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Design of Transmission
Systems
Prepared by Dr.A.Vinoth Jebaraj
To avoid the slipping
Exact velocity ratio  Transmit large power  Used for small centre
distances  High efficiency  Reliable service  Compact layout
Require special tools and equipments to produce  Improper cutting of teeth
produce vibration and noise  Lubrication is must
TERMINOLOGIES USED IN GEARS
Driver pinion
Driven gear wheel
Arc of contact: Path traced by a point on the pitch circle from
the beginning to the end of the engagement of a given pair of
teeth. It consists of two parts.
Arc of approach: Portion of the path of contact from the
beginning of engagement to the pitch point.
Arc of recess: Portion of the path of contact from the pitch point
to the end of the engagement of a pair of teeth.
Line of Action
Arc of approach Arc of recess
Spur gear Helical gear
Double helical or Herringbone gear Cross helical gear
Straight bevel gear Spiral bevel gear
Worm and worm wheel
Rack & Pinion
Pressure Angle or Angle of Obliquity:
Angle between common normal to two gear teeth at the point
of contact (line of contact) and the common tangent at the
pitch point. Standard values include 14.5, 20 and 25
degrees.
Backlash:
It is the difference between tooth space and the tooth thickness as measured
along pitch circle. Theoretically backlash should be zero. But in actual practice
some backlash must be allowed to prevent jamming of the teeth due to the tooth
errors and thermal expansion.
Module (m): Pitch diameter divided by number of teeth. The
pitch diameter is usually specified in inches or millimeters;
It is a measure of the tooth strength. Higher the module
bigger the size of the gear. More important, higher the
module, wider the tooth at the base and larger the height of
the tooth.
Main parameters to be designed:
Center Distance
Module
Face width
Let Mt be the torque transmitted by the pinion
Normal force on the tooth Fn = Torque / lever arm
Radius of the base circle = ½ d1 cos α
1
Diameter d1 can be expressed in terms of center distance ‘a’ as
Substituting the value of d1 in Eq. 1
Therefore, Fn is inversely proportional to the centre
distance.
 As center distance decreases the normal force will
increase and hence the surface compressive stress
increases.
Therefore the centre distance is limited by the
permissible surface compressive stress of the
material of the pinion.
IMPORTANT POINTS TO BE NOTED:
Minimum centre distance depends upon the surface compressive strength
of the material
So induced surface compressive stress < Design surface compressive
strength of the material
Minimum module depends upon the bending strength
So induced bending stress < Design bending strength of the material
Design surface compressive strength [σc]
Surface strength is proportional to the hardness of the
surface.
σc α HB or RC
Therefore,
σC = CB × HB N/cm2
= CR × RC N/cm2
CB and CR are constants depending on the material
and heat treatment.
Also the design compressive strength depends on load conditions.
Hence correction factor is introduced.
Design surface compressive strength
[σC ] = CB HB Kcl in N/cm2
[σC] = CR HRC Kcl in N/cm2
Where Kcl is the life factor for surface compressive strength.
Kcl =
Where N – number of fatigue cycles the pinion teeth has undergone
in its life period of T hours.
Number of fatigue cycles per hour = 60 n
Number of cycles in life period N = 60 n T
Design Bending Stress [σb]
It depends on endurance limit, stress concentration factor at the root and life
factor for bending.
[σb] = For gears having both directions of rotation
[σb] = × 1.4 For gears having one direction of rotation only
= endurance limit stress in bending
= life factor in bending
= stress concentration of fillet at the root
n = factor of safety
Gear materials
Commonly used materials  cast iron and steel
For large power transmission and reduction in size  Alloy steel of
Nickel, chromium & vanadium (with proper heat treatment to obtain
sufficient surface strength)
For corrosive environment  Brass and bronze
Non metallic materials  Laminated fabric, Bakelite and mica (to reduce
noise)
Gear Failures
Teeth breakage: due to fatigue
Pitting: hard and smooth working surfaces of the teeth reduce the danger
of pitting
Surface abrasion: due to sliding of the teeth
Seizure: surface of the teeth mesh so tightly together causes particles of
softer material to break away from the teeth surface and groove it.
Law of gearing
The common normal to the tooth profile at the point of contact should
always pass through a fixed point, in order to obtain a constant
velocity ratio.
Only involute and cycloidal curves satisfies the fundamental law of
gearing.
Involute Profile Cycloidal Profile
Helical Gears and Herringbone Gears
They have teeth cut in the form of helix on their pitch cylinders. Teeth are not
parallel to the axis of rotation.
More than one pair of teeth are in engagement. Runs smoothly because of the
gradual engagement of teeth. Higher peripheral speeds are permissible in
helical gears.
Limitation: Axial thrust
By providing another helical gear of opposite hand, the axial thrust can be
balanced. They are called as double helical or herringbone gears.
Helix angle is helical gears are in between 8° and 25°
Axial pitch = π m , where m is the axial module
Normal pitch = π mn , where mn is the normal module
Cos β = π mn / π m
Therefore,
Cos β = mn / m
Centre distance =
Forces acting on a Helical gear tooth
Design of Bevel Gear
Straight Bevel Gear Spiral Bevel Gear
Direction of shaft’s rotation can be changed by means of bevel
gears. Usually two shafts are arranged at an angle of 90°. But the
other angles are also possible.
Bevel gears in differential
AXES MUST INTERSECT EACH OTHER AND MUST LIE IN
THE SAME PLANE IN BEVEL GEAR ARRANGMENT
Bevel Gear - Nomenclature
Terminology of bevel gears
Pitch cone: Imaginary cone that the surface of which contains the pitch lines of all
teeth in the bevel gear.
Cone center: The apex of the pitch cone is called cone center.
Cone distance: Length of the pitch cone element also called as pitch cone radius.
Pitch angle: Angle that the pitch line makes with the axis of the gear is called the
pitch angle.
Addendum angle: Angle subtended by the addendum at the cone center.
Face angle: Angle subtended by the face of the tooth at the cone center.
Transverse module mt : It is based on the pitch circle diameter at the outer portion.
Average module mav : It is based on pitch circle diameter at the centers of the teeth.
Miter Gear
 When two identical gears are mounted on
shafts, that are intersecting at right angles,
then they are called as Miter gears.
 Pitch angles of pinion and gear of Miter
gears are same and each is equal to 45°.
 Pinion and gear of Miter gears rotate at
same speed.
Crown Gear
 In a pair of bevel gear, when one of the gear has a pitch
angle of 90°, then that gear is called as crown gear.
 They are intersecting at an angle that is more than 90°.
Internal Bevel gear
 When the teeth of a bevel gear are cut inside the pitch cone,
then it is called as internal bevel gear.
 In this case the pitch angle of the internal gear is more than 90°
and the apex point is on the backside of the teeth on the gear.
Skew bevel gear: When two straight bevel gears are mounted on
shafts, which are non parallel and non intersecting, then they are
called as skew bevel gears
Hypoid Bevel Gear
They are similar to spiral bevel gears that are mounted on
shafts, which are non-parallel and non-intersecting.
Face gears: They consists of a spur or helical pinion mating with
a pair gear of disk form.
Force Analysis
on Bevel gear
tooth
Design of worm and worm wheel
Worm
(Driver)
Worm wheel
(Driven)
Worm always drives the worm wheel. It is a self locking drive. Reversible
direction of power transmission is not possible.
Higher speed
reduction and
more torque
at the output
is possible
through
worm drive.
Consider a single start worm and a 20 teeth worm gear will reduce the
speed by the ratio of 20:1.
The gear ratio of a worm gear is
i =
The worm acts as a single toothed gear so the ratio is;
i =
Gear Ratio = 20:1
(Rotary velocity is reduced by 20:1)
 If this speed reduction is achieved by spur gears, then a gear of 12 teeth (the
smallest size permissible) would have to be matched with a 240 tooth gear to
achieve the same ratio of 20:1.
 Therefore according to the physical size of the 240 tooth gear to that of the 20
tooth gear, the worm arrangement is considerably smaller in volume.
Applications
Self-locking Worm Gear
 The worm always acts as a driving gear and the spur gear as a driven gear- vice
versa is not possible. If you try to run it in opposite direction, it will lock
automatically.
 A worm and gear will be self-locking depends on the lead angle, the pressure angle,
and the coefficient of friction;
 If the tangent of the lead angle of the worm gear is less than the coefficient of
friction between the worm and the gear, then the worm gear train should be a self-
locking type.
The self-locking worm gear USED for the
applications where loading against the
gravitational force is required.
This is because the angle on the worm is so
shallow that when the gear tries to spin it,
the friction between the gear and the worm
holds the worm in place.
 Losses in worm gears are high, they need costly materials like
bronze and the manufacturing cost is high.
 Power transmission between worm and worm wheel happens
through sliding. Therefore, the materials used should have low
coefficient of friction.
 Seizure and wear are the two major failures in worm gear drive.
 Proper lubrication and cooling surfaces should be provided to limit
the operating temperature between 60° and 70°C.
Bearing : Machine element used to
support a rotating member with the
very minimum frictional power loss.
Types:
 Rolling contact bearings
 Sliding contact bearings
Anti-friction bearing  due to its low friction characteristics  used for
radial load, thrust load and combination of thrust and radial load 
relatively lower price  maintenance free  friction increases at high
speeds  noisy while running  Types : Ball bearing and Roller bearing
Single row deep groove ball bearing
Radial load but it can also take up
considerable amount of axial load.
Functions of bearings :
Ensure free rotation with
minimum friction
Act as a support for shaft and
axle and holds in correct position
Takes up the forces acting on the
shaft and axle and transmits them
to the frame or foundation
Advantages
1. Low starting and running friction except at
very high speeds.
2. Accuracy of shaft alignment.
3. Low cost of maintenance, as no lubrication is
required while in service.
4. Small overall dimensions.
5. Reliability of service.
6. Easy to mount and erect & Cleanliness.
Disadvantages
1. More noisy at very high speeds.
2. Low resistance to shock loading.
3. More initial cost.
4. Design of bearing housing complicated.
Applications of rolling contact bearings:
Machine tool spindles  automobile front and rear axles  gear boxes 
small size electric motors  rope sheaves, crane hooks and hoisting drums
Single row Angular Contact Ball Bearing
Used for radial loads and heavy axial loads
Double Row Angular Contact Bearing
Has two rows of balls. Axial displacement of
the shaft can be kept very small even for axial
loads of varying magnitude
Single thrust ball bearing
Used for unidirectional axial load
Taper Roller Bearing
Used for simultaneous
heavy radial load and
heavy axial load
Roller bearings has more contact area than a
ball bearing, therefore, they are generally
used for heavier loads than the ball bearings
Spherical Roller Bearing
Cylindrical Roller Bearing
For heavy radial load and
high speed use, cylindrical
roller bearings
It is mainly used for heavy axial loads.
However, considerable amount of
loads in either direction can also be
applied
Self aligning principle
Static load carrying capacity: The static load which corresponds to a total
permanent deformation of balls and races, at the most heavily stressed
point of contact, equal to 0.0001 of the ball diameter. [Load acting on the
bearing when the shaft is stationary]
STIBECK’S EQUATION
Static load CO = (k.d2.z) / 5
Where
k = factor depends upon the radii of curvature at the point of contact
d = ball diameter
z = number of balls
Dynamic load carrying capacity: (fatigue life of the bearing)
Life of an individual bearing is defined as the number of revolutions
which the bearing runs before the first evidence of fatigue crack in
balls and races.
The dynamic load carrying capacity of a bearing is defined as the
radial load in radial bearings that can be carried for a minimum life
of one million revolutions.
The minimum life in this definition is the L10 life, which 90% of the
bearings will reach or exceed before fatigue failure.
Equivalent bearing load [P]:
Two components of load acting on the bearing  single hypothetical load
The equivalent dynamic load is defined as the constant radial load in radial
bearings (or thrust load in thrust bearings), which if applied to the bearing would
give same life as that which the bearing will attain under actual condition of forces.
Where
Fr  radial load
Fa  axial load
X and Y  radial and thrust factors from manufacturer’s catalogues
V  Race factor
P = X .V. Fr + Y . Fa
Load factor in bearings:
Load factors are used in applications involving gear, chain and belt drives.
Gear drives  additional dynamic load due to inaccuracies of the tooth
profile and the elastic deformation of the teeth.
Chain and belt drives  additional dynamic load due to vibrations
Bearing failure – causes and remedies
 breakage of parts like races and cages
 crushing of balls due to misalignment leads to overload
 failure of a cage due to centrifugal force acting on balls
 surface wear  abrasive wear, corrosive wear, pitting, scoring (breakage
lubrication film leads to excessive heat in the contact surfaces)
Journal Bearing ( Hydrodynamic bearing)
Journal bearing is a sliding contact bearing working on hydrodynamic lubrication
and which supports the load in radial direction. The portion of the shaft inside the
bearing is called journal and hence the name ‘Journal bearing’
Since the pressure is created within
the system due to rotation of the
shaft, this type of bearing is known
as ‘self acting bearing’.
Can take load in any radial direction
[many industrial applications)
Can take load in only one radial direction
[rail road cars]
Hydrostatic bearing: In a system of lubrication, load supporting fluid film,
separating the two surfaces is created by an external source, like pump,
supplying sufficient fluid under pressure. This is also called as externally
pressurized bearings.
Advantages: High load carrying capacity even at low speeds, no starting
friction, no rubbing action at any operating speed or load
 Bearing which operates without any lubricant  Zero film bearings
 Two surfaces of the bearing in relative motion are completely separated by
a lubricant  Thick film bearings
 Lubricant film is relatively thin and there is partial metal to metal contact 
Thin film bearings
The factor ZN / p is termed as bearing characteristic number and
is a dimensionless number
 Between Q and R  Partial metal to metal contact
(The viscosity (Z) or the speed (N) are so low, or the pressure ( p) is so
great that their combination ZN / p will reduce the film thickness)
 Between R and S  Thin film or boundary lubrication or imperfect
lubrication
(This is the region where the viscosity of the lubricant ceases to be a
measure of friction characteristics but the oiliness of the lubricant is
effective in preventing complete metal to metal contact and seizure of the
parts)
 Between P and Q  Stable operating conditions
(Since from any point of stability, a decrease in viscosity (Z) will reduce ZN
/ p. This will result in a decrease in coefficient of friction (μ) followed by a
lowering of bearing temperature that will raise the viscosity (Z ))
Bearing should not be operated at ‘K’ (Bearing modulus).
Because, a slight decrease in speed or slight increase in pressure will
break the oil film and make the journal to operate with metal to metal
contact. This will result in high friction, wear and heating.
In order to prevent such conditions, the bearing should be designed for
a value of ZN / p at least three times the minimum value of bearing
modulus (K). If the bearing is subjected to large fluctuations of load and
heavy impacts, the value of ZN / p = 15 K may be used.
On the other hand, when the value of ZN / p is less than K, then the oil
film will rupture and there is a metal to metal contact.
Critical pressure of the journal bearing
The pressure at which the oil film breaks down so that metal to
metal contact begins, is known as critical pressure or the
minimum operating pressure of the bearing.
 Clutch is a mechanical device which
transmits power from the driving shaft to the
driven shaft when it is engaged and cuts the
power when it is disengaged.
 Example: Engine to road wheels , Drilling
machine motor to spindle
Clutch Engaged position Clutch disengaged position
Multiplate Clutch
Single plate clutch
Method of Analysis
The torque transmitted by a clutch is a function of
Geometry
The magnitude of the actuating force applied
The condition of contact prevailing between the
members
Uniform Pressure Theory
If the applied force keep the frictional surfaces together with a
uniform pressure all over its contact area , then the analysis is
based on uniform pressure condition .
Uniform Wear Theory
However, as the time progresses some wear takes place between
the contacting members and this may alter or vary the contact
pressure appropriately and uniform pressure condition may no
longer prevail. Hence the analysis here is based on uniform wear
condition. [Wear α contact pressure and sliding velocity]
Cone Clutches
Consider a small ring of radius “r” and thickness “dr”
“dl” is the length of ring of the friction surface = dl = dr cosec α
Area of ring = 2π r. dl = 2π r.dr cosec α
1. Considering uniform pressure
The normal force acting on the ring
δWn = Normal pressure × Area of ring = pn × 2π r.dr cosec α
The axial force acting on the ring
δW = Horizontal component of δWn (i.e. in the direction of W)
δWn × sin α = pn × 2π r.dr cosec α × sin α = 2π × pn.r.dr
Total axial load transmitted to the clutch or the axial spring
force required
Frictional force on the ring acting tangentially at radius r
Fr= μ.pn × 2πr.dr cosec α
Frictional torque acting on the ring
Tr = Fr × r = μ.pn × 2πr.dr cosec α × r
Tr = 2π μ.pn cosec α.r2 dr
Centrifugal clutch
centrifugal force > spring force
(Outward) (Inward)
Increase of speed causes the shoe to press harder the rim
inner surface and enables more torque to be transmitted.
Design of a centrifugal clutch
Mass of the shoes
Consider one shoe of a centrifugal clutch m = Mass of each shoe,
n = Number of shoes
r = Distance of centre of gravity of the shoe
from the centre of the spider,
R = Inside radius of the pulley rim,
N = Running speed of the pulley in r.p.m.,
ω = Angular running speed of the pulley in
rad / s = 2 π N / 60 rad/s,
ω1 = Angular speed at which the
engagement begins to take place, and
μ = Coefficient of friction between the shoe
and rim.
Centrifugal force acting on each shoe at the running speed
Since the speed at which the engagement begins to take place is generally
taken as 3/4th of the running speed, therefore the inward force on each
shoe exerted by the spring is given by
Therefore, Net outward radial force (i.e. centrifugal force) with which the
shoe presses against the rim at the running speed
The frictional force acting tangentially on each shoe
Frictional torque acting on each shoe
Total frictional torque transmitted
Size of the shoes
l = Contact length of the shoes
b = Width of the shoes
R = Contact radius of the shoes. It is same as the inside radius of the rim
of the pulley
θ = Angle subtended by the shoes at the centre of the spider in radians
p = Intensity of pressure exerted on the shoe. In order to ensure
reasonable life, it may be taken as 0.1 N/mm2.
Area of contact of the shoe = l.b
The force with which the shoe presses against the rim = p×A = p.l.b
Since the force with which the shoe presses against the rim at the
running speed is (Pc – Ps), therefore
Dimensions of the spring obtained from the relation below
Classification of Mechanical drives
Friction drives
(Belt and Rope drives)
Toothed drives
(Gears and chain drives)
According to
physical
condition
According to
method of
linking
Direct contact drives
(Gear drives)
Drives with intermediate
link
(Belt, rope and chain drives)
Flat belt joints
Cemented
joints
Laced
joints
Hinged
joints
Open belt drives Cross belt drives
No crossing
between belts,
Pulleys are rotating
in same direction,
Pulleys are rotating
in opposite direction
due to crossing,
More angle of
contact
Vibration due to long centre
distance, slip due to low
frictional grip
Belts rubs during crossing
leads to wear, bending in two
different planes
Friction between the belt and the pulley is responsible for transmitting
power from one pulley to the other. Due to the presence of friction between
the pulley and the belt surfaces, tensions on both the sides of the belt are
not equal.
Relationship between belt tensions
Free body diagram of a belt segment
The length of the belt segment
frictional force N
Centrifugal force due to the motion of the belt
Important terms
The motion of the belt and pulley assuming a firm frictional grip between the belts
and pulleys. Sometimes, the frictional grip becomes insufficient and may cause
forward motion of a pulley without carrying the belt. This is called slip of the belt.
When the belt passes from the slack side to the tight side, a certain portion
of the belt extends and it contracts again when the belt passes from the tight
side to slack side. Due to these changes of length, there is a relative motion
between the belt and the pulley surfaces. This relative motion is termed as
creep.
Classification of Belt Drives
Based on power
transmission
Light duty drives
About 5 kW power, velocity up to 10m/s
Example: Pumps
medium duty drives
5 kW to 20 kW power, velocity up to 20
m/s
Example: punch and printing
machinery
Heavy duty drives
More than 20 kW power, more than 20
m/s
Example: Turbines
Belt materials
Leather
(Oak tanned or chrome tanned)
fabrics
(Canvas or woven cotton ducks)
rubber
(Canvas or cotton duck
impregnated with rubber, For
greater tensile strength, the
rubber belts are reinforced with
steel cords or nylon cords)
plastics
(Thin plastic sheets with rubber
layers )
Based on centre
distance
Flat belts
V belts ( single V belt, multiple V belt, ribbed belt)
Toothed or timing belt
Round belt
Based on cross
section
For long distance about 5m to 20m  Flat belts
For short distance less than 5m  V belts, toothed belts etc.
Factors considered for
selection of belt drives
Based on wear resistance,
durability, strength, flexibility
& coefficient of friction
Power to be
transmitted
Space
availability for
installation
Speed of the
machinery
shaft
Velocity ratio
Center
distance
Service
conditions
Advantages: long distance power transmission, withstand shock and vibration,
adjusting misalignment between driving and driven machine, simple in design, low
cost
Disadvantages: large space, belt slipping, exert heavy load on the shaft and bearings,
power loss due to friction, shorter life
Flat belt drive Applications
Packing Industry
Baggage Handling
Coal Industry
Applications of belt drives
 The belt thickness can be built up with a number of layers. The number of layers is
known as ply.
Typical Belt drive specifications  Material  No. of ply and Thickness  Maximum
belt stress per unit width  Coefficient of friction of the belt material  Density of
Belt material
Centrifugal Tension in the Belt
When a belt runs over a pulley, some centrifugal force is caused,
whose effect is to increase tension on both tight side and slack
side of the drive. This tension caused by centrifugal force is
known as centrifugal tension.
 At high speed greater than 10 m/s,
effect of centrifugal force is
considerable .
If the effect of centrifugal tension is considered,
Then, the total tension in the tight side Tmax = T1 + TC
Total tension in the slack side Tmin = T2 + TC
Where,
T1 = Tension in the tight side of the belt
T2 = Tension in the slack side of the belt
TC = Centrifugal tension
Therefore, centrifugal tension has no effect on the power
transmission.
Condition for Maximum Power Transmission
when the power transmitted is
maximum, 1/3rd of the maximum
tension (T) is absorbed as
centrifugal tension (TC) .
Crowning of Pulley
 Pulleys are provided with a slight conical shape or convex shape in their
outer rim surface to prevent the belt from running off the pulley due to
centrifugal force. This is known as crowing of pulley.
 Usually crowning height may be 1/96 th of the pulley width.
Sag in the belt drive
 In horizontal belt drive, loose side is usually kept on the top. On the
upper side, the sag of the belt due to its own weight slightly increases the
arc of contact with the pulleys and increases the efficiency of the drive.
 If the lower side is slack side, then sag will reduce the angle of contact
with the pulleys. This has to be avoided to gain the power transmission.
 In case of vertical belt drive, due to gravitational force on the belt, it will
try to fall away from the lower surface of the lower pulley. This causes
slip and reduces the efficiency of the drive. To run such a drive, the belt
has to run with excessive tension with consequent increase in bearing
reactions and reduced belt life.
Timing belt or Ribbed belt
 Timing belt has toothed shape in
their inner surface. Their
engagement with toothed pulley
will provide positive drive without
any belt slip where as in the case of
ordinary V – belts chances for slip
are more.
 Hence toothed shape belts ( i.e.
timing belts) are always superior
than V – belts.
Initial tension not required – reduces the bearing action – high strength to
weight ratio – costlier than the V and flat belts – more sensitive to
misalignment
Timing belt or Ribbed belt
Timing belt or Ribbed belt
Round Belts
Round belts are made of leather, canvas and rubber. The diameter of
the round belts are usually 3 to 12 mm.
They are suitable for , 90° twist, reverse bending or serpentine
applications.
Round belts are limited to light duties dish washer drives, sewing
machines, vacuum cleaner, light duty textile machinery.
Trapezoidal Half round
groove groove
Quarter turn Belt Drive
The quarter turn belt drive (also known as right angle belt drive) as is used with
shafts arranged at right angles and rotating in one definite direction.
In order to prevent the belt from leaving the pulley, the width of the face of the
pulley should be greater or equal to 1.4 b, where b is width of belt.
when the reversible motion is desired, then a quarter turn belt drive with a guide
pulley, may be used.
Design of V – Belt Drive
 In case of V – belt drive, power is transmitted by the wedging action between
the belt and the v – groove in the pulley or sheave.
 A clearance should be provided at the bottom of the groove to prevent
touching of the bottom as it becomes narrower from wear.
 To increase the power transmission, multiple V – belts can be operated side
by side. All the belts should stretch at the same rate so that the load is equally
shared between them.
 When one of the set of belts break, the entire set should be replaced at the
same time. If only one belt is replaced, the new unworn and unstretched belt
will be more tightly stretched and will move with different velocity.
Forces acting on an element of V – Belt
The force components T, T+ dT and Centrifugal force are same as like flat
belt element. But the normal reaction which act on the sides of the V – belt.
Different failures in
belt drives
Wire rope is a type of rope which consists of several strands of metal wire
twisted into a helix. Lighter in weight  silent operation  withstand shock
loads  do not fail suddenly  more reliable
Applications: Elevators - mine hoists – cranes – conveyors - hauling devices -
suspension bridges
Right-hand Lang's lay (RHLL) wire rope
Strands are twisted into a right hand side
Left-hand Lang's lay (RHLL) wire rope
Strands are twisted into a left hand side
Design of Wire rope
When a large amount of power is to be transmitted over long distances from
one pulley to another (i.e. when the pulleys are upto 150 meters apart), then
wire ropes are used.
Rope construction Wire diameter dw
where d = rope diameter
Area of cross section
(Approx.
6 x 7 0.106 d 0.38 d2
6 x 19 0.063 d 0.38 d2
6 x 37 0.045 d 0.38 d2
8 x 19 0.05 d 0.38 d2
Cross or regular lay ropes  direction of twist of wires in the strands is
opposite to the direction of twist of the stands
Parallel or lang lay ropes  direction of twist of the wires in the strands is
same as that of strands in the rope
Composite or reverse laid ropes  wires in the two adjacent strands are
twisted in the opposite direction
Wire rope
applications
Stresses in Wire Ropes
Direct stress due to axial load lifted and weight of the rope
Bending stress when the rope winds round the sheave or drum
The approximate value of the bending stress in the wire as proposed by Reuleaux
Equivalent bending load on the rope
Load on the whole rope due to bending
Impact load and stress during starting
Effective stresses in the wire rope at different situations
Impact Loading: The load which is rapidly applied to the machine
component is known as impact load.
Impact stress = Twice the stress produced by gradual load
Special offset thimble with clips
Regular thimble with clips
Three bolt wire clamps
Thimble with four or five wire tucks
Wire rope socket with zinc
Design of Chain Drives
Positive drive – No slip – No Creep –
high temperature service – Easier to
install – compact than belt drives
Classification of Chains
Hoisting and hauling chains Conveyor chains
Chain with oval links
Chain with square links
Detachable or hook joint type chain
Closed joint type chain
Used for suspending, raising or lowering loads
in material handling equipments
Used for carrying materials
continuously in conveyors by sliding
Roller chain
Power transmitting chains
Used for transmitting
power from one shaft to
another shaft
Types of roller chain
Silent chain
Inverted tooth chain – formed by laminated steel plates – each plate has two teeth
with space to accommodate tooth of the sprocket – for high speed applications –
silent operation
Breaking load: The maximum tensile
load which if applied will result in chain
failure is known as breaking load.
Chain sag: catenary effect
Over tensioned chain will wear faster due to high pressure
loading between the roller and pin and high pressure
between the roller and sprocket. Over tensioning will also
result in higher bearing and shaft loads.
Under tensioning can result in the chain ratcheting
1. Drop lubrication
2. Oil bath lubrication
3. Forced feed lubrication
1 2
3

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Design of transmission systems by A.Vinoth Jebaraj

  • 2.
  • 3. To avoid the slipping Exact velocity ratio  Transmit large power  Used for small centre distances  High efficiency  Reliable service  Compact layout Require special tools and equipments to produce  Improper cutting of teeth produce vibration and noise  Lubrication is must
  • 6. Arc of contact: Path traced by a point on the pitch circle from the beginning to the end of the engagement of a given pair of teeth. It consists of two parts. Arc of approach: Portion of the path of contact from the beginning of engagement to the pitch point. Arc of recess: Portion of the path of contact from the pitch point to the end of the engagement of a pair of teeth.
  • 7. Line of Action Arc of approach Arc of recess
  • 8. Spur gear Helical gear Double helical or Herringbone gear Cross helical gear
  • 9. Straight bevel gear Spiral bevel gear Worm and worm wheel Rack & Pinion
  • 10. Pressure Angle or Angle of Obliquity: Angle between common normal to two gear teeth at the point of contact (line of contact) and the common tangent at the pitch point. Standard values include 14.5, 20 and 25 degrees.
  • 11. Backlash: It is the difference between tooth space and the tooth thickness as measured along pitch circle. Theoretically backlash should be zero. But in actual practice some backlash must be allowed to prevent jamming of the teeth due to the tooth errors and thermal expansion.
  • 12. Module (m): Pitch diameter divided by number of teeth. The pitch diameter is usually specified in inches or millimeters; It is a measure of the tooth strength. Higher the module bigger the size of the gear. More important, higher the module, wider the tooth at the base and larger the height of the tooth.
  • 13. Main parameters to be designed: Center Distance Module Face width Let Mt be the torque transmitted by the pinion Normal force on the tooth Fn = Torque / lever arm Radius of the base circle = ½ d1 cos α 1
  • 14. Diameter d1 can be expressed in terms of center distance ‘a’ as Substituting the value of d1 in Eq. 1
  • 15. Therefore, Fn is inversely proportional to the centre distance.  As center distance decreases the normal force will increase and hence the surface compressive stress increases. Therefore the centre distance is limited by the permissible surface compressive stress of the material of the pinion.
  • 16. IMPORTANT POINTS TO BE NOTED: Minimum centre distance depends upon the surface compressive strength of the material So induced surface compressive stress < Design surface compressive strength of the material Minimum module depends upon the bending strength So induced bending stress < Design bending strength of the material
  • 17. Design surface compressive strength [σc] Surface strength is proportional to the hardness of the surface. σc α HB or RC Therefore, σC = CB × HB N/cm2 = CR × RC N/cm2 CB and CR are constants depending on the material and heat treatment.
  • 18. Also the design compressive strength depends on load conditions. Hence correction factor is introduced. Design surface compressive strength [σC ] = CB HB Kcl in N/cm2 [σC] = CR HRC Kcl in N/cm2 Where Kcl is the life factor for surface compressive strength. Kcl = Where N – number of fatigue cycles the pinion teeth has undergone in its life period of T hours. Number of fatigue cycles per hour = 60 n Number of cycles in life period N = 60 n T
  • 19. Design Bending Stress [σb] It depends on endurance limit, stress concentration factor at the root and life factor for bending. [σb] = For gears having both directions of rotation [σb] = × 1.4 For gears having one direction of rotation only = endurance limit stress in bending = life factor in bending = stress concentration of fillet at the root n = factor of safety
  • 20. Gear materials Commonly used materials  cast iron and steel For large power transmission and reduction in size  Alloy steel of Nickel, chromium & vanadium (with proper heat treatment to obtain sufficient surface strength) For corrosive environment  Brass and bronze Non metallic materials  Laminated fabric, Bakelite and mica (to reduce noise)
  • 21. Gear Failures Teeth breakage: due to fatigue Pitting: hard and smooth working surfaces of the teeth reduce the danger of pitting Surface abrasion: due to sliding of the teeth Seizure: surface of the teeth mesh so tightly together causes particles of softer material to break away from the teeth surface and groove it.
  • 22. Law of gearing The common normal to the tooth profile at the point of contact should always pass through a fixed point, in order to obtain a constant velocity ratio. Only involute and cycloidal curves satisfies the fundamental law of gearing.
  • 24. Helical Gears and Herringbone Gears They have teeth cut in the form of helix on their pitch cylinders. Teeth are not parallel to the axis of rotation. More than one pair of teeth are in engagement. Runs smoothly because of the gradual engagement of teeth. Higher peripheral speeds are permissible in helical gears.
  • 25. Limitation: Axial thrust By providing another helical gear of opposite hand, the axial thrust can be balanced. They are called as double helical or herringbone gears. Helix angle is helical gears are in between 8° and 25°
  • 26. Axial pitch = π m , where m is the axial module Normal pitch = π mn , where mn is the normal module Cos β = π mn / π m Therefore, Cos β = mn / m Centre distance =
  • 27. Forces acting on a Helical gear tooth
  • 28. Design of Bevel Gear Straight Bevel Gear Spiral Bevel Gear Direction of shaft’s rotation can be changed by means of bevel gears. Usually two shafts are arranged at an angle of 90°. But the other angles are also possible.
  • 29.
  • 30. Bevel gears in differential
  • 31. AXES MUST INTERSECT EACH OTHER AND MUST LIE IN THE SAME PLANE IN BEVEL GEAR ARRANGMENT
  • 32. Bevel Gear - Nomenclature
  • 33. Terminology of bevel gears Pitch cone: Imaginary cone that the surface of which contains the pitch lines of all teeth in the bevel gear. Cone center: The apex of the pitch cone is called cone center. Cone distance: Length of the pitch cone element also called as pitch cone radius. Pitch angle: Angle that the pitch line makes with the axis of the gear is called the pitch angle. Addendum angle: Angle subtended by the addendum at the cone center. Face angle: Angle subtended by the face of the tooth at the cone center.
  • 34. Transverse module mt : It is based on the pitch circle diameter at the outer portion. Average module mav : It is based on pitch circle diameter at the centers of the teeth.
  • 35. Miter Gear  When two identical gears are mounted on shafts, that are intersecting at right angles, then they are called as Miter gears.  Pitch angles of pinion and gear of Miter gears are same and each is equal to 45°.  Pinion and gear of Miter gears rotate at same speed.
  • 36. Crown Gear  In a pair of bevel gear, when one of the gear has a pitch angle of 90°, then that gear is called as crown gear.  They are intersecting at an angle that is more than 90°.
  • 37. Internal Bevel gear  When the teeth of a bevel gear are cut inside the pitch cone, then it is called as internal bevel gear.  In this case the pitch angle of the internal gear is more than 90° and the apex point is on the backside of the teeth on the gear.
  • 38. Skew bevel gear: When two straight bevel gears are mounted on shafts, which are non parallel and non intersecting, then they are called as skew bevel gears
  • 39. Hypoid Bevel Gear They are similar to spiral bevel gears that are mounted on shafts, which are non-parallel and non-intersecting.
  • 40. Face gears: They consists of a spur or helical pinion mating with a pair gear of disk form.
  • 42. Design of worm and worm wheel Worm (Driver) Worm wheel (Driven) Worm always drives the worm wheel. It is a self locking drive. Reversible direction of power transmission is not possible. Higher speed reduction and more torque at the output is possible through worm drive.
  • 43. Consider a single start worm and a 20 teeth worm gear will reduce the speed by the ratio of 20:1. The gear ratio of a worm gear is i = The worm acts as a single toothed gear so the ratio is; i = Gear Ratio = 20:1 (Rotary velocity is reduced by 20:1)  If this speed reduction is achieved by spur gears, then a gear of 12 teeth (the smallest size permissible) would have to be matched with a 240 tooth gear to achieve the same ratio of 20:1.  Therefore according to the physical size of the 240 tooth gear to that of the 20 tooth gear, the worm arrangement is considerably smaller in volume.
  • 45. Self-locking Worm Gear  The worm always acts as a driving gear and the spur gear as a driven gear- vice versa is not possible. If you try to run it in opposite direction, it will lock automatically.  A worm and gear will be self-locking depends on the lead angle, the pressure angle, and the coefficient of friction;  If the tangent of the lead angle of the worm gear is less than the coefficient of friction between the worm and the gear, then the worm gear train should be a self- locking type. The self-locking worm gear USED for the applications where loading against the gravitational force is required. This is because the angle on the worm is so shallow that when the gear tries to spin it, the friction between the gear and the worm holds the worm in place.
  • 46.  Losses in worm gears are high, they need costly materials like bronze and the manufacturing cost is high.  Power transmission between worm and worm wheel happens through sliding. Therefore, the materials used should have low coefficient of friction.  Seizure and wear are the two major failures in worm gear drive.  Proper lubrication and cooling surfaces should be provided to limit the operating temperature between 60° and 70°C.
  • 47. Bearing : Machine element used to support a rotating member with the very minimum frictional power loss. Types:  Rolling contact bearings  Sliding contact bearings
  • 48.
  • 49. Anti-friction bearing  due to its low friction characteristics  used for radial load, thrust load and combination of thrust and radial load  relatively lower price  maintenance free  friction increases at high speeds  noisy while running  Types : Ball bearing and Roller bearing Single row deep groove ball bearing Radial load but it can also take up considerable amount of axial load. Functions of bearings : Ensure free rotation with minimum friction Act as a support for shaft and axle and holds in correct position Takes up the forces acting on the shaft and axle and transmits them to the frame or foundation
  • 50. Advantages 1. Low starting and running friction except at very high speeds. 2. Accuracy of shaft alignment. 3. Low cost of maintenance, as no lubrication is required while in service. 4. Small overall dimensions. 5. Reliability of service. 6. Easy to mount and erect & Cleanliness. Disadvantages 1. More noisy at very high speeds. 2. Low resistance to shock loading. 3. More initial cost. 4. Design of bearing housing complicated.
  • 51. Applications of rolling contact bearings: Machine tool spindles  automobile front and rear axles  gear boxes  small size electric motors  rope sheaves, crane hooks and hoisting drums
  • 52. Single row Angular Contact Ball Bearing Used for radial loads and heavy axial loads Double Row Angular Contact Bearing Has two rows of balls. Axial displacement of the shaft can be kept very small even for axial loads of varying magnitude Single thrust ball bearing Used for unidirectional axial load
  • 53. Taper Roller Bearing Used for simultaneous heavy radial load and heavy axial load Roller bearings has more contact area than a ball bearing, therefore, they are generally used for heavier loads than the ball bearings Spherical Roller Bearing Cylindrical Roller Bearing For heavy radial load and high speed use, cylindrical roller bearings It is mainly used for heavy axial loads. However, considerable amount of loads in either direction can also be applied
  • 55. Static load carrying capacity: The static load which corresponds to a total permanent deformation of balls and races, at the most heavily stressed point of contact, equal to 0.0001 of the ball diameter. [Load acting on the bearing when the shaft is stationary] STIBECK’S EQUATION Static load CO = (k.d2.z) / 5 Where k = factor depends upon the radii of curvature at the point of contact d = ball diameter z = number of balls
  • 56. Dynamic load carrying capacity: (fatigue life of the bearing) Life of an individual bearing is defined as the number of revolutions which the bearing runs before the first evidence of fatigue crack in balls and races. The dynamic load carrying capacity of a bearing is defined as the radial load in radial bearings that can be carried for a minimum life of one million revolutions. The minimum life in this definition is the L10 life, which 90% of the bearings will reach or exceed before fatigue failure.
  • 57. Equivalent bearing load [P]: Two components of load acting on the bearing  single hypothetical load The equivalent dynamic load is defined as the constant radial load in radial bearings (or thrust load in thrust bearings), which if applied to the bearing would give same life as that which the bearing will attain under actual condition of forces. Where Fr  radial load Fa  axial load X and Y  radial and thrust factors from manufacturer’s catalogues V  Race factor P = X .V. Fr + Y . Fa
  • 58. Load factor in bearings: Load factors are used in applications involving gear, chain and belt drives. Gear drives  additional dynamic load due to inaccuracies of the tooth profile and the elastic deformation of the teeth. Chain and belt drives  additional dynamic load due to vibrations Bearing failure – causes and remedies  breakage of parts like races and cages  crushing of balls due to misalignment leads to overload  failure of a cage due to centrifugal force acting on balls  surface wear  abrasive wear, corrosive wear, pitting, scoring (breakage lubrication film leads to excessive heat in the contact surfaces)
  • 59. Journal Bearing ( Hydrodynamic bearing) Journal bearing is a sliding contact bearing working on hydrodynamic lubrication and which supports the load in radial direction. The portion of the shaft inside the bearing is called journal and hence the name ‘Journal bearing’
  • 60. Since the pressure is created within the system due to rotation of the shaft, this type of bearing is known as ‘self acting bearing’.
  • 61. Can take load in any radial direction [many industrial applications) Can take load in only one radial direction [rail road cars]
  • 62. Hydrostatic bearing: In a system of lubrication, load supporting fluid film, separating the two surfaces is created by an external source, like pump, supplying sufficient fluid under pressure. This is also called as externally pressurized bearings. Advantages: High load carrying capacity even at low speeds, no starting friction, no rubbing action at any operating speed or load
  • 63.  Bearing which operates without any lubricant  Zero film bearings  Two surfaces of the bearing in relative motion are completely separated by a lubricant  Thick film bearings  Lubricant film is relatively thin and there is partial metal to metal contact  Thin film bearings
  • 64. The factor ZN / p is termed as bearing characteristic number and is a dimensionless number
  • 65.
  • 66.  Between Q and R  Partial metal to metal contact (The viscosity (Z) or the speed (N) are so low, or the pressure ( p) is so great that their combination ZN / p will reduce the film thickness)  Between R and S  Thin film or boundary lubrication or imperfect lubrication (This is the region where the viscosity of the lubricant ceases to be a measure of friction characteristics but the oiliness of the lubricant is effective in preventing complete metal to metal contact and seizure of the parts)  Between P and Q  Stable operating conditions (Since from any point of stability, a decrease in viscosity (Z) will reduce ZN / p. This will result in a decrease in coefficient of friction (μ) followed by a lowering of bearing temperature that will raise the viscosity (Z ))
  • 67. Bearing should not be operated at ‘K’ (Bearing modulus). Because, a slight decrease in speed or slight increase in pressure will break the oil film and make the journal to operate with metal to metal contact. This will result in high friction, wear and heating. In order to prevent such conditions, the bearing should be designed for a value of ZN / p at least three times the minimum value of bearing modulus (K). If the bearing is subjected to large fluctuations of load and heavy impacts, the value of ZN / p = 15 K may be used. On the other hand, when the value of ZN / p is less than K, then the oil film will rupture and there is a metal to metal contact.
  • 68. Critical pressure of the journal bearing The pressure at which the oil film breaks down so that metal to metal contact begins, is known as critical pressure or the minimum operating pressure of the bearing.
  • 69.
  • 70.  Clutch is a mechanical device which transmits power from the driving shaft to the driven shaft when it is engaged and cuts the power when it is disengaged.  Example: Engine to road wheels , Drilling machine motor to spindle
  • 71.
  • 72. Clutch Engaged position Clutch disengaged position
  • 74. Method of Analysis The torque transmitted by a clutch is a function of Geometry The magnitude of the actuating force applied The condition of contact prevailing between the members
  • 75. Uniform Pressure Theory If the applied force keep the frictional surfaces together with a uniform pressure all over its contact area , then the analysis is based on uniform pressure condition . Uniform Wear Theory However, as the time progresses some wear takes place between the contacting members and this may alter or vary the contact pressure appropriately and uniform pressure condition may no longer prevail. Hence the analysis here is based on uniform wear condition. [Wear α contact pressure and sliding velocity]
  • 76.
  • 77.
  • 78.
  • 79.
  • 80.
  • 81.
  • 82.
  • 84.
  • 85.
  • 86. Consider a small ring of radius “r” and thickness “dr” “dl” is the length of ring of the friction surface = dl = dr cosec α Area of ring = 2π r. dl = 2π r.dr cosec α 1. Considering uniform pressure The normal force acting on the ring δWn = Normal pressure × Area of ring = pn × 2π r.dr cosec α The axial force acting on the ring δW = Horizontal component of δWn (i.e. in the direction of W) δWn × sin α = pn × 2π r.dr cosec α × sin α = 2π × pn.r.dr
  • 87. Total axial load transmitted to the clutch or the axial spring force required Frictional force on the ring acting tangentially at radius r Fr= μ.pn × 2πr.dr cosec α Frictional torque acting on the ring Tr = Fr × r = μ.pn × 2πr.dr cosec α × r Tr = 2π μ.pn cosec α.r2 dr
  • 88.
  • 89. Centrifugal clutch centrifugal force > spring force (Outward) (Inward) Increase of speed causes the shoe to press harder the rim inner surface and enables more torque to be transmitted.
  • 90. Design of a centrifugal clutch Mass of the shoes Consider one shoe of a centrifugal clutch m = Mass of each shoe, n = Number of shoes r = Distance of centre of gravity of the shoe from the centre of the spider, R = Inside radius of the pulley rim, N = Running speed of the pulley in r.p.m., ω = Angular running speed of the pulley in rad / s = 2 π N / 60 rad/s, ω1 = Angular speed at which the engagement begins to take place, and μ = Coefficient of friction between the shoe and rim.
  • 91. Centrifugal force acting on each shoe at the running speed Since the speed at which the engagement begins to take place is generally taken as 3/4th of the running speed, therefore the inward force on each shoe exerted by the spring is given by Therefore, Net outward radial force (i.e. centrifugal force) with which the shoe presses against the rim at the running speed
  • 92. The frictional force acting tangentially on each shoe Frictional torque acting on each shoe Total frictional torque transmitted
  • 93. Size of the shoes l = Contact length of the shoes b = Width of the shoes R = Contact radius of the shoes. It is same as the inside radius of the rim of the pulley θ = Angle subtended by the shoes at the centre of the spider in radians p = Intensity of pressure exerted on the shoe. In order to ensure reasonable life, it may be taken as 0.1 N/mm2. Area of contact of the shoe = l.b The force with which the shoe presses against the rim = p×A = p.l.b
  • 94. Since the force with which the shoe presses against the rim at the running speed is (Pc – Ps), therefore Dimensions of the spring obtained from the relation below
  • 95.
  • 96.
  • 97.
  • 98. Classification of Mechanical drives Friction drives (Belt and Rope drives) Toothed drives (Gears and chain drives) According to physical condition According to method of linking Direct contact drives (Gear drives) Drives with intermediate link (Belt, rope and chain drives)
  • 100. Open belt drives Cross belt drives No crossing between belts, Pulleys are rotating in same direction, Pulleys are rotating in opposite direction due to crossing, More angle of contact Vibration due to long centre distance, slip due to low frictional grip Belts rubs during crossing leads to wear, bending in two different planes
  • 101. Friction between the belt and the pulley is responsible for transmitting power from one pulley to the other. Due to the presence of friction between the pulley and the belt surfaces, tensions on both the sides of the belt are not equal.
  • 102. Relationship between belt tensions Free body diagram of a belt segment
  • 103. The length of the belt segment frictional force N Centrifugal force due to the motion of the belt
  • 104. Important terms The motion of the belt and pulley assuming a firm frictional grip between the belts and pulleys. Sometimes, the frictional grip becomes insufficient and may cause forward motion of a pulley without carrying the belt. This is called slip of the belt.
  • 105. When the belt passes from the slack side to the tight side, a certain portion of the belt extends and it contracts again when the belt passes from the tight side to slack side. Due to these changes of length, there is a relative motion between the belt and the pulley surfaces. This relative motion is termed as creep.
  • 106. Classification of Belt Drives Based on power transmission Light duty drives About 5 kW power, velocity up to 10m/s Example: Pumps medium duty drives 5 kW to 20 kW power, velocity up to 20 m/s Example: punch and printing machinery Heavy duty drives More than 20 kW power, more than 20 m/s Example: Turbines Belt materials Leather (Oak tanned or chrome tanned) fabrics (Canvas or woven cotton ducks) rubber (Canvas or cotton duck impregnated with rubber, For greater tensile strength, the rubber belts are reinforced with steel cords or nylon cords) plastics (Thin plastic sheets with rubber layers )
  • 107. Based on centre distance Flat belts V belts ( single V belt, multiple V belt, ribbed belt) Toothed or timing belt Round belt Based on cross section For long distance about 5m to 20m  Flat belts For short distance less than 5m  V belts, toothed belts etc.
  • 108. Factors considered for selection of belt drives Based on wear resistance, durability, strength, flexibility & coefficient of friction Power to be transmitted Space availability for installation Speed of the machinery shaft Velocity ratio Center distance Service conditions Advantages: long distance power transmission, withstand shock and vibration, adjusting misalignment between driving and driven machine, simple in design, low cost Disadvantages: large space, belt slipping, exert heavy load on the shaft and bearings, power loss due to friction, shorter life
  • 109. Flat belt drive Applications Packing Industry Baggage Handling Coal Industry
  • 111.  The belt thickness can be built up with a number of layers. The number of layers is known as ply. Typical Belt drive specifications  Material  No. of ply and Thickness  Maximum belt stress per unit width  Coefficient of friction of the belt material  Density of Belt material
  • 112. Centrifugal Tension in the Belt When a belt runs over a pulley, some centrifugal force is caused, whose effect is to increase tension on both tight side and slack side of the drive. This tension caused by centrifugal force is known as centrifugal tension.  At high speed greater than 10 m/s, effect of centrifugal force is considerable .
  • 113.
  • 114. If the effect of centrifugal tension is considered, Then, the total tension in the tight side Tmax = T1 + TC Total tension in the slack side Tmin = T2 + TC Where, T1 = Tension in the tight side of the belt T2 = Tension in the slack side of the belt TC = Centrifugal tension Therefore, centrifugal tension has no effect on the power transmission.
  • 115. Condition for Maximum Power Transmission when the power transmitted is maximum, 1/3rd of the maximum tension (T) is absorbed as centrifugal tension (TC) .
  • 116. Crowning of Pulley  Pulleys are provided with a slight conical shape or convex shape in their outer rim surface to prevent the belt from running off the pulley due to centrifugal force. This is known as crowing of pulley.  Usually crowning height may be 1/96 th of the pulley width.
  • 117. Sag in the belt drive  In horizontal belt drive, loose side is usually kept on the top. On the upper side, the sag of the belt due to its own weight slightly increases the arc of contact with the pulleys and increases the efficiency of the drive.  If the lower side is slack side, then sag will reduce the angle of contact with the pulleys. This has to be avoided to gain the power transmission.  In case of vertical belt drive, due to gravitational force on the belt, it will try to fall away from the lower surface of the lower pulley. This causes slip and reduces the efficiency of the drive. To run such a drive, the belt has to run with excessive tension with consequent increase in bearing reactions and reduced belt life.
  • 118.
  • 119. Timing belt or Ribbed belt  Timing belt has toothed shape in their inner surface. Their engagement with toothed pulley will provide positive drive without any belt slip where as in the case of ordinary V – belts chances for slip are more.  Hence toothed shape belts ( i.e. timing belts) are always superior than V – belts. Initial tension not required – reduces the bearing action – high strength to weight ratio – costlier than the V and flat belts – more sensitive to misalignment
  • 120. Timing belt or Ribbed belt
  • 121. Timing belt or Ribbed belt
  • 122. Round Belts Round belts are made of leather, canvas and rubber. The diameter of the round belts are usually 3 to 12 mm. They are suitable for , 90° twist, reverse bending or serpentine applications. Round belts are limited to light duties dish washer drives, sewing machines, vacuum cleaner, light duty textile machinery. Trapezoidal Half round groove groove
  • 123. Quarter turn Belt Drive The quarter turn belt drive (also known as right angle belt drive) as is used with shafts arranged at right angles and rotating in one definite direction. In order to prevent the belt from leaving the pulley, the width of the face of the pulley should be greater or equal to 1.4 b, where b is width of belt. when the reversible motion is desired, then a quarter turn belt drive with a guide pulley, may be used.
  • 124.
  • 125. Design of V – Belt Drive  In case of V – belt drive, power is transmitted by the wedging action between the belt and the v – groove in the pulley or sheave.  A clearance should be provided at the bottom of the groove to prevent touching of the bottom as it becomes narrower from wear.  To increase the power transmission, multiple V – belts can be operated side by side. All the belts should stretch at the same rate so that the load is equally shared between them.  When one of the set of belts break, the entire set should be replaced at the same time. If only one belt is replaced, the new unworn and unstretched belt will be more tightly stretched and will move with different velocity.
  • 126. Forces acting on an element of V – Belt The force components T, T+ dT and Centrifugal force are same as like flat belt element. But the normal reaction which act on the sides of the V – belt.
  • 127.
  • 128.
  • 130. Wire rope is a type of rope which consists of several strands of metal wire twisted into a helix. Lighter in weight  silent operation  withstand shock loads  do not fail suddenly  more reliable Applications: Elevators - mine hoists – cranes – conveyors - hauling devices - suspension bridges Right-hand Lang's lay (RHLL) wire rope Strands are twisted into a right hand side Left-hand Lang's lay (RHLL) wire rope Strands are twisted into a left hand side Design of Wire rope
  • 131. When a large amount of power is to be transmitted over long distances from one pulley to another (i.e. when the pulleys are upto 150 meters apart), then wire ropes are used. Rope construction Wire diameter dw where d = rope diameter Area of cross section (Approx. 6 x 7 0.106 d 0.38 d2 6 x 19 0.063 d 0.38 d2 6 x 37 0.045 d 0.38 d2 8 x 19 0.05 d 0.38 d2
  • 132. Cross or regular lay ropes  direction of twist of wires in the strands is opposite to the direction of twist of the stands Parallel or lang lay ropes  direction of twist of the wires in the strands is same as that of strands in the rope Composite or reverse laid ropes  wires in the two adjacent strands are twisted in the opposite direction
  • 134. Stresses in Wire Ropes Direct stress due to axial load lifted and weight of the rope Bending stress when the rope winds round the sheave or drum The approximate value of the bending stress in the wire as proposed by Reuleaux
  • 135. Equivalent bending load on the rope Load on the whole rope due to bending Impact load and stress during starting
  • 136. Effective stresses in the wire rope at different situations
  • 137. Impact Loading: The load which is rapidly applied to the machine component is known as impact load. Impact stress = Twice the stress produced by gradual load
  • 138. Special offset thimble with clips Regular thimble with clips Three bolt wire clamps Thimble with four or five wire tucks Wire rope socket with zinc
  • 139. Design of Chain Drives Positive drive – No slip – No Creep – high temperature service – Easier to install – compact than belt drives
  • 140. Classification of Chains Hoisting and hauling chains Conveyor chains Chain with oval links Chain with square links Detachable or hook joint type chain Closed joint type chain Used for suspending, raising or lowering loads in material handling equipments Used for carrying materials continuously in conveyors by sliding
  • 141. Roller chain Power transmitting chains Used for transmitting power from one shaft to another shaft
  • 142. Types of roller chain
  • 143. Silent chain Inverted tooth chain – formed by laminated steel plates – each plate has two teeth with space to accommodate tooth of the sprocket – for high speed applications – silent operation
  • 144.
  • 145.
  • 146. Breaking load: The maximum tensile load which if applied will result in chain failure is known as breaking load.
  • 147. Chain sag: catenary effect Over tensioned chain will wear faster due to high pressure loading between the roller and pin and high pressure between the roller and sprocket. Over tensioning will also result in higher bearing and shaft loads. Under tensioning can result in the chain ratcheting
  • 148. 1. Drop lubrication 2. Oil bath lubrication 3. Forced feed lubrication 1 2 3