Gears are toothed wheels used for transmitting motion and power from one shaft to
another when they are not too far apart and when a constant velocity ratio is desired. In
comparison with belt, chain and friction drives, gear drives are more compact, can operate at
high speeds and can be used where precise timing is required.Also gear drives are used when
large power is to be transmitted.
Advantages and Limitations of Gear Drive Over Chain and Belt Drives
1. Since there is no slip, so exact velocity ratio is obtained.
2. It is capable of transmitting larger power than that of the belt and chain drives.
3. It is more efficient (upto 99%) and effective means of power transmission.
4. It requires less space as compared to belt and rope drives.
5. It can transmit motion at very low velocity, which is not possible with the belt
1. The manufacture of gears require special tools and equipments.
2. The manufacturing and maintenance costs are comparatively high.
3. The error in cutting teeth may cause vibrations and noise during operation.
Definition of Gear
A circular body of cylindrical shape or that of the shape of frustum of a cone and of
uniform small width, having teeth of uniform formation, provided on its outer circumferential
surface, is called a gear or toothed gear or toothed wheel.
CLASSIFICATION OF GEARS
Gears may be classified in different manners as given below:
1. Classification based on the relative position of their shaft axes:
2. Classification based on the relative motion of the shafts:
3. Classification based on peripheral speed (v):
4. Classification based on the position of teeth on the wheel:
5. Classification based on the type of gearing:
i. External gearing
ii. Internal gearing
iii. Rack and pinion
But from our subject point of view, gears are broadly classified into four groups, viz., spur,
helical, bevel and worm gears.
Spur gears (sometimes called straight spur gears) have teeth parallel to the axis of rotation are
used to transmit motion from one shaft to another parallel shaft.
Helical gears have teeth inclined to the axis of rotation. The double helical gears connecting two
parallel shafts are known as herringbone gears.
Bevel gears have teeth formed on conical surfaces. They are mostly used for transmitting motion
between intersecting shafts. A straight-tooth bevel gear.
Worm gears consist of a worm and a worm wheel. Worm and worm wheel can be visualized as
a screw and nut pair. They are used to transmit motion between non-parallel non-intersecting
SPUR GEARS TERMINOLOGY
(a) Circular pitch (pc)
It is the distance measured along the circumference of the pitch circle from a point on one
tooth to the corresponding point on the adjacent tooth.
Where D = Diameter of pitch circle, and
Z = Number of teeth on the wheel.
(b) Diametral pitch (pd):
It is the ratio of number of teeth to the pitch circle diameter.
(c) Module pitch (m):
It is the ratio of the pitch circle diameter to the number of teeth.
Velocity ratio: It is the ratio of speed of driving gear to the speed of the driven gear.
Where NA and NB = Speeds of driver and driven respectively, and
zA and zB = Number of teeth on driver and driven respectively.
Advantages of 141/2
It provides smooth and noiseless operation.
It has stronger tooth.
Advantages of 200
It reduces the risk of undercutting.
It has stronger tooth with a higher load carrying capacity.
It has greater length of contact.
In modern industries, a wide variety of gear materials are used. The gear materials are
broadly grouped into two groups viz., metallic and non-metallic materials.
1. Metallic materials:
(a) Steel: So far, the most widely used material in gear manufacture is steel. Almost all
types of steels have been used for this purpose.
To combine the property of toughness and tooth hardness, steel gears are heat
The plain carbon steels used for medium duty applications are 50 c 8, 45 C 8, 50
C 4 and 55 C 8. For heavy duty applications, alloy steels 40 Cr 1, 30 Ni 4 Cr 1
and 40 Ni 3 Cr 65 Mo 55 are used. For planetary gear trains, alloy steel 35Ni 1 Cr
(b) Cast iron: It is used extensively as a gear material because of its low cost, good
machinability, and moderate mechanical properties.
Generally, large size gears are made of grey cast iron of Grades FG 200, FG 260 or FG
Disadvantage: It has low tensile strength.
(c) Bronze: It is mainly used in worm gear drives because of their ability to withstand heavy
Bronze gears are also used where corrosion and wear are a problem.
Disadvantage: They are costlier.
The bronze alloys are either aluminium bronze, manganese bronze, silicon bronze, or
2. Non-metallic materials: The non-metallic materials like wood, rawhide, compressed paper
and synthetic resins like nylon are used for gears.
Advantages: (i) Noiseless operation; (ii) Cheaper in cost; and (iii) Damping of shock
Disadvantages: (i) Low load carrying capacity; and (ii) Low heat conductivity.
Selection of Gear Material
The selection of the gear material depends upon:
Type of service
Method of manufacture
Wear and shock resistance
Space and weight limitations
Safety and other considerations
Degree of accuracy required
Cost of the material
High loads, impact loads, and longer life requirements.
Gears can be manufactured by various processes that can be classified under the
following three topics.
1. Gear milling:
2. Gear generating:
3. Gear molding:
GEAR TOOTH FAILURE
The two modes of gear tooth failure are:
1. Tooth breakage (due to static and dynamic loads), and
2. Tooth wear (or surface deterioration)
(b) Pitting, and
(c) Scoring or seizure
1. Tooth breakage: The load on any gear tooth is cyclic and therefore fatigue fracture of tooth
may occur at the root. Tooth breakage may also be caused by an unexpected heavy load imposed
on the teeth.
2. Tooth wear (or surface deterioration):
(a) Abrasion: When some foreign materials such as dirt, rust or metal particles deposited in
between the mating teeth, there will be wear of tooth surfaces. This wear is known as abrasion
(b) Pitting and spalling: Pitting is the process during which small pits are formed on the active
surfaces of gear tooth. It is a surface fatigue failure which occurs when the load on the gear tooth
exceeds the surface endurance strength of the material.
(c) Scoring or seizure: Scoring can occur under heavy loads and inadequate lubrication. At this
condition, the lubrication oil film breaks down and metal-to-metal contact occurs. Hence high
temperatures result and the mating spots of the two surfaces weld together. This phenomenon is
known as scoring or seizure.
Tooth Stresses (Beam Strength of Gear Tooth – Lewis Equation)
The first analysis of gear tooth stresses was done by Wilfred Lewis in 1892. The formula
given by Lewis (also known as Lewis equation) still serves as the basis for gear-tooth bending
stress analysis. In the Lewis analysis, the gear tooth is considered as a cantilever beam.
The Lewis equation is based on the following assumptions:
The effect of radial component Fr, which induces compressive stresses, is
The tangential component Ft is uniformly distributed across the full face width.
The tangential force Ft is applied to the tip of a single tooth. In other words, it is
assumed that at any time only one pair of teeth is in contact and takes the total
Stress concentration in the tooth fillet is negligible.
Forces which are due to tooth sliding friction are negligible.
DYNAMIC TOOTH LOAD (Buckingham’s Equation for Dynamic Load)
In addition to the static load due to power transmission, there are dynamic loads between
the meshing teeth. The dynamic loads are due to the following reasons:
Inaccuracies of tooth spacing,
Irregularities in tooth profiles,
Elasticity of parts,
Misalignment between bearings,
Deflection of teeth under load, and
Dynamic unbalance of rotating masses.
Let Fd = Total dynamic load on the gear tooth,
Ft = Transmitted load i.e., steady load due to transmitted torque, and
F1 = Incremental load due to dynamic action.
Helical gears are simple modification of ordinary spur gears. A helical gear has teeth in
the form of helix around the gear.
The use of helical gears is most common in automobiles, turbines and high speed applications. It
can be seen that the teeth of the two wheels are of opposite hand. The helixes may be right
handed on one wheel and left handed on the other.
Advantages of Helical Gears
There are three main reasons why helical gears are preferred than spur gears. They are:
1. Noise:Helical gears produce less noise than spur gears of equivalent quality because the total
contact ratio is increased.
2. Load carrying capacity: Helical gears have a greater load carrying capacity than equivalent
size spur gears because the total length of the line of contact is increased.
3. Manufacturing: A limited number of standard cutters are used to cut a wide variety of helical
gears simply by varying the helix angle.
Disadvantage of Helical Gears
Since the teeth are inclined to the axis of rotation, helical gears are subjected to
axial thrust loads. This axial thrust load can be eliminated by using Herringbone (i.e., double
TYPES OF HELICAL GEARS
1. Parallel helical gears:
They operate on two parallel shafts.
The magnitude of the helix angle is the same for the pinion and the gear.
They have opposite hand of the helix. i.e., a right hand pinion meshes with a left hand
gear and vice versa.
2. Crossed-helical (or spiral) gears:
The operate on two non-parallel shafts.
They have the same or opposite hand of the helix.
1. Helix angle (or Spiral angle) (β):
It is the angle between the tooth axis and the plane containing the wheel axis. The helix
angle varies from 150
It is the distance advanced by each tooth per revolution measured along the axis parallel
to the axis.
3. Transverse circular pitch (pt):
The distance between corresponding points on adjacent teeth measured in a plane
perpendicular to the shaft axis is known as transverse circular pitch.
4. Axial pitch (pa):
The distance between corresponding points on adjacent teeth measured in plane parallel
to the shaft axis is known as axial pitch.
HERRINGBONE (DOUBLE HELICAL) GEARS
Herringbone or double helical gear consists of teeth having a right and left handed helix
cut on the same blank. One of the disadvantages of the single helical gear is the existence of
axial thrust load. They are eliminated by the Herringbone configuration because the thrust force
of the right hand is balanced by that of the left hand helix. Helix angles are usually greater for
Herringbone gears than for single helical gears because of the absence of the thrust reactions.
Crossed-helical or spiral or screw or skew gears
A pair of crossed-helical gears, also known as spiral gears. Spiral gears are used to
connect and transmit motion between two non-parallel and non-intersecting shafts. As the
contact between the mating teeth is always a point, these gears are suitable only for transmitting
a small amount of power.
In order for two helical gears to operate as crossed-helical gears, they must have the same
normal diametral pitch and normal pressure ϕn. But the gears need not to have the same helix
angle or be opposite of hand. In most crossed gear applications, the gears have the same hand.
Advantages of Spiral Gears
They provide noiseless operation due to smooth engagement.
They can be used at any angles other than 900
They permit a wide range of speed ratios without change of centre distance or gear size.
Limitations of Spiral Gears
They transmit relatively small amounts of power because of point contact between teeth.
They have lower efficiency than that of toothed gears because of sliding action.
Bevel gears are used to transmit power between two intersecting shafts. Bevel gears are
commonly used in automotive differentials. The gears are formed by cutting teeth along the
elements of frustum of a cone. That is, the pitch surface in the bevel gears are truncated cone,
one of which rolls over the other. When teeth formed on the cones are straight, the gears are
known as straight beveland when inclined, they are known as spiral or helical bevel.
Bevel Gear terms
Bevel gears are mounted on intersecting shafts at any desired angle, although 90o
angle is most common. Bevel gears are not interchangeable. Because they are designed and
manufactured in pairs.
The bevel gear teeth can be cast, milled, or generated. But the generated teeth is more
accurate than cast and milled teeth.
TYPES OF BEVEL GEARS
Classification Based on the Teeth Shape
1. Straight Bevel Gears
2. Spiral Bevel Gears
3. Zero Bevel Gears
4. Hypoid Gears
The worm gears are used to transmit power between two non-intersecting, non-parallel
shafts. The angle between the non-intersecting shafts is usually, but not necessarily, a right angle.
As discussed in the previous chapters, crossed helical and hypoid gears are also used to connect
non-intersecting non-parallel shafts. But crossed-helical and hypoid gears are suitable only for
low speed ratios (upto 8) and low power ratings. Whereas worm gears can be used for high speed
ratios as high as 300:1.
The worm gear drive consists of a worm and a worm wheel. If a tooth of a helical gear
makes complete revolutions on the pitch cylinder, the resulting gear is known as a worm.The
matting gear is called worm gear or worm wheel. The worm in worm and worm gear drive is
same as screw in screw and nut pair.
Apllications of Worm Gear Drives
Worm gear drives are widely used as a speed reducer in materials handling equipment,
machine tools and automobiles.
ADVANTAGES AND DISADVNTAGES OF WORM GEAR DRIVE
Advantages of Worm Gear Drives
The worm gear drives can be used for speed ratios as high as 300:1.
The operation is smooth and silent.
The worm gear drives are compact compared with equivalent spur or helical gears for the
same speed reduction.
The worm gear drives are irreversible. It means that the motion cannot be transmitted
from worm wheel to the worm. This property of irreversible is advantageous in load
hoisting applications like cranes and lifts.
Disadvantages of Worm Gear Drives
The efficiency is low compared with other types of gear drives.
They are costly.
Since sliding occurs, the amount of heat generation is quite high.
The power transmitting capacity of worm gear drive is low (upto 100 kW).
TYPES OF WORM GEAR DRIVES
Two types of worms in use are:
1. Single-enveloping worm drive:
2. Double-enveloping worm drive:
SPECIFICATION OF A PAIR OF WORM GEARS
A pair of worm gears can be specified and designated by four parameters as
(z1 / z2 / q / mx)
Where z1 = Number of starts on the worm,
Z2 = Number of teeth on the worm wheel,
Q = Diametral quotient or diameter factor = d1/mx,
D1 = Pitch circle diameter of the worm, and
Mx = Axial module.
For example, a R5/25/7/5 worm drive means, a right hand worm of starts 5, meshes with
a worm wheel of 25 teeth and of diameter quotient 7, and with module 5 mm.
1.Axial pitch or linear pitch (px): It is the distance between two consecutive teeth, measured
along the axis of the worm. In other words, it is the distance between a point on a worm thread
and a corresponding point on the adjacent thread measured parallel to the axis.
2. Lead (L): It is the distance travelled by a thread when one complete revolution is given to the
Lead, L = px z1 = π mx z1
= Axial pitch Number of threads in the worm
3. Lead angle (γ): It is the angle between the tangent to the pitch helix and the plane of rotation.
4.Helix angle (β): It is the angle between the tangent to the thread helix on the pitch cylinder and
the axis of the worm. The worm helix angle is the complement of worm lead angle, i.e.,
β = 900
FAILURE OF WORM GEARING
The different worm gear tooth failures are:
Since significant sliding occurs between the teeth of the worm wheel and
thread of the worm, the possibility of seizure is very high in worm gear
The seizure has greater probability to occur in the zone where oil has
2. Pitting and Rupture:
The worm wheel wears off more. Because the worm wheel is softer than
Only the worm wheel is affected by pitting phenomenon.