Balancing by Gaurav Patel

8/14/2019 Balancing by Gaurav Patel

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B L NCINGBy: Gaurav Patel


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Static balance

Topics


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Balancing The technique of designing or modifying

unwanted inertia forces andmomentsof rotating

orreciprocatingmassesinamachinesothatthe

unbalanceisreducedtoanacceptablelevelandif

possible,entirelyeliminated.

Necessity:

Reducesthenegativeeffectsofvibration Increasesservicelifeandeconomyofoperation.


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Benefits of BalancingBalancing

Reduces:

Noise

Vibration

Airframedamage

Avionicsdamage

Fatigue and stress

onpassengers

Increases:

Economyofoperation

Service life of

airframe and

components

Comfort


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Static Balance

When a shaft carries a

number of eccentric

masses and if the sum ofthe moments of all the

masses about the axis of

rotationisequaltoZeroforall angular positions, the

shaftassemblyissaidtobeinStatic Balance


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Static Balance

Consider a light arm pivoted freely at the fulcrumO andcarrying masses m1, m2 at distances r1, r2 from Orespectively.IngeneralthearmwillrotateaboutOandthesystem is said to be outof balance. For equilibrium theremustbebalanceofmomentsaboutO.i.e.

m1gxr1=m2gxr2or

m1r1=m2r2

Wheninbalancethearmmaybesetinanypositionandwillremainatrestinthatposition.Theweightsaresaidtobein

static balance and the center of gravity of the system islocatedatO.

Static balance (two

masses in a plane)


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Static balance (two

masses in a plane)


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Dynamic Balance

Dynamicbalancingisawayofcontrollingvibrationsbyarranging the overall summation of out-of balanceforces and couples cancels out or reduced to more

acceptablevalue

Therearetwogroupsofforcesandcouples-relatedto:

revolving mass reciprocating mass

Rotating mass balance is quite easily obtained bychoiceofcranksequenceandbalanceweight

Reciprocatingmassbalanceismorecomplicated.


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Dynamic BalanceDynamic balance (two

masses in a plane)

NowconsidertwolightarmsfixedtoashaftatbearingOandrotatingwithangularvelocity Thearmsareinthesameplaneandcarrymassesm1,m2atradiir1,r2respectively.OwingtotherotationeachmassesexertsaninertiaforceradiallyoutwardonthebearingO.Theforceduetom1ism1

2

r1(OAintheforcediagram)Theforceduetom2ism22r2(ABintheforcediagram)


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TheresultantoutofbalanceforceonthebearingisgivenbyOBintheforcediagram.

whenthedynamicloadonthebearingiszerothe

rotatingsystemissaidtobeindynamicbalance.TheconditionfornoloadatOisthattwoinertiaforceshall:

1. actalongthesamestraightlinebutwithoppositesense

2. Beequalinmagnitude

therelativepositionsofthemassesareasinthefigureCshownearlier.Theconditionforequalinertiaforcesis:

m12r1=m2

2r2

Thus,since2isthesamebothmasses

m1r1=m2r2

Twobodiesinthesameplaneareinstaticbalancewhenpivotedaboutagivenaxistheywillbeindynamicbalance

atanyspeedwhenrotatingaboutthesameaxis.

Dynamic balance (two

masses in a plane)


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Itwas shownearlier that for a twomass system to be instaticbalancethemrproductforeachmasshadtobethesame. This is also the condition for the masses to bebalancedwhenrotatingandsuggestsamethodforensuringbalance for rotating rotors such as turbine disks or carwheelassemblies.

Method of

balancing

Rotors Method of Balancing Rotors


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CentrifugalForce

When a mass rotates in a circle, centripetal forceactsonit,whichistowardsthecenterofthecircle

AccordingtoNewtons3rd

Law,centrifugalforceactsonthemassintheoppositedirectioni.e.awayfrom

thecenterofthecircle

Both these forces are same in magnitude. Thatkeepsthemassrotatinginthecircle


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Forcesonamassrotatinginacircle


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CentrifugalForce

CentripetalForce=mv2/r

CentrifugalForce=-mv2/ r

Replacinglinearvelocitybyangularvelocity:

Centrifugal Force = - m2r


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Imbalance

Theeffectofthecentrifugalforceistobendtheshaft

with which the mass is attached, and hence to

produceunwantedvibrationsintheshaft

This creates imbalance in thewholesystem


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Balancing

In order to balanceout the imbalanceproduced bythecentrifugalforceofthedisturbingmass,another

massisattachedtotheshaftinsuchawaythatthe

centrifugal force of this mass (balancing mass)

cancels out the effects of the centrifugal forceproducedbythedisturbingmass


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CasesofBalancing

Balancingofasinglemassbyasinglemassinthe

sameplane

Balancing of a single mass by two masses in

differentplanes

Balancingofseveralmassesindifferentplanes


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SamePlanes


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DifferentPlanes


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masses in a plane) Case:1

Balancingofasinglerotatingmassbyasinglemassrotatinginthesameplane


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masses in a plane)

Fc1=(W1/g)2r1

Fc2=(W2/g)2r2

For a balancedsystem, the

centrifugal force of

W1shouldbeequalto

the centrifugal forceofW2.Hence:

W1r1=W2r2


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masses in a plane)

Fc1=(W1/g)2r1

Fc2=(W2/g)2r2

Forabalancedsystem,thecentrifugalforceof

W1shouldbeequalto

thecentrifugalforceof

W2.Hence:

W1r1=W2r2


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Case:2

Balancing of a single rotating mass by two

massesrotatingindifferentplanes

Thiscasehasfurthertwopossibilities

(a) When the disturbing mass is in the

middleofthebalancingmasses

(b) Whenthedisturbingmassisononeside

ofthebalancingmasses


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Possibility:1

Whentheplaneofthedisturbingmasslieinbetweentheplanesoftwobalancingmasses


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ForStaticbalancing:

Fc=Fc1+Fc2

Wr=W1r1+W2r2

For Dynamic balancing, taking plane M as

reference:

Fc1 * l = Fc * l2

W1 * r1= (W * r * l2) / l


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Possibility:2 Whentheplaneofthedisturbingmassliesonone

endoftheplanesofthetwobalancingmasses


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For Static balancing:

Fc1= Fc2 + Fc

W1r1= W2r2+ Wr

For Dynamic balancing, taking plane M as

reference:

Fc1 * l = Fc * l2

W1 * r1= (W * r * l2) / l


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Case:3

Balancingofseveralmassesrotatinginthesameplane


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AnalyticalSolution

Fcx=W1r1Cos1+W2r2Cos2+ ..

Fcy= W1r1Sin1+ W2r2Sin2+ ..

Fc = (Fcx)2+ (Fcy)

2

Fc (balancing) = Fc = (W/g)*2r

tan = Fcy / Fcx

(balancing) = + 180


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GraphicalSolution

First find out the resultant FcwhichisactuallyW*r

The balancing Fc=(W/g)*2r, which

issameinmagnitudebutoppositeindirectiontotheaboveFc

As the balancingweight is attached

onthesameshaft,hence,willbe

thesameforallmasses

Inordertofindoutbalancingweight

W,itsradiusrshouldbeknown


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Thank you

Balancing by Gaurav Patel

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