Dept. of Mech & Mfg. Engg. 1 TRANSMISSION OF POWER
Feb 23, 2016
1Dept. of Mech & Mfg. Engg.
TRANSMISSION OF POWER
2Dept. of Mech & Mfg. Engg.
What is a transmission system?
The rotational motion can be transmitted from one mechanical element to the other with the help of certain systems known as transmission system (Drive).
3Dept. of Mech & Mfg. Engg.
The methods of power transmission are (Types of drives)
i. Belt driveii. Chain drive.iii. Gear drive.iv. Rope drive.
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Open belt drive It is employed when the two parallel shafts have to rotate in the same direction.
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Open belt drive
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Open belt drives
– When the shafts are placed far apart, the lower side of the belt should be the tight side and the upper side must be the slack side.
– When the upper side becomes the slack side, it will sag due to its own weight and thus increases the arc of contact.
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Open belt drive
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Flat belt drives of the open systemshould always have:
• Their shaft axes either horizontal or
inclined.
• They should never be vertical
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CROSSED BELT DRIVEIt is employed when:
• Two parallel shafts have to rotate in the opposite
direction.
• At the junction where the belt crosses, it rubs against
itself and wears off.
• To avoid excessive wear, the shafts must be placed at a
maximum distance from each other
• Operated at very low speeds.
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Crossed belt drive
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Pulley
Pulleys are used to transmit power from one shaft to the
other at a moderate distance away by means of a belt or
strap running over them.
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What is crowning in a pulley?
When the flat belt on cylindrical pulley is off-center
and the pulley rotating the belt quickly moves up to the
largest radius at the top of the crown and stays there.
The crown is important to keep the belt "tracking" stable,
preventing the belt from "walking off" the edge of the
pulley.
A crowned pulley eliminates the need for pulley flanges
and belt guide rollers.
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About Crowning
• When a flat belt runs over two pulleys, only one of them
needs to be crowned to achieve lateral stability.
• The amount of curvature required in actual machinery is
small.
• The method works for belts of leather or rubberized fabric
that have some elasticity.
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Benefits of Crowning of a pulley
• Crowning of pulleys provides an automatic correction to
mis-tracking caused by transient forces that are applied to
the belt.
• Without crowning these transient forces cause the belt to
be displaced without consistent means of returning to its
normal path.
• This can cause belt edge cupping and wear.
For this reason it is wise to select a conveyor with pulley
crowning.
15Dept. of Mech & Mfg. Engg.
Pulley crowning
Critical dimensions:
Crowning of pulleys should not exceed 25mm on the
dia. / mtr of width
Width of the pulley should be 1/4th greater than width of
the belt
Min. dia. of the belt should be at least 25 times thickness of
the belt used to run the pulley
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Types of pulleys
• Stepped cone pulley (Speed cone)
• Fast and loose pulleys
• Guide pulley (Right angled drive)
• Jockey pulley
• Grooved pulley
• Wrought-iron pulley
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Stepped cone pulley
• When speed of the driven shaft is to be changed
very frequently
• Used in lathe, drilling m/c etc..
• Integral casting
• One set of stepped cone pulley mounted in
reverse on the driven shaft
Link
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Stepped cone pulley
f
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Fast and Loose pulley• When many machines obtain the drive from a
main driving shaft,• Run some machines intermittently without having
to Start and stop the main driving shaft
Fast pulley• Securely keyed to the machine shaft
Loose pulley (with brass brush)• Mounted freely on the machine shaft• Rotates freely
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Fast and Loose pulley
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WorkingWhen the belt is on the fast pulley,
– Power transmitted to the machine shaftWhen machine shaft is to be brought to rest,
– Belt is shifted from fast pulley to loose pulleyNote:1. Axial movement of the loose pulley towards
fast pulley is prevented
2. Axial movement of the loose pulley away fast pulley is prevented
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Jockey PulleyIf • Center distance is small• One pulley is very small• Arc of contact smallThen■ Use idler pulley■ Placed on the slack side of the beltResult* Increase in arc of contact* Increase in tension* Increase in power transmission
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Jockey Pulley
fk
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Use:
• To connect non-parallel shafts those which intersect and
those which do not intersect to guide the belt in to the
proper plane
• When two shafts to be connected are close together
Guide pulley (Right angled drive)
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Guide pulley (Right angled drive)
Guide Pulley
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The effect of groove is to increase the frictional grip
of the rope on the pulley.
This reduces tendency to slip.
The groves are V-shaped.
Angle between 2 faces: 400 – 600
Uses:
• Used in V-belts, rope.
• Transmission of large powers over great distances
Grooved Pulley
27Dept. of Mech & Mfg. Engg.
Wrought-iron pulley
• Light, strong and durable
• Entirely free from initial strains
• To facilitate the errection of pulleys on the main shaft,
they are usually made in halves and parts are securely
bolted together.
28Dept. of Mech & Mfg. Engg.
Length of a beltOpen belt drive:
h(r1+ r2)L = + 2
+ (r1 - r2)2
29
Length of a belt
L =e
+(r1+ r2) (r1 + r2)2
Crossed belt drive:
30Dept. of Mech & Mfg. Engg.
Effect of sum of pulley diameter on the length of belt for open type
• Any variation in which (r1+ r2) is kept constant will vary
the length of the belt because of the term containing r1- r2
• If speed cones are connected by an open belt, the belt
will be slacker in some position than in others
31Dept. of Mech & Mfg. Engg.
Effect of sum of pulley diameter on the length of belt for crossed type
• Here r1 and r2 only occur in the form of sum,
• If sum is kept constant by varying r1 and r2, length of
the belt will be constant
In speed cones:
They are connected by crossed belt, hence
– Length of belt remains constant
– Sum of diameters of the corresponding steps should
be constant.
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Equation for arc of contact (angle of lap) for open belt drive (theta)
= =Cos 2
r2-r1
Dd2-d1
2D
Dia. of the larger pulley - Dia. of the smaller pulley
Centre distance between the two pulleys=
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Equation for arc of contact (angle of lap) for crossed belt drive (theta)
2
- = =r2 + r1
Dd2 + d1
2DCos
Dia. of the larger pulley + Dia. of the smaller pulley
2 Centre distance between the two pulleys=
34Dept. of Mech & Mfg. Engg.
Define Velocity Ratio of Belt Drive. (Speed Ratio)
The velocity ratio of a belt drive is defined
as the ratio of the speed of the driven
pulley to the speed of the driving pulley.
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Obtain the expression for velocity ratio of belt drive. Let d1= Diameter of the driving pulley (mm)d2= Diameter of the driven pulley (mm)N1= Speed of the driving pulley (Revolutions/min
OR RPM)N2= Speed of the driven pulley (Revolutions/min
or RPM)
If there is no relative slip between the pulleys and the portions of the belt which are in contact with them
The speed at every point on the belt will be same
36Dept. of Mech & Mfg. Engg.
The circumferential speeds of the driving and driven pulleys and the linear speed of the belt are equal.
belttheof
dLinearspee
pulleydrivingtheofspeedntialCircumfere
pulleydrivenof
speedntialCircumfere= =
= d1N1 = d2N2
= Πd1N1 = Πd2N2
Velocity Ratio = N2 / N1 = d1/d2
Velocity Ratio pulleydrivingtheSpeedof
pulleydriventheofSpeedpulleydriventheDiameterofpulleydrivingtheofDiameter==
37Dept. of Mech & Mfg. Engg.
Initial tension in belt drive
DefinitionIt is a uniform tension that exists initially when the drive
is not in motion. It is designated as To.
Formula: To =
T1 + T2
2
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The polygon of forces acting on the element is represented by the closed quadrilateral as shown in figure.
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Derive the expression for the ratio of tensions in belt drive. The driving pulley drives the driven pulley only if one side of the belt has higher tension than the other sideThe figure shows a driving pulley rotating in clockwise directionConsider a small element AB of belt,
T1= Higher tension, T2= Lower tension, δθ = angle subtended by the element of AB T =tension on the slack side of the belt. μ = co efficient of friction between the belt surface and
pulley rim
40Dept. of Mech & Mfg. Engg.
Let the tension in the tight side of the belt element AB
be greater than the slack side by δT.
Therefore the tension in the tight side of the belt
element is T +δT.
If R is the normal reaction exerted by the pulley on the
element of the belt.
Then,
The force of friction μR acts perpendicular to the
normal reaction R in the direction opposite to the
direction of motion as shown in figure.
41Dept. of Mech & Mfg. Engg.
Element AB will be in equilibrium only when following forces act on it
1. Tension T on the slack side at A
2. Tension T +δT on the slack side at A
3. Normal reaction R
4. Frictional force μR acting perpendicular to R
42Dept. of Mech & Mfg. Engg.
Resolving all the forces in the direction of R.
R =
2SinT +
2
SinTT
=
22 SinT +
2SinT
For small angles the following assumptions can be made.
Sin δθ/2 = δθ/2 & δT. δθ /2 is neglected.
R= 2T2
R =T δθ ------------------------------ (1)
43Dept. of Mech & Mfg. Engg.
Resolving all the forces perpendicular to R
μR =
2CosTT -
2
CosT
=
2CosT +
2CosT -
2CosT
=
2CosT
For small angles Cos δθ/2 = 1
μR = δT ---------------------- (2)
Substituting equation (1) in (2)
μT δθ = δT
44Dept. of Mech & Mfg. Engg.
Substituting equation (1) in (2)
μT δθ = δT
TT = μ δθ
Integrating δθ between 0 and θ and tension δT between T2 and T1
0
1
2
T
T TT
log e
2
1
TT
= μθ
2
1
T
T = e μ θ
45Dept. of Mech & Mfg. Engg.
Slip
What is slip?
–The sliding motion of the belt which
causes a relative motion between the
pulley and the belt.δT= μR The equation is,
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Creep in Flat belt drive
• The phenomena of alternate stretching
and contraction of the belt results in a
relative motion between the belt and the
pulley surface.
• This relative motion is called creep.
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This results in:
–Loss of power
–Decrease in the velocity ratio
Creep in Flat belt drive
48Dept. of Mech & Mfg. Engg.
Power transmitted in a belt drive
P = (T1-T2) * v
4500 HP
v= d N in m/min
T1, T2 in kgf
49Dept. of Mech & Mfg. Engg.
Power transmitted in a belt drive
P = (T1-T2) * v60,000
kW
v= d N in m/min
T1, T2 in Newton
50Dept. of Mech & Mfg. Engg.
What are the different types of gears used in gear drives? Explain. The different types of gears used are:1. Spur Gears - For Parallel Axes shafts.2. Helical Gears - For both Parallel and Non-parallel
and non-intersecting axes shafts. 3. Spiral Gears - For Non-parallel and Non-intersecting
axes shafts.
4. Bevel Gears - For Intersecting Axes shafts.
5. Worm Gears - For Non-Parallel and Non-co-planar axes shafts.
6. Rack and Pinion - For converting Rotary motion into linear motion.
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52Dept. of Mech & Mfg. Engg.
Spur Gears• When the axes of the driving and driven shafts are
parallel and co-planar. • The teeth of the gear wheels are parallel to the axes• The contact between the mating gears will be along a line• Can transmit higher power. • Noise will be very high. Applications:o Machine tools, o Automobile gear boxes and in o All general cases of power transmission where gear
drives are preferred.
53Dept. of Mech & Mfg. Engg.
Spiral Gears
• Used to connect only two non-parallel, non-
intersecting shafts
• There is a point contact in spiral gears
• Because of the point contact the spiral gears are
more suitable for transmitting less power.
54Dept. of Mech & Mfg. Engg.
Helical Gears • Similar to the spur gears • But teeth are cut in the form of the helix around the gear • Used for transmitting power between two parallel shafts
and also between non parallel, non-intersecting shafts. • Contact between the mating gears will be along a
curvilinear path.• Helical gears are preferred to spur gears when smooth
and quiet running at higher speeds are necessary. • Generally they are used in automobile power
transmission.Disadvantage:It produces end thrusts on the driving and driven shafts.
55Dept. of Mech & Mfg. Engg.
Bevel gears • Used when the axes of the two shafts are inclined
to one another, and intersect when produced. • Teeth are cut on the conical surfaces. • The most common examples of power
transmission are those in which the axes of the two shafts are at right angles to each other.
• When two bevel gears have their axes at right angles and are of equal sizes, they are called Miter gears.
56Dept. of Mech & Mfg. Engg.
Rack and Pinion • Used when a rotary motion is to be converted into
a linear motion.• Rack is a rectangular bar with a series of straight
teeth cut on it.• Theoretically rack is considered to be a spur gear
of infinite diameter. Application:• Machine tools, such as, lathe, drilling, planing
machines,• Some steep rail tracks, where the teeth of the
locomotive wheel mesh with a rack embedded in the ground, offering the locomotive improved traction.
57Dept. of Mech & Mfg. Engg.
What are the Advantages and Disadvantages of Gear Drives? Advantages;
1. They are positive non-slip drives.
2. Most convenient for very small centre distances.
3. By using different types of gears, it will be possible to
transmit the power when the axes of the shafts are not
only parallel, but even when non parallel, intersecting, non-
intersecting and co-planar or non-coplanar.
4. The velocity ratio will remain constant throughout.
5. They can be employed conveniently for low, medium and
high power transmission.
58Dept. of Mech & Mfg. Engg.
6. Any velocity ratio as high as, even upto 60 : 1 can be obtained.
7. They have very high transmission efficiency.
8. Gears can be cast in a wide range of both metallic and non-metallic materials.
9. If required gears may be cast integral with the shafts.
10. Gears are employed for wide range of applications like in watches, precision measuring instruments, machine tools, gear boxes fitted in automobiles, aero engines, etc.
59Dept. of Mech & Mfg. Engg.
Disadvantages1. They are not suitable for shafts of very large
centre distances.
2. They always require some kind of lubrication.
3. At very high speeds noise and vibrations will be
more.
4. They are not economical because of the
increased cost of production of precision gears.
5. Use of large number of gear wheels in gear trains
increases the weight of the machine.
60Dept. of Mech & Mfg. Engg.
Define pitch and module of spur gear.
Circular pitch(p): It is the distance from a point on one teeth to the corresponding point on the next tooth measured along the pitch circle. Module(m): It is the ratio of the pitch circle diameter of a gear to the number of teeth on a gear.
i. e. m=d/Z
61Dept. of Mech & Mfg. Engg.
Define velocity ratio of Gear drive
The velocity ratio of a gear drive is defined as the ratio of the speed of the driven gear to the speed of the driving gear.
62Dept. of Mech & Mfg. Engg.
Obtain an expression for gear drive.Let d1 = pitch circle diameter of the driving gear d2 = pitch circle diameter of the driven gear T1 = Number of teeth on the driving gearT2 = Number of teeth on the driven gear. N1 =speed of the driving gear in revolutions per minute.N2 = speed of the driven gear in revolutions per minute.
63Dept. of Mech & Mfg. Engg.
Since there is no slip between the pitch cylinders of the two gear wheels, The linear speed of the two pitch cylinders must be equal.
gearDrivingthengrepresenticylinder
pitchtheofspeedLinear=
geardrivenngrepresenticylinder
pitchtheofspeedLinear
π d1N1 = π d2N2
1
2
NN
=
2
1
dd
……………… (1)
The circular pitch for both the meshing gears remains same.
i.e. pc =
1
1
Td
=2
2
Td
64Dept. of Mech & Mfg. Engg.
i.e.,
2
1
dd
2
1
TT
= ……………………..(2)
From equation (1) and (2)
Velocity Ratio of a Gear Drive =1
2
NN
=2
1
dd
=2
1
TT
Velocity ratio of the worm and worm wheel is expressed as:
Speed of the WormSpeed of the Worm Wheel
Number of Teeth on Worm WheelNumber of Threads on the Worm
==Velocity ratio
65Dept. of Mech & Mfg. Engg.
A gear train is an arrangement of number of
successively meshing gear wheels through
which the power can be transmitted between
the driving and driven shafts.
What do understand by a gear train?
66Dept. of Mech & Mfg. Engg.
The gear wheels used in gear train may be spur ,
bevel or helical etc.
The different types of gear trains are:
1. Simple gear train.
2. Compound gear train.
3. Reverted gear train.
4. Epicyclic Gear train.
67Dept. of Mech & Mfg. Engg.
Draw a neat sketch of a simple gear train and derive an expression for the velocity ratio of the same.
In a simple gear train a series of gear wheels are mounted on different shafts between the driving and driven shafts each gear carrying only one gear.
A → Driving gear B → Intermediate gear C → Intermediate gear
D → Driven gear Simple gear train
Gear AGear B
Gear C
Gear D
68Dept. of Mech & Mfg. Engg.
Let NA = speed in RPM of gear ANB = speed in RPM of gear BNC = speed in RPM of gear CND = speed in RPM of gear D
TA = Number of teeth of gear ATB = Number of teeth of gear BTC = Number of teeth of gear CTD = Number of teeth of gear D Simple gear
train
Gear AGear B
Gear C
Gear D
69Dept. of Mech & Mfg. Engg.
i. A drives B
ii. B drives C
iii. C drives D
A
B
NN
=B
A
TT
B
C
NN
=C
B
TT
C
D
NN
=D
C
TT
Simple gear train
Gear AGear B
Gear C
Gear D
70Dept. of Mech & Mfg. Engg.A
D
NN
D
A
TT
= Velocity Ratio
.
.
B
A
TT
C
B
TT
D
C
TT
= . .
Velocity Ratio = A
D
NN
Substituting from (i), (ii) and (iii) .
.
A
D
NN
Velocity Ratio =
C
D
NN
B
C
NN
A
B
NN
= . .
Velocity ratio between the driving and driven gears is given by,
Simple gear train
Gear AGear B
Gear C
Gear D
71Dept. of Mech & Mfg. Engg.
Draw a neat sketch of a compound gear train and derive
an expression for the velocity ratio of the same.
A compound gear train is one in which each shaft carries two or more gears and keyed to it.
Gear B →Compound gearGear C →Compound gear
Gear C
Gear A
Gear B
Gear D
Compound gear train
72Dept. of Mech & Mfg. Engg.
Gear A drives B,
B
A
A
B
TT
NN
……….(1)
Gear C
Gear A
Gear B
Gear D
Compound gear train
Since gears B and C are keyed to the same shaft,
NB = Nc but TB Tc
Gear C drives D,
D
C
C
D
TT
NN
Both of them rotate at the same speed
………(2)
73Dept. of Mech & Mfg. Engg.
Gear C
Gear A
Gear B
Gear D
Compound gear train
Velocity ratio between driving and driven gear
C
D
A
D
NN
NN
. A
C
NN
=
Substituting from (1) and (2)
D
C
A
D
TT
NN
B
A
TT
Velocity ratio = .
74Dept. of Mech & Mfg. Engg.
PROBLEMS1) A compound gear train is formed by 4 gears P,Q,R and S. Gear P meshes with gear Q and gear R meshes with gear S. Gears Q and R are compounded. P is connected to driving shaft and S connected to the driven shaft and power is transmitted. The details of the gear are,
Gears P Q R SNo. of
Teeth30 60 40 80
If the gear S were to rotate at 60 rpm. Calculate the speed of P. represent the gear arrangement schematically.
75Dept. of Mech & Mfg. Engg.
SOLUTION:
Velocity ratio =
S
R
P
S
TT
NN
.
Q
P
TT
PN60
=
8040 .
6030
Speed of P, NP = 240 rpmGear R,TR=40
Gear P,TP=30
Gear Q,TQ=60
Gear S,TS=80
Gear arrangement
76Dept. of Mech & Mfg. Engg.
2) An electric motor provides 6 KW power to an open belt
drive. The diameter of the motor pulley is 200mm and it
rotates at 900 rpm. Calculate tight and slack side tension
in the belt if the ratio of tension is 2.
Solution:P = 6kW
d1 = 200 mm
n1 = 900 rpm
2
1
TT
= 2.
77Dept. of Mech & Mfg. Engg.
P = 6kW, d1 = 200 mm, n1 = 900 rpm , 2
1
TT
= 2.
Linear velocity of belt v =
1000.6011 Nd
=
1000.60900.200.
= 9.425 m/sec
Power P =
10000)( 21 vTT
T1 – T2 =
vP.1000
= 425.9
6.1000 = 636.6 N
78Dept. of Mech & Mfg. Engg.
By data,2
1
TT
= 2.
From equations, (1) & (2)
We get, 2T2 – T2 = 636.6N
Slack side tension T2 = 636.6 N
Tight side tension T1= 2T2 = 1273.2 N
79Dept. of Mech & Mfg. Engg.
3) A leather belt transmits 20kW power from a pulley of
750mm diameter which runs at 500 rpm. The belt is
in contact with the pulley over an arc of 1600 and
the coefficient of friction between the belt and the
pulley is 0.3. Find the tension on each side of the
open belt drive.
Solution: P = 20 k W
d = 750 mm n = 500 rpm = 1600 = 0.3
80Dept. of Mech & Mfg. Engg.
Linear velocity of belt v =
1000.60nd
=1000.60
500.750.
= 19.635 m / sec
Power P =1000
)( 21 vTT
T1 – T2 = vp.1000
=
635.1920.1000
= 1018.6 N …………….(1)
81Dept. of Mech & Mfg. Engg.
By data,
2
1
TT
= e
= e ((0.3 ) (160) /180 )= 2.311 ………….(2)
From equations (1) and (2)
2.311 T2 – T2 = 1018.6
Slack side tension T2 = 776.96 N
Tight side tension T1 = 776.96 (2.311) = 1795.6 N
82Dept. of Mech & Mfg. Engg.
4) Power is transmitted by an open belt drive from a
pulley 300 mm. diameter running at 600rpm. to a pulley 500 mm. in diameter. The distance between the centre lines of the shaft is 1m. and the coefficient of friction in the belt drive is 0.25. If the safe pull in the belt is not to exceed 500 N, determine the power transmitted by the belt drive.
Solution: d1 = 300 mm.
n1 = 600 rpm
d2 = 500mm
c= 1m. = 1000 mm
= 0.25
T1 = 500 N
83Dept. of Mech & Mfg. Engg.
Linear velocity of belt v =
1000.60nd =
1000.60600.300.
Radius of driver pulley r1 =
21d
=
2300
= 150 mm.
Radius of driven pulley r2 =
22d
= 2
500= 250 mm.
Angle of lap on smaller pulley = - 2 sin -1
crr 12
(because r2 – r1)
= - 2 sin -1
1000150250
= 2.94 rad.
84Dept. of Mech & Mfg. Engg.
Power P =
100021 vTT
P =
1000425.98.239500
= 2.425 kW
Slack side tension T2 = eT1
085.2500
= 239.8 N
Ratio of tensions2
1
TT= e
= e (0.25 ) . (2.94) = 2.085
85Dept. of Mech & Mfg. Engg.
Higher tension is in the tight side of the belt and
Lower tension is in the slack side of the belt.
Back
86Dept. of Mech & Mfg. Engg.
The centrifugal force developed in the belt
combined with the force of gravity causes
the belt to stretch and tend to leave the rim
of the pulleys, thereby losing contact with
their rim surfaces.
Back
87Dept. of Mech & Mfg. Engg.
Integral casting– Single component having 3 or 4 pulleys of
different sizes one adjacent to another
How speed of driven shaft can be varied?Answer:By shifting the belt from one pair of pulley to other.
Back
88Dept. of Mech & Mfg. Engg. Back
How?
1.Abutting its (loose pulley) boss to that of fast pulley
2.Collar fixed to the machine shaft