Gears: definition, classification with various parameters, detail of each gears, basic and important terms used in gears, Gear trains: definition, classification, detail of each gear train, speed ration and train value of each gear train.
Instrumentation, measurement and control of bio process parameters ( Temperat...
Gears and gear trains may 2020
1. Theory of Machines
Gears and Gear Trains
[It will be also useful in MTT (5th SEM)]
Gaurav Mistry
Assistant Professor
Diwaliba Polytechnic, UTU.
2. Gaurav Mistry 2
❑ Gears Theory of Machines
What is gear?
When a number of projections (called teeth) are provided on the periphery of the
friction wheel (a), such a wheel with the teeth cut on it is known as toothed wheel or
GEAR (b).
When and where it is required?
1. In precision machines, in which a definite velocity ratio is of importance (as in
watch mechanism), the only positive drive is by means of gears or toothed wheels.
2. A gear drive is also provided, when the distance between the driver and the follower
is very small.
3. Gaurav Mistry 3
Theory of Machines
❑ Gears
1. Classification of Gear according to the position of axes of the
shafts (and position of teeth on the gear surface):
The axes of the two shafts may be
1. Parallel (Gears which connect parallel shafts):
When the two parallel and co-planar shafts are connected by the gears, the arrangement
is known as spur gearing.
a. Spur Gear (Straight teeth)
b. Helical Gear (Inclined Teeth)
c. Double Helical or Herringbone Gear (Inclined Teeth)
4. Gaurav Mistry 4
Theory of Machines
❑ Gears
a. SPUR GEAR
❖ Teeth is parallel to axis of shaft
❖ Transmit power from one shaft to another parallel
shaft
❖ Used in Electric screwdriver, oscillating sprinkler,
alarm clock, washing machine and clothes dryer
b. HELICAL GEAR
❖ The teeth on helical gears are cut at an angle to the
axis of the gear (helix angle.)
❖ Helical Gear is used in Automobile gear box because
it produces less noise than spur gear.
c. HERRINGBONE GEAR
(double helical gears)
❖ To avoid axial thrust, two helical gears of opposite hand
can be mounted side by side, to cancel resulting thrust forces.
❖ Herringbone gears are mostly used on heavy machinery.
INTERNAL SPUR
GEAR
EXTERNAL SPUR
GEAR
SINGLE
HELICAL
GEAR
DOUBLE
HELICAL
GEAR
DOUBLE
HELICAL
GEAR
SPUR GEAR
5. Gaurav Mistry 5
Theory of Machines
❑ Gears
1. Classification of Gear according to the
position of axes of the shafts:
2. Intersecting (Gears would intersect at some angle):
When The two non-parallel or intersecting, but coplanar shafts
connected by gears, the arrangement is known as bevel
gearing.
Bevel gears with Straight (spur) and Spiral teeth’s
(Curved teeth):
❖ Bevel gears are useful when the direction of a shaft's
rotation needs to be changed.
❖ They are usually mounted on shafts that are 90 degrees
apart, but can be designed to work at other angles as well
❖ The teeth on bevel gears can be straight or spiral
❖ Locomotives, marine applications, automobiles, printing
presses, cooling towers, power plants, steel plants, railway
track inspection machines, etc.
When equal bevel gears (having equal teeth) connect two
shafts whose axes are mutually perpendicular, then the
bevel gears are known as miter. (Gear ratio 1:1)
BEVEL GEAR
STRAIGHT OR SPUR BEVEL GEAR
MITER GEAR
6. Gaurav Mistry 6
Theory of Machines
❑ Gears
1. Classification of Gear according to the
position of axes of the shafts:
3. Non parallel and Non intersecting (Gears would not
intersect and are not parallel):
When The two non-parallel, non intersecting and non coplanar
shafts connected by gears, the arrangement is known as spiral
gearing.
Hypoid Gears: They are similar to Spiral bevel gears with
only difference that their shafts are non intersecting.
Worm and Worm gears (Curved teeth):
❖ A worm drive is a cylindrical gear with a shallow
spiral thread that engages the worm gear in a non intersecting,
perpendicular axes configuration.
❖ The worm can easily turn the gear, but the gear cannot
turn the worm
❖ Worm gears are used widely in material handling and
transportation machinery, machine tools, automobiles, etc.
HYPOID GEAR
7. Gaurav Mistry 7
Theory of Machines
❑ Gears
2. Classification of Gear according to the peripheral velocity of the
gear :
a. Low Velocity: The gears having velocity less than 3 m/s are termed as low
velocity gears.
b. Medium Velocity: The gears having velocity between 3 m/s to 15 m/s are termed
as medium velocity gears.
c. High Velocity: The gears having velocity greater than 15 m/s are termed as high
speed gears.
3. Classification of Gear according to the type of gearing :
a. External Gearing
b. Internal Gearing
c. Rack and Pinion
(Discussed in subsequent slide)
8. Gaurav Mistry 8
Theory of Machines
❑ Gears
3. Classification of Gear according to the
type of gearing :
a. External Gearing: In external gearing, the gears of the
two shafts mesh externally with each other. The larger of
these two wheels is called spur wheel and the smaller
wheel is called pinion. In an external gearing, the motion
of the two wheels is always unlike.
b. Internal Gearing: In internal gearing, the gears of the
two shafts mesh internally with each other. The larger of
these two wheels is called annular wheel and the smaller
wheel is called pinion. In an internal gearing, the motion
of the two wheels is always like.
c. Rack and Pinion: Sometimes, the gear of a shaft
meshes externally and internally with the gears in a
straight line. Such type of gear is called rack and pinion.
The straight line gear is called rack and the circular wheel
is called pinion. A little consideration will show that with
the help of a rack and pinion, we can convert linear
motion into rotary motion and vice-versa.
(A Rack can be considered as a gear with infinite diameter.)
EXTERNAL GEARS
INTERNAL GEARS
RACK AND
PINION
10. Gaurav Mistry 10
Theory of Machines
❑ Gears
Terms used in Gears:
1. Pitch circle: It is an imaginary circle on
which the teeth of the mating gears are
meshed. (Very imp term in design of gear.)
2. Pitch Point: The common point of contact
between two pitch circles of mating gears.
3. Pitch circle diameter (PCD): It is the
diameter of the pitch circle. The size of the
gear is usually specified by the pitch circle
diameter.
4. Circular pitch (Pc ): It is the arc distance measured on the circumference of the pitch circle
from a point of one tooth to the corresponding point on the next tooth. Pc = π* D/T = π*m.
5. Diametral pitch (Pd): It is the ratio of number of teeth to the pitch circle diameter in
millimeters. It is denoted by Pd= T /D = π/ Pc.
6. Module (m): It is the ratio of the pitch circle diameter in mm to the number of teeth (indicates
how big or small a gear is), m = 1/ Pd =D/T= Pc /π.
11. Gaurav Mistry 11
Theory of Machines
❑ Gears
Terms used in Gears:
7. Addendum: It is the radial distance of a
tooth from the pitch circle to the top of the
tooth.
8. Dedendum: It is the radial distance of a
tooth from the pitch circle to the bottom of the
tooth.
9. Addendum circle: It is the circle drawn through the top of the teeth and is concentric with the
pitch circle.
10. Dedendum circle: It is the circle drawn through the bottom of the teeth.
11. Total Depth: It is the radial distance between addendum circle and dedendum circle. It is the
sum of addendum and dedendum.
12. Clearance: It is the radial distance from the top of the tooth of first gear to the bottom of the
tooth of second meshing gear. i.e. The difference between the dedendum of one gear and the
addendum of the mating gear. The circle passing through clearance distance is known as
clearance circle.
13. Working Depth: The difference between total depth and clearance in radial direction.
12. Gaurav Mistry 12
Theory of Machines
❑ Gears
Terms used in Gears:
14. Top Land: It is the surface of the top of the
tooth.
15. Tooth Face: It is the surface of the gear
tooth above the pitch circle.
16. Tooth Flank: It is the surface of the gear
below the pitch circle.
17. Face Width: It is the width of the gear tooth measured parallel to the axis.
18. Tooth thickness: It is the width of the gear tooth measured along the pitch circle
19. Tooth space: It is the width of the space between two adjacent teeth measured along the
pitch circle.
20. Backlash: It is the difference between tooth space and tooth thickness, measured along the
pitch circle. (Theoretically, the backlash must be zero. But in actual practice, some backlash
should be purposefully allowed to prevent jamming of the teeth due to tooth errors or thermal
expansion.)
13. Gaurav Mistry 13
Theory of Machines
❑ Gears
Other Important terms of Gears:
1. Path of Contact: It is the path traced by a point of contact of the two mating teeth
from beginning to the end of engagement.
2. Arc of Contact: It is the path traced by a point on the pitch circle from beginning to
the end engagement.
3. Contact Ratio: It is the ratio of length of arc of contact on pitch circle to the circular
pitch. (Number of pairs of teeth in contact.)
4. Law of Gearing (Condition of Constant angular
velocity ratio of gear):
{In order to have a constant angular velocity ratio for all
positions of the wheel, the point P must be the fixed point
(called pitch point) on the line joining centres of the two
wheels O1O2.}
➢ In other words, The common normal (line MN) at the
Point of contact (Q) between a pair of teeth must meet the line
joining two centers (O1O2) at a fixed point (P). i.e.
➢ The common normal (MN) at point (Q) must always pass
through the pitch point (P). It is known as Law of Gearing. Law of Gearing
14. Gaurav Mistry 14
Theory of Machines
❑ Gears
Other Important terms of Gears:
5. Velocity of Sliding of teeth: The sliding between a pair of teeth in contact at Q occurs
along the common tangent TT to the tooth curves.
The velocity of sliding is the velocity of one tooth relative to its mating tooth along the
common tangent at the point of contact Q.
, (velocity of sliding is proportional to the distance of point
of contact Q from the pitch point P.)
6. Forms of teeth (Teeth profiles): There are basically two forms of teeth:
1. Cycloidal Teeth: Epicycloid and Hypocycloid.
2. Involute Teeth. (In actual practice, involute teeth are more commonly used compared to
cycloidal teeth.)
The phenomenon when the tip of tooth undercuts the root on its mating gear is known as
INTERFERENCE of involute gears.
7. System of Gear Teeth: The following four system of gear teeth are commonly used in
practice. (pressure angle in degrees)
i. 14
1
2
° composite system: used for general purpose gears
ii. 14
1
2
° full depth involute system: used with gear hobs for spur and helical gears.
iii. 20 ° full depth involute system: stronger than 14
1
2
° full depth involute system
iv. 20 ° stub involute system: strong tooth to take heavy loads.
15. Gaurav Mistry 15
Theory of Machines
❑ Gears Trains
Advantages and Disadvantages of Gear Drive/Train compared to
Belt, Rope and Chain Drive:
Advantages:
1. It transmits exact velocity ratio.
2. It may be used to transmit large power.
3. It has high efficiency.
4. It has reliable service.
5. It has compact layout.
Disadvantages:
1. The manufacture of gears require special tools and equipment.
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.
DEFINITION:
When two or more gears are made to mesh with each other to transmit power from one
shaft to another, such a combination is called ‘gear train or train of toothed wheels’.
16. Gaurav Mistry 16
Theory of Machines
❑ Gears Trains
Types of Gear Trains:
i. Simple Gear Train.
ii. Compound Gear Train. Axes of the shafts are fixed relative to each other.
iii. Reverted Gear Train.
iv. Epicyclic Gear Train. Axes of the shafts may move relative to a fixed axis.
Speed Ratio (Velocity Ratio) of Gear Train: The ratio of the speed of the driver to
the speed of the driven or follower and ratio of speeds of any pair of gears in mesh is
the inverse of their number of teeth, therefore
(It is reverse of VR of belt drive)
(It is also known as Gear Ratio =
𝑻 𝟐
𝑻 𝟏
)
Train Value: It may be noted that ratio of the speed of the driven or follower to the
speed of the driver is known as train value of the gear train. Mathematically,
(It is reciprocal of Speed Ratio)
17. Gaurav Mistry 17
Theory of Machines
❑ Gears Trains
i. Simple Gear Train:
• When there is only one gear on each shaft as shown in fig, it is known as simple
gear train.
• Sometimes, the distance between the two gears is large. The motion from one gear
to another, in such a case, may be transmitted by either of the following two
methods :
1. By providing the large sized gear, or
2. By providing one or more intermediate gears.
• It may be noted that when the number of intermediate gears are odd, the motion of
driver and driven gears is in same direction, but if the number of intermediate gears
are even, the motion of driver and driven gears is in opposite direction.
18. Gaurav Mistry 18
Theory of Machines
❑ Gears Trains
i. Simple Gear Train:
• These intermediate gears are called idler gears, as they do not effect the speed ratio
or train value of the system.
• The idler gears are used for the following two purposes :
1. To connect gears where a large distance is required, and
2. To obtain the desired direction of motion of the driven gear (i.e. clockwise or
anticlockwise).
𝑵 𝟏
𝑵 𝟐
𝐱
𝑵 𝟐
𝑵 𝟑
𝐱
𝑵 𝟑
𝑵 𝟒
=
𝑻 𝟐
𝑻 𝟏
x
𝑻 𝟑
𝑻 𝟐
x
𝑻 𝟒
𝑻 𝟑
or
𝑵 𝟏
𝑵 𝟒
=
𝑻 𝟒
𝑻 𝟏
• It is seen that the speed ratio and the train value of simple gear train, is independent
of the size and the number of intermediate gears.
19. Gaurav Mistry 19
Theory of Machines
❑ Gears Trains
ii. Compound Gear Train:
• When there are more than one gear on
an intermediate shaft, as shown in Fig.
it is called a compound train of gear.
• Whenever the distance between the
driver and the driven or follower has
to be bridged over by intermediate
gears and at the same time a great ( or
much less ) speed ratio is required,
then the advantage of intermediate
gears is intensified by providing
compound gears on intermediate
shafts.
• In this case, each intermediate shaft
has two gears rigidly fixed to it so that
they may have the same speed.
• One of these two gears meshes with
the driver and the other with the
driven or follower attached to the next
shaft as shown in Fig.
20. Gaurav Mistry 20
Theory of Machines
❑ Gears Trains
ii. Compound Gear Train:
• The speed ratio of compound gear train is obtained by multiplying the equations:
• Since the two gears mounted on same
intermediate shaft have same speed.
• 𝑁2 = 𝑁3 and 𝑁4 = 𝑁5
• The advantage of Compound is that a much
larger speed reduction from the first shaft to the
last shaft can be obtained with small gears.
21. Gaurav Mistry 21
Theory of Machines
❑ Gears Trains
iii. Reverted Gear Train:
• When the axes of the first gear (i.e.
first driver) and the last gear (i.e. last
driven or follower) are co-axial, then
the gear train is known as reverted
gear train as shown in Fig.
• Since the gears 2 and 3 are mounted
on the same shaft, they rotate in same
direction with same speed. And also
will rotate the gear 4 in same direction
as the gear 1.
• Thus the motion of first and last gear
in reverted gear train is always in
same direction.
• The reverted gear trains are used in
automotive transmissions, lathe back
gears, industrial speed reducers, and in
clocks (where the minute and hour
hand shafts are co-axial).
C
C
22. C =
Gaurav Mistry 22
Theory of Machines
❑ Gears Trains
iii. Reverted Gear Train:
23. Gaurav Mistry 23
Theory of Machines
❑ Gears Trains
iv. Epicyclic Gear Train:
• In an epicyclic gear train, the axes of
the shafts, over which the gears are
mounted, may move relative to a fixed
axis. A simple epicyclic gear train is
shown in Fig.
• A gear A and the arm C have a
common axis at O1 about which they
can rotate. The gear B meshes with
gear A and has its axis on the arm at
O2, about which the gear B can rotate.
• If the arm is fixed, the gear train is
simple and gear A can drive gear B or
vice- versa.
• If gear A is fixed and the arm is rotated about the axis of gear A (i.e. O1), then the
gear B is forced to rotate upon and around gear A. Such a motion is called epicyclic
and the gear trains arranged in such a manner that one or more of their members
move upon and around another member are known as epicyclic gear trains (epi.
means upon and cyclic means around). The epicyclic gear trains may be simple or
compound.
24. Gaurav Mistry 24
Theory of Machines
❑ Gears Trains
Velocity Ratio of Epicyclic Gear Train:
• The following two methods may be used for finding out the velocity ratio of an
epicyclic gear train.
1. Tabular method and 2. Algebraic method.
• Assuming anticlockwise rotation as +ve and clockwise rotation as –ve, when the
arm is fixed, we may say that when gear A makes +1 revolution, then
Tabular method
(clockwise
rotation as
–ve)
Tabular method
25. Gaurav Mistry 25
REFERENCES:
1. Theory of Machines, R. S. Khurmi, S. Chand.
2. www.google.com
3. Presentation (PPT) of Gaurav Kumar, from LinkedIn
Theory of Machines