me-311 machine design - lecture 19

8/20/2019 ME-311 Machine Design - Lecture 19

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Instructor: Dr. Samiur Rahman Shah

NUST School of Mechanical and Manufacturing Engineering

ME-311 Machine Designecture 1!


2/25

Clutches, Brakes, Couplings & Flywheels: Internal E#$anding Rim %lutches & 'ra(esE#ternal %ontracting Rim %lutches & 'ra(es)rictional %ontact *#ial %lutches

%one %lutches & 'ra(esEnerg+ considerations & Tem$erature rise)riction MaterialsMiscellaneous %lutches & %ou$lings

,age


3/25

,age 3

*n a#ial clutch isone in hich themating surfaces

are $er$endicularto the rotationala#is%lutches ma+ /eof single $late ormulti-$late t+$e

•

)rictional-contact a#ial clutches


4/25

,age 0


5/25

* clutch ith dis( ofe#ternal diameter D andinternal diameter d issho n

e are interested ino/taining a thrust forceF for re2uired tor2ue T and $ressure p

T o methods of sol ing

the $ro/lem are in useUniform ear 4 dis(is rigidUniform $ressure 4dis( is su$$le ,age 5


6/25

•

)rictional contact a#ial clutches -uniform ear

,age 6

In this anal+sis7 the dis( is considered to /e rigid*t 8rst use7 the greatest ear is at the outerradius here tangential elocit+ is greatest

*fter sometime7 the ear e2ualises and theclutch ears e2uall+ o er the hole surface

The a#ial ear can thus /e e#$ressed as

In hich onl+ P and V ar+ along the radius of theclutch dis('+ de8nition7 ear is constant7 hence

t KPV f f w 21=

( ) 1C const PV == 2C prw = 2max3d

pr pC pr ai ===


7/25

e can ta(e the earlier e#$ression hich is thecondition for ha ing the same or( done atradius r and at radius d /2Referring to 8gure7 e ha e an element of radiusr and thic(ness dr *rea of this element is 2πrdr )orce on this element is thus dF 9 2πprdr

e can 8nd the total normal force /+ integratingo er r hich aries /et een d /2 and D /2

Thus ith pr constant

,age

( )d Dd pdr d p prdr F a D

d a

D

d −=== ∫ ∫ 22

2

2

2

2

π π π


8/25

The tor2ue is found /+ integrating the $roduct ofthe frictional force and the radius

'+ su/stituting the alue of F from the forcee2uation7 e ma+ o/tain a more con eniente#$ression for the tor2ue. Thus;

In use7 the force e2uation gi es the actuatingforce for the selected ma#imum $ressure p a . Thise2uation holds for an+ num/er of friction $airs orsurfaces. The tor2ue e2uation a/o e gi es tor2ueout$ut for one surface ,age <

( )2222

2

2

2

82 d D

d fprdr d fpdr fpr T a

D

d a

D

d −=== ∫ ∫

π π π

( )d D Ff T +=4


9/25

• )rictional contact a#ial clutches - uniform $ressure

,age !

In this t+$e of clutch arrangement7 s$rings areem$lo+ed to o/tain a uniform $ressure o er the

hole dis( surface

hen uniform $ressure can /e assumed o er thearea of the dis(7 the actuating force F is sim$l+the $roduct of the $ressure and area. This gi es;

Tor2ue is thus an integral of the $roduct of thefrictional force and the radius

( )224

d D p

F a −= π

( )3322

2

122 d D

fpdr r fpT

D

d −== ∫

π π


10/25

Since $ 9 $a from earlier e2uation7 e can rite

The a/o e tor2ue alue should /e multi$lied /+the num/er of surfaces to get o erall tor2ue for amulti-$late clutch

Tor2ue for uniform ear

)or uniform $ressure

,lot of the a/o e t o e2s. on right ,age 1=

−−= 22

33

3 d Dd D Ff

T

4

1 Dd fFD

T +=

( )( )2

3

1

1

3

1

Dd Dd

fFDT

−−=


11/25

•

Dis( /ra(es

,age 11

There is no f undamentaldi>erence /et een adis( /ra(e and a clutch

%an /e of a slidingcali$er ?one side $iston@or a 8#ed cali$er ?dualside $iston@ t+$e


12/25

The go erning a#ial ear e2uation is

here 9 ear in length units

f 1 9 o$erational conditions for motion t+$e7load and s$eedf 9 conditions for tem$erature andcleanlinessA 9 material ear $ro$ert+, 9 $ressure on materialB 9 elocit+ of sliding

t 9 time of o$eration ,age 1

KPVt f f w 21=


13/25

The coordinate ṝ locates the line of action of FCf interest is e>ecti e radius r e 7 hich is thee2ui alent of an in8nitesimal radial thic(ness

,age 13

( )∫ ∫ ∫ −== 21 12θ

θ θ θ θ

o

i

o

i

r

r

r

r prdr prdrd F

( )∫ ∫ ∫ −== 21 2122θ

θ θ θ θ

o

i

o

i

r

r

r

r dr pr f drd fpr T


14/25

The e2ui alent radius can thus /e found from fFr e = T

The locating coordinate ṝ of the acti ating force isfound /+ ta(ing moments a/out the #-a#is

,age 10

∫ ∫

==o

i

o

i

r

r

r

r e

prdr

dr pr

fF T

r

2

( ) ( )∫ ∫ ∫ −=== 21 221 coscossinθ

θ θ θ θ θ

o

i

o

i

r

r

r

r x dr pr drd r pr r F M

( ) e x fr F M r 1221 coscos θ θ

θ θ

−−==


15/25

•

Dis( /ra(es 4 uniform ear

,age 15

)or ear to /e uniform7 PV has to /e constant,ressure p e#$ressed in terms of largestallo a/le $ressure p a ?occurring at the inner

radius r i @ as p = p a r i /r

Tor2ue e2uation then /ecomes

( ) ( )ioia r r r p F −−= 12 θ θ

( ) ( ) ( )2212122

1ioia

r

r ia r r r fprdr r fpT

o

i

−−=−= ∫ θ θ θ θ

2

1

2

22

io

io

ior

r ia

r

r ia

er r

r r r r

dr r p

rdr r pr

o

i

o

i +=−−==

∫ ∫

2coscos

12

21 io r r r

+−−

= θ θ θ θ


16/25


17/25

• %ircular ?'utton or ,uc(@ $ad cali$er /ra(e

,age 1

In this situation7 r e = δe The actuating force is gi en /+

*nd the tor2ue is gi en /+av p R F

2π =

e fFr T =


18/25

•

Energ+ considerations

,age 1<

hen a rotating mem/er of a machine is causedto sto$ /+ a /ra(e7 the (inetic energ+ of rotationmust /e a/sor/ed /+ the /ra(e 4 heat

Similarl+7 hen a clutch engages dri e /et eent o mem/ers of hich one is mo ing and theother is initiall+ at rest7 (inetic energ+ is dissi$ateddue to the initial sli$$age

* clutch or /ra(e ma+ /e destro+ed /+ it s o ngenerated heat%a$a/ilit+ of a clutch de$ends on

T+$e of material of clutch

*/ilit+ of the clutch to dissi$ate heat


19/25

%onsidering the sim$li8ed diagram of clutch

riting the e2uations for moments of inertia s. Tfor the t o mem/ers

Instantaneous elocities are

,age 1!

11θ I T =− 22θ I T =

11

1 ω θ +−= t I T

22

2 ω θ += t

I T


20/25

here and at t =0 The di>erence in elocities ?relati e elocit+@ isgi en /+

The clutching o$eration is com$leted at theinstant hen the relati e elocit+ or w 1 - w 2 /ecomes ero7 hence

,age =

11 ω θ = 22 ω θ =

+−+−=−= 2

2

1

1

21 ω ω θ θ θ t

I T

t I T

t I I

I I T

+−−=

21

2121

ω ω θ

( )( )21

21211 I I T

I I t

+−=

ω ω


21/25

If e assume the clutch tor2ue duringengagement constant7 hence7 e get the rate ofenerg+-dissi$ation ?$o er units@ during the$rocess to /e

This sho s that the energ+ dissi$ation rate isgreatest at the start hen t = 0 . The total energ+dissi$ated during the clutching o$eration of/ra(ing o$eration is o/tained /+ integrating thea/o e e2uation from t = 0 to t = t 1

,age 1

+−−== t I I

I I T T T u

21

2121

ω ω θ

dt t I I

I I T T udt E

t t

∫ ∫

+−−== 11

021

2121

0ω ω

( )

( )21

2

2121

2 I I

I I E

+

−= ω ω


22/25

•

Tem$erature rise

,age

The tem$erature rise of a clutch F /ra(e assem/l+can /e a$$ro#imated /+

hereGT 9 Tem$erature rise%$ 9 S$eci8c heat for materialm 9 Mass of clutch or /ra(e $arts

mC

E T

p

=∆


23/25

If an o/Hect is at initial tem$erature T 1 in anen ironment of tem$erature T inf 7 then Ne ton scooling model is e#$ressed as

here T # 9 Tem$eraturesh

cr 9 C erall heat transfer coe cient

* 9 ateral heat transfer area%ooling of dis( /ra(e F clutch is go erned /+another Ne tonian e2uation

,age 3

−=−

−∞

∞ t mC Ah

T T T T

p

cr exp1

( ) ( ) ( )∞∞ −+=−= T T Ah f hT T Ah H cr CRoss υ


24/25

hereJ loss 9 Rate of energ+ lossh %R 9 C erall heat transfer coe cienth r 9 Radial com$onent of h %R

h 3 9 Bentilation factor

,age 0


25/25

,age 5

Than( +ou

me-311 machine design - lecture 19

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