DR Flywheel

7/25/2019 DR Flywheel

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Department of AutomobileEngineeringPSG College of Technology

2/6/161

Flywheel


2/119


2/6/162

Necessity

In a combution engine! " epeciallyin one #ith one or t#o cylin$er!energy i imparte$ to the cran%haftintermittently! " in or$er to %eep itrotating at a fairly uniform pee$

un$er a ubtantially contant loa$! iti neceary to pro&i$e it #ith a'y#heel(

)ly#heel


3/119


2/6/16*

In a single cylinder engine(4Stroke)! in #hich there i only onepo#er tro%e in t#o re&olution of thecran%haft! a coni$erable fraction of

energy generate$ per cycle i tore$ inthe 'y#heel! " the proportion thutore$ $ecreae #ith an increae in

the +o( of cylin$er In a 4 cylinder engineabout ,-. of

the energy of the cycle i temporarily

tore$(

)ly#heel


4/119


2/6/16,

o#e&er!not all of thi energy goe into'y#heel

During the 1thalf of the po#er tro%e!#hen energy i being upplie$ in e0ceby the burning gae! all of thereciprocating part of the engine arebeing accelerate$ " aborb energy

bei$e! the rotating part other than the'y#heel alo ha&e ome 'y#heelcapacity! " thi re$uce the proportion ofthe energy of the cycle #hich mut be

tore$ in the 'y#heel(

)ly#heel


5/119


2/6/16

In a 6 cylinder enginethe proportion ofthe energy #hich mut be aborbe$ "returne$ by the mo&ing part amount to

about 2-.(

The greater the No. of cylinders thesmaller the ywheel capacity

re!ired per !nit of pistondisplacement! becaue the o&erlap ofpo#er tro%e i greater " bei$e other

rotating part of the engine ha&e greater

)ly#heel


6/119


2/6/166

o#e&er! the 'y#heel ha by far thegreatet inertia e&en in a multi cylin$erengine(

"side from its principle f!nction#the y wheel ser$es as a mem%erof the friction cl!tch# & it !s!allycarries also the ring gear of theelectric starter.

)ly#heel


7/119


2/6/163

)ly#heel


8/119


2/6/164

)ly#heel


9/119


2/6/165

)ly#heel


10/119


2/6/161-

)ly#heel

Energy accumulatorEnergy re$itributor

A 'y#heel er&e a a reser$oir#hich

storesenergy $uring the perio$ #henthe upply of energy i more than there7uirement " releases! it $uring the

perio$ #hen the re7uirement of energy imore than upply(

A 'y#heel help to %eep the cran%haftrotating at a uniform pee$


11/119


2/6/1611

In internal com%!stion engines! the energy i $e&elope$ d!ring one

strokean$ the engine i to run for the#hole cycle on the energy pro$uce$$uring thi one tro%e(

the energy i $e&elope$! only d!ringpower stroke#hich i much more than

the engine loa$ an$ no energy i being$e&elope$ $uring suction! compressionan$ exhaust strokesin cae of , tro%e

engine " $uring compressionin cae of2 tro%e en ine(

)ly#heel


12/119


2/6/1612

The e0ce energy $e&elope$ $uringpo#er tro%e i aborbe$ by the 'y#heelan$ releae it to the cran%haft $uringother tro%e in #hich no energy i

$e&elope$! thu rotating the cran%haftat a uniform pee$(

8hen the 'y#heel aborb energy! it

pee$ increae an$ #hen it releae! thepee$ $ecreae( ence a 'y#heel $oenot maintain a contant pee$! it simplyred!ces the !ct!ation of speed(

)ly#heel


13/119


2/6/161*

The function of a go&ernor in engine i entirely$i9erent from that of a 'y#heel

'o$ernor reg!lates the mean speedofan engine #hen there are &ariation in theloa$!e(g(! #hen the loa$ on the engineincreae it become neceary to increae theupply of 8or%ing 'ui$( :n the other han$!#hen the loa$ $ecreae! le #or%ing 'ui$ ire7uire$(

The go&ernor automatically control theupply! of #or%ing 'ui$ to the engine #ith the&arying loa$ con$ition an$ keeps the meanspeed within certain limits.

)ly#heel


14/119


2/6/161,

The 'y#heel $oe not maintain contantpee$

It imply re$uce the 'uctuation of pee$( " ywheel controls the speed

$ariations ca!sed %y the !ct!ation

of the engine t!rning moment d!ringeach cycle of operation.

It does not control the speed

$ariations ca!sed %y the $arying

)ly#heel


15/119


2/6/161

apacity & iameter

The 'y#heel capacity of a gi&en ma increae#ith it $itance from the a0i of rotation cone7uently! if the 'y#heel i ma$e large in$iameter it nee$ not be o hea&y(

:n the other han$ there are t#o reaon forlimiting the $iameter( At high rpm! 'y#heel i ub;ecte$ to $irupti&e or

burting force! " by %eeping $o#n the $iameter! the) : S can be %ept high(

A it i cat or cat " pree$ teel houing! thinee$ not #eigh o much if the $iameter i maller

)ly#heel


16/119


2/6/1616

)ly#heel

A )ly#heel i gi&en a high rotationalinertia i(e(! mot of it #eight i #ell outfrom the a0i


17/119


2/6/1613

onstr!ction ofFlywheels


18/119


2/6/1614

Contruction of )ly#heel

The 'y#heel of malleri are cate$ in onepiece(

The rim " hub are ;oine$together by mean of #eb(

The hole in the #eb may

be ma$e for han$lingpurpoe(


19/119

Department of Automobile

EngineeringPSG College of Technology

2/6/1615

In cae the 'y#heeli of larger i! the

arm are ma$eintea$ of #eb(

The number of

arm $epen$ uponthe i


20/119



2/6/162-

The split fywheelsareabo&e 2(m$iameter " are uually cate$ in t#opiece(

Itha a$&antage of relie&ing hrin%age

tree in arm $ue to une7ual rate of

Contruction of )ly#heel


21/119



2/6/1621

*a+im!m Fl!ct!ation of Speed

&

oe,cient of Fl!ct!ation of Speed


22/119



2/6/1622

The*a+im!m Fl!ct!ation of Speed

the $i9erence bet#een the ma0imum "

minimum pee$ $uring a cycle( i.e.,=(N

1

-N2

)

8here! +1?@a0imum pee$ in r(p(m( $uring the cycle!

+2?@inimum pee$ in r(p(m( $uring the cycle

The oe,cient of Fl!ct!ation ofSpeedi the ratio of the ma0imum'uctuation of pee$ to the mean pee$(

)ly#heel

)ly#hee


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2/6/162*

( )[ ]

( ) ( )

( )

( ) ( )( )

( )

( ) ( )

( ) ( )

1/CsmSteadinessoftCoefficien

flywheel.ofdesigntheinfactorlimitingaisCThe

....vv

vv2

v

vv

.....

2

NN

NN2

N

NNC

CSpeedofnl!ct!atiotCoefficien

NNmprinSpeed"eanN

s

21

2121

21

2121

21

2121s

s

21

speedslinearoftermsin

speedsang!laroftermsin

==

+

=

=

+==

+

=

=

=

+== 2/

)ly#heel


24/119



2/6/162,

Fl!ct!ation of-nergy

The Fluctuation of Energmaybe $etermine$ by the turningmoment $iagram for one

complete cycle of operation

)l h


25/119



2/6/162

turning momenti


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2/6/1626

#or% $one?turning moment 0 angle turne$ The area of the turning moment $iagram

repreent the #or% $one per re&olution Engine i aume$ to #or% againt the mean

reiting tor7ue! Since it i aume$ that

#or% $one by the turning moment / re&olution? #or% $one againt the mean reiting

tor7ueTherefore!

area of rectangle =aA)e> i proportional to #or%$one againt the mean reiting tor7ue(

)ly#heel

)l h


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2/6/1623

8hen cran% mo&e from !a! to !p!

#or% $one by the engine i ? area a"p,

#herea the energy re7uire$ ? areaa#"p.

In other #or$! the engine ha $one le#or% than the re7uirement( Thi amountof energy i ta%en from the 'y#heel an$hence the pee$ of the 'y#heel$ecreae(

)ly#heel

)l h


28/119



2/6/1624

+o# the

cran% mo&e from p to 7!

#or% $one by the engine ? area pBbC7

re7uirement of energy ? area pBC7 Therefore the engine ha $one more #or%

than the re7uirement(

Thi e0ce #or% i tore$ in the 'y#heelan$ hence the pee$ of the 'y#heelincreae #hile the cran% mo&e from p to 7(

)ly#heel

)l hee


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2/6/1625

Similarly #hen the cran% mo&e from $ to r,more #or% i ta%en from engine than i$e&elope$? area %c.

To upply thi lo! the 'y#heel gi&e upome of it energy an$ thu the pee$$ecreae #hile the cran% mo&e from $ to r.

A the cran% mo&e from r to s,e0ce energy i again $e&elope$ ? area 'E

" the pee$ again increae( A the piton mo&e from s to e,

again there i a lo of #or% " the pee$$ecreae(

)ly#heel

)ly#hee


30/119



2/6/16*-

The &ariation of

energy abo&e an$belo# the meanreiting tor7ueline are calle$!ct!ation ofenergy.

The area "%,

%c, 'E etc(repreent'uctuation ofenergy(

)ly#heel


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2/6/16*1

Engine ha a ma0( pee$ either at 7 or at (

Thi i $ue to the fact that 'y#heel aborb energy#hile the cran% mo&e from p to 7 an$ from r to (

Engine ha a minimum pee$ either at p or at r(

The reaon i that 'y#heel gi&e out ome of itenergy #hen the cran% mo&e from a to p an$ 7 tor(

The $i9erence bet#een the ma0imum an$ theminimum energie i %no#n a ma+im!m!ct!ation of energy.

)ly#hee


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2/6/16*2

)ly#heel

*eanSpeed

*a+im!m

Speed

Speed

rankangle *in.Speed

)ly#hee


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2/6/16**

)ly#heel

The Fl!ct!ation of -nergythe &ariation of

Energy abo&e " belo# mean reiting tor7ueline(

)ly#hee


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2/6/16*,

)or a , Stro%e IC Engine!

During s!ction stroke#ince the pr( ini$e theengine cylin$er i le than the atmopheric pr(! anegati$e loop is formed

During compression stroke#the #or% i $one onthe gae! there ahigher negati$e loop is o%tained

In the working stroke#the fuel burn " the gaee0pan$! therefore a large positi$e loop is formed

During e+ha!st stroke#the #or% i $one on thegae! therefore a negati$e loop is o%tained

)ly#heel


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2/6/16*

*a+im!m Fl!ct!ation of-nergy


36/119



2/6/16*6

*a+im!m

Fl!ct!ation of -nergy


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2/6/16*3

( ) ( )#$211 aaaa%a%&%%nergy'ofnl!ct!atio"a(im!m

ly.respective%)*atis%nergiestheseof"in.)"a(.the+et

,at%nergy

aaaaaa%-at%nergy

aaaaa%at%nergy

aaaa%%at%nergy

aaa%at%nergy

aa%Cat%nergya%*at%nergy

fig.'fromthen%',atflywheelin%nergy+et

0#$21

0#$21

#$21

$21

21

1

+++=

=+++=

+++=++=

++=+= +=

=


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2/6/16*4

oe,cient ofFl!ct!ation of -nergy


39/119



2/6/16*5

( )

( )

( ) ( ) lyrespective%nginesCst.)fornstroes/miworingofNo.

n

345

rad/secin

wattsin45

N26

34cycleperdone7oror

rad/secin

wattsin4

N26

34m8Nintor9!e"eanT)

lyrespective%nginesCst.)for)rad/secint!rned,ngle5where'

%

#2N/2)Nn

#2#626

Tcycleperdone7or

%nergy"in.8%nergy"a(.

cycleperdone7or%nergyofnl!ct!atio"a(.C

rpmin

rpminmean

mean

%

:;Cenergyofnfl!ct!atiooftCoefficien

==

=

=

==

=

==

=

==

==

n

EE

P 60


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2/6/16,-

-nergy stored in aywheel


41/119



2/6/16,1

( ) ( )

==

=

==

===

===

+=+==

2

2121

2121

m)://;:/NN;Ns

:/2;mean:/2'N;Nmean

C

Nwhere'or

s

22C

2

1

2

1


42/119



2/6/16,2

( )

( ) o!tfo!nd>ecant)>'2!s!ally>/tratio>/tetorimofareac/s,ss!ming

densityvol.mrimflywheelof"ass

determined>emayflywheelofmassthisrom

CmvCm?&%

??imofradi!smeangyrationof?adi!s

s

2

s

22

diameter'tocomparedsmallveryisrimofthicness,s

====

==

==

=

=

of rimthicknesswidth & twhere,b

rim.ofareac/sfindmaywethisFrom

neglectedhub & arms& that ofconsideredof rim is

nertiaoment of inly mass mression, ovein the abo

A!

!v

2,

exp

,


43/119



2/6/16,*

-+ample/

E l 1


44/119



2/6/16,,

E0ample1

The turning moment $iagram for a

Petrol engine i $ra#n to follo#ing caleTurning moment! 1 mm ? +m Cran% angle! Imm ? 1

The turning moment $iagram repeat itelf at

e&ery half re&olution of the engine an$ the areaabo&e an$ belo# mean turning moment line!ta%en in or$er are 25! 64! ,-! *,-! 56-! 23-mm2(

etermine the massof *-- mm $iameter

'y#heel rim #hen the coecient of 'uctuationof pee$ i -(*. an$ the engine run at 14--r(p(m((

Alo determine the crosssectionof the rim

#hen the #i$th of the rim i t#ice of thic%ne(Aume $enity of rim material a 32- %g/m*(


45/119



2/6/16,

E0ample1Solution

Gi&enF ? 32- %g/m*

C ? -(*. ?-(--*

D ? *-- mm or ? 1- mm

? -(1 m

+ ?14--r(p(m(

orH ? 2 0 14-- /6- ?144(ra$/

m# %# t 0 1

J E ? IH2C? m(2(H2C

m ? FK

? F(=D(A>? F(=2(A>

A ? b 0 t!

b?2t


46/119



2/6/16,6

*ass of the ywheel (m kg)

A per gi&en cale!on the turning moment $iagram!1 mm2? +m 0 1-? 0=1-0 /14-> ? -(-43

+m

@a0( 'uctuation of energy ? J E ? m(2(H2CLet the total energy at A ? E!from Mg(! Energy at B ? E N 25

Energy at C ? E N 25 64 ? E *5-Energy at D ? E *5- N ,- ? E *-Energy at E ? E *- *,- ? E 65-Energy at ) ? E 65- N 56- ? E N 23-

Energy at G ? E N 23- 23- ?E?Energy at

E0ample1

E l 1


47/119



2/6/16,3

. @a0imum energy ?EN25 at B"

@inimum energy ?E65- at E@a0imum 'uctuation of energy!

i(e( J E ?@a0( energy O @in( energy

?=E N 25> =E 65-> ? 54 mm2

?54 0 -(-43?46 +m

Alo! @a0imum 'uctuation of energy!

i(e( J E ? 46 ?m(2(H2C

?m =-(1>2=144(>2=-(--*> ? 2(,0m

( m 0 263.4 0 5.2 kg777"ns.

E0ample1

E l 1


48/119



2/6/16,4

E0ample1rosssection of the ywheel rim

@a of the 'y#heel rim! m ?Kol( 0 $enity ?=A 0 2> 0F

Let! 8i$th of rim! %0 + t#thic%ne of rim

.Croectional area of rim! A?b 0 t ? 2t 0 t

? 2 t2

ma of the fly#heel rim =m> ? *(4 ? A 0 20F

?2 t22 0 -(1 0 32-

?1*664 t2

( t2?*(4/1*664 ?-(--26

or t 08.8/ m 0 /mm7."ns.

& % 0 t 0 + / 0 /8 mm7."ns.


49/119



2/6/16,5

-+ample

l


50/119



2/6/16-

E0ample2A ingle cylin$er! ingle acting!,

tro%e oil engine $e&elop 2- %8 at*-- r(p(m(

The #or% $one by the gae $uring

e0pan( tro%e i 2(* time the #or% $oneon the gae $uring the compreion an$#or% $one $uring the uction an$ e0haut

tro%e i negligible(The pee$ i to be maintaine$ #ithin

Q1.( etermine the mass moment of

inertiaof the 'y#heel(

l 2


51/119



2/6/161

Sol!tion

Gi&enP ? 2-%8

?2-0 1-*8

+ ?*--r(p(m( or

H?20*--/6-

?*1(,2ra$/C?Q1. or

H1 H2?

Q1.H

E0ample2

J E ?IH2C

E0ample 2


52/119



2/6/162

E0ample2

( )[ ]

( )[ ]

===

=

==

=

==

=

"m/

/nPycledone #er calso, work

8000150601020

60

3

Nm@3336#A$.05ATyclewordone/c

Nm$.0$3326

(31323(

N2

4(3T

engine'>ydtransmittetor9!e"ean

(Cs(%

energy'ofnfl!ct!atio"a(im!m

mean

$

mean

2

inertia'ofmoment"ass

E l 2


53/119



2/6/16*

E0ample2

[ ]( )[ ]

( )

1#13Nm

@333/3.007

3.007

/2.$77@333Nmor77cycleperwordonedoneworNet

stroee(pn.d!ringdonewor7)

stroecomprn.d!ringdonewor7

let'

%

%

%%

C%

%

C

==

==

==

==


54/119



2/6/16,

The #or% $one $uring e0pan( tro%e

i ho#n by triangle ABC in )ig(! in #hichbae AC ? ra$ian " height B) ?Tma0

.8or% $one $uring e0panion tro%e!

8E ?1,16- ?=1/2> Tma0? 1(31

Tma0

:r Tma0

? 1,16-/1(31 ? 5-1* +m

eight abo&e the mean tor7ue line!

BG ? B) )G ? Tma0 Tmean

? 5-1* 6*6( ? 4*36( +m

E0ample2

E0ample 2


55/119



2/6/16

E0ample2

havewe;*-:2'l=%,of,rea

tion'Brel.lgeometricafromtherefore

=

( )

( ) ( )

( )( )( )

( )( )( )

( ) ( ) "$m.%.%/% &E % '(/'&E)lea of *+i.e., are. *.

rad..

-

)mean$-+-A

'F

'(&Eor

'F

'(

A

&Eand 'A,ngles '&Emilar trias, From sias followcalculated*E may bealso,

12230583769222121

922

9013

58376

max

max

====

====

=

===

==

=

Nm122$331$

@$D.01#13T

:T8;T7%&

*

;*-:7

*

;*-:,*C&of,rea%i.e.&

*%:'&of,rea;i.e.energyofnfl!ct!atio"a(.

'*

;*-:

,*C&of,rea

*%&of,rearelation'lgeometricafrom

2

2

2

ma(

2meanma(

%

2

2

%2

2le

le

2

2

le

le

E l 2


56/119



2/6/166

E0ample2

( ) .,ns..........1.0gm#122$3/1.D 21.D#3.32;$1.#2:C122$3i.e.

C&%

%energy'ofnfl!ct!atioma(im!mthatnow7e

.gminflywheeltheofinertiaofmoment"ass+et

3.32

8Cspeed'ofnfl!ct!atiooftcoefficienand

3.32E28speedofnfl!ct!atiototalthereforespeed'meantheof

1Ewithinmaintained>etoisspeedtheSince

2

s

2

s

2

2

21s

21

=====

=

=

==

==


57/119



2/6/163

Stresses in a Flywheel 9im


58/119



2/6/164

Stresses in a Flywheel 9im

A 'y#heel! conit of a rim at #hich ma;orportion of ma or #eight i concentrate$(

)ollo#ing type of tree are in$uce$ in therim

1( Tenile tre $ue to centrifugal force!

2( Tenile ben$ing tre caue$ by theretraint of the arm! an$

*( The hrin%age tree $ue to une7ual rateof cooling of cating( Thi tre i ta%en careof by a factor of afety(

Stresses in a Flywheel


59/119



2/6/165

Stresses in a Flywheel9im

b 0 :idthof rim#

t0Thickness of rim#

A 0 rosssectionalarea ofrim 0 b +

t.

Stree in


60/119



2/6/166-

Stree inim

1( Tensile stress d!e to centrif!gal force

The tenile tre in the rim $ueto the centrifugal force! aumingthat rim i untraine$ by arm! i$etermine$ in a imilar #ay a a

thin cylin$er ub;ecte$ to internal pr((Tensile stress#

>t?F(2(H2 ?F(&2 ...(* = +.)

(hen is in kg/m0an' * is in m/s, then till e inN/m2or a)Note )rom the abo&e e0preion the mean $iameter ()of the 'y#heel may be obtaine$ by uing the relation

v0?DN 3 68

Stree in


61/119



2/6/1661

[ ]

[ ] [ ]

tn

!v.b

v /!)ing+0ubstitut

tn

!1.

bt

n

!!bt

bt

wl

2

3b

==

=

===

2

2

7419

6

2

12

6

12

7419

2

32

2

22

2

2

>Fstress'*endingloaded'!niformlyandends

>othatfi(ed>eamalie>ehavesarmsofpaira>etn.rim

ofportioneachthatass!mptiontheon>asedisarmsof

restraintthetod!erimtheinstress>endingtensileThearmstheofrestraint

>yca!sedstress>endingTensile2.im

Stree in


62/119



2/6/1662

+=

=

+=

+

+=

tn

!v

bt

bt

tn

!v.v

b

t

2

2 935.475.04

1

4

3

,

2

27419

4

12

4

3

'Te(pansion.freefornecessary

amo!nttheof#

$a>o!tstretchflywheelaofarmsThe

Gero.>ewilli.e.'arms'thetod!erestraint

no>ewillthereaction'lcentrif!gatod!erimtheofe(pansion

freeallowtoeno!ghstretchedarearmsifhandothertheHn

Gero>ewilli.e.'rim'instress!psetnotwillforcelcentrif!gathentogether'closeveryplacedare)stretchnotdoarmsf

rimtheinstressotal

rim'theinstresstotalNow

th

im


63/119



2/6/166*

-+ample5

E0ample *


64/119



2/6/166,

E0ample*

A multicylin$er engine i to run at a contant loa$at a pee$ of 6-- r(p(m(:n $ra#ing the cran% e9ort

$iagramto cale of 1 m ? 2- +m an$ 1 mm ? *!The area in mm2abo&e " belo# mean tor7ue lineare N 16-! 132! N 164! 151! N 153! 162 mm2

The pee$ i to be %ept #ithin Q1. of the meanpee$ of the engine( alc!late the necessarymoment of inertia of the ywheel(etermine s!ita%le dimensions for cast ironywheel#ith a rim #hoe brea$th i t#ice it

ra$ial thic%ne( The $enity of cat iron i 32-%g/m*! an$ it #or%ing tre in tenion i 6@Pa(Aume that rim contribute 52. of 'y#heel e9ect(

E0ample *


65/119



2/6/166

E0ample*Sol!tion. Gi&en

N ?6-- r(p(m( orH ?2 0 33/3 ?62(4, ra$/

F ?32- %g/m* Rt?6 @Pa ?6 0 1-6+/m2

J E ? IH2CRt?F($

2

& ? =+>/6-

J E ? m(2(H2Cm ? FK ? F(=D(A>? F(=2(A>A ? %0 t!

b?2t

E0ample *


66/119



2/6/1666

*oment of inertia of the ywheel

8e %no# that!@a0imum 'uctuation of energy! JE?I0H20C

Scale for the turning moment i

1 mm ? 2- +m " cale for the cran%

angle i1 mm ? *? *0/14-? /6- ra$!therefore

1 mm2

on the turning moment $iagram

E0ample*

E0ample*


67/119



2/6/1663

Let total energy at# ? E. .from )ig(!

Energy at " ?E N 16-

Energy at C ?E N 16- 132 ? E 12 Energy at ?E 12 N 164 ?E N 16

Energy at E ?E N 16 151 ?E O * (min. energy)

Energy at F ? E * N 153 ?E N 162 (ma+. energy)

Energy at G ?E N 162 162 ? E ?Energy at#

@a0( 'uctuation of energy!

J E ?@a0( energy O @in( energy

? (E N 162> (E *> ? 153 mm2

J E ?153 0 1*(1?241 +m

E0ample*


68/119



2/6/1664

E0ample*


69/119



2/6/1665

Since the 'uctuation of pee$ iQ1.

of the mean pee$ =H>!therefore total 'uctuation of pee$!

H1H2? 2. H ? -(-2H

" coecient of 'uctuation of pee$!

C?=H1H2>/H ? -(-2

ma0imum 'uctuation of energy! JE!

JE! ? 241 ? I(H2(C? I =62(4,>2-(-2 ?

350I

( I ? 241/35 ? 5.@ kgm

7.."ns

E0ample *

E0ample*


70/119



2/6/163-

imensions of a ywheel rim

8e %no# that! @a of the 'y#heel rim!m ? Kol( 0 $enity ?2 0 A 0 F ? D 0 =b 0 t >0F b?2t =gi&en>

Peripheral &elocity =&> " mean $iameter =D>

8e %no# that! tenile tre! Rt?F(&2

i(e(! Rt?6 0 1-6?F(&2 ?32- &2

So! &2?=6 0 1-6>/32- ?423(6 or $02.@6 m3s

8e alo %no# that! peripheral &elocity!& ?=D+>/6-

i(e(! &?24(36 ? =D+>/6- ? =D06-->/6- ? *1(,2

E0ample *

E0ample*


71/119



2/6/1631

*ass of ywheel rim

Since rim contribute 52. of 'y#heel e9ect!

( Energy of 'y#heel rim! -rim? -(52 0 total Energy ofthe 'y#heel! -

@a0( 'uctuation of energy! JE? E 0 2 C

i(e(! JE ?241 ? E 0 2 C ?E 0 2 0 -(-2 ? -(-, E

( E ? 241/ -(-, ? 6,2 +m" Energy of 'y#heel rim! Erim? -(52 E

=&?H>? -(52 0 6,2 ? 5*6* +m

Alo!Erim? =1/2>IH2? =1/2>m%2H2? =1/2>m2H2 ? =1/2>0m0&2

i(e(! 5*6* ? 1/2 0 m 0 &2? 1/2 0 m =24(36>2? ,1*(6m

( m 0 A56534/5.6 0 /45. kg

p

E0ample*


72/119



2/6/1632

The mass o the fywheel rim may also

be obtained by using ollowing relations(

Since the rim contribute 52. of the 'y#heel e9ect!

Irim? -(520I'y#heelor m(%2? -(52 0 *2(3 ?*- %gm2

Since ra$iu of gyration! % ? ?D/2 ? -(51/2

?-(,3m!i(e(! m0(583k) 0(5838.4@)0(5838.8A)0/45.kg

=J E> rim? -(52 =J E >'y#heelm( K2(CS? -(52 =J E >'y#heel

m =24(36>20-(-2? -(520 241

16!0m ? 2*3,(

or m 0 [email protected]/6.0 /45.kg

E0ample *

E0ample*


73/119



2/6/163*

m 0 A56534/5.6 0 /45.

kgAlo! ma of the 'y#heel rim!

m? =b 0 t >0 D 0 F " b?2t=gi&en>

1,*( ? b 0 t 0 D 0 F

?2 t t 0 -(51 0 32- ? ,1646 t2

t2 ? 1,*(/,1646 ?-(--*,,

t 08.82@ say 8.86 m 068 mm

"ns.

E0ample *


74/119



2/6/16

3,

-+ample4


75/119



2/6/16

3

E0ample,

An otto cycle engine $e&elop - %8 at1- r(p(m( #ith 3 e0ploion per minute(The change of pee$ from the commencement

to the en$ of po#er tro%e mut not e0cee$ -(.of mean on either i$e(

esign a s!ita%le rim sectionha&ing #i$thfour time the $epth o that the hoop tre $oenot e0cee$ , @Pa(

Aume that the 'y#heel tore 16/1 time

theenergy tore$ by the rim an$ that the #or%$one$uring po#er tro%e i 1(,- time the #or%$one$uring the cycle( Denity of rim material i 32--

%g/m*

E0ample,


76/119



2/6/16

36

Solution(

Gi&enP ?- %8

?- 1-*8

+ ?1-r(p(m(

n ?3

Rt?, @Pa

?, 0 1-6+/m2

F ?32--%g/m*

E0ample,

E0ample,


77/119



2/6/16

33

8e %no# that! @a of the 'y#heel rim!m ?Kol( 0 $enity?2 0 A 0 F

i(e(! m?=% + t>0 D 0 F " b?,t =gi&en>

)urther! Energy of the 'y#heel rim!Erim? =1/2>IH

2 ? =1/2>m%2H2? =1/2>m2H2

=&?H>? =1/2>0m0&2 -rim?=1/16>E gi&en

An$ @a0( 'uctuation of energy! JE? -0 2 C

" hoop Stre?Rt?F&2 " &?+/6-

E0ample,

E0ample,


78/119



2/6/16

34

Tmeantranmitte$ by the engine or 'y#heel(

Po#er tranmitte$! P? =200+0Tmean>/6-

i(e(! -01-*? =2001-0Tmean>/6- ?1(31 TmeanTmean? - 0 1-*/1(31? 5/2.@ Nm

:orkdone3cycle? Tmean0 U ? *142(3 0 , ?

48888 Nm

{r 4he ork'one per ccle for a 5 stroke engine,6ork'one l ccle =7(x3)/(No. of explosions/min)8

=(x3)/n = (93333x3)/:9=53333 Nm!

( 8or%$one $uring po#er tro%e?1(,08or%$one/cycle ?1(,0,---- ?6--- +m

E0ample ,

E0ample,


79/119



2/6/16

35

The #or%$one $uring po#er tro%e i ho#n

by Jle

ABC in )igin #hich bae AC ? ra$ian an$ height B) ?

Tma0( 8or%$one $uring #or%ing tro%e? 1/20Tma0

? 1(31 Tma0( Alo 8or%$one $uring #or%ing tro%e?6---+m

( Tma+?=6---/1(31> ?5646Nm

eight abo&e the mean tor7ue line!

BG ? B))G ? Tma0Tmean? ?

E0ample ,

E0ample,


80/119



2/6/16

4-

a p e

Nm##@3% 3.@$(3330

$0#$2#$.$(0333

:;*

;*-:(,*Ctriangleof,rea%*%of,rea

*%:'triangleofarea;i.e.'energyofnfl!ct!atio"a(im!m

:;*

;*-:

,*Cof,rea

*%of,rearelationlgeometrica

from%:';energyofnfl!ct!atioma(.

representslinetor9!emeanthea>ove

ig:inshaded;shown*%areatheSince

2

2

2le

2

2

le

le

==

=

==

=

E0ample,


81/119



2/6/16

41

*ean diameter of the ywheel ()

oop tre! Rt?F&2

i(e(! , 0 1-6? F(*2? 32-- *2

( *2?, 1-6/32-- ? 6

or * ? 2*(4 m/s

Peripheral &elocity!& ? D+/6-

i(e(! 2*(4 ? D+/6-? D01-/6-?3(4

DD ?2*(4/3(4

05 m 7"ns(

p

E0ample,


82/119



2/6/16

42

rosssectional dimensions of the rim

Croectional area of the rim!#= x t= 5t x t =5t2 (=5t..gi*en)Since N1 N2= -(. + either i$e! =..gi*en)

.total 'uctuation of pee$!

N1 N2? 1. of mean pee$ ?-(-1 N" coecient of 'uctuation of pee$!

C( ? =N1 N2)/N ? -(-1

E ? Total energy of the 'y#heel(

@a0imum 'uctuation of energy =J E),,6,4- ? Ex 2 C ? E 0 2 0 -(-1 ? -(-2 E

. " 0 4642838.8 054 + /85Nm

p

E0ample,


83/119



2/6/16

4*

Since the energy tore$ by the 'y#heel i16/1 time the energy tore$ by rim!

Therefore the energy of the rim!Erim? =16/1>E? =16/1>0 2*2, 0 1-

*? 2134(4 01-*+mAlo Erim? =1/2>0m0&

2

i(e(! 2134(4 1-*? =1/2>0m0=2*(4>2?2340m

. m? 2134(4 01-*/ 234 ?@25@ kgAlo! ma of the fly#heel rim! m? A 0 D 0 F

i(e(!34*3 ? A 0 D 0 F ?, t2

* 0 32--?231,65 t2

or t2? 34*3 / 231,65 ? -(-244

or t 0 8./@ m 0 /@8 mm 7"ns.

% 04 t 04 + /@8 0 628 mm 7"ns.

p


84/119



2/6/16

4,

-+ample


85/119



2/6/16

4

E0ample

.7200kg/mastakenbemayironcastofDensity.39.23/mm

astakenbemaykeyan!s"aftforstresss"ear#afe$"e

tor%&e.meant"et'iceiss"aftt"eontor%&emaxim&m$"ecyc(e.

'"o(et"e!&ring!one'orka)eraget"etimes3

11isstrokepo'er

t"e!&ring!one'orkt"et"atass&me!bemay*tspee!.meanof

4+to(imite!betoisspee!ofnf(&ct&atiotota($"e.3.92/mm

excee!tonotismateria(t"einstress"oop$"e800rpm.at36.8k

De)e(oping-ngineDiese(stroke4afor(y'"ee(ironcastaDesign

32

2

E l


86/119



2/6/16

46

E0ample

3

2

s

meanmax

s

2

7200kg/mironcastofDensity

39.23/mmfstresss"ear#afe

$2$

cyc(e'"o(et"e!&ring

!one'orka)e.3

11strokepo'er!&ring!oneork

0.04spee!ofn(&ct&atio

3.92/mmmateria(instressoop

800rpm36.8k'o'er

(y'"ee(ironasti)en,

#o(&tion

=

== =

=

==

=


87/119



2/6/16

43

J E ? IH2

CRt?F($

2

& ? =+>/6-

J E ? m(2(H2Cm ? FK ? F(=D(A>? F(=2(A>A ? %0 t!

b?2t

E0ample


88/119



2/6/16

44

p

E0ample


89/119



2/6/16

45

( )

( )

03mmisdiametershaft'di.e.'

03mm#mm3.3#md13$.2$6

1@[email protected]#d

f1

d6

@[email protected]#Nm#$.2D2T2T*!t

#$.2DNm@3362

3333$.@

N62

33334owerT

73333

TN624owerthat'now7e

s

s

$

s

s

$s

meanma(

mean

mean

>oohanddataine9n.$.1ref.'

==

=

=

===

=

=

=

=

E0ample


90/119


2/6/16

5-

E0ample


91/119


2/6/16

51

( )

sddiameter'oss

bookhanddataine4nref

=

,8.17..,

( )

0@3Nm#

0023D$3

%nergy"in.%nergy"a(.energyofnl!ct!atio

D$3Nm$

110023

done/cycle7or$11stroepowerd!ringdone7or

0023Nm#6#$.2DD23#$.2D

t!rned5,nglemomentTT!rningdone/cycle7or

133mm032d2diameterh!>ordiameter*oss

3

mean

s

>oohanddataine9n.1D.@ref.'

==

=

==

=

===

====

E

p

E0ample


92/119


2/6/16

52

E0ample

( )( )

0#mmrimofdia."eani.e.'

3.0#3mor1.32N62$.$$I

'N6

I,lso

2$.$$m/sIorID23313$.2

'IJFstressKoop,s

ec21.$3N.m.sN623.3#0@3%

C%,lso'

1.32N:ma(Nspeed'meanof#Etolimitedspeedofnfl!ct!atiototal;

rimofvelocityI)densityJ

speedofnfl!ct!atiooftcoefficiens

C)speedang!lar"ean

ma(

2

2

ma(

22

'2

s

==

===

=

==

=

==

=

==

==

60

60

60

E0ampleth t7


93/119


2/6/16

5*

p

( )

( ) ( )

( ) 3.3D1mtt#t3.0#63.3$D

#t>let''t>6,rea?2I,lso'

3.3$Dm

.@1D233

2@3$

gJ

2@3$

w'

7'If!rther'

2@3$N77eight'

2

3.0#

.@1

7

2

g

7

21.$

wheelLrimmedthinfor?rim'ofradi!smeanM

mgyrationofradi!sflywheelofmass

rotationofa(isa>o!tinertiaofmomemtmass

that'now7e

rim

$

rim

22

22

density

7eight

=====

=

=

==

=

=

==

====

=

.,.ei


94/119


2/6/16

5,

E0ample

#.mm

22.1mm

$3#.#mm

D.1##t>

D.1mm't

3.#m

3.3D13.0#tflywheeltheofdiameternside

3.221m

3.3D13.0#tflywheeltheofdiameterH!tside

or

mean

mean

==

====

+=+=

===

=


95/119


2/6/16

5

Stresses in Flywheel"rms


96/119


2/6/16

56

Stree in )ly#heel Arm

)ollo#ing tree are in$uce$ in the armof a 'y#heel

Tenile tre $ue to centrifugal force

acting on the rim(Ben$ing tre $ue to tor7ue tranmitte$from the rim to the haft or from the haft

to the rim(Shrin%age tree $ue to une7ual rate ofcooling of cating( Thee tree are

$icult to $etermine


97/119


2/6/16

53

Tenile tre $ue to centrifugal force

Due to the centrifugal force acting onthe rim! the arm #ill be ub;ecte$ to

$irect tenile tre #hoe magnitu$e i!.Tenile tre in the arm!

Rt1? =*/,>Rt? =*/,>F0&2



98/119


2/6/16

54

Ben$ing tre $ue to tor7uetranmitte$

4 ?@a0imum tor7ue tranmitte$ by the

haft!V ? Section mo$ulu for the c/ of arm"

?@ean ra$iu of rimr ?a$iu of the hub

n ?+umber of arm


Stree in Arm


99/119


2/6/16

55

11 bt

+=

==

=

=

=

end'h!>theatarmstheinstresstensileTotal

r:8;?

n?

T

"arms'instress*ending

r:8;?n?

T"i.e.'h!>'theat

armtheonlieswhichmoment>endingma(.)

n?Tarmeachon+oad

?Trim'theofradi!smeantheat+oad

>1


100/119


2/6/16

1--

esign of Flywheel"rms

D/n of Arm


101/119


2/6/16

1-1

D/n of Arm

( ) ( )

( )

;2:);1:e9!ations>yo>taineddimensionsarms'>2a,ss!ming

2r:.......8;?n?

T

"F

arms'instressding"a(im!m*en

r:8;?n?

T"

moment'>endingma(im!mthatnow7e

1.......a>($2

6mod!l!s'Section

stress.>endingma(.fordesgnednedisit)a(is'minorthetwiceasa(ismaOorwith

elliptical!s!allyisarmstheofc/sThe

11

>

2

11

=

==

=

=


102/119


2/6/16

1-2

esign of Shaft# B!% andCey


103/119


2/6/16

1-*

Deign of Shaft! ub an$ Wey

( )

shaft.ofmaterialtheforstressshear,llowa>le)shaft'theofiameterd

where'

1Td'transmittetor9!e"a(im!m

d.transmittetor9!ema(im!mthefromo>tained

isflywheelforshaftofdiameterThe

1

ma(

==

=

3

1d

Shaft! ub an$ Wey


104/119


2/6/16

1-,

therim.ofwidthtoe9!altaengenerallyist

diameter.shaftthetimes2.0to2fromlengthK!>)

dia.shaftthetwiceastaen!s!allyisdiameterK!>

shaft.ofdiameterorh!>ofdiameternnerd

)h!>'ofdiameterH!terdwhere'

1Td'transmittetor9!e"a(.

d.transmittetor9!ema(im!mthe

forshaft'hollowaasdesignedish!>The

1

ma(

==

=

d

dd 4

1

4

Deign of Shaft ub an$


105/119


2/6/16

1-

shaft.ofiameterd

aley.materitheforstressShear

ey'theof+ength+where'

2

d(+( w (Tma(shaft'>ydtransmitteTor9!e

shearing.ineyoffail!re

thegconsiderin>yo>tainediseyoflengthThe

h!>.)shaftthefor!sediseys!nstandard,

1

1

===

=

Deign of Shaft! ub an$Wey


106/119


2/6/16

1-6

-+ample6

E0ample6


107/119


2/6/16

1-3

esign and draw a cast iron ywheel

ue$ for a four tro%e I(C engine$e&eloping14- %8 at 2,- r(p(m(The hoop or centrifugal tre $e&elope$

in the 'y#heel i (2 @Pa! the total

'uctuation of pee$ i to be limite$ to *.of the mean pee$( The #or% $one $uringthe po#er tro%e i 1/* more than thea&erage #or% $one $uring the #hole cycle(

The ma0( tor7ue on haft i t#ice themean tor7ue( The $enity of cat iron i322- %g/m*(

E0ample6


108/119


2/6/16

1-4

Sol!tion(Gi&en =14-%8 ?14- 1-*8N ? 2,-r(p(m(

Rt ? (2@Pa ? (20 1-6N/m2;+l N2? *. N;

F ? 322- kg/m0

(

Turning moment $iagram ofa , tro%e engine i ho#nin )ig(

%:;ffl t ti" iE0ample6


109/119

Department of AutomobileEngineering

PSG College of Technology

2/6/16

1-5

"m%%cycledone5ork.

"ine, nstroke engForg strokesof workin"owhere n

,n

Pcycle5orkdonetained asalso be obcycle mayworkdone

90000120

6010180/

2/4.min/.

60/,/

3

40

==

==

=

===

=

=

=

Nm3333#(D11(Tyclewordone/c

NmD1122

3(131@3(

N2

34(T

flywheel'the>ydtransmittetor9!e"ean

%:;energyofnfl!ct!atio"a(im!m

mean

$

mean

E0ample6


110/119



2/6/16

11-

( )

( ) NmD$@#2123333(T123333TA(

TA(stroepowerd!ring7ordone

T*height)radians,C>asewhich'inig.in,*Ca>yshownisstroepowerthed!ring7ordone

Nm1233333333($

13333

stroeworing:;orpowerthed!ring7ordone

cycle'wholed!ringwordoneaveragethanmore

times1/$isstroepowerd!ringwordoneSince

ma(

ma(

ma(

ma(

le

===

=

==

=+=

21

21

E0ample6litth>K i ht


111/119



2/6/16

111

Nm@000;D$@#:

;22$:123333

;*:

;*-:(,*C&of,rea

*%&of,rea%energy'ofnfl!ct!atio"a(.

';*:;*-:P

,*C&of,rea*%&of,rearelation'lgeometricafrom

%:';energynoffl!ct!atioma(.therepresentslinetor9!e

meanthea>oveig.inshadedshown*%areatheSince

Nm22$D118D$@#

T8T-8**-

line'tor9!emeanthea>oveKeight

2

2

2

2le

le

2

2

le

le

meanma(

==

=

==

=

==

==

E0ample6ifl h lthfi t1


112/119



2/6/16

112

,ns....m2.3#2.@/1$.1

rimflywheeltheofiameter1.

1$.13

203

N

2.@v

velocity'4eripheral

or

D23/D22313A0.2I

IAD223.I13(0.2rim'flywheeltheindevelopedstressKoop

m/s2.@v

2

22t

===

===

==

===

=

60

E0ample6ifl h lthf"2


113/119



2/6/16

11*

( ).....,ns.g#0000/1.D$@m

rimflywheeltheof"ass2.

1.D$m3.3$;20.1#:2

2.3#m@000%

C'.m.?@000%

energy'ofnfl!ct!atio"a(.

3.3$N

N8N

Csspeed'ofnfl!ct!atiooftCoefficien)

rad/s20.1#3

(2032

3(N2rim'flywheeltheofspeed,ng!lar

22

s

22

21

=====

==

==

===

E0ample6ifdi iti lC$


114/119



2/6/16

11,

,nsmm...#D32$02t2>

......,ns.mm2$0tor

rimofdimensionssectional8Cross$.

)

m3.2$0say3.2$2tor

3.30##0/200t

t200D223(2.3#t2m

(, (#0mrim'flywheelthe"assof

t2tt2t>,rim'theofareasectional8Cross

t;,ss!me:2metresinrimtheof7idth>)

metres'inrimofthicnessoreptht+et

2

22

2

====

===

==

=====

===

E0ample6


115/119



2/6/16

11

,S.mm3.#Dmm#D3>and

m20Q3mm203120(2dl2dd:..;QR888........

'

rim.theofwidthtoe9!al

ish!>oflengthandshaftofdiameterthetwicetoe9!almadeish!>theofdiameterThe

,ns.12Smmsay122d1or

13$(1@2$13$1D.@SS($221#;dl:$.P

N/mm2:#3"4a#3tR...;Taing

1.1111.

:$;dD@SS:$;d#38(:$;dtRA813$($221#1t.1t

fl==C:';Tshafttheonactingtor9!ema(im!mthethatnow7e

mm8N13$($221#m8N1#$22D11(2Tmtl=(2CTfl==..

:...;,ss!me

..shaft'theonactingtor9!ema(.

tor9!e'meanthetwiceisshaftontor9!ema(.Since

h!>.theof+ength+)

shaft'ofiameterdh!>'ofiameterd+et 1

h!>oflengthandiameter#.

===

====

=

==

==

===

====

=

==

nsmm........0.47mm470b*

m0.25mm250125x21

!2!,

........ns125mmsay122

1

!or2/mm40:a40;$aking

;!7.855;!4016

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