelerometer- It is an instrument used to measure the acceleration of a !ibratin

system"


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From the stand#oint of instrument construction we need to select the masses and s#rins

accordin to the ty#es and frequencies we wishto measure For am#litude measurement we require a low

natural frequency" This is achie!ed with a soft

s#rin and a lare mass" For acceleration measurements we require a

hih natural frequency" +hich is a achie!ed with a stiff s#rin and a small mass


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Accelerometer

An accelerometer is a de!ice that measures the !ibration, or acceleration of motion of a structure"

The force caused by !ibration or a chane in

motion 9acceleration; causes the mass to squee.ethe #ie.oelectric material which #roduces anelectrical chare that is #ro#ortional to the forceeerted u#on it"

Since the chare is #ro#ortional to the force, andthe mass is a constant, then the chare is also#ro#ortional to the acceleration"


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Pie.o *lectric Accelerometer

The #ie.oelectric effect #roduces an o##osed accumulation of chared#articles on the crystal" This chare is #ro#ortional to a##lied force orstress" A force a##lied to a quart. crystal lattice structure altersalinment of #ositi!e and neati!e ions, which results in anaccumulation of these chared ions on o##osed surfaces"

In an accelerometer, the stress on the crystals occurs as a result of theseismic mass im#osin a force on the crystal" 8!er its s#ecifiedfrequency rane, this structure a##roimately obeys $ewton%s law ofmotion, FBma"

Therefore, the total amount of accumulated chare is #ro#ortional to

the a##lied force, and the a##lied force is #ro#ortional to acceleration"*lectrodes collect and wires transmit the chare to a sinal conditioner

that may be remote or built into the accelerometer"


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Seismic >is#lacement Sensin Accelerometer

+hen a s#rin 5 mass 5 dam#er system is subjected toacceleration, the mass is dis#laced, and this dis#lacement of themass is #ro#ortional to the acceleration" 6ence a measure ofdis#lacement of the mass becomes a measure of acceleration"

!eration The accelerometer is fitted on to the structure whose acceleration is to be

measured"

>ue the acceleration, the seismic mass e#erience a dis#lacement and thisdis#lacement of the mass is #ro#ortional to the acceleration"

As the mass is connected to an electric dis#lacement transducer, the out#utof the transducer de#ends on the etent 5 to which the mass is dis#laced"

6ence the out#ut of the transducer is calibrated to i!e a direct indicationof the acceleration characteristics of the structure"


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-eed ty#e Vibrometer

The !ariable7lenth reed !ibrometer shown in Fiure isused to measure the main frequency com#onent of the !ibration"

In #ractice the lenth l is ad2usted until the ma.imum reed

vibration occurs, when its resonant frequency is the sameas the frequency of the !ibratin mechanism or structure"

The lenth l is calibrated directly in /1! 3 small mass maybe added to the cantilever if the !ibrometer is to be used for

!ery7low frequency in!estiation, but the scale readins would then need to be corrected for the additional mass"

The rane of measurement is quoted as 0 6. to /@6."


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Force Torque Shaftpower Vibration

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