Post on 25-Feb-2018
transcript
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Department of AutomobileEngineeringPSG College of Technology
2/6/161
Flywheel
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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$e it #ith a'y#heel(
)ly#heel
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Department of AutomobileEngineeringPSG College of Technology
2/6/16*
In a single cylinder engine(4Stroke)! in #hich there i only onepo#er tro%e in t#o re&olution of thecran%haft! a coni$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$(
)ly#heel
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o#e&er!not all of thi energy goe into'y#heel
During the 1thalf of the po#er tro%e!#hen energy i being upplie$ 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
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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$e other
rotating part of the engine ha&e greater
)ly#heel
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o#e&er! the 'y#heel ha by far thegreatet inertia e&en in a multi cylin$erengine(
"side from its principle f!nction#the y wheel ser$es as a mem%erof the friction cl!tch# & it !s!allycarries also the ring gear of theelectric starter.
)ly#heel
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)ly#heel
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)ly#heel
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)ly#heel
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)ly#heel
Energy accumulatorEnergy re$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$
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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
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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
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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
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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
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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
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)ly#heel
A )ly#heel i gi&en a high rotationalinertia i(e(! mot of it #eight i #ell outfrom the a0i
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onstr!ction ofFlywheels
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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(
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In cae the 'y#heeli of larger i! the
arm are ma$eintea$ of #eb(
The number of
arm $epen$ uponthe i
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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
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*a+im!m Fl!ct!ation of Speed
&
oe,cient of Fl!ct!ation of Speed
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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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( )[ ]
( ) ( )
( )
( ) ( )( )
( )
( ) ( )
( ) ( )
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
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Fl!ct!ation of-nergy
The Fluctuation of Energmaybe $etermine$ by the turningmoment $iagram for one
complete cycle of operation
)l h
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turning momenti
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#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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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
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+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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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
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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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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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)ly#heel
*eanSpeed
*a+im!m
Speed
Speed
rankangle *in.Speed
)ly#hee
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)ly#heel
The Fl!ct!ation of -nergythe &ariation of
Energy abo&e " belo# mean reiting tor7ueline(
)ly#hee
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)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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*a+im!m Fl!ct!ation of-nergy
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*a+im!m
Fl!ct!ation of -nergy
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( ) ( )#$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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oe,cient ofFl!ct!ation of -nergy
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( )
( )
( ) ( ) 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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-nergy stored in aywheel
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( ) ( )
==
=
==
===
===
+=+==
2
2121
2121
m)://;:/NN;Ns
:/2;mean:/2'N;Nmean
C
Nwhere'or
s
22C
2
1
2
1
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( )
( ) 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
,
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-+ample/
E l 1
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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*(
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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
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*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
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. @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
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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.
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-+ample
l
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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
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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
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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
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E0ample2
[ ]( )[ ]
( )
1#13Nm
@333/3.007
3.007
/2.$77@333Nmor77cycleperwordonedoneworNet
stroee(pn.d!ringdonewor7)
stroecomprn.d!ringdonewor7
let'
%
%
%%
C%
%
C
==
==
==
==
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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
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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
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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
=====
=
=
==
==
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EngineeringPSG College of Technology
2/6/163
Stresses in a Flywheel 9im
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EngineeringPSG College of Technology
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
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Department of Automobile
EngineeringPSG College of Technology
2/6/165
Stresses in a Flywheel9im
b 0 :idthof rim#
t0Thickness of rim#
A 0 rosssectionalarea ofrim 0 b +
t.
Stree in
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Department of Automobile
EngineeringPSG College of Technology
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
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Department of Automobile
EngineeringPSG College of Technology
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
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Department of Automobile
EngineeringPSG College of Technology
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
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EngineeringPSG College of Technology
2/6/166*
-+ample5
E0ample *
7/25/2019 DR Flywheel
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Department of Automobile
EngineeringPSG College of Technology
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 *
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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 *
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Department of Automobile
EngineeringPSG College of Technology
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*
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Department of Automobile
EngineeringPSG College of Technology
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*
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EngineeringPSG College of Technology
2/6/1664
E0ample*
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Department of Automobile
EngineeringPSG College of Technology
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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*
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EngineeringPSG College of Technology
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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*
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Department of Automobile
EngineeringPSG College of Technology
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*
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Department of Automobile
EngineeringPSG College of Technology
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 5@4.3/6.0 /45.kg
E0ample *
E0ample*
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Department of Automobile
EngineeringPSG College of Technology
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 *
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EngineeringPSG College of Technology
2/6/16
3,
-+ample4
7/25/2019 DR Flywheel
75/119
Department of Automobile
EngineeringPSG College of Technology
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,
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Department of Automobile
EngineeringPSG College of Technology
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,
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EngineeringPSG College of Technology
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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,
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EngineeringPSG College of Technology
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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,
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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,
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Department of Automobile
EngineeringPSG College of Technology
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,
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Department of Automobile
EngineeringPSG College of Technology
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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,
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Department of Automobile
EngineeringPSG College of Technology
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,
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Department of Automobile
EngineeringPSG College of Technology
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
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Department of Automobile
EngineeringPSG College of Technology
2/6/16
4,
-+ample
7/25/2019 DR Flywheel
85/119
Department of Automobile
EngineeringPSG College of Technology
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
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Department of Automobile
EngineeringPSG College of Technology
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
=
== =
=
==
=
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EngineeringPSG College of Technology
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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
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2/6/16
44
p
E0ample
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45
( )
( )
03mmisdiametershaft'di.e.'
03mm#mm3.3#md13$.2$6
1@D@.0#d
f1
d6
@D@.0#Nm#$.2D2T2T*!t
#$.2DNm@3362
3333$.@
N62
33334owerT
73333
TN624owerthat'now7e
s
s
$
s
s
$s
meanma(
mean
mean
>oohanddataine9n.$.1ref.'
==
=
=
===
=
=
=
=
E0ample
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2/6/16
5-
E0ample
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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
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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
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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
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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
==
====
+=+=
===
=
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5
Stresses in Flywheel"rms
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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
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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
Stree in )ly#heel Arm
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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 )ly#heel Arm
Stree in Arm
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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
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1--
esign of Flywheel"rms
D/n of Arm
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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
=
==
=
=
7/25/2019 DR Flywheel
102/119
Department of AutomobileEngineeringPSG College of Technology
2/6/16
1-2
esign of Shaft# B!% andCey
7/25/2019 DR Flywheel
103/119
Department of AutomobileEngineeringPSG College of Technology
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
7/25/2019 DR Flywheel
104/119
Department of AutomobileEngineeringPSG College of Technology
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
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=
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4
Deign of Shaft ub an$
7/25/2019 DR Flywheel
105/119
Department of AutomobileEngineeringPSG College of Technology
2/6/16
1-
shaft.ofiameterd
aley.materitheforstressShear
ey'theof+ength+where'
2
d(+( w (Tma(shaft'>ydtransmitteTor9!e
shearing.ineyoffail!re
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h!>.)shaftthefor!sediseys!nstandard,
1
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===
=
Deign of Shaft! ub an$Wey
7/25/2019 DR Flywheel
106/119
Department of AutomobileEngineeringPSG College of Technology
2/6/16
1-6
-+ample6
E0ample6
7/25/2019 DR Flywheel
107/119
Department of AutomobileEngineeringPSG College of Technology
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
7/25/2019 DR Flywheel
108/119
Department of AutomobileEngineeringPSG College of Technology
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
7/25/2019 DR Flywheel
109/119
Department of AutomobileEngineering
PSG College of Technology
2/6/16
1-5
"m%%cycledone5ork.
"ine, nstroke engForg strokesof workin"owhere n
,n
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90000120
6010180/
2/4.min/.
60/,/
3
40
==
==
=
===
=
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Nm3333#(D11(Tyclewordone/c
NmD1122
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flywheel'the>ydtransmittetor9!e"ean
%:;energyofnfl!ct!atio"a(im!m
mean
$
mean
E0ample6
7/25/2019 DR Flywheel
110/119
Department of AutomobileEngineering
PSG College of Technology
2/6/16
11-
( )
( ) NmD$@#2123333(T123333TA(
TA(stroepowerd!ring7ordone
T*height)radians,C>asewhich'inig.in,*Ca>yshownisstroepowerthed!ring7ordone
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13333
stroeworing:;orpowerthed!ring7ordone
cycle'wholed!ringwordoneaveragethanmore
times1/$isstroepowerd!ringwordoneSince
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le
===
=
==
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21
21
E0ample6litth>K i ht
7/25/2019 DR Flywheel
111/119
Department of AutomobileEngineering
PSG College of Technology
2/6/16
111
Nm@000;D$@#:
;22$:123333
;*:
;*-:(,*C&of,rea
*%&of,rea%energy'ofnfl!ct!atio"a(.
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2
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le
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le
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==
E0ample6ifl h lthfi t1
7/25/2019 DR Flywheel
112/119
Department of AutomobileEngineering
PSG College of Technology
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
7/25/2019 DR Flywheel
113/119
Department of AutomobileEngineering
PSG College of Technology
2/6/16
11*
( ).....,ns.g#0000/1.D$@m
rimflywheeltheof"ass2.
1.D$m3.3$;20.1#:2
2.3#m@000%
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energy'ofnfl!ct!atio"a(.
3.3$N
N8N
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rad/s20.1#3
(2032
3(N2rim'flywheeltheofspeed,ng!lar
22
s
22
21
=====
==
==
===
E0ample6ifdi iti lC$
7/25/2019 DR Flywheel
114/119
Department of AutomobileEngineering
PSG College of Technology
2/6/16
11,
,nsmm...#D32$02t2>
......,ns.mm2$0tor
rimofdimensionssectional8Cross$.
)
m3.2$0say3.2$2tor
3.30##0/200t
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t2tt2t>,rim'theofareasectional8Cross
t;,ss!me:2metresinrimtheof7idth>)
metres'inrimofthicnessoreptht+et
2
22
2
====
===
==
=====
===
E0ample6
7/25/2019 DR Flywheel
115/119
Department of AutomobileEngineering
PSG College of Technology
2/6/16
11
,S.mm3.#Dmm#D3>and
m20Q3mm203120(2dl2dd:..;QR888........
'
rim.theofwidthtoe9!al
ish!>oflengthandshaftofdiameterthetwicetoe9!almadeish!>theofdiameterThe
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fl==C:';Tshafttheonactingtor9!ema(im!mthethatnow7e
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tor9!e'meanthetwiceisshaftontor9!ema(.Since
h!>.theof+ength+)
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===
====
=
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nsmm........0.47mm470b*
m0.25mm250125x21
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........ns125mmsay122
1
!or2/mm40:a40;$aking
;!7.855;!4016
;!16
10x14322$
s"aft,on t"eactingtor%&emaxim&m(so,
mm
7/25/2019 DR Flywheel
116/119
Department of AutomobileEngineering
PSG College of Technology
2/6/16
116
Nmm13(23#.0Nm23#.0
Nm3.20:8;2.3#2.3#
1#$22d:8;
n
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armsellipticalof
dimensionssectionalCross0.
==
=
=
=
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====
==
E0ample6dimensionssectionalCross
7/25/2019 DR Flywheel
117/119
Department of AutomobileEngineering
PSG College of Technology
2/6/16
113
....,nsmmD31#3(3.01
a3.01>
....,ns.mm1#31a
arms.....ellipticalof
dimensionssectionalCross
or
13(2D$/1013(@3#1:;a
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arm.theofsection8crosstheformod!l!ssectionThe
$$$1
$
1
$
$
1
$
>
$1
211
211
====
==
====
===
3232
E0ample6
7/25/2019 DR Flywheel
118/119
Department of AutomobileEngineering
PSG College of Technology
2/6/16
114
( ) ( ) ....,ns.mm13say10+
......,nsmm23eyofthicness)
s........,nmm$weyof7idth
eyofimensions.
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ma(
133/13(1#$22
+1332
120(#3($(+
dw+13(1#$22T
'shaftthe>ydtransmittetor9!e"a(.
.
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shearingineyoffail!regconsiderin>yo>td.is;+:eyof+ength
==
====
=
=
21
hi hiitt t lfCh
E0ample6
7/25/2019 DR Flywheel
119/119
( ) ( )
safeisdesign"4a10thanlessisSince
"4a.10thangreater>enotsho!ld
whichriminstresstotalforChec
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N/m3.2$0
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tn
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rim'theinstresstotalthat'now7e
2
2
2
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2
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==+=
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