Unit2 Gear

F T ra n sf o F T ra n sf o
PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/1
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.
A B B Y Y.c A B B Y Y.c

UNIT 2 GEAR

OBJECTIVES

General Objective : To understand the concept of gears and gearing

Specific Objectives : At the end of the unit you will be able to:

Ø Know the types and functions of gears in engineering.
Ø Know, sketch and label the parts of gears.
Ø Understand the method of measuring spur gear.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/2
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

INPUT

2.0 INTRODUCTION

Gears are used to transmit power positively from one shaft to another by
means of successively engaging teeth (in two gears). They are used in place of
belt drives and other forms of friction drive when exact speed ratios and power
transmission must be maintained. Gears may also be used to increase or
decrease the speed of the driven shaft, thus decreasing or increasing the torque
of the driven number.

2.1. TYPES OF GEARS

2.1.1. Spur gear

Spur gears, Fig. 2.1, are generally used to transmit power between
two parallel shafts. The teeth on these gears are straight and parallel to
the shafts to which they are attached. When two gears of different sizes
are in mesh, the larger is called the gear while the smaller is called the
pinion. Spur gears are used where slow to moderate- speed drive are
required.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/3
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Gear

.

Pinion

Figure 2.1. Spur gears Figure 2.2. Internal gears

2.1.2. Internal gears

Internal gears, Fig. 2.2., are used where the shafts are parallel and
the centers must be closer together and that could be achieved with spur
or helical gearing. This arrangement, provides a stronger drive since
there is the greater area of contact than with the conventional gear drive.
It also provides speed reductions with a minimum space requirement.
Internal gears are used on heavy duty tractors where much torque is
required.

2.1.3. Helical gears

Helical gears, Fig.2.3, may be used to connect parallel shafts or
shafts which are at an angle. Because of the progressive rather than
intermittent action of the teeth, helical gears run more smoothly and
quietly than spur gears. Since there is more than one tooth in
engagement at any one time, helical gears are stronger than spur gears of
the same size and pitch. However, special bearing (thrust bearings) are
often required on shafts to overcome the end thrust produced by these
gears as they turn.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/4
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Figure 2.3. Helical gears Figure 2.4. Herringbone gears

2.1.4. Herringbone gears

Herringbone gears, Fig. 2.4., are resembles of two helical
gears placed side by side, with one half having a left-hand helix and the
other half a right-hand helix. These gears have a smooth continuous
action and eliminate the need for thrust bearings.

2.1.5. Bevel gears

When two shafts are located at an angle with their axial lines
intersecting at 90o, power is generally transmitted by means of bevel
gears, Fig. 2.5.

Figure 2.5. Bevel gears

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/5
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

2.1.6. Miter gears

When the shafts are at right angles and the gears are of the same
size, they are called miter gears, Fig. 2.6..

Figure 2.6. Miter gears Figure 2.7. Angular bevel gears

2.1.7. Angular bevel gears

However, it is not necessary that the shafts be only at right angles
in order to transmit power. If the axes of the shafts intersect at any angle
other 90o, the gears are known as angular bevel gears, Fig. 2.7.

2.1.8. Hypoid gears

Bevel gears have straight teeth very similar to spur gears.
Modified bevel gears having helical teeth are known as hypoid gears. The
shafts of these gears, although at right angles, are not in the same plane
and, therefore, do not intersect. Hypoid gears are used in automobile
drives, Fig. 2.8.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/6
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Worm

Worm gear

Figure 2.8. Hypoid gears Figure 2.9. Worm and worm gears

2.1.9. Worm and worm gear

When shafts are at right angles and considerable reduction in speed
is required, a worm and worm gear may be used, Fig. 2.9. The worm,
which meshes with the worm gear, may be single or multiple start thread.
A worm with a double-start thread will revolve the worm gear twice as
fast as a worm with a single-start thread and the same pitch.

2.1.10. Rack and pinion

When it is necessary to convert rotary motion to linear motion, a
rack and pinion may be used, Fig. 2.10. The rack, which is actually a
straight or flat gear, may have straight teeth to mesh with a spur gear, or
angular teeth to mesh with a helical gear.

Pinion

Rack

Figure 2.10. Rack and pinion

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/7
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

2.2. GEAR TERMINOLOGY

top land/peak

face width 2
Fig.
root addendum circle
face
circular pitch
flank
thooth
thickness pitch
addendum liner
pitch circle

clearance
dedendum
pitch
diamete outside base dedendum
diamete diamete circle

Fig. 2.11 Parts of a spur gear

2.2.1. Addendum

Addendum is the radial distance between the pitch circle and the
outside diameter or the height of the tooth above the pitch.

2.2.1. Dedendum

Dedendum is the radial distance from the pitch circle to the bottom
of the tooth space.

2.2.3. Pitch diameter

Pitch diameter is the diameter of the pitch circle which is equal to
the outside diameter minus two addendums.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/8
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

2.2.4. Base diameter

The diameter of the circle from which the involute is generated;
which is equals to pitch diameter times the cosine of the pressure angle.

2.2.5. Pitch circle

Pitch circle is the circle through the pitch point having its centre at
the axis of the gear.

2.2.6. Pitch line

The line formed by the intersection of the pitch surface and the
tooth surface.

2.2.7. Face width - The width of the pitch surface.

2.2.8. Tooth thickness

The thickness of the tooth measured on the pitch circle.

2.2.9. Top land - The surface of the pitch cylinder.

2.2.10. Base diameter - The diameter of the root circle.

2.2.11. Root - The bottoms of the tooth surface.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/9
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

2.3. MEASUREMENT AND TESTING OF GEARS

2.3.1. Gear-tooth vernier caliper

The gear-tooth vernier, Fig.2.12, is an instrument for measuring
the pitch-line thickness of a tooth. It has two scales and must be set for
the width (w) of the tooth, and the depth (h) from the top, at which the
width occurs.

AO = R

Figure 2.12. The gear-tooth vernier caliper

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/10
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

NOTE: The following considerations of gear elements, the symbols
below will be used for the quantities.

T/t = No. of teeth
P = Diametral pitch ( inch gear )
P = Circular pitch
D/d = Diameter of pitch circle
R/r = Radius of pitch circle
Y = pressure angle
M = Modul
Add/A = Addendum
Ded/D = Dedendum
Circular pitch = P x Modul M

The angle subtended by a half tooth at the centre of the gear
( AOB), Fig. 2.12, is given by,

1 360 90
= x = ; T = no. of teeth
4 T T
w 90 90
AB = = AO sin = R sin
2 T T

D = Modul x No. of Teeth, and

MT
R =R
2

MT
i.e. D = 2R =MT and R=
2

w 90 MT 90
Hence = R sin = sin
2 T 2 T

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/11
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

90
and w = MT sin (1)
T

To find h we have that h = CB = OC – OB

MT
But OC = R + Add = +M
2

90 MT 90
And OB = R cos = cos
T 2 T

MT MT 90
Hence h= +M - cos
2 2 T

MT MT 90
= +M - cos ] (2)
2 2 T

MT 90
=M+ [ 1- cos ]
2 T

T 90
For diametral-pitch gears, (1) becomes w = sin
P T

1 T 90
And (2) becomes h= [1+ ( 1 – cos )
P 2 T

Example:
To calculate the gear tooth vernier setting to measure a gear of 33T,
6 modul.
90 90
w = MT sin = 6 x 33 sin
T 33

= 198 sin 2o 43.5’ = 198 x 0.0476

= 9.42 mm.

T T
h= M[1+ ( 1 – cos )]
2 2

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/12
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

33 90
=6[1+ ( 1 – cos )]
2 33

33
=6[1+ (0.0011) ]
2

= 6.11 mm

2.4. PLUG METHOD OF CHECKING FOR PITCH DIAMETER AND DIVIDE
OF TEETH

The tooth vernier gives us a check on the size of the individual tooth, but
does not give a measure of either the pitch diameter or the accuracy of the
division of the teeth.

Figure 2.13

Fig. 2.13 shows a rack tooth symmetrically in mesh with a gear tooth
space, the curved sides of the gear teeth touching the straight rack tooth at the
points A and B on the lines of action. O is the pitch. If now we consider the rack

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/13
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

tooth as an empty space bounded by its outline, a circle with centre at O and
radius OB would fit in the rack tooth and touch it at A and B (since OA and OB
are perpendicular to the side of the rack tooth). Since the rack touches the gear
at these points, the above circle (shown dotted) will rest against the gear teeth at
points A and B and will have its centre on the pitch circle.

In triangle OBD: OB = radius of plug required.
1
OD = circular pitch
4
pm
=
4

< B = 90o, <O=y
OB = OD cos y
pm
= cos y
4

Dia of plug = 2OD
pm
= cos y
2

This is the diameter of a plug which will rest in the tooth space and have
its centre on the pitch circle. Notice that the plug size remains the same for all
gears having the same pitch and pressure angle.
With such plugs placed in diametrically opposite tooth spaces, it is a
simple matter to verify the gear pitch diameter. The accuracy of the spacing
over any number of teeth may be found as shown in chordal calculations.

Example:
Calculate for a 36Tgear of 5 mm module and 20o pressure angle, (a) plug size (b)
distance over two plugs placed in opposite spaces, (c) distance over two plugs
spaced 10 teeth apart.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/14
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Solutions:
pm
(a) Dia of plug = cos y
2
5p
= cos 20o
2

= 7.854 x 0.9397
= 7.38 mm
Pitch dia of gear = mT
= 5 x 36
= 180 mm

(b) Distance across plugs in opposite spaces = 180 + 7.38
= 187.38 mm

(c) Distance across plugs spaced 10 teeth apart (Fig.2.14)

Figure 2.14

360
Angle subtended by 10 teeth = 10 x
36

= 100o.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/15
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

In triangle OAB:
AB = OA sin 50o
= 90 x 0.766
= 68.94
Centre distance of plugs = 2 x AB
= 2 x 68.94
= 137.88 mm.
Distance over plugs = 137.88 + 7.38
= 145.26 mm.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/16
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

ACTIVITY 2

2.1. State three (3) characteristics of the following gears
i. helical gear
ii. spur gear

2.2. Sketch and name six (6) parts of a spur gear

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/17
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

FEEDBACK ON ACTIVITY 2

2.1. (a) 3 characteristics of helical gears;

i) connect parallel shafts or shafts which are at an angle
ii) runs more smoothly and quietly than spur gears.
iii) gears are stronger than spur gears of the same size and pitch.

(b) 3 characteristics of spur gears;

i) transmits power between two parallel shafts.
ii) the teeth on these gears are straight and parallel to the shafts to
which they are attached.
iii) they are used where slow to moderate-speed drive are required.
2.2.

top land/peak

face width

root addendum circle
face
circular pitch
flank
thooth
thickness pitch
addendum liner
pitch circle
clearance

dedendum
pitch
diamete outside base dedendum
diamete diamete circle

Parts of a Spur Gear

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/18
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

SELF-ASSESSMENT 2

1. Calculate the diameter of plug which will lie in the tooth space of a 5 mm
module gear with its centre on the pitch circle. If the gear has 50T, find (a)
distance over two such plugs spaced in opposite spaces, (b) distance over two
plugs spaced 12 spaces apart (y = 20o)

2. Determine the diameter of a plug which will rest in the tooth space of a 4 mm
module 20o rack, and touch the teeth at the pitch line. Calculate (a) the distance
over two such plugs spaced 5 teeth apart. (b) The depth from the top of the plug
to the top of the teeth.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/2/19
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

FEEDBACK OF SELF-ASSESSMENT 3

1. 7.38 mm (a) 257.38 mm (b) 178.52 mm

2. 5.9 mm (a) 59 mm (b) 10.664 mm

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