mechanical vibrations lab manual

8/9/2019 Mechanical Vibrations Lab Manual

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Mechanic

alVibrations

Mte-321l

Tahir HasanInstitute of MechatronicsEngineering, UET,Peshawar12PWMT!1"#

lass $ !%Instructor& 'ir (ai)Muha**a+


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ab $ 1aout of Mechanical Vibrations

ab.

Objectives: The basic ob/ecti0e of this lab is to gain nowle+ge about +ierent in+s of

aaratus that are resent in the Mechanical Vibrations lab. 4 brief +escrition an+

alication of each instru*ent is shown.

• Free Vibration Apparatus:

Vibrations are a *a/or art of the real worl+. There are0ibrations in *an of the hsical heno*enon we see

for e5a*le a car engine, a hanging bri+ge or e0en our

0oice is trans*itte+ in the for* of 0ibrations. The free

0ibration aaratus is use+ to 0isuali)e free 0ibrations.

It consists of a sring *ass sste* an+ a +a*er. The

whole asse*bl is calle+ a free 0ibration aaratus

because no e5ternal force is alie+ +uring the 0ibration. The e5citation force is /ust

ro0i+e+ once an+ then its resonse is lotte+.

It can be use+ to erfor* a nu*ber of e5eri*ents such as +eter*ining the

+a*ing in a sste*, in0estigating the nature of 0ibration, 6n+ing the +a*ing

coe7cient an+ *an *ore.

• Forced Vibration Apparatus:4 force+ 0ibration aaratus is the sa*e as a free

0ibration aaratus but it is use+ to +e*onstrate

the force+ 0ibrations. It consists of a *otor an+ a

sring *ass sste* that causes force+ oscillations

of so*e fre8uenc, which is in the control of the

user. 4 0ertical bar is attache+ to the *otor 0ia asring. When the *otor rotates the 0ertical bar

oscillates an+ ro+uces force+ oscillations.

4 +a*ing sste* is also resent in this aaratus. 9a*er is use+ as an energ

absorbent in the 0ibrating sste*. The +a*ing of the 0ibration can also be 0arie+

using a nob on to of it.


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• Torsional Vibration

Apparatus: This e5eri*ental unit is use+ to

e5lain torsion an+ torsional 0ibration

in e5eri*ents. The core of the

e5eri*ent is a *etal torsion bar. With

the ai+ of chucs, *ass +iscs of 0aring inertia can be attache+ to the bar. It this

wa it is ossible to asse*ble torsional 0ibrator sste*s with u to three *asses.

Vibrations can be in+uce+ on the sste* using an electrical e5citer sulie+ fro*

the control unit. 4n a+/ustable +a*er can be use+ to in:uence the 0ibrations. 'haftenco+ers on the chucs ro0i+e the a*litu+e of 0ibration as an electrical signal.

The control unit con+itions these signals an+

*aes the* a0ailable

• Static and Dynamic

Balancing Apparatus: The *ain ele*ent of the bench to unit is a

s*ooth shaft to which four 0ariable unbalance

weights can be attache+ at an angle or+istance. The rotor is suorte+ hori)ontall in

ball bearings an+ is +ri0en b a see+-

controlle+ *otor. The see+ is *easure+

electronicall an+ shown on a +igital +isla. (or +eter*ination of the unbalance

weight b *easuring the balance of *o*ents the +ri0ing belt can be re*o0e+.

Using +ierent weights +ragging on the ulle +e6ne+ *o*ents can be e5erte+ to

the shaft. The can be co*are+ with those cause+ b the unbalance weights when

rotating. The transarent hoo+ re0ents contact with the rotating arts an+

ro0i+es a goo+ 0iew of the rotor. (astening of the

suorting base with elastic ele*ents neutrali)esun+esirable 0ibrations.

• Inverted Pendulum Trainer:In0erte+ en+ulu* sste* is a nonlinear

unstable sste*, an i+eal e5eri*ent latfor* for

teaching control theories an+ con+ucting 0arious


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control e5eri*ents. Man abstract control concets, such as the stabilit an+ the

controllabilit of a control sste*, can all be shown 0isuall through the in0erte+

en+ulu* sste*. In a++ition to e+ucational uroses, an in0erte+ en+ulu* is also

a research area for *an researchers of *o+ern control theories. Through the

continuous research on new was of controlling in0erte+ en+ulu*, researchers

ha0e +e0eloe+ new control *etho+s, an+ al the* to the high tech areas suchas aeronautical engineering and robotics, thans to the characteristics of the

sste*, such as high-or+er, instabilit *ulti-

0ariables, non-linearit an+ strong couling.

• yroscope:;roscoe is a +e0ice for *easuring or

*aintaining orientation, base+ on the

rinciles of angular *o*entu*. Mechanical

groscoes ticall co*rise a sinningwheel or +isc in which the a5le is free to

assu*e an orientation. 4lthough the

orientation of the sin a5is changes in

resonse to an e5ternal tor8ue, the a*ount of change an+ the +irection of the

change is less an+ in a +ierent +irection than it woul+ be if the +is were not

sinning.

4lications of groscoes inclu+e inertial na0igation sste*s where *agnetic

co*asses woul+ not wor


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• #$irling o" S$a"t

Apparatus: The *o+es of oscillation an+ resonances of

rotors with continuous *ass +istribution

can be clearl +e*onstrate+ using this

unit. 9ue to the use of thin, elastic rotor shafts *a+e of high-strength steel, the

oscillator heno*ena can be easil un+erstoo+. 4 range of shaft +ia*eters an+ the

free choice of the bearing arrange*ent *ae it ossible to erfor* a wi+e 0arietof e5eri*ents. 4+aters in the bearings co*ensate for +ierent +ia*eters, catch

bearings li*it the a*litu+e of the oscillation. The free+o* of *o0e*ent of the

rotor is assure+ b an elastic couling. 4 a0al rotor with +iscrete *ass +istribution

can be asse*ble+ using a *ass +isc.

• %ompre$ensive Fly #$eel Apparatus:4 :wheel is a rotating *echanical +e0ice that is use+ to store rotational energ.

(lwheels ha0e a signi6cant *o*ent of inertia an+ thus resist changes in

rotational see+. The a*ount of energ store+ in a :wheel is roortional to the

s8uare of its rotational see+. Energ is transferre+ to a :wheel b aling

tor8ue to it, thereb increasing its rotational see+, an+ hence its store+ energ.

on0ersel, a :wheel releases store+ energ b aling tor8ue to a

*echanical loa+, thereb +ecreasing the :wheel>s rotational see+.


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• %entri"ugal Force Apparatus:

This aaratus is use+ to 0erif that centrifugal force 0aries with the s8uare of the

see+, the rotating *ass, an+ the ra+ius of gration. The bench-*ounte+ unit

houses a see+-controlle+ *otor, which carries a hori)ontal asse*bl. Thisasse*bl co*rises a boo* which rotates. The see+ of rotation of the boo* is

+islae+ on the front anel along with the +igital force rea+ing. 4 uni8ue feature is

that all three 0ariables can be set an+ the centrifugal force +irectl rea+ fro* the

+igital force +isla.

Ot$er Apparatus:'o*e other aaratus which are resent are *ass attache+ to sring aaratus,

torsion 0ibration aaratus, connecting ro+s,

co*ressional srings.

4ll of the aaratus are use+ to +e*onstrate the

natural ti*e erio+ an+ fre8uenc of 0ibrations.

?alancing of *asses aaratus is resent which is

use+ to +e*onstrate the heno*enon of balancing of

*asses base+ on the rincile of *o*entu* an+

0ibrations.


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ab $ !2 To 6n+ the @atural (re8uenc an+ti*e erio+ of a Torsional 'ste*.

Apparatus:• Torsional 'ste* or


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Procedure:• Ensure that the aaratus is in e8uilibriu* osition.

• Deset the stowatch to )ero.

• Then al a coule on the circular +is, but be sure that it is in the safe

li*its an+ will not +a*age the aaratus.

• 4s soon as ou release the +is start the sto watch. The +is will start an

oscillator *otions.

• ount the nu*ber of oscillations an+ the ti*e taen to co*lete the

oscillations.

• @ow bring the aaratus to rest again, an+ al a coule on the +is. @ow

again count the oscillations an+ the ti*e taen to co*lete the oscillations.

• Deeat these stes 3 to C ti*es.

Observations and %alculations:

&at$ematical Formulation:

W n=√

K T

I

W n A natural (re8uenc

K T =GJ

L

; A oungs *o+ulus

F A G+232


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2+¿ f 3

f ¿3¿

avg=¿¿

f ¿

Time period ' ()" avg '

ab $ !3

9eter*ine the ti*e erio+ an+natural fre8uenc of *assattache+ to sring

Apparatus:• Mass string sste*

• 'to watch

T$eory:Mass attache+ to sring is the si*lest for* of a en+ulu*. The string use+ is an

ine5tensible one. When so*e e5citation is gi0en to the *ass in articular +irection it

oscillates about its *ean osition. These oscillations are erio+ic an+ are calle+ as

0ibrations. The *ass string sste* can be oerate+ in three *o+es. In 6rst *o+e it


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0ibrates fro* left to right. In the secon+ *o+e its 0ibrations are torsional in nature,

while it the thir+ *o+e it 0ibrates in to an+ fro *anner.

Procedure:

• Ensure that the aaratus is in its e8uilibriu* osition• Deset the stowatch

• @ow +islace the aaratus towar+s an e5tre*e osition i.e. left or right.

• @ow as soon as ou release the aaratus start the sto watch.

• ount the nu*ber of oscillations it *aes an+ the ti*e taen to *ae those

oscillations.

• @ow again bring the aaratus to rest an+ reeat the abo0e stes, 3 ti*es.

&ode *:

• To oerate in *o+e 2 the *ass is sub/ecte+ to a coule.

• When the force is release+ the *ass starts to oscillate in a torsional *anner.

• The sa*e roce+ure is reeate+ i.e. noting the ti*e erio+ an+ the nu*berof oscillations.

• Deeat the roce+ure 3 ti*es to get an a0erage 0alue.

&ode +:

• The roce+ure is sa*e but the e5citation this ti*e is in an e5tre*e osition

towar+s the bac or forth .

• Ti*e an+ oscillations are note+ to calculate the ti*e erio+ an+ natural

fre8uenc.


• Mo+e 1

s.

no

@u*be

r

f

oscillat

ions

Ti*

e


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s.

no

@u*be

r

f

oscillat

ions

Ti*

e


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Apparatus:• (ree 0ibration aaratus

• 'to watch

• Masses

• ;rah aer

• Pencil

T$eory:(ree 0ibrations are the te of 0ibrations in

which e5citation force is ro0i+e+ once an+

then re*o0e+. The 0ibrations +een+ uon

the *ass an+ the sring constant. There is a

+a*er also resent +ue to which there

e5ists a logarith*ic +ecre*ent in the

0ibration an+ with the assage of ti*e thea*litu+e beco*es )ero.

Procedure:• ut a longitu+inal sheet of grah

aer an+ wra it aroun+ the roller on

the aaratus. Put a encil or a en to

note the resonse of the 0ibration.

• @e5t a++ *asses to the aaratuss ro0i+e+ slots for *asses.

• n the +a*er bloc there is a screw which can be use+ to increase or

+ecrease the +a*ing in the sste*

• @ow gi0e +e:ection to the sli+er of the aaratus, as soon as ou gi0e

+e:ection start the *otor.

• 4t the sa*e ti*e start the sto watch to *easure the ti*e taen for

oscillations, an+ count the nu*ber of oscillations also.

• When the a*litu+e of 0ibration beco*es )ero, sto the *otor.

• @ow a++ *ore weights an+ reeat the abo0e stes.

• Each ti*e ou see the resonse on the grah aer ou will notice a change

in the a*litu+e of the 0ibration.

• This change in a*litu+e is +ue to the change of *asses in the sste*,

which can ro0e the fact that *asses eect the 0ibrations.


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ab $ !%?alancing of unbalance+ *asses

using balancing *achine.

Apparatus:• ?alancing *achine aaratus

• Masses

T$eory:

The aaratus consists of eccentric +is of nown *asses attache+ to a hori)ontal

shaft. The shaft is connecte+ to outut of a *otor through a J0ee beltK. There are

slots ro0i+es on the +iss to ass *asses to the*. In a balance+ con+ition there is aless 0ibration while in an unbalance+ con+ition there is a huge a*ount of 0ibration.

Procedure:

• 9isconnect the *otor fro* ower outlet to eli*inate the +anger of an electric

shoc.

• @ow a++ *asses to the eccentric +iss, two *asses are a++e+ on a nown

angle an+ the other two are a++e+ in unnown ositions at constant ra+ii

+iss.

• The *asses are tightene+ carefull to a0oi+ sliage +uring oeration.

• When the *otor is turne+ on the shaft start to rotate an+ there is a large

a*litu+e of 0ibration +ue to unbalance+ *asses.• If the *achine is oerate+ in balance+ con+ition there will be *ini*u*

0ibration.

• The angles of two *asses are nown an+ two are et unnown an+

+eter*ine+.

• When the unnown angles are foun+ out the *asses are lace+ at those

angles an+ it is obser0e+ that the a*litu+e of 0ibration now +ecreases to a

*ini*u* le0el.

Observations and %alculations:Place Mass


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ab $ ! To balance unbalance+ *assesusing static an+ +na*icbalancing aaratus.

Apparatus:

• 'tatic an+ +na*ic balancing aaratus

• 4llen e

• Masses

T$eory: The *ain ele*ent of the bench to unit is a s*ooth shaft to which four 0ariable

unbalance weights can be attache+ at an angle or +istance. The rotor is suorte+

hori)ontall in ball bearings an+ is +ri0en b a see+-controlle+ *otor. The see+ is

*easure+ electronicall an+ shown on a +igital +isla. (or +eter*ination of theunbalance weight b *easuring the balance of *o*ents the +ri0ing belt can be

re*o0e+. Using +ierent weights +ragging on the ulle +e6ne+ *o*ents can be

e5erte+ to the shaft. The can be co*are+ with those cause+ b the unbalance

weights when rotating. The transarent hoo+ re0ents contact with the rotating

arts an+ ro0i+es a goo+ 0iew of the rotor. (astening of the suorting base with

elastic ele*ents neutrali)es un+esirable 0ibrations.

Procedure:

• 9isconnect the aaratus fro* ower sul.

• @ow re*o0e the transarent to, an+ on the shaft there are rectangular

blocs in which *asses can be attache+.• The rectangles can rotate as well as the can sli+e on the shaft.

• To *easure the +istance fro* the *ean osition a 0ertical scale is resent

an+ the to *easure the angle fro* the *ean osition a gra+uate+ +is with

angles is also resent.

• We can a+/ust the angular osition an+ the linear osition to our own +esire.

• Then weights are a++e+ an+ are fastene+ tightl.


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• @ow the to is again lace+ on the aaratus an+ the *otor is starte+.

• The see+ of the *otor can be seen on the +isla unit.

• We can also control the see+ of the *otor.

• In an unbalance+ con+ition there will be a 0ibration in the aaratus.

• This rocess can be use+ to either 6n+ the osition of the unbalance+

*asses, or the unbalance+ *asses the*sel0es, if osition is nown.

Observations and calculations:

Place Mass


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ab $!B To 6n+ the ti*e erio+ an+fre8uenc of an E+ge susen+e+onnecting ro+

Apparatus:

• E+ge susen+e+ connecting ro+

• 'tan+

T$eory: The connecting ro+ or con ro+ connects the iston to the

cran or cranshaft. Together with the cran, the for*

a si*le *echanis* that con0erts recirocating *otion

into rotating *otion. It ser0es as the inter*e+iate

con0ersion +e0ice between two tes of *otion.

Procedure:

• The connecting ro+ is lace+ on the stan+ s*aller en+ uwar+ an+ larger en+

+ownwar+.

• The aaratus is brought into e8uilibriu* osition.

• @ow a s*all angular +islace*ent is gi0en to the ro+ in either +irection.

• @ow start the stowatch to count the ti*e taen to co*lete the oscillations

• This rocess is reeate+ three ti*es.

• @ow the ro+ is lace+ usi+e +own i.e. the larger +ia*eter hole is uwar+s

an+ the other +ownwar+s.

• The sa*e roce+ure is reeate+ for this osition as well an+ the oscillationsan+ ti*e is note+ to calculate the fre8uenc.


'.n

o

@u*ber

of

0ibratio

Ti*e for

oscillatio

ns

(re8uen

c


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19/22

• 4s soon as the a*litu+e beco*es )ero sto the *otor.

• 4++ *ore *ass to the sste* an+ again gi0e +e:ection an+ note the

resonse of the sste* with the hel of a grah aer.

• This rocess can be reeate+ an ti*es with the change of *asses to ensure

there is a change in force which results +islace*ent.



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ab $ !"(in+ the natural ti*e erio+ an+

fre8uenc of a co*rehensi0e:wheel aaratus.

Apparatus:

• o*rehensi0e :wheel aaratus

• 'to watch

T$eory:4 :wheel is a rotating *echanical +e0ice that is use+ to store rotational energ.

(lwheels ha0e a signi6cant *o*ent of inertia an+ thus resist changes in rotational

see+. The a*ount of energ store+ in a :wheel is roortional to the s8uare of its

rotational see+. Energ is transferre+ to a :wheel b aling tor8ue to it,

thereb increasing its rotational see+, an+ hence its store+ energ. on0ersel, a

:wheel releases store+ energ b aling tor8ue to a *echanical loa+, thereb

+ecreasing the :wheel>s rotational see+. o**on uses of a :wheel inclu+e,

ro0i+ing continuous energ when the energ source is +iscontinuous. (or e5a*le,

:wheels are use+ in recirocating engines because the energ source, tor8ue fro*

the engine, is inter*ittent.

Procedure:• Mae sure that the :wheel aaratus is in an e8uilibriu* osition

• @ow reset the sto watch.

• ;i0e a slight +islace*ent to the :wheel an+ release it, an+ at the sa*e

ti*e start the sto watch.

• @ote the nu*ber of oscillations an+ also the ti*e taen to co*lete it.

• @ow again bring the aaratus to rest an+ reeat the abo0e rocess three to

four ti*es an+ *easure ti*e for a seci6c nu*ber of 0ibrations.


'.

n

o

@u*b

er of

oscilla

tions

Ti*e


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22/22

ab $1!9e*onstration an+ use of the

(orce+ Vibration 4aratus.Apparatus:

• (orce+ 0ibration aaratus

• ;rah aer

T$eory: The oscillator consists of a bea* *ounte+ in ball bearings at one en+N a helical

sring is hung on the other en+ of the bea*. The attach*ent of srings, the e5citer

an+ a +a*er to a erforate+ anel er*its a wi+e range of +ierent set-us to be

rero+uce+. Either an unbalance e5citer or a +islace*ent e5citer generate0ibrationsN the fre8uenc of the 0ibrations can be a+/uste+ using the electronic

control unit. The +islace*ent e5citer can be 6tte+ +irectl to the base of the

sring. The 0ibrations can be +a*e+ using the a+/ustable 0iscosit +a*er. To

recor+ 0ibration rocesses o0er ti*e, a *echanical +ru* lotter is inclu+e+.

Procedure:

• 4 grah aer is rolle+ on to the +ru* roller to recor+ the 0ibration.

• @ow the aaratus is connecte+ to a ower sul unit.

• There is a controller resent that controls the see+ of the *otor which

*eans it can control the fre8uenc of 0ibration.• 4 linear +ashot is also resent, with a bolt to 0ar its +a*ing o0er a wi+e

range.

• The +a*ing is re+uce+ to a low 0alue an+ the *otor is turne+ on.

• We will see that the bea* starts to 0ibrate.

• @ow the see+ of the *otor is increase+.

• 4s the see+ of the *otor increases the fre8uenc of 0ibrations also

increases.

• @ow for the secon+ ti*e the +a*ing 0alue is a+/uste+ to a *a5i*u* 0alue.

• 4gain the *otor is starte+ at the sa*e fre8uenc, now we can note that there

is less 0ibration in the bea*.

• The osition of the +a*er can also be 0arie+.• It it is *ore close to the 0ibrating en+ there will be *ore +a*ing an+ less

0ibration, but on the other if it is far awa fro* the 0ibrating en+ the

*agnitu+e of 0ibration will increase.

mechanical vibrations lab manual

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