kom Unit-V

8/16/2019 kom Unit-V

1/19

Unit V: Friction in Machine Element KOMUNIT V FRICTION IN MACHINE ELEMENTS

Surface contacts-Sliding and Rolling friction-Friction drives-Friction in screwthreads-Bearings and lubrication-Friction clutches-Belt and Rope drives-Friction in

brakes-Band and Block brakes.

FRICTIONWhen a body slides over another, the motion is resisted by a force called the

force of friction.

n lathe slides and !ournal bearings power transmitted reduced due to friction. nsuch case, the friction reduced by lubricated surface. "ttempts are made to increase friction where the power is transmitted throughfriction. #$amples are friction clutches, belt drives, etc. #ven the tightness of nut and bolt is dependent mainly on the force of friction.

LAWS OF FRICTION #$periments have shown that the force of solid friction

• is directly proportional to normal reaction between the two surfaces• opposes the motion between the surfaces• depends upon the materials of the two surfaces• is independent of the area of contact•

is independent of the velocity of sliding. %he last of these laws is not true in the strict sense as it has been found that thefriction force decreases slightly with the increase in velocity.

KINDS OF FRICTION&sually, three kinds of friction, depending upon the conditions of surface considered.1. Dry Friction 'ry friction is said to occur when there is relative motion between twocompletely unlubricated surfaces. t is further divided into two types( (a) So i! Friction When the two surfaces have a sliding motion relative to each other, it is calleda solid friction.(") Ro in# Friction

Friction due to rolling of one surface over another )e.g. ball and roller bearings*is called rolling friction.

$. S%in or #r&a'y riction When the two surfaces in contact have a minute thin layer of lubricant betweenthem, it is known as skin or greasy friction. +igher spots on the surface break through the lubricant and come in contact with the other surface.

Skin friction is also termed as boundary friction.*. Fi + riction When the two surfaces in contact are completely separated by a lubricant,friction will occur due to the shearing of different layers of the lubricant. %his isknown as film friction or viscous friction.

FRICTION CLUTCHES " lutch is a device used to transmit the rotary motion of one shaft to another

when desired. %he a$es of the two shafts are coincident.. Single plate )or* 'isc clutch. /ulti-plate clutch

0. one clutch1. entrifugal clutch

1. Sin# & , at& (or) Di'c c -tc

When disengaged, the springs pressed against a cover attached to the flywheel.%hus, both the flywheel and the pressure plate rotate with the input shaft. %hemovement of the clutch pedal is transferred to the pressure plate through a thrust

bearing. Figure shows the pressure plate pulled back by the release levers and the frictionlinings on the clutch plate are no longer in contact with the pressure plate or theflywheel. %he flywheel rotates without driving the clutch plate and thus, the drivenshaft .

Department of Mechanical, AAMEC Page 1

" disc clutch consists of a clutch plate attached to a splined hub whichis free to slide a$ially on splines cuton the driven shaft.

%he clutch plate is made of steeland has a ring of friction lining oneach side. %he engine shaft supportsa rigidly fi$ed flywheel. " spring-loaded pressure plate

presses the clutch plate firmly againstthe flywheel when the clutch isengaged.


2/19

Unit V: Friction in Machine Element KOM When the foot is taken off the clutch pedal, the pressure on the thrust bearing isreleased. "s a result, the springs become free to move the pressure plate to bring it incontact with the clutch plate.

%he clutch plate slides on the splined hub and is tightly gripped between the pressure plate and the flywheel. %he friction between the linings on the clutch plate, and the flywheel on one sideand the pressure plate on the other, cause the clutch plate and hence, the driven shaftto rotate.

$. M- ti/, at& c -tc n a multi-plate clutch, the number of frictional linings and the metal plates isincreased which increases the capacity of the clutch to transmit tor2ue. Figure showsa simplified diagram of a multi-plate clutch.

%he friction rings are splined on their outer circumference and engage withcorresponding splines on the flywheel. %hey are free to slide a$ially. %he frictionmaterial thus, rotates with the flywheel and the engine shaft. %he number of frictionrings depends upon the tor2ue to be transmitted.

%he driven shaft also supports discs on the splines which rotate with the drivenshaft and can slide a$ially. f the actuating force on the pedal is removed, a spring

presses the discs into contact with the friction rings and the tor2ue is transmitted between the engine shaft and the driven shaft. f n is the total number of plates both on the driving and the driven members, thenumber of active surfaces will be n - .

*. Con& c - tc

When the clutch is engaged, the tor2ue is transmitted from the driving shaft to thedriven shaft through the flywheel and the friction cones. For disengaging the clutch,the cone B is pulled back through a lever system against the force of the spring. %he advantage of a cone clutch is that the normal force on the contact surfaces ishigher than other types of clutches

0. C&ntri -#a c - tc

entrifugal clutches are being increasingly used in automobiles and machines." centrifugal clutch has a driving member consisting of four sliding blocks as shownin figure. %hese blocks are kept in position by means of flat springs provided for the

purpose. "s the speed of the shaft increases, the centrifugal force on the shoesincreases.


n a cone clutch as shown infigure, the contact surfaces are in theform of cones.

n engaged position, the frictionsurfaces of the two cones A and B arein complete contact due to spring

pressure that keeps one cone pressedagainst other all the time.


3/19

Unit V: Friction in Machine Element KOM When the centrifugal force e$ceeds the resisting force of the springs, the shoesmove forward and press against the inside of the rim and thus, tor2ue is transmittedto the rim. n this way, the clutch is engaged only when the motor gains sufficientspeed to take up the load in an effective manner. %he outer surfaces of the shoes arelined with some friction material.

Sin# & , at& c - tc

p 3 ntensity of pressure

r 3 4uter radiusr 3 nner radiusW 3"$ial thrust acting on the clutch platen 3 5umber of effective sides of plate% 3Frictional %or2ue6 3 oefficient of friction between the surfaceUni or+ , r&''-r& t &ory

( )r r 7W

p pressureof ntensity−

=

%or2ue % 8 n6WR

( )( )

..

.-

0.

0-

r r

r r

0

.R radius/ean

−

−=

For Single plate clutchn8 for one side effectiven8 for both sides effectiveFor /ulti-plate clutchn8n 9n -

n - 5o. of discs on the driving shaftn - 5o. of discs on the driven shaft

Uni or+ &ar t &ory p.r 8 onstant 8 /a$.pressure at inner radius 8 p ma$.r 8 /in.pressure at outer radius 8 p min.r 8

( )r r 7W

, −=

( )r r 7W

p pressure"verage−

=

%or2ue % 8 n6WR

R radius/ean r r +=

:ower : 8 %.;%or2ue % 8 .<"ngular acceleration< 8 ;= t

D-rin# ' i,,in#"ngle turned by the driving shaft > 8 ; t

"ngle turned by the driven shaft > ? +=#nergy lost due to friction 8 %)> - > *

For 5ew clutch &niform pressure theory For 4ld clutch &niform wear theory

1. A 'in# & , at& c -tc "ot 'i!&' & &cti2&3 a' o-t&r an! inn&r !ia+&t&r'*44++ an! $44++ r&',&cti2& y. T & +a5i+-+ int&n'ity o ,r&''-r& at any,oint in t & contact '-r ac& i' not to &5c&&! 4.1N6++ $. I t & co& ici&nt o

riction i' 4.*3 !&t&r+in& t & ,o &r tran'+itt&! "y a c -tc at a ',&&! $744r,+or t o ty,&' o a''-+,tion'3 t at i'3 or -ni or+ ,r&''-r& an! -ni or+ &ar.

8i2&nSingle plate clutchBoth sides effective4uter diameter of clutch plate d 8 0?? mm

4uter radius r 8 @?mmnner diameter of clutch plate d 8 ?? mm



4/19

Unit V: Friction in Machine Element KOM nner radius r 8 ??mm/a$imum intensity of pressure p ma$ 8 ?. 5=mm

offecient of friction 6 8 ?.0Speed 5 8 @?? r.p.m.

To in!:ower transmitted by a clutch at a speed @??rpm for two types of assumptions )i* For uniform pressure and

)ii* For uniform wear

So -tion1. Uni or+ &ar t &ory9o &r tran'+itt&! "y a c -tc 3 9 : T.;Tor C (r 1 ? r $)

ntensity of pressure )p* is ma$imum at the inner radius )r * for uniform wear, pma$.r 8

8 ?. A ?? 8 ? 5=mm W 8 7 )r 3 r * 8 7 A ? ) @? 3 ??* 8 0 1 5M&an ra!i-' o t & riction '-r ac&' or -ni or+ &ar3

R radius/ean r r += ??@? += 8 @mm 8 ?. @m

Tor


5/19

Unit V: Friction in Machine Element KOM)iv* Ratio of :ower transmitted with uniform wear to that of uniform pressure

So -tion(i) Ti+& to attain t & - ',&&! "y t & +ac in&

onaccelerati"ngularlocity"ngular ve

<;

t == =t

ω α

B?locity"ngular ve

N π ω =

B?@? ×= π

; 8 . C rad=s

inertiaof /omentedtransmitt%or2ue%

8 ; t

B?

N π ω =

B?@? ×= π 8 . C rad=s

> 8 ; t 8 . CA .0@ 8 .@ rad"ngle turned by the driven shaft >

? t t α ω θ += ( )

××+×= [email protected]@.0@.? 8 0?.E@ rad

#nergy lost in friction 8 % )> -> * 8 E .0C A ) .@-0?.E@* 8 5-m 8 . k5-m(iii) Int&n'ity o ,r&''-r& or -ni or+ ,r&''-r& con!ition

( )r r 7W

p pressureof ntensity −="$ial thrust same for both uniform pressure and uniform wear theory

%herefore, W 8 @?E.D 5

( )??B.?.?7@?E.DB

p pressureof ntensity−

=

p 8 E@??? 5=m 8 E@ k5=m

(i2) Ratio o 9o &r tran'+itt&! it -ni or+ &ar to t at o -ni or+ ,r&''-r&:ower transmitted : 8 %;

For &niform wear% 8 E .0C 5-m

; 8 . C rad=s:ower transmitted for uniform wear: 8 E .0CA . C 8 CD1.D W

For &niform :ressure%or2ue % 8 n6WR

n 8 ,for both sides of plate effective 68?.0 )cofficient of friction*"$ial thrust same for both uniform pressure and uniform wear theory%herefore, W 8 @?E.D 5

( )( )...-

0.

0-

r r

r r

0

.R radius/ean

−

−=

( )( )

00

?B.?.?

?B.?.?0 −

−=

R8?.?C mTor


6/19

Unit V: Friction in Machine Element KOM : 8 %.; 8 E0.CD A . C 8 D01.11 W

11.D01D.CD1

pressureuniform:ower with wear uniform:ower with = 8?.DC

*. A riction c -tc o +- ti/, at& ty,& i' +&ant or tran'+ittin# a ,o &r o 77%W at 1B44 r,+. Co& ici&nt o riction or t & riction '-r ac&' i' 4.1. A5iaint&n'ity o ,r&''-r& i' not to &5c&&! 1@4 %N6+ $ . T & int&rna ra!i-' i' B4 ++an! i' 4. ti+&' t & &5t&rna ra!i-'. D&t&r+in& t & n-+"&r o , at&' n&&!&! totran'+it t & r&


7/19

Unit V: Friction in Machine Element KOM "n open belt drive is used when the driven pulley is desired to be rotated in samedirection as the driving pulley as shown in Figure enerally, the centre distance for an open-belt drive is 1 to m.

$. Cro''&! or t i't "& t !ri2&

V& ocity Ratio o & t Dri2& d 8 'iameter of the driver,d 8 'iameter of the follower,

5 8Speed of the driver in r.p.m and 58 Speed of the follower in r.p.mGength of the belt that passes over the driver, in one minute 8 7d 5

dd

5 5 ratioHelocity =

When the thickness of the belt )t* is considered, then velocity ratio

t

t

+

+=dd

5 5 ratioHelocity

:eripheral velocity of the belt on the driving pulley,B?

d N v

π =

:eripheral velocity of the belt on the driven or follower pulley,B?

d N v

π =

When there is no slip, then v 8 v

B?d

B?d N N π π =

.

-

-

.

d

d

5

5=

V& ocity ratio o co+,o-n! "& t !ri2&

Helocity ratio of pulleys and

.

-

.

- d

d N

N = ------- )i*

Helocity ratio of pulleys 0 and 1,

1

0

0

1 dd N

N = ------------- )ii*

/ultiplying e2uations )i* and )ii*,

1

0

0

1 dd d

d

N

N

N

N

×=×

1

01 dd d

d

N

N ×=

)5 85 0, being keyed to the same shaft*

Department of Mechanical, AAMEC Page #

" crossed-belt drive isadopted when the driven

pulley is to be rotated inopposite direction to that of the driving pulley " cross belt drive cantransmit more power than anopen-belt drive as the angle of wrap is more.

+owever, the belt has to bend in two different planesand it wears out more.


8/19

Unit V: Friction in Machine Element KOMif there are si$ pulleys, then

B

@

1

0B dd

d

d d

d

N

N ××=

drivensof diametersof :roductdriversof diametersof :roduct

driver firstof Speeddrivenlastof Speed =

S i, o & t Helocity of the belt passing over the driver per second

−=

??B?

s N d v

Helocity of the belt passing over the follower per second

−=

??B?

s N d v

−=

??

s

d

d

N

N

)s8s 9s *f thickness of the belt )t* is considered, then

−

++=

??

s

t d

t d

N

N

Cr&&, o & t I , I - Stress in the belt on the tight and slack side respectively, and# 8 JoungKs modulus for the material of the belt

σ

σ

++×=

E

E

d

d

N

N

L&n#t o O,&n & t Dri2&

( ) ( ) x

r r xr r L

−+++=π

( ) ( ) x

d d xd d L

1.

.

..-

.-

−+++=

π

L&n#t o a Cro'' & t Dri2& (

( ) ( ) x

r r xr r L.

.-.- .

++++= π

( ) ( ) x

d d xd d L

1.

.

..-

.-

++++=

π

9o &r Tran'+itt&! "y a & t

Department of Mechanical, AAMEC Page $


9/19

Unit V: Friction in Machine Element KOM% and % 8 %ensions in the tight and slack side of the belt respectively in 5r and r 8 Radii of the driver and follower respectively, andv 8 Helocity of the belt in m=s%he effective turning )driving* force at the circumference of the follower is thedifference between the two tensions )i.e. % - % *Work done per second )or* power transmitted 8 )% - % * v

Ratio o Dri2in# T&n'ion' or F at & t Dri2&

µθ eT T =

An# & o contact or a,

O,&n "& t ! ri2&

( ) rad C?7

C?> α −=

−=

x- r r sin<

Cro'' "& t !ri2&

( ) rad C?7C?> α +=

+=

x- r r sin<

C&ntri -#a T&n'ion mvT c =

%r 3 /a$imum or %otal tension in the beltNot&'

. When the centrifugal tension is taken into account, then total tension in the tightside,

%r 8 % 9% and total tension in the slack side, % r 8 % 9%

. :ower transmitted : 8 )% r -%r * v 8 L)%9% * 3 )% -% *M v 8 )%-% * v%hus we see that centrifugal tension has no effect on the power transmitted.

0. %he ratio of driving tension may also be written as

µθ =

−−

C r

C r

T T

T T log0.

Ma5i+-+ T&n'ion in t & & t entrifugal tension is considered, then % 8 % 9 %

:ower transmitted by a belt : 8 )% -% * v: 8 )%-% * v.

8 )%-mv * v.8 )%.v-mv 0* )Substituting % c 8 mv *% -0mv 8 ?

% -0% 8?%80%

Not&' (. % 8%-% and for ma$imum power

00

T T T T =−=

. Helocity of the belt for the ma$imum powerm

T v

0=

Initia T&n'ion in t & & t (

?

T T T += C

T T T ++=0. Fin! t & ,o &r tran'+itt&! "y a "& t r-nnin# o2&r a ,- &y 44++ !ia+&t&rat *44 r,+3 μ :4.* an! an# & o a, 1@4 4 an! +a5i+-+ t&n'ion in t & "& t i'$.07*%N.

8i2&n:ulley diameter d 8 E?? mm8?.EmSpeed 5 80?? rpm

oefficient of friction 6 8 ?. C"ngle of lap > 8 ? ? 8 .ED0 rad

/a$imum tension in belt % 8 .1@0 k5 8 .1@0A ?0 5

To in!:ower transmitted by the belt

So -tion:ower transmitted : 8 )% - % * v

Department of Mechanical, AAMEC Page %


10/19

Unit V: Friction in Machine Element KOM

µθ eT

T =

ED0.C.? ×= eT

T

CB.=T

T

CB.

T T =

CB.?1@0. 0×=

5.00% =

B?B?

d N d N vvv

π π ====

B?

d N vv

π ==

B?E.?0?? ××= π 8 ?.DD m=s

:ower transmitted : 8 )% - % * v8 ) 1@0 3 .00* A ?.DD

8 0@0 .D W 8 0.@0 kW

7.T o ,- &y'3 on& 074 ++ !ia+&t&r an! ot &r $44++ !ia+&t&r ar& in ,ara &' a t' 1. 7+ a,art an! ar& conn&ct&! "y a cro'' "& t. Fin! t & &n#t o t & "& tr&


11/19


12/19


µθ eT

T =

E..? ×= eT

T

C.=T

T

.C%

% =:ower transmitted : 8 )% - % * v

@[email protected].

?@ 0 ×

−=×

T T

−=

C.C.

10.1 1 T T

C..@B? T T −=

= C.?.@B?

T

5B1.B?0=

b.t%

b.t%

IStress ma$ == B 5=m?0. B?B?.??.

0 B?.B1 ×=×=

I 8 0. ? 5=mm

Cro'' "& t !ri2&

b.t%

b.t%

IStress ma$ ==:ower transmitted : 8 )% - % * v

m=s@[email protected]=v

µθ eT

T

=

( ) rad C?7

C?> α +=

+=

x- r r sin<

+=

@..?@@.?

sin - 8 0?.CE ?

( ) rad C?7

C?> α += ( )( ) C?7

CE.?0C? ×+= 8 1. rad

µθ eT

T =

.1.? ×= eT

T

@0.=T

T

.@0%


@[email protected]@0.

?@ 0 ×

−=×

T T

−=

@0.@0.

10.1 1 T T

@0.D1.0@EC T T −=

=

@0.D1.0@EC

T

5E.00D% =

b.t%

b.t%

IStress ma$ ==

B 5=m?00D.?.??.

00D. E ×=×

= I 8 .00D 5=mm

. Fin! t & ,o &r tran'+itt&! "y a "& t r-nnin# o2&r a ,- &y 44++ !ia+&t&rat *44 r,+3 μ :4.* an! an# & o a, 1@4 4 an! +a5i+-+ t&n'ion in t & "& t i'$.07*%N.8i2&n



13/19

Unit V: Friction in Machine Element KOM:ulley diameter d 8 E?? mm8?.EmSpeed 5 80?? rpm

oefficient of friction 6 8 ?. C"ngle of lap > 8 ? ? 8 .ED0 rad

/a$imum tension in belt % 8 .1@0 k5 8 .1@0A ?0 5

To in!:ower transmitted by the belt

So -tion:ower transmitted : 8 )% - % * v

µθ eT

T =

ED0.C.? ×= e

T

T

CB.=T

T

CB.

T T

=

CB.?1@0. 0×=T 5.00=

B?B?

d N d N vvv

π π ====

B?

d N vv

π ==

B?E.?0?? ××= π 8 ?.DD m=s

:ower transmitted : 8 )% - % * v 8 ) 1@0 3 .00* A ?.DD 8 0@0 .D W : 8 0.@0 kW

B. A "& t !ri2& tran'+it' B %W o ,o &r ro+ a ' a t rotatin# at $04 r,+ toanot &r ' a t rotatin# at 1@4 r,+. T & "& t i' B ++ t ic%. T & !ia+&t&r o t &'+a &r ,- &y i' @44 ++ an! t & t o ' a t' ar& 7 + a,art. T & co& ici&nt o

riction i' 4.$7. I t & +a5i+-+ 'tr&'' in t & "& t i' i+it&! to *N6++ $3 in! t &i!t o t & "& t or (1) An o,&n "& t !ri2& ($) A cro''/"& t !ri2&.

8i2&n:ower transmitted by the belt 8 CkW

Speed of smaller shaft 5 8 1? rpmSpeed of bigger shaft 5 8 ? rpm%hickness of belt t 8CmmSmaller pulley diameter d 8 ?? mm

entre distance 8 @ moefficient of friction 6 8 ?. @

/a$imum stress in the belt 8 0 5=mmTo in!

Width of the belt by)i* "n open belt drive) ii* " cross-bel t drive

So -tionO,&n "& t !ri2&

b.t%

Stress ma$=σ

I.t

% bwidth ma$=

%ma$ 8 % :ower transmitted : 8 )% - % * v

( ) ( )B?

d

B?

d ..--.-

t N t N vvv

+=

+===

π π

( )B?

d ...

t N vv

+==

π ( )B?

?C.?B.?1? +××= π m=s@[email protected]=

µθ eT

T =



14/19


( ) rad C?7

C?> α −=

−=

x- r r sin<

.

-

.

-

-

.

r

r

d

d

N

N ==

N

N d d ×=

B?1?

B.? ×=

d 8?.Dmr 8 d = 8?.D= 8 ?.1@ m

−=

x- r r sin<

−=

@0.?1@.?

sin - 8 .E D?

( ) rad C?7

C?> α −= ( )( ) C?7

E D.C? ×−= 8 0.?C rad

µθ eT

T

=?C.0@.? ×= e

T

T

B.=T

T

. B%


@[email protected].?C0

×

−=× T T

−=

B.B.

.D0B T T

B.E.? 0 T T −=

=

B.E.? 0

T

5B.E1% =

I.t%

.tI%

bWidth ma$ == m?E. B?C.??0

E1 .B 0-B ×=××

=

b 8 E. mm

Cro'' "& t !ri2&

I.t%

bwidth ma$=:ower transmitted : 8 )% - % * v

m=s@[email protected]=v

µθ e

T

T =

( ) rad C?7C?> α +=

+=

x- r r sin<

+=

@0.?1@.?

sin - 8 C. E?

( ) rad C?7

C?> α += ( )( ) C?7

B E.CC? ×+= 8 0.110 rad

µθ eT

T =

110.0@.? ×= e

T

T

0B@.=T

T

.0B@%

% =



15/19

Unit V: Friction in Machine Element KOM:ower transmitted : 8 )% - % * v

@[email protected].

?C 0 ×

−=×

T T

−=

[email protected]@.

.D0B T T

[email protected] T T −=

=

[email protected] 5.B=

I.t%

.tI%

bWidth ma$ == m?B.EB?C.??0

B . 0-B ×=××

=

b 8 .E mm

. T o ,- &y'3 on& 074++ !ia+&t&r an! ot &r $44++ !ia+&t&r ar& on ,ara &' a t' $.1 + a,art an! ar& conn&ct&! "y a "& t3 a' a cro'' "& t !ri2&. T & ar#&r,- &y rotat&' at $$7 r,+. T & +a5i+-+ ,&r+i''i" & t&n'ion in t & "& t i' 1%Nan! t & co& ici&nt o riction "&t &&n t & "& t an! ,- &y i' 4.$7.Fin! t & ,o &rt at can "& tran'+itt&!.

8i2&n'iameter of the pulley one d 8 E?? mm8?.Em r 8?.0@m'iameter of the second pulley d 8 ?? mm8?. m r 8?. m

entre distance x 8 . mSpeed of larger pulley 5 8 @ rpm/a$imum tension in belt % 8 k5 8 A ? 0 5

oefficient of friction 6 8 ?. @To in!:ower transmitted by the beltSo -tion:ower transmitted : 8 )% - % * v

µθ eT

T =

( ) rad C?7

C?> α −= )"ssume, open belt drive*

−=

x- r r sin<

−=

.?.0@.?

sin - 8 .C0E?

( ) rad C?7

C?> α −= ( )( ) C?7

C0E.BC? ×−= 8 .D?0 rad

µθ eT

T =

D?0.@.?0? ×=× e

T

% 8 1C0.D 5

B?d

B?d N N

vvv π π ====

B?d N vv

π ==

B?E.?@××= π 8 C. 1E m=s

:ower transmitted : 8 )% - % * v 8 ) ??? 3 1C0.D * A C. 1E 8 1 @@. W14. A &at &r "& t i' r&


16/19


t

% b ma$

σ =

%ma$ 8 % 9%:ower transmitted : 8 )% - % * v

B?d

B?d N N

vvv π π ====

B?d N

vv π

==

B?.@? ××= π

v 8 @.E m=s

µθ eT

T =

CC.0.? ×= eT

T

0E0.

T T =:ower transmitted : 8 )% - % * v

E.@0E0.

[email protected] 0 ×

−=×

T T

−=

0E0.0E0.

1?0.1EE T T

0E0.CC.0 T T −=

=

0E0.CC.0

T

5.C @% =% 8 mv

V m ×= ρ GH ××= t b

"ssume, G 8 m?.?H ××= b

V m ×= ρ ?.???? ×××= bm8 ? b

% 8 mv 8 ?b A @.E 8 1 C.?1 b

%ma$ 8 % 9% 8 C @. 9 1 C.?1b

I.t

% bwidth ma$=

?.??.@

1BC.?1bC @. b B ××

+=

@??? b 8 C @. 9 1 C.?1b@0 .D b 8 C @.

DB.@0C @.

b =

m?.?B@C1 b = 8 @.C1 mm

9art/A. Gist down the laws of friction. (May6G-n& $41*3 R$44B6$414). State the laws of dry friction. (May6G-n& $41*3 R$4406$44 )

0. 'ifferentiate between self locking and overhauling of screw. (May6G-n& $41$3R$44B)1. State the condition of self locking of screw !ack (No26D&c $4103 R$4406$44 )@. Why self locking screws have lesser efficiencyO (No26D&c $41$3 R$44B)

. What is the ma$imum efficiency a screw !ackO (May6G-n& $4103 R$4406$44 )E. What is friction angleO (No26D&c $4103 R$44B6$414)C. 'efine anti -friction bearing. (No26D&c $41*3 R$44B6$414)

D. 'ifferentiate multiplate clutch and cone clutch. (No26D&c $41*3 R$44B6$414)?. /ention the significance of multi-plate clutch. (No26D&c $41*3 R$4406$44 )

. 'efine velocity ratio (May6G-n& $4103 R$44B6$414)

. 'istinguish between open and cross belt drive in terms of its application.(May6G-n& $41*3 R$44B6$414)

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17/19

Unit V: Friction in Machine Element KOM0. n an open belt drive the diameter of the smaller pulley is @? mm. %he diameter

of the bigger pulley is 1?? mm, and the centre distance is .? m. find the angle of lapfor the smaller pulley. (May6G-n& $41*3 R$4406$44 )

1. State the functional difference between a clutch and a brake. (May6G-n& $41$3R$44B)

@. P%he brake drum of a single block brake of diameter 0 ? mm is rotating at 1 ?rpm. f the angle of contact is D? ?, co-efficient of friction between the drum and

brake block is ?. @, determine the e2uivalent co-efficient of friction (No26D&c $41*3

R$4406$44 ). What is meant by a self-locking and self-energised brakeO (No26D&c $41$3R$44B)

9art/Friction in 'cr& t r&a!'

. Gist the various types of friction. )1* (No26D&c $41*3 R$44B6$414)

. 'erive the force analysis of a body resting on an inclined plane with force inclinedto the plane. ) * (No26D&c $41*3 R$44B6$414)

0. 'erive an e$pression for the effort re2uired to raise a load with screw !ack taking

friction into consideration.)C* (May6G-n& $4103 R$44B6$414)

1. " s2uare threaded bolt with a core diameter of @ mm and pitch of ?mm istightened by screwing a nut. %he mean diameter of the bearing surface of the nut is

? mm. %he coefficient of friction for the nut and bolt is ?( and for the nut and bearing surface it is ?. @. 'etermine theQ force re2uired at the end of a 1?? mm longspanner, if the load on the bolt is k5. ) * (No26D&c $410 R$4406$44 3 No26D&c$41*3 R$4406$44 )

@. " @?mm diameter value, against a steam pressure of /5=m is acting, is closed by means of a s2uare threaded screw @?mm in e$ternal diameter with mm pitch. f the coefficient of friction is ?. , find tor2ue re2uired to turn the handle. )C*(May6G-n& $4103 R$44B6$414)

. %he mean diameter of the screw !ack having pitch of ?mm is @?mm. " load of ?k5 is lifted through a distance of E? mm. Find the work done in lifting the load

and efficiency of the screw !ack when )i* the load rotates with the screw, and )ii* theload rests on the loose head which does not rotate with screw. %he e$ternal andinternal diameter of the bearing surface of the loose head is ?mm and ?mm

respectively. %he coefficient of friction for the screw as well as the bearing surfacemay be taken as ?.?C. (May6G-n& $41*3 R$4406$44 )

E. " screw-!ack has a s2uare thread of mean diameter ?mm and pitch Cmm.%hecoefficient of friction at the screw thread is ?.?D." load of 0k5 is to be lifted through

?mm. 'etermine the tor2ue re2uired and the work done in lifting the load through?mm.Find also the efficiency of the !ack.)C* (No26D&c $41$3 R$44B)

C. %he following data related to a screw !ack :itch of a thread screw 8 Cmm,diameter of the screw thread 8 1?mm, oefficient of friction between screw and nut8 ?. , Goad 8 ?k5."ssuming that the load rotates with screw, determine(

(i) %he ratio of tor2ues re2uired to raise and lower the load.(ii) %he efficiency of the machine.) * (May6G-n& $41$3 R$44B)

&arin#'D. n a thrust bearing, the e$ternal and internal diameters of the contacting surfacesare 0 ?mm and ??mm respectively. %he total a$ial load is C?k5 and the intensity of

pressure is 0@?k5=m . %he shaft rotates at 1??rpm. %aking the coefficient of frictionas ?.? , calculate the power lost in overcoming the friction and the number of collarsre2uired. )C*(No26D&c $41$3 R$44B)

?. " vertical shaft of ??mm diameter rotating at @? rpm rests on a flat end footstep bearing. %he coefficient of friction is e2ual to ?.?@ and shaft carries a verticalload of @ k5. Find the power lost in friction assuming the following conditions( ) * &niform pressure ) * &niform wear. ) * (May6G-n& $41*3 R$44B6$414)

. " vertical shaft 1? mm diameter rotating at ? rpm rests on a flat end foot step bearing. %he shaft carries a vertical load of 0? k5. %he coefficient of friction is ?.? .#stimate the power lost is friction, assuming uniform pressure and uniform wear. )C*(No26D&c $41*3 R$44B6$414)

C -tc &'

. With a neat sketch, e$plain the working of a multi-plate clutch. )C*(No26D&c $4103 R$4406$44 )

. " single plate clutch both sides effective, has outer and inner diameters 0??mmand ??mm respectively. %he ma$imum intensity of pressure at any point in thecontact surface is not to e$ceed ?. 5=mm . f the coefficient of friction is ?.0,determine the power transmitted by a clutch at a speed @??rpm for two types of

Department of Mechanical, AAMEC Page 1#


18/19

Unit V: Friction in Machine Element KOMassumptions, that is, for uniform pressure and uniform wear ) ?* (May6G-n& $41$3R$44B)

0. " friction clutch of multi-plate type is meant for transmitting a power of @@ kW atC?? rpm. oefficient of friction for the friction surfaces is ?. . "$ial intensity of

pressure is not to e$ceed ? kN/m2. %he internal radius is C? mm and is ?.E times thee$ternal radius. 'etermine the number of plates needed to transmit the re2uired

tor2ue. ) ?* (May6G-n& $41*R$44B6$4143 No26D&c $41*3 R$44B6$414)

@. " friction clutch is used to rotate a machine from a shaft rotating at a uniformspeed of @? rpm. %he disc-type clutch has both of its sides effective, the coefficientof friction being ?.0. %he outer and the inner diameters of the friction plate are ??mm and ? mm respectively. "ssuming uniform wear of the clutch, the intensity of

pressure is not more than ?? k5=m . f the moment of inertia of the rotating parts of the machine is .@ kg-m . 'etermine the time to attain the full speed by the machineand the energy lost in slipping of the clutch. What will be the intensity of pressure if the condition of uniform pressure of the clutch is consideredO "lso, determine theratio of power transmitted with uniform wear to that of uniform pressure. (No26D&c$41*3 R$4406$44 )

& tE. 'erive an e$pression for the centrifugal tension in a belt passing round a pulley

rim ) * (No26D&c $41$3 R$44B)

C.%wo pulleys, one 1@? mm diameter and other ??mm diameter are in parallelshafts .D@m apart and are connected by a cross belt. Find the length of the beltre2uired and angle of contact between the belt and each pulley. What power can betransmitted by the belt when the larger pulley rotates at ?? rpm if the ma$imum

permissible tension in the belt is k5 and the co efficient of friction between the beltand pulley is ?. @O ) * (May6G-n& $4103 R$44B6$414)

D. " ?? mm wide and ? mm thick belt transmits @ kW of power, between two

parallel shafts. %he distance between the shaft centres is .@ m and the diameter of the smaller pulley is 11? mm. %he driving and driven shafts rotate, atQ ? rpm and

@? mm respectively. %he coefficient of function is ?. . Find the stress in the belt if the two pulleys are connected by) * "n open belt and )@*) * " cross belt. )@* (No26D&c $4103 R$4406$44 )

?. %wo shafts whose centres are m apart are connected by a H belt drive.%he driving pulley is supplied with ?? W and has an effective diameter of 0??mm. t runs at 0E@ rpm. %he angle- of groove on the pulley is 1?T .%he permissibletension in 1?? mm cross sectional area of the belt is . /:a. %he density of the beltis ?? kg=mm 0 and oefficient of friction is?. C. #stimate number of belts re2uired.(May6G-n& $41*3 R$4406$44 )

. Find the power transmitted by a belt running over a pulley E??mm diameter at

0?? rpm, μ 8?.0 and angle of lap ?? and ma$imum tension in the belt is .1@0k5.) * (May6G-n& $41*3 R$44B6$414)

. " belt drive transmits C kW of power from a shaft rotating at 1? rpm to another shaft rotating at ? rpm. %he belt is C mm thick. %he diameter of the smaller pulleyis ?? mm and the two shafts are @ m apart. %he coefficient of friction is ?. @. f thema$imum stress in the belt is limited to 0 5=mm , find the width of the belt for ) * "n open belt drive )@* ) * " cross-belt drive. )@* (No26D&c $41*3 R$4406$44 )

0. %wo pulleys, one 1@?mm diameter and other ??mm diameter are on parallelshafts . m apart and are connected by a belt, as a cross belt drive. %he larger pulleyrotates at @ rpm. %he ma$imum permissible tension in the belt is k5 and the

coefficient of friction between the belt and pulley is ?. @.Find the power that can betransmitted. )C* (May6G-n& $41$3 R$44B)

1. " leather belt is re2uired to transmit E.@ kW from a pulley . m in diameter,running at @? rpm. %he angle embraced is @ ? and the coefficient of friction

between the belt and the pulley is ?.0. %he safe working stress for the leather belt is.@/:a the density of leather is ???kg=m 0 and thickness of belt is ?mm.

'etermine the width of the belt taking centrifugal tension into account. ) ?*(No26D&c $41$3 R$44B)

Ro,&@. %he following data relate to a rope drive(

:ower transmitted 8 ? kW 'iameter of pulley 8 1C?mm Speed 8 C?rpm

"ngle of lap on smaller pulley 8 ?U 5umber of ropes 8 C/ass of rope=m length 8 1C kgGimiting working tension 8 0 k5

oefficient of friction 8 ?.0"ngle of groove 8 11 ?

f is the girth of rope in m. 'etermine the initial tension and diameter, of eachrope. (No26D&c $4103 R$4406$44 )

Department of Mechanical, AAMEC Page 1$


19/19


ra%&

. " simple brake as shown in Figure is used on a shaft carrying a flywheel of mass1@? kg. %he radius of gyration of the flywheel is @?? mm. and runs at 0 ? rpm. %hecoefficient of friction is ?. and the diameter of brake drum is @? mm, determine thefollowing( ) * %or2ue applied due to a hand load of @?5 )1*

) * %he number of turns of the wheel before it is brought to rest. )1* )0* %he time re2uired to bring it to rest from the moment of application of the brake. ) * (May6G-n& $41*3 R$44B6$414)

E. n a simple band brake, one end of the band is attached to the fulcrum of a lever.%he other end is attached at a distance of b from the fulcrum. %he effort is applied at

the end of the lever. 'erive an e$pression for braking tor2ue, in terms of effort. )C*(May6G-n& $41$3 R$44B)

Department of Mechanical, AAMEC Page 1%

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