GEARS PPT.pptx

Introduction
We have discussed earlier that the slipping of a belt
or rope is a common phenomenon, in the
transmission of motion or power between two
shafts.
The effect of slipping is to reduce the velocity ratio
of the system. In precision machines, in which a
definite velocity ratio is of importance (as in watch
mechanism), the only positive drive is by gears or
toothed wheels.
A gear drive is also provided, when the distance
between the driver and the follower is very small

FRICTION WHEELS
GEAR OR TOOTHED WHEEL

The motion and power transmitted by gears is
kinematically equivalent to that transmitted by frictional
wheels or discs.
Let the wheel A is keyed to the rotating shaft and the
wheel B to the shaft to be rotated.
A little consideration will show that when the wheel A is
rotated by a rotating shaft, it will rotate the wheel B in
the opposite direction as shown in above fig.
The wheel B will be rotated by the wheel A so long as
the tangential force exerted by the wheel A does not
exceed the maximum frictional resistance between the
two wheels.
But when the tangential force (P) exceeds the *frictional
resistance (F), slipping will take place between the two
wheels.

In order to avoid the slipping, a number of projections
(called teeth) as shown in above Fig. are provided on the
periphery of the wheel A which will fit into the
corresponding recesses on the periphery of the wheel B.
A friction wheel with the teeth cut on it is known as gear
or toothed wheel.
Gears are defined as toothed wheels which
transmit power and motion from one shaft to
another by means of successive engagement
of teeth.
DEFINITION

Advantages and Disadvantages of Gear Drives
 The following are the advantages and disadvantages of the gear drive as
compared to other drives, i.e. belt, rope and chain drives :
Advantages
1. It transmits exact velocity ratio.
2. It may be used to transmit large power.
3. It may be used for small centre distances of shafts.
4. It has high efficiency.
5. It has reliable service.
6. It has compact layout.
Disadvantages
1. Since the manufacture of gears require special tools and equipment, therefore
it is costlier than other drives.
2. The error in cutting teeth may cause vibrations and noise during operation.
3. It requires suitable lubricant and reliable method of applying it, for the proper
operation of gear drives

Classification of Gears
• Spur Gears
• Helical Gears
• Bevel Gears
• Worm Gears

Spur Gears
• In spur gears the teeth are cut parallel to the
axis of the shaft.
• As the teeth are parallel to the axis of the
shaft, spur gears are used only when the
shafts are parallel.
• The profile of the gear tooth is in the shape of
an involute curve and it remains identical
along the entire width of the gear wheel.
• Spur gears impose radial loads on the shaft.

ADVANTAGES:
1.SIMPLE IN CONSTRUCTION.
2.EASY TO MANUFACTURE.
3.LOW COST.
4.EXCELLENT PRECISION RATING.
DISADVANTAGES:
1.CENTRE DISTANCE IS LIMITED.
2.NOISE AT HIGH SPEED.
3.STRESS.

Helical Gears
• The teeth of these gears are cut at an angle with the
axis of the shaft.
• They have an involute profile similar to that of spur
gears.
• This involute profile is in a plane, which is
perpendicular to the tooth element.
• The helix angle of pinion and gear is same; however,
the hand of the helix is opposite.
• A right hand pinion meshes with a left hand gear and
vice versa.
• They impose radial and thrust loads on the shafts.

ADVANTAGES:
1.HIGHER LOAD CARRYING CAPACITY.
2.SMOOTHER & QUITER.
3.LESS WEAR & TEAR.
4.CONSTANT OUTPUT.
DISADVATAGES:
1.COSTLIER THAN SPURGEARS.
2.REQUIRED THRUST BEARING.
3.GENERATION OF HEAT.

Herringbone Gears
• A herringbone gear consists of two helical
gears with the opposite hand of helix.
• The construction results in equal and opposite
thrust reactions, balancing each other and
imposing no thrust load on the shaft.
• Used only for parallel shafts.

ADVANTAGES:
1.SHAFT IS FREE FROM AXIAL FORCE.
2.HIGH POWER TRANSMISSION CAPACITY.
DISADVANTAGES:
1.MANUFACTURING COST IS MORE.
2. LOAD MUST BE EQUALLY DISTRIBUTED.

ADVANTAGES:
1.Easiest way of conversion.
2.Compact.
3.Robust.
4.Cheaper.
DISADVANTAGES:
1.NOISE.
2.FRICTION.

Bevel Gears
• They have the shape of a frustum of a cone.
• The size of the gear tooth, including the thickness
and height, decreases towards the apex of the
cone.
• Generally used for shafts, which are at right
angles to each other.
• The tooth of the bevel gears can be straight or
spiral.
• They impose radial and thrust loads on the shafts.

ADVANTAGES:
1.HIGH SPEED AND LOAD.
2.1:1 VELOCITY RATIO.
DISADVANTAGES:
1.COMPLICATED IN DESIGN AND MANUFACTURE.
2.MORE PRECISSION.

Worm Gears
• The gears consist of a worm and worm wheel as shown
in the figure.
• The worm is in the form of a threaded screw which
meshes with the matching wheel.
• The threads on the worm can be single or multi-start
and usually have a small lead.
• They are used for shafts, the axes of which do not
intersect and are perpendicular to each other.
• The worm imposes high thrust load, while the worm
wheel imposed high radial load on the shafts.
• They are characterised by high speed reduction ratio.

ADVANTAGES:
1.HIGHER REDUCTION RATIO.
2.COMPACT.
3. SELF LOCKING FEATURE.
4.EFFECTIVE MESHING.
5.REDUCE SPEED AND TORQUE.
DISADVANTAGES:
1.HEAT AT CONTACT POINT.
2.LOW EFFICIENCY.
3.MANUFACTURING COST IS MORE.
4.HIGH POWER LOSSES.

Selection of Gears
The factors for deciding the type of gear
are:
• layout of the shafts
• speed reduction
• power to be transmitted
• input speed
• cost.

• Spur and helical gears are used when the
shafts are parallel.
• When the shafts intersect at right angles,
bevel gears are used.
• Worm gears are recommended when the
axes of the shafts are perpendicular and non-
intersecting.

• The speed reduction ratio for a pair of spur or
helical gears is normally taken as 6:1, can be
raised up to 10:1.
• When the velocity ratio increases, the size of
the gear wheel increases resulting in increase in
the size of the gear box.
• For high speed reductions, two-stage or three-
stage constructions are used.
• The normal velocity ratio for bevel gears is 1:1,
which can be increased up to 3:1.
• For high speed reduction, worm gears offer the
best choice with a velocity ratio of 60:1, which
can be increased up to 100:1.

• Spur gears generate noise in high speed
applications, due to sudden contact over the
entire face width between two meshing teeth.
• In helical gears the contact between the two
meshing teeth begins with a point and gradually
extends along the tooth, resulting in quiet
operations. Hence used for high speed
applications.
• On cost basis spur gears are the cheapest and
easy to manufacture.
• Helical, bevel and worm gears manufacturing is a
specialized and costly operation.

Condition for Constant Velocity Ratio of Toothed Wheels – Law of Gearing
 Consider the portions of the two teeth, one on the wheel 1 (or
pinion) and the other on the wheel 2.
 Let the two teeth come in contact at point Q, and the wheels
rotate in the directions as shown in the figure.
 Let T T be the common tangent and MN be the common
normal to the curves at the point of contact Q. From the
centres O1 and O2, draw O1M and O2N perpendicular to MN.
 A little consideration will show that the point Q moves in the
direction QC, when considered as a point on wheel 1, and in
the direction QD when considered as a point on wheel 2.
 Let v1 and v2 be the velocities of the point Q on the wheels 1
and 2 respectively. If the teeth are to remain in contact, then
the components of these velocities along the common
normal MN must be equal.

From above, we see that the angular velocity ratio is inversely
proportional to the ratio of the distances of the point P from
the centers O1 and O2, or the common normal to the two
surfaces at the point of contact Q intersects the line of centers
at point P which divides the center distance inversely as the
ratio of angular velocities.
Therefore in order to have a constant angular velocity ratio for
all positions of the wheels, the point P must be the fixed point
(called pitch point) for the two wheels.
In other words, the common normal at the point of contact
between a pair of teeth must always pass through the
pitch point.
This is the fundamental condition which must be satisfied
while designing the profiles for the teeth of gear wheels. It is
also known as law of gearing.

The common normal to the tooth profile at
the point of contact should always pass
through a fixed point, called pitch point, in
order to obtain a constant velocity ratio.
Law of gearing definition

Curves Satisfying Fundamental Law of Gearing
• Involute : A curve traced by a point on a line as it rolls
without slipping on a circle
• Cycloid : A curve traced by a point on the
circumference of a generating circle as it rolls without
slipping along the inside and outside of another circle.
Cycloidal tooth is made of two curves , hypocycloid
below the pitch circle and epicycloid above the pitch
circle.

Advantages of Cycloidal tooth over Involute tooth
• In cycloidal gears, a convex flank on one tooth comes
in contact with concave flank of mating teeth,
increasing the contact area and wear strength. In
involute gears, the contact is between two convex
surfaces on mating teeth, resulting in smaller contact
area and lower wear strength.
• Phenomenon of interference does not occur at all in
cycloidal gears.

• Pinion: Smaller of the two mating gears.
• Gear: Larger of the two mating gears.
• Velocity ratio(i): The ratio of the number of revolutions of the
driving (or input) gear to the number of revolutions of the
driven (or output) gear, in a unit of time.
• Transmission ratio(il ): The ratio of angular velocity of first
gear to the angular velocity of last gear in a gear train.
• Pitch surface: The pitch surfaces of the gears are imaginary
planes, cylinders or cones that roll together without slipping.
• Pitch circle: A right section of the pitch surface.
• Pitch circle diameter : It is the diameter of the pitch circle.
The size of the gear is specified by the pitch circle diameter,
usually denoted by dl
• Pitch point: The point of tangency of the pitch circles of a pair
of mating gears.

• Top Land: The surface of the top of the gear
tooth.
• Bottom Land: It is the surface of the gear
between the flanks of adjacent teeth.
• Base circle :An imaginary circle used in involute
gearing to generate the involutes that form the
tooth profiles.
• Addendum circle: A circle bounding the ends of
the teeth, in a right section of the gear.
• Root (or dedendum) circle: The circle bounding
the spaces between the teeth, in a right section of
the gear.
• Addendum(ha): The radial distance between the
pitch circle and the addendum circle.

• Dedendum(hf): The radial distance between the pitch
circle and the root circle.
• Clearance(c):The difference between the dedendum of
one gear and the addendum of the mating gear.
• Face of a tooth: That part of the tooth surface lying
outside the pitch surface.
• Flank of a tooth: The part of the tooth surface lying
inside the pitch surface.
• Face width(b): Width of the tooth measured parallel to
the axis.
• Fillet Radius: The radius that connects the root circle to
the profile of the tooth.
• Circular thickness (also called the tooth thickness) :
The thickness of the tooth measured on the pitch circle.
It is the length of an arc and not the length of a straight
line.

• Tooth space: The distance between adjacent teeth
measured on the pitch circle.
• Working Depth(hk): It is the depth of engagement of two
gear teeth, that is, sum of their addendums.
• Whole Depth(h): It is the total depth of the tooth space,
that is, sum of addendum and dedendum.
• Pressure angle (α ) : The angle between the common
normal at the point of tooth contact and the common
tangent to the pitch circles. It is also the angle between
the line of action and the common tangent.
• Line of action: A line normal to a pair of mating tooth
profiles at their point of contact.
• Common tangent: The line tangent to the pitch circle at
the pitch point.
• Path of contact: The path traced by the contact point of a
pair of tooth profiles.

• Arc of Contact: It is the arc of the pitch circle
through which a tooth moves from the beginning
to the end of contact with mating tooth.
• Arc of Approach: It is the arc of the pitch circle
through which a tooth moves from its beginning
of contact until the point of contact arrives at the
pitch point.
• Arc of Recess: It is the arc of the pitch circle
through which a tooth moves from the contact at
the pitch point until the contact ends.
• Contact Ratio(mp): The number of pairs of teeth
that are simultaneously engaged. If there are two
pairs of teeth in contact all the time, the contact
ratio is 2. The contact ratio for smooth transfer of
motion is usually taken as 1.2.

• Backlash: The amount by which the width of tooth
space exceeds the thickness of the engaging tooth
measured along the pitch circle.
• Circular pitch p: The width of a tooth and a space,
measured on the pitch circle.
p = πdl/z
• Diametral pitch P: Ratio of number of teeth to the
pitch circle diameter. A toothed gear must have an
integral number of teeth.
P = z/dl
Hence, P x p = π
• Module(m): Pitch diameter divided by number of
teeth. The module is the inverse of diametral pitch.
m = 1 / P = d l/ z or d l = mz

Standard systems of gear tooth
All standard systems use involute tooth profile due
to the following reasons.
•Satisfies fundamental law of gearing.
•All involute gears of given pressure angle and
module can be machined from one single tool.
•All involute gears of given pressure angle and
module are interchangeable.
•Basic rack of involute profile has straight edges,
hence easy to manufacture.
•A slight change in centre distance can be
accommodated.

Standard systems for involute gear tooth
• 14.5o Full depth involute system
• 20o Full depth involute system
• 20o Stub involute system

Basic Rack
• As the number of teeth on the gear is
increased the involute outline becomes
straighter and straighter. When the number of
teeth is infinity or PCD is infinity, the gear
becomes a rack. This is known as basic rack.

Interference
• As the involute profile begins above the base circle, the
portion below the base circle is not involute.
• The tip of the tooth on the mating gear, which is
involute interferes with this non-involute portion of the
dedendum.
• This phenomenon of overlapping of profiles and
cutting into each other is called interference.
• Results in nonconjugate action and wear, vibrations
and jamming takes place.

Undercutting
• The profile of the cutting tool is such that it
removes the interfering portion of the flank.
This is called under cutting.
• Under cut tooth is considerably weaker. As
undercutting removes a small portion of the
involute adjacent to the base circle, serious
reduction in length of contact takes place.

Methods to eliminate Interference
• Increase the No. of teeth on the pinion.
• Increase pressure angle.
• Use long addendum for the pinion and use
shorten addendum for the mating gear than
standard addendum.

14.5o Full depth involute system
• Basic rack consists of straight edges except for
the fillet arcs.
• Interference occurs when the No. of teeth on
pinion is less than 32.

20o Full depth involute system
• Basic rack consists of straight edges except for the
fillet arcs.
• Widely used and recommended by BIS.
• Interference occurs when the No. of teeth on
pinion is less than 17.
• Increasing pressure angle increases tooth
strength but decreases the duration of contact.
Decreasing pressure angle requires more No. of
teeth on the pinion to avoid interference. Hence
this profile is a good compromise.

Advantages of 20o pressure angle over 14.5o
pressure angle
• Reduces risk of under cutting.
• Reduces interference.
• Increases tooth strength and hence load
carrying capacity increases.

20o stub involute teeth system
• Have shorter addendum and shorted dedendum,
thus removing the interfering portion of the
tooth addendum.
• Minimum No. of teeth on the pinion to avoid
interference is 14.
• Stub teeth are stronger, hence transmits heavy
load. Also compact and production cost is less.
• Contact ratio is reduced, thus resulting in
insufficient overlap due to which vibrations occur.

Backlash
• Backlash is defined as the amount by which the
width of the tooth space exceeds the thickness
of the engaging tooth measured along the
pitch circle.
• Objectives of providing backlash
– Prevents the mating teeth from jamming as the
mating teeth do not make contact on both sides
simultaneously.
– Compensates for machining errors.
– Compensates for thermal expansion of teeth.

Methods to provide backlash
• The teeth of the gear are cut slightly thinner.
• The centre distance between the mating gears
is slightly increased.

Gear tooth failures
• Basic modes of gear tooth failure
– Breakage of tooth due to static and dynamic loads.
– Surface destruction.
• Breakage of the tooth can be avoided by adjusting the
parameters in gear design such as module and face width, so
that the beam strength of the gear tooth is more than the
sum of static and dynamic loads.

Principle types of wear tooth
• Abrasive wear:
– Foreign particles in the lubricant causes abrasive wear.
– This can be avoided by using oil filters, increasing surface
hardness and use of high viscosity oils.
• Corrosive wear:
– Caused by corrosive element such as additives in
lubricating oils and foreign materials due to external
contamination.
– Remedies against this wear are providing complete
enclosure for gears, selecting proper additives and
replacing the lubricating oil at regular intervals.

• Initial pitting:
– Initial pitting is characterized by small pits at high spots due to
errors in tooth profile, surface irregularities and misalignment.
– Such spots progressively wear out.
– The remedies against pitting are precise manufacturing of gears,
correct alignment, uniform load distribution and reducing
dynamic loads.
• Destructive pitting:
– It is surface fatigue failure, which occurs when the load on the
gear tooth exceeds the endurance strength of the material.
– It can be avoided by designing the gears in such a way that the
wear strength of the gear tooth is more than the sum of static
and dynamic loads.
– Surface endurance strength can be improved by increasing the
surface hardness.

• Scoring:
– Excessive frictional heat and over heating due to excessive
surface pressure, high surface speed, and inadequate
supply of lubricant oil causes scoring.
– Scoring is a stick-slip phenomenon in which alternate
welding and shearing takes place at the high spots.
– Scoring can be avoided by selecting appropriate surface
speed, surface pressure, and flow of lubricant so that the
resulting temperature at the contacting surfaces is within
permissible limit.
– If required, heat dissipation system can be provided.

Gear Lubrication
• Is essential for satisfactory performance and durability of
the gears.
• Gears are lubricated by grease, mineral oils or extreme
pressure lubricants.
• Grease is used in applications where the pitch line
velocity is low and the operation is intermittent.
• For medium velocities gears are enclosed in a box and
immersed in lubricating oil.
• In some cases a jet of lubricating oil is sprayed towards
the meshing teeth.
• For medium duty SAE 80, SAE 90 or SAE 140 are used.
• For Heavy duty mineral oils with additives are used.

Selection of gear materials
• The desirable properties of gear material are:
– Ultimate tensile strength or yield strength. When the gear
tooth is subjected to fluctuating loads endurance strength
is the deciding factor.
– Wear rating. The resistance to wear depend upon alloying
elements, grain size, % of carbon, and surface hardness.
– Low coefficient of friction.
– Due to warping(thermal distortion due to heat treatment),
load gets concentrated at one corner of the gear tooth.
Alloy steels are superior to plain carbon steels in this
aspect.

Gear Materials
• Cast iron, steel, bronze and phenolic resins.
• Large size gears are made of cast iron(FG 200, FG260, FG 350). They have
good wear resistance, cheap, and generate less noise. They have poor
strength.
• Case-hardened steel grade offers wear resistance and shock absorbing
core.
• Plain carbon steels (50C8, 45C8, 50C4 & 55C8) are used for medium duty
applications.
• Alloy steels (40Crl, 30Ni4Crl & 40Ni3Cr65Mo55) are used for heavy duty
applications.
• Bronze is mainly used for worm wheels.
• Non-metalic gears are used in the following conditions:
– Light load & low pitch line velocity
– Long life
– Quiet operation
– If gears are effected by water and oil.
• In non metalic gears the pinion is made from non metals(Nylon,
laminated phenolics) which mates with cast iron gear.

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