clutch final 01

7/29/2019 Clutch Final 01

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Clutch Theory of machines II Prof. Pradeepkumar Suryawanshi

DON BOSCO INSTITUTE OF TECHNOLOGY, MUMBAI

Department of Mechanical EngineeringTheory of Machine II (T.E. Sem- V)

Module 01

CLUTCH1.1 Clutch:A clutch is a device used to transmit the rotary

motion of one shaft to another when desired. Theaxes of the two shafts are coincident. It can also

be described as a machine member used to

connect a driving shaft to a driven shaft so thatthe driven shaft may be started or stopped at will,

without stopping the driving shaft. Thus it is an

interruptible connection between two shafts.

1.2 Classification of Clutches:Clutches can be classified as follows:

Positive Clutches:

a) Square Jaw Clutch

b) Spiral Jaw Clutch

Friction Clutches:

a) Single Plate Clutchb) Diaphragm spring type single

plate clutch

c) Multiplate Clutchd) Cone clutch

e) Semi-centrifugal Clutchf) Centrifugal Clutchg) Wet Clutch

Fluid Flywheel

1.3 Positive Clutches:

The positive clutches are used when a positive

drive is required. This type of clutch is designed

to transmit torque without slip. It is the simplestof all shaft connectors, sliding on a keyed shaft

section or a splined portion and operating with a

shift lever on a collar element. The simplest typeof a positive clutch is a jaw or claw clutch. The

jaw clutch permits one shaft to drive another

through a direct contact of interlocking jaws. Itconsists of two halves one of which is

permanently fastened to the driving shaft by a

sunk key. The other half of a clutch is movable

and it is free to slide axially on the driven shaft,but it is prevented from turning relatively to its

shaft by means of feather key. The jaws of the

clutch may be of square type or spiral type as

shown in Fig. 1.1

Fig. 1.1 Positive clutches. (a) Square-jaw clutch. (b)

Spiral-jaw clutch.

Fig. 1.2 Square-jaw clutch.

A square jaw type is used where engagement and

disengagement in motion and under load is not

necessary. This type of clutch will transmitpower in either direction of rotation. The spiral

jaws may be left-hand or right-hand, because

power transmitted by them is in one directiononly. This type of clutch is occasionally used

where the clutch must be engaged and

disengaged while in motion. Engagement speedshould be limited to 10 rpm for a square-jaw

TE Mech Sem-V/TOM-II/Module:01 Page 1


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clutch and 150 rpm for a spiral-jaw clutch. If

disengagement under load is required, the jawsshould be finish-machined and lubricated. The

use of jaw clutches are frequently applied to

sprocket wheels, gears and pulleys. In such a

case the non-sliding part is made integral with

the hub. Fig 1.3 shows the photographic views ofsquare and spiral jaw clutches.

Fig 1.3 Photographic views of square and spiral jaw

clutches

1.4 Principle of Friction Clutches:

The principle of friction clutch may be explained

by means ofFig.1.4

Fig.1.4 Principle of Friction ClutchesLet disc C keyed to shaft A, rotates at some

speed, say N rpm. Initially when clutch is not

engaged shaft B and disc D keyed to it arestationary. Now apply some axial force W to the

disc D so that it comes in contact with disc C. As

soon as the contact is made the force of friction

between C and D will come into play andconsequently the disc D will start rotating. The

speed of D depends upon friction force present,

which in turn, is proportional to the force Wapplied. If W is increased gradually, the speed of

D will be increased consequently till the stage

comes when the speed of D becomes equal to the

speed of C. Then the clutch is said to be fully

engaged.

1.5 Single Plate Clutch:

A single disc or plate clutch shown in Fig.1.5consists of a clutch plate C whose both sides are

faced with a friction material G.

Fig.1.5 Single disc or plate clutchIt is mounted on a hub which is free to move

axially along the splines of the driven shaft Dand is held between the flywheel A and the

pressure plate E. The pressure plate is mounted

inside the clutch body which is bolted to theflywheel. Both the pressure plate and flywheel

rotate with engine crankshaft or the driving shaft.

The pressure plate pushes the clutch plate

towards the flywheel by a set of coil springs S.The springs are arranged circumferentially which

provide axial force to keep the clutch in engagedposition. The three levers known as releaselevers or fingers are carried on pivots suspended

from the case of the body as shown in Fig 1.6.

These are arranged in such a manner that thepressure plate moves away from the flywheel by

the inward movement of a thrust bearing. A

pedal is provided to pull the pressure plate



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against the spring force whenever it is required

to be disengaged. Ordinarily clutch remains inengaged position.

Fig.1.6 Single disc or plate clutch with linkage

When the clutch pedal is pressed down, itslinkage forces the thrust release bearing to move

in towards the flywheel and pressing the longer

ends of the lever inward. The levers are forced toturn on their suspended pivot and the pressure

plate moves away from the flywheel by the knife

edges, thereby comprising the clutch springs as

shown in Fig 1.7. With the movement of thepressure plate, the friction plate is released and

clutch is disengaged. On the other hand, whenthe foot is taken off from the clutch pedal, the

thrust bearing is moved back by the levers. This

allows the springs to extend and thus the

pressure plate pushes the clutch plate backtowards the flywheel.

Fig 1.7 Operation of the release levers

The axial pressure exerted by the spring providesa frictional force in the circumferential direction

when the relative motion between driving and

driven members tends to take place. If the torquedue to this frictional force exceeds the torque to

be transmitted, then no slipping takes place and

power is transmitted from the driving shaft to the

driven shaft.

Fig 1.7 shows exploded photographic view and

Fig 1.8 shows cut away section of clutchassembly of single plate clutch.

Fig 1.7 Exploded photographic view of single plate clutch



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Fig 1.8 Cut away section of clutch assembly of single plate

clutch

Advantages:

1. As compared to cone clutch, the pedalmovement is less in this case which leads

to easier gear changing.

2. It is more reliable compared to cone

clutch

Disadvantages:

As compared to cone clutch, the springshave to be stiffer and this means greater force

required to be applied by the driver while

disengaging.

1.6 Diaphragm spring type single plate clutch:

The construction of this type of clutch is similarto the single plate type of clutch described above

except that here diaphragm springs (also knownas Belleville springs) are used instead of theordinary coil springs. In the free condition, the

diaphragm spring is of conical form, but when

assembled, it is constrained to an approximately

flat condition because of which it exerts a loadupon the pressure plate. A diaphragm spring type

clutch is shown in Fig 1.9 and Fig 1.10 shows a

diaphragm spring in free condition.

Fig 1.9 A diaphragm spring type clutch

Fig 1.10 A diaphragm spring in free condition

Advantages:

This type of clutch has now virtually

superseded the earlier coil spring design in many

countries in clutch sizes ranging upto 270 mm indiameter. However in case of heavy vehicles, the

coil spring type clutches are still being used,

because of the difficulty to provide sufficientclamping force by a single diaphragm spring.

The diaphragm spring offers following distinct

advantages.

1. It is more compact means of storingenergy. Thus compact design results in

smaller clutch housing.

2. As the diaphragm spring iscomparatively less affected by the

centrifugal forces, it can withstand higher

rotational speed. On the other hand, thecoil springs have tendency to distort in

the transverse direction at higher speeds.

3. In case of coil springs, load-

deflection curve is linear. Therefore with



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the wear of the clutch facing the springs

have less deflection due to which theywould apply less force against the clutch

plate. On the other hand, in case of

diaphragm spring the load-deflection

curve is not linear (Fig 1.11).

Fig 1.11 Load- Deflection curve

Therefore in this case as the clutch facing

wears, force on the plate gradually

increases, which means that even in wornout condition, the spring force is not less

than its value in case of new clutch.Further it is also seen from Fig 1.12 that

the load-deflection curve depends uponthe ratios h/t, where h is the free dish

height and tis the thickness of the spring.

Therefore in this case with suitabledesign, the load-deflection curve can be

improved to give lower release loads.

Fig 1.12 Effect ofh/ton Load- Deflection curve

4. The diaphragm acts as both clampingspring and release levers. Therefore many

extra parts like struts, eye bolts, levers,

etc. are eliminated in the diaphragmspring because of which the loss of

efficiency due to friction wear of these

parts also does not occur, which results inelimination of squeaks and rattles.



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Fig 1.13 Cut away section of clutch assembly of single

plate clutch (Diaphragm spring type)

Fig 1.13 shows cut away section of clutch

assembly and Fig 1.14 shows explodedphotographic view of Diaphragm spring type

single plate clutch

Fig 1.14 Exploded photographic view of single plate

clutch (Diaphragm spring type)

1.7 Design of Single plate Clutch:

Consider two friction surfaces maintained in

contact by an axial thrust W as shown in Fig1.15(a). Let,

T = Toque Transmitted by clutch p = Intensity of pressure with which the

contact surfaces are held togetherr2 = ri = Inner radius of the friction surfacer1 = ro= Inner radius of the friction surface

= Coefficient of friction

Consider an elementary ring of radius r andthickness dr as shown in Fig 1.15(b).

Fig 1.15 Forces on a single plate clutch

We know that,

Area of the contact surface or friction surface,

dA = 2r.drNormal or axial force on the ring,dW = Pressure x Area = p . 2r.dr (i)

The friction force acting on the ring tangentially

at radius r,Fr = . dW = . p . 2r.dr

Hence Friction torque acting on the ring,

Tr = r. Fr = . p . 2r2.dr (1)

Friction torque of a clutch is usually calculated

on the basis of two assumptions. Each

assumption leads to a different value of torque.

In one case it is assumed that the intensity ofpressure on the contact surface or friction surface

is constant whereas in the second case, it is

uniform wearing of the contact surface or frictionsurface.

i) Considering uniform pressure:

Under this assumption, pressure is assumed to beuniform over the surface area and the intensity of

pressure is given by,

( ) (2)

areasectional-Cross

ForceAxial

22

io rrWp

pressure

=

=

Equation (2) can be obtained by integratingequation (i) within the limits from ri to ro.The total friction torque can be found by

integrating equation (1) within the limits from rito ro.



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The total friction torque acting on thefriction surface or on the clutch,

Substituting expression for p from equation (2),

( )

=

3.2

33

22

io

io

rr

rr

WT

)3(3

222

33

RWrr

rrWT

io

io =

=

SurfaceFrictionofRadiusMean3

222

33

=

=

io

io

rr

rrR

Where

ii) Considering uniform axial wear:

For uniform wear over an area, the intensity of

pressure should vary inversely proportional to

the elementary areas, i.e. it should decrease withincrease in the elementary area and vice-versa.

This can be illustrated by drawing a line with a

chalk. In doing so a little quantity of chalk isworn from the stick. Now if it is desired that the

chalk is worn by the same amount, but the length

of the line is doubled, the pressure on the chalkhas to be reduced to half that in the previous

case. Therefore for uniform wear, product of the

pressure applied and the distance traveled mustbe constant. For uniform wear of the surface, let

)4(CConstant

r2r2

rradiiatarearradiiatareawidt(equalrandrradiiatsurfacetheofwidth

ratsurfacesobetween twpressureNormal

ratsurfacesobetween twpressureNormal

oi

oi

oi

o

i

==

==

==

=

=

pr

rprp

bpbp

ppb

p

p

ooii

oi

oi

o

i

Thus in case of uniform wear of the twosurfaces, product of the normal pressure and the

corresponding radius must be constant. This

means the pressure is less where the radius ismore and vice-versa. Pressure on an elemental

area at radius r can be found as given below.

We know that,

dr2r.dr2rC=r.dr2.p=dW = C

[ ] ( )

( ))5(

2

222

force,axialTotal

io

io

r

r

r

r

rr

WC

rrCrCdrCW oi

o

i

=

==.=

We know that the friction torque acting on the

ring,Tr = r. Fr = . p . 2r

2.dr = 2..C.r. dr The total friction torque acting on thefriction surface or on the clutch,

Substituting expression for C from equation (5),

( )

( )

( )SurfaceFrictionofRadiusMean

2

)6(2

1

22.2

22

=+

=

=+=

=

io

io

io

io

rrR

Where

RWrrWT

rr

rr

WT

In general, total friction torque acting on the

friction surface or on the clutch is given by,

surfacesfrictionofpairsofNumberWhere

)7(

==

n

RWnT

Important points:

1. For a single plate clutch normally both sides

of the plate are effective. Hence a single plate

clutch has two pairs of surfaces in contact.

(i.e. n = 2)


=

=.=

3.2

3.22p..

33

32

io

r

r

r

r

rrpT

rpdrrT

o

i

o

i

=

=.=

2.2

2.2C2

22

2

io

r

r

r

r

rrCT

rCdrrT

o

i

o

i


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2. Since the intensity of pressure is maximum atthe inner radius(ri) of the friction surface,

equation (4) may be written as

Crp i =max3. Since the intensity of pressure is minimum at

the outer radius(ro) of the friction surface,

equation (4) may be written asCrp o =min

4. In case of a new clutch the intensity of

pressure is approximately uniform, but in an

old clutch, the uniform wear theory is more

approximate.

5. The uniform pressure theory gives higher

torque than the uniform wear theory. Hence

in case of friction clutches, uniform wear

theory should be considered, unless

otherwise stated.

1.8 Multiplate Clutch:The Multiplate clutch is an extension of the

single plate clutch where the number of friction

and metal plates is increased. The increase innumber of friction surfaces obviously increases

capacity of the clutch to transmit torque, the size

remaining fixed. Alternatively the overall

diameter of the clutch is reduced for same torquetransmission as a single plate clutch. Therefore

this type of clutch is in some heavy transport

vehicles and racing cars where high torque is to

be transmitted. Also, it finds application inscooters and motor cycles where space available

is limited.

The construction of a multiplate clutch as shown

in Fig 1.16 is similar to that of single plate typeexcept that all the friction plates in this case are

in two sets i.e. one set of plates slides in grooves

on the flywheel and the other one slides on the

pressure plate hub. Alternate plates shown in Fig

1.17 belong to each set.

In another way of arranging plates in a multiplateclutch, the inside plates usually made of steel are

fastened to the driven shaft to permit axial

motion except for the last plate. The outsideplates usually made of bronze are held by bolts

and are fastened to the housing which is keyed to

the driving shaft.

Fig 1.16 Multi-plate Clutch

Fig 1.17 Multi-plate Clutch (Inner and outer plates)

Design of a multiplate clutch:The total friction torque acting on the friction

surface or on the clutch is given by,

surfacefrictionofpairsofNumberWhere

)8(

==

n

RWnT

1. If N is the total number of friction plates inthe multiplate clutch, then 1= Nn

2. If1n is the number of plates on the

driving shaft and2

n is the number of

plates on the driven shaft, then

121 += nnn

1.9 Cone Clutch:



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Fig 1.18 Cone clutch

Fig 1.18 shows simplified diagram of the cone

clutch. It was extensively used in automobiles,but now-a-days it has been completely replaced

by the plate clutch. It consists of only one pair of

friction surface which is in the form of cones. In

the engaged position the male cone is fully insidethe female cone so that the friction surfaces are

in complete contact. This is done by means of

springs which keep the male cone pressed all thetime.

Advantages:

The only advantage of cone clutch is that the

normal force acting on the contact surfaces is

larger than the axial force as compared to thesingle plate clutch in which the normal force

acting on the contact surfaces is equal to the

axial force.

Disadvantages:

The cone clutch is practically obsolete because

of certain inherent disadvantages.1. If the angle of cone is made smaller that

200 the male cone tends to bind or join in

the female cone and it becomes difficultto disengage the clutch.

2. A small amount of wear on the cone

surface results in considerable amount of

axial movement of the male cone forwhich it is difficult to allow

1.10 Design of Cone Clutch:

Consider a pair of friction surfaces of a cone

clutch maintained in contact by an axial thrust Was shown in Fig 1.19(2). Let

T = Toque Transmitted by clutch

p = Intensity of pressure with which the

conical contact surfaces are held togetherri = Inner radius of the friction surface

ro= Inner radius of the friction surface = Coefficient of friction

= Semi-angle of the cone or the angle of the

friction surface with the axis of the clutchb = Width of the friction surface (also

known as face width or cone face)

Consider an elementary ring of radius r and

thickness dr as shown in Fig 1.19(1).

Let dl is the length of ring of the friction

surface, such that

sin

cosdr

ecdrdl ==

We know that,

Area of the contact surface or friction surface,

dA = 2r. dl=

sin

r2dr



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Fig 1.19 Forces on Friction surface of Cone Clutch

Normal force on the ring,

dP = Pressure x Area = p . dA=

sin

r2dr

p

Axial force on the ring,

)9(2

sinsin

2sin

drprdW

drprdPdW

=

==

The friction force acting on the ring tangentially

at radius r,

Fr = . dP = .

sin

r2dr

p

Hence Friction torque acting on the ring,

Tr = r. Fr = . )10(sin

r22

dr

p

i) Considering uniform pressure:

The total axial force can be found by integratingequation (9) within the limits from ri to ro.

( ) )11(2

22

force,axialTotal

222

io

r

r

r

r

rrpr

pdrprW

o

i

o

i

=

=.=

Equation (11) shows that the total axial force is

independent of the cone angle.

The total friction torque can be found by

integrating equation (10) within the limits from rito ro.


Substituting expression forp from equation

(11),

( )

SurfaceFrictionofRadiusMean3

2

)12(sin3

2

3.

sin

2

22

33

22

33

33

22

=

=

=

=

=

io

io

io

io

io

io

rr

rrR

Where

RWrr

rrWT

rr

rr

WT

ii) Considering uniform axial wear:

We know that,

dr2r.dr2rC=r.dr2.p=dW = C

[ ] ( )

( ))13(

2

222

force,axialTotal

io

io

r

r

r

r

rr

WC

rrCrCdrCW oi

o

i

=

==.=

We know that the friction torque acting on the

ring,

Tr

= r. Fr

=

sinr22 dr

p =

sinr2

drC



=

=.=

3sin

.2

3sin

.2

sin2p..

33

32

io

r

r

r

r

rrpT

rpdrrT

o

i

o

i

=

=.=

2sin

.2

2sin

.2

sinC2

22

2

io

r

r

r

r

rrCT

rCdrrT

o

i

o

i


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Substituting expression for C from equation (13),

( )

( )

( )SurfaceFrictionofRadiusMean

sin2

)14(sin2

22.sin

222

=+

=

=+

=

=

io

io

io

io

rrR

Where

RWrrW

T

rr

rr

W

T

Equation (14) gives the more conservativeresults as compared to equation (12) and hence

can be safely used for design of cone clutch.

1.11 Centrifugal Clutch:

The centrifugal clutches are usually incorporated

in motor pulleys. It consists of a number of shoes

on the inside of pulley as shown in Fig 1.20

Fig 1.20 Centrifugal Clutch

The outer surfaces of the shoes are covered witha friction material. These shoes, which can move

radially in guides, are held against the boss of

spider on the driving shaft by means of springs.The springs exert a radially inward force which

is assumed constant. When rotating, under the

action of centrifugal force, the shoes are moved

radially outwards. The magnitude of thiscentrifugal force depends upon the speed at

which the shoe is rotating. When centrifugal

force is equal to the spring force, the shoe is justfloating. However when the centrifugal force

exceeds the spring force, the shoe moves

outwards and comes in contact with the driven

member. Further increase in the centrifugalforce, presses the shoe against the driven

member. The force with which the shoe presses

against the driven member is the difference

between the centrifugal force and the spring

force. The increase of speed causes the shoe topress harder and enables more torque to be

transmitted.

Fig 1.21 shows another means of arrangement

for centrifugal clutch and Fig 1.22 shows

photographic view of shoes of centrifugal clutch.

Fig 1.21 Centrifugal Clutch

Fig 1.22 Photographic view of shoes of centrifugal clutch

1.12 Design of Centrifugal Clutch:

Design of a centrifugal clutch involves

determination of mass or weight of the shoe, size

of the shoe and dimensions of the spring.



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i) Mass of the shoes:

Consider one shoe of a centrifugal clutch asshown in Fig 1.23.

Fig 1.23 Forces on a shoe of centrifugal clutch.

Let,m = Mass of each shoe

n = Number of shoes

r = Distance of C.G. of shoe from the

centre of the spiderR = Inside radius of the pulley rim

N = Running speed of the pulley in rpm

= Angular running speed of the pulley

in rad/s (60

2 N= )

e = Angular speed at which the

engagement begins to take place = Coefficient of friction between the

shoe and rim

The centrifugal force acting on each shoe at the

running speed,

rmPc

2=

The speed at which the engagement begins to

take place is generally taken as 3/4th of the

running speed. Hence the inward force on eachshoe exerted by the spring is given by

rmrmrmP es2

2

2

16

9

4

3 =

==

Therefore net outward radial force (i.e.centrifugal force) with which the shoe presses

against the rim at the running speed,

rmrmrmPPP sco222

16

7

16

9 ===

The friction force acting tangentially on each

shoe,

)( scor PPPF == The friction torque acting on each shoe,

RPPRPRFT scorr === )(

And the total friction torque transmitted,

)15()( RPPnT

RPnRnFnTT

sc

orr

=

===

The mass of the shoe can be evaluated from

equation (15).

ii) Size of the shoes:

Let,l = Contact length of the shoe

b = Width f the shoeR = Radius of the shoe when it presses

against the pulley rim (same as the

inside radius of the pulley)= Angle subtended by the shoe at the

centre of spider in radp = Intensity of pressure exerted on the

shoe (In order to ensure reasonable

life, it may be taken as 0.1 N/mm2)

Now, Rl=Area of contact o the shoe, lbA =The force with which the shoe presses against

the rim= p . plbA =

Since the force with which the shoe presses

against the rim at the running speed is

sco PPP = ,

Therefore )16(sc PPplb =

The width of the shoe can be obtained from

equation (16).

iii) Dimensions of the springs:

We have discussed above that the load on thespring is given by,

)17(16

9

4

3 22

21 rmrmrmPs =

==



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By using the load value from eqn (17), the

dimensions of spring may be obtained as usual.

References:

1) Theory of Machines by S S Rattan, Tata

McGraw Hill Education Pvt ltd.2) Automobile Engineering Vol. 1 by Kirpal

Singh, Standard Publishers Distributors.3) Theory of Machines by R S Khurmi, S

Chand Technical

4) Design of Machine Elements by V BBhandari, Tata McGraw Hill Education

Pvt ltd.

5) http://books.google.com

6) http://www.google.co.in/imghp?hl=en&tab=wi

http://books.google.com/http://www.google.co.in/imghp?hl=en&tab=wihttp://www.google.co.in/imghp?hl=en&tab=wihttp://books.google.com/http://www.google.co.in/imghp?hl=en&tab=wihttp://www.google.co.in/imghp?hl=en&tab=wi


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