Unit3 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
J3103/3/1
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 3 GEAR

OBJECTIVES

General Objective : To understand the technology of gears manufacturing

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

Ø Know the methods of gear manufacturing
Ø Know the methods of direct and simple indexing
Ø Apply direct and simple indexing when cutting
gears on a milling machine.
Ø Apply various formula to calculate gear-tooth
dimensions.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/2
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

INPUT

3.0. GEAR MANUFACTURING

Gears can be manufactured by casting, forging, extrusion, drawing,
thread rolling, powder metallurgy, and blanking sheet metal (for making thin
gears such as those used in watches and small clocks). Nonmetallic gears can
be made by injection molding and casting.
Gears may be as small as those used in watches or a large as 9 m in
diameter. The dimensional accuracy and surface finish required for gear
teeth depend on its intended use. Poor gear-tooth quality contributes to
inefficient energy transmission and noise and adversely affects the gear’s
frictional and wear characteristics. Submarines gears, for examples, have to
be of extremely high quality so as to reduce noise levels, helping the
submarine avoid detection.
There two basic gear manufacturing methods which involve the
machining of a wrought or cast gear blank: form cutting and generating.

3.1. FORM CUTTING

In form cutting, the cutting tool is similar to a form-milling cutter
made in the shape of the space between the gear teeth (Fig. 3.1). The 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
J3103/3/3
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

tooth shape is produced by cutting the gear blank around its periphery. The
cutter travels axially along the length of the gear tooth at the appropriate
depth to produce the gear tooth profile. After each tooth is cut, the cutter is
withdrawn, the gear blank is rotated (indexed), and the cutter proceeds to cut
another tooth. The process continues until all teeth are cut.
Each cutter is designed to cut a range of number of teeth. The
precision of the form cut tooth profile depends on the accuracy of the cutter
and on the machine and its stiffness. Although inefficient, form cutting can
be done on milling machines, with the cutter mounted on an arbor and the
gear blank mounted in a dividing head.

Form
cutter

Gear
blank

Figure 3.1. Producing gear teeth on a blank by form cutting

Because the cutter has a fixed geometry, form cutting can only be used
to produce gear teeth that have constant width, that is, on spur or helical
gears but not on bevel gears. Internal gears and gear teeth on straight
surfaces, such as in rack and pinion, are form cut with a shaped cutter, using
a machine similar to a shaper.
Broaching can also be used to produce gear teeth and is particularly
applicable to internal teeth. The process is rapid and produces fine surface
finish with high dimensional accuracy. However, because broaches are

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/4
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

expensive and a separate broach is required for each gear size, this method is
suitable almost exclusively for high-quantity production.
Gear teeth may be cut on special machines with a single-point cutting
tool that is guided by a template in the shape of the gear tooth profile. As the
template can be made much larger than the gear tooth, dimensional accuracy
is improved.
Form cutting is relatively a simple process and can be used for cutting
gear teeth with various profiles, however, it is a slow operation, and some
types of machines require skilled labor. Consequently, it is suitable only for
low-quantity production. Machines with semiautomatic features can be used
economically for form cutting on a limited production basis.

3.2. GEAR GENERATING

The cutting tool used in gear generating may be one of the following:
3.2.1. A pinion-shaped cutter
3.2.2. A rack-shaped straight cutter
3.2.3. A hob

3.2.1. The pinion-shaped cutter can be considered as one of
gears in a conjugate pair and the other as the gear blank (Fig 3.2);
it is used on machines called gear shapers (Fig 3.3). The cutter has
an axis parallel to that of the gear blank and rotates slowly with
the blank at the same pitch-circle velocity in an axial reciprocating
motion. A train of gears provides the required relative motion
between the cutter shaft and the gear-blank shaft.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/5
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Gear cutter Base circle Pitch circle

Gear blank

Base circle
Figure 3.2. Gear generating in a gear shaper using a pinion-shaped cutter

Cutter spindle Gear
teeth
Spacer

Pinion-shape
cutter

Gear blank

Figure 3.3.. Gear generating with a pinion-shaped gear cutter

Cutting may take place at either the down stroke or the
upstroke of the machine. Because the clearance required for cutter
travel is small, such as flanges (Fig 3.3). The process can be used
for low-quantity as well as high-quantity production.

3.2.2. On a rack shaper, the generating tool is a segment of a
rack (Fig.3.4) which reciprocates parallel to the axis of the gear
blank. Because it is not practical to have more than 6 to 12 teeth
on a rack cutter, the cutter must be disengaged at suitable intervals
and returned to the starting point; the gear blank remain fixed.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/6
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Figure 3.4. Gear generating with rack-shaped cutter

3.2.3. A gear-cutting hob (Fig. 3.5) is basically a worm, or screw,
made into a gear-generating tool by machining a series of longitudinal
slots or gashes into it to form the cutting teeth. When hobbing a spur
gear, the angle between the hob and gear blank axes is 90o minus the
lead angle at the hob threads. All motions in hobbing are rotary, the
hob and gear blank rotate continuously, much as two gears meshing
until all teeth are cut.

Top view

Gear
blank

Hob

Gear
blank

Figure 3.5. View of gear cutting with a hob

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/7
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Hobs are available with one, two, or three threads. If the hob
has a single thread and the gear is to have 40 teeth, for example, the
hob and gear spindle must be geared together so that the hob makes 40
revolutions while the gear blank makes one revolution. Similarly, if a
double-threaded hob is used, the hob would make 20 revolutions to the
gear blank’s one revolution.
In addition, the hob must be fed parallel to the gear axis for a
distance greater than the face width of the gear tooth (Fig. 3.5) in
order to produce straight teeth on spur gears. The same hobs and
machines can be used to cut helical gears by tilting the axis of the hob
spindle.
Because it produces a variety of gears rapidly and with good
dimensional accuracy, gear hobbing is used extensively in industry.
Although the process is suitable for low-quantity production, it is most
economical for medium to high-quantity production.
Gear–generating machines can also produce spiral-bevel and
hypoid gears. Like most other machine tools, modern gear-generating
machines are computer controlled. Multi axes computer-controlled
machines are capable of generating many types and sizes of gears
using indexable milling cutters.

3.3. CUTTING BEVEL GEARS

Straight bevel gears are generally roughed out in one cut with a form
cutter on machines that index automatically. The gear is then finished to the
proper shape on a gear generator. The generating method is analogous to the
rack-generating method already described. The cutters reciprocate across the
face of the bevel gear as does the tool on a shaper (Fig 3.6).

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/8
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Gear
blank

Cutter

Figure 3.6. Cutting a straight bevel gear blank with two cutter

The machines for spiral bevel gears operate on essentially the
same principle. The spiral cutter is basically a face-milling cutter that
has a number of straight-sided cutting blades protruding from its
periphery ( Fig.3.7 ).

Cutter

Gear blank

Figure 3.7. Cutting a spiral bevel gear with a single cutter

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/9
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

3.4 GEAR-FINISHING PROCESSES

As produced by any of the process described, the surface finish and
dimensional accuracy of gear teeth may not be sufficiently accurate for
certain applications. Moreover, the gears may be noisy or their mechanical
properties, such as fatigue life, may not be sufficiently high.
Several finishing processes are available to improve the surface quality
of gears. The choice of process is dictated by the method of gear manufacture
and whether the gears have been hardened by heat treatment. Heat treating
can cause distortion of parts. Consequently, for precise gear-tooth profile,
heat-treated gears should be subjected to appropriate finishing operations.

3.4.1. Shaving

The gear shaving process involves a cutter, made in the exact
shape of the finished tooth profile, which removes small amounts of
metal from the gear teeth. The cutter teeth are slotted or gashed at
several points along its width, making the process similar to fine
broaching. The motion of the cutter is reciprocating. Shaving and
burnishing can only be performed on gears with a hardness of 40 HRC
or lower.
Although the tools are expensive and special machines are
necessary, shaving is rapid and is the most commonly used process for
gear finishing. It produces gear teeth with improved surface finish and
improved accuracy of tooth profile. Shaved gears may subsequently be
heat treated and then ground for improved hardness, wear resistance,
and accurate tooth profile.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/10
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

3.4.2. Burnishing

The surface finish of gear teeth can also be improved by
burnishing. Introduced in the 1960s, burnishing is basically a surface
plastic-deformation process using a special hardened gear-shaped
burnishing die that subjects the tooth surfaces to a surface rolling
action (gear rolling). Cold working of tooth surfaces improves the
surface finish and induces surface compressive residual stresses on the
gear teeth, thus their fatigue life. However, burnishing does not
significantly improve gear-tooth accuracy.

3.4.3. Grinding, honing and lapping

For the highest dimensional accuracy, tooth spacing and form,
and surface finish, gear teeth may subsequently be ground, honed, and
lapped. Specially-dressed grinding wheels are used for either forming
or generating gear-tooth surfaces. There are several types of grinders
of gears, with the single index form grinder being the most commonly
available. In form grinding, the shape of the grinding wheel is
identical to that of the tooth spacing (Fig. 3.8)
The honing tool is plastic gear impregnated with fine abrasive
particles. The process is faster than grinding and is used to improve
surface finish. To further improve the surface finish, ground gear
teeth are lapped using abrasive compounds with either a gear-shaped
lapping tool (made of cast iron or bronze) or a pair of mating gears that
are run together. Although production rates are lower and costs are
higher, these finishing operations are particularly suitable for
producing hardened gears of very high quality, long life, and quiet
operation.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/11
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Grinding wheel

Gear

Position: 15o or 0o Position: 0o

Figure 3.8. Grinding by generating with two wheels

3.5. METRIC GEARS AND GEAR CUTTING

Countries which have been using a metric system of measurement
usually use the module system of gearing. The module (M) of a gear equals
the pitch diameter (PD) divided by the number of teeth (N), or M = only,
N
whereas the DP of a gear is the ratio of N to the PD, or DP = . The DP of
PD
a gear is the ratio of the number of teeth per inch diameter, whereas M is an
actual dimension. Most of the term used in DP gears remains the same for
module gears; however, the method of calculating the dimensions has
changed in some instances. Table 3.2. gives necessary rules and formulas for
metric spur 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
J3103/3/12
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

3.6. METRIC MODUL GEAR CUTTERS

The most common metric gear cutters are available in moduls ranging
from 0.5 to 10 mm. However metric modul gear cutters are available in sizes
up to 75 mm. Any metric modul size is available a set of eight cutters,
number from #1 to #8. The range of each cutter is the reverse of that of a DP
cutter. For instance, a #1 metric modul cutter will cut from 12 to 13 teeth; a
#8 DP cutter will cut from 135 teeth to a rack. Table 3.1. shows the cutters
available and the range of each cutter in the set.

Table 3.1 Metric module gear cutter

Milling Cutter Numbers
Module size (mm)
Cutter No. For Cutting
0.50 3.50
0.75 3.75 1 12 – 13 teeth
1.00 4.00 2 14 – 16 teeth
1.25 4.50 3 17 – 20 teeth
1.50 5.00 4 21 – 25 teeth
1.75 5.50 5 26 – 34 teeth
2.00 6.00 6 35 – 54 teeth
2.25 6.50 7 55 – 134 teeth
2.50 7.00 8 135 teeth to rack
2.75 8.00
3.00 9.00
3.25 10.00

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/13
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Table 3.2. Formula for calculating metric gear

To Obtain Knowing Rule Formula
Addendum (A) Normal Module Addendum equals module A=M
Module Multiply module by p CP = M x 3.1416
Pitch diameter 3.1416
Multiply pitch diameter by p
and number of CP = M x
and divide by number of teeth N
Circular pitch (CP) teeth
Outside diameter Multiply outside diameter by OD x 3.1416
and number of p and divide by number of CP =
teeth teeth minus 2 N-2
Divide 90 by number of teeth.
Module and Find the sine of this angle and 90
CT = PD x sin
outside diameter multiply by the pitch N
diameter.
Chordal thickness
(CT) Multiply module by p and M x 3.1416
Module CT =
divide by 2 2
CP
Circular pitch Divide circle pitch by 2 CT =
2
Clearance (CL) Module Multiply module 0.166 mm CL = M x 0.166
Dedendum (D) Module Multiply module 1.166 mm D = M x 1.166
Pitch diameter PD
Divide pitch diameter by the
and number of M=
module N
teeth
CP
Module (M) Circular pitch Divide circular pitch by p M=
3.1416
Outside diameter OD
Divide outside diameter by
and number of M=
number of teeth N+2
teeth
Pitch diameter Divide pitch diameter by the PD
N=
and module module M
Number of teeth (N) Multiply pitch diameter by p
Pitch diameter PD x 3.1416
and divide product by N=
and circular pitch CP
circular pitch
Number of teeth Add 2 to the number of teeth
OD = (N + 2) x M
Outside diameter and module and multiply sum of module
(OD) Pitch diameter Add 2 modules to pitch
OD = PD + 2M
and module diameter
Module and Multiply module by number of
PD = M x N
number of teeth teeth
Outside diameter Subtract 2 modules from
PD = OD – 2M
and module outside diameter
Pitch diameter (PD)
Multiply number of teeth by
Number of teeth N x OD
outside diameter and divide
and outside PD =
product by number of teeth N+2
diameter
plus 2
Whole depth (WD) Module Multiply module by 2.166 mm WD = M x 2.166
Centre-to-centre Divide the sum of the pitch PD1 + PD 2
Pitch diameters CD =
distance(CD) diameters by 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
J3103/3/14
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Example 1.
1. A spur gear has PD of 60mm and 20 teeth. Calculate:

(a) Modul
(b) Circular Pitch
(c) Addendum
(d) Outside diameter
(e) Dedendum
(f) Whole depth
(g). Cutter number
Solutions:
(a) Modul = PD/N
= 60/20
= 3 mm

(b) CP =M×p
= 3 × 3.1416
= 9.425 mm

(c) Addendum = Modul
= 3 mm

(d). Outside diameter = ( N + 2 ) × M
= 22 × 3
= 66 mm

(e). Dedendum = M × 1.666
= 3 × 1.666
= 4.998 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
J3103/3/15
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

(f) Working depth = Modul × 2.166
= 3 × 2.166
= 6.498 mm

(g). Cutter number ( see Table 3.2 ) = 3

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/16
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

ACTIVITY 3A

3.1. Two identical gears in mesh have a CD of 120 mm. Each gear
has 24 teeth. Calculate;

(a) Pitch diameter
(b) Modul
(c) Outside diameter
(d) Whole depth
(e) Circular pitch
(f) Chordal thickness

3.2. Name 3 methods of gear generating.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/17
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

PD
FEEDBACK ON ACTIVITY 3A
N

2xCD
3.1.(a)PD = ( equal gears )
2
2x120
=
2
240
=
2
= 120 mm

PD
(b) M =
N
120
=
24
= 5

(c) OD = (N + 2 ) x M
= 26 x 5
= 130 mm

(d) WD = M x 2.166
= 5 x 2.166
= 10.83 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
J3103/3/18
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

(e) CP = MxP
= 5 x 3.1416
= 15.708 mm

MxÕ
(f) CT =
2

5x3.1416
=
2
7.85 mm

3.2. 1. Pinion- shaped cutter
1. Rack-shaped straight cutter
2. A hob

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/19
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

3.7. THE INDEXING OR DIVIDING HEAD

The indexing or dividing head is one of the most important
attachments for the milling machine. It is used to divide the circumference of
a work piece into equally spaced divisions when milling gears, splines,
squares and hexagons. It may also be used to rotate the work piece at a
predetermined ratio to the table feed rate to produce cams and helical
grooves on gears, drills, reamers, and other parts.

3.8. INDEX HEAD PARTS

The universal dividing head set consists of the headstock with index
plates, headstock change and quadrant, universal chuck, footstock, and the
centre rest ( Fig 3.9 ). A swiveling block mounted in the base enables the
headstock to be tilted from 5o below horizontal position to 10o beyond the
vertical position. The side of the base and the blocks are graduated to
indicate the angle of the setting. Mounted in the swiveling block is a spindle,
with 40-tooth worm wheel attached, which meshes with a worm ( Fig. 3.10 ).
The worm , at right angles to the spindle, is connected to the index crank, the
pin of which engages in the index plate. A direct indexing plate is attached to
the front of the spindle.
A 60o centre may be inserted into the front of the spindle, and a
universal chuck may be threaded onto the end of the spindle.
The footstock is used in conjunction with the headstock to support
work held between centers or the end of work held in a chuck. The footstock
centre may be adjusted longitudinally to accommodate various lengths of
work and may be raised or lowered off centre. It may also be tilted out of
parallel with the base when cuts are being made on tapered work.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/20
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Long, slender work held between centers is prevented from bending by
the adjustable centre rest.

Figure 3.9. A universal dividing head set

Figure 3.10 Section through a dividing head, showing
the worm wheel and worm shaft

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/21
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

3.9 METHODS OF INDEXING

The main purpose of the indexing or dividing head is to divide the
work piece circumference accurately into any number of divisions. This may
be accomplished by the following indexing methods: direct, simple, angular,
and differential. However, this modul will only cover direct and simple
indexing.

3.9.1. Direct indexing

Direct indexing is the simplest form of indexing. It is performed
by disengaging the worm shaft from the worm wheel by means of an
eccentric device in the dividing head. Some direct dividing heads do
not have a worm and worm wheel but rotate on bearings. The index
plates contain slots, which are numbered , and a spring-loaded tongue
lock is used to engage in the proper slot. Direct indexing is used for
quick indexing of the work piece when cutting flutes, hexagons,
squares, and other shapes.
The work is rotated the required amount and held in place by a
pin which engages in to a hole or slot in the direct indexing plate
mounted on the end of the dividing head spindle. The direct indexing
plate usually contains three sets of hole circles or slots: 24, 30, and 36.
The number of divisions it is possible to index is limited to numbers
which are factors of either 24, 30, or 36. The common divisions that
can be obtain by direct indexing are listed in Table 3.3

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/22
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Table 3.3. Direct Indexing Divisions

Plate
Hole
Number
24 2, 3, 4, -, 6, 8, - ----- 12 …………24
30 2, 3, -, 5, 6, -, -, -, 10, -, -, 15, ……….30
36 3, 4, -, 6, -, 9, -, 12, -, 18,…………… 36

Example:
What direct indexing is necessary to mill eight flutes on a reamer blank?
As the 24 hole circle is the only one divisible by eight (the required of
divisions), it is the only circle which can be used in this case.

24
Indexing = = 3 holes on a 24-hole circle.
8

Note: Never count the hole or slot in which the index pin is engaged.

To mill a square by direct indexing
1. Disengage the worm and worm shaft by turning the worm
disengaging shaft lever if the dividing head is so equipped.
2. Adjust the plunger behind the index plate into the 24-hole circle or
slot (Fig. 3.11. ).

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/23
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Plunger pin
lever

Figure 3.11. Adjusting the plunger pin to fit into the
proper hole circle or slot

3. Mount the work piece in the dividing head chuck or between centers.
4. Adjust the cutter height and cut the first side.
5. Remove the plunger pin using the plunger pin lever ( Fig. 3.11.).
6. Turn the plate, attached to the dividing head spindle, one-half turn
(12 holes or slots) and engage the plunger pin.
7. Take the second cut.
8. Measure the work across the flats and adjust the work height if
required.
9. Cut the remaining sides by indexing every six holes until all
surfaces are cut.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/24
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Figure 3.12 The plunger pin and the direct indexing plate are used for
indexing a limited number of divisions.

3.9.2. Simple Indexing

In simple indexing, the work is positioned by means of the
crank, index plate, and sector arms. The worm attached to the crank
must be engaged with the worm wheel on the dividing head spindle.
Since there are 40 teeth on the worm wheel, one complete turn of the
index crank will cause the spindle and the work to rotate one-fortieth
of a turn. Similarly, 40 turns of the crank will revolve the spindle and
work one turn. Thus there is a ratio of 40:1 between the turns of the
index crank and the dividing head spindle.
To calculate the indexing or the number of turns of the crank for
most divisions, it is necessary only to divide 40 by the number of

division (N) to be cut, or
40
Indexing =
N

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/25
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Example:

The indexing required to cut eight flutes would be:
40
= 5 full turns of the index crank
8
If, however, it was necessary to cut seven flutes, the indexing would be
40 5
=5 turns
7 7

Five complete turns are easily made; however, the five seventh of a turn
involves the use of the index plate and sector arms.

Index plate and sector arms

The index plate is a circular plate provided with a series of equally spaced
holes into which the index crank pin engages. The sector arms fit on the
front of this plate and may be set to any portions of a complete turn.
To get five-sevenths of a turn, choose any hole circle ( Table 3.4.) which is
divisible by the denominator 7, such as 21, then take five-sevenths of 21 = 15
holes on a 21-hole circle. Therefore, the indexing for seven flutes would be
40 5
=5 turns or 5 complete turns plus 15 holes on the 21-hole circle.
7 7

When extreme accuracy is required for indexing, choose the circle with the
most holes.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/26
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Table 3.4. Index plate hole circle

Brown and Sharpe
Plate 1 15-16-17-18-19-20-
Plate 2 21-23-27-29-31-33
Plate 3 37-39-41-43-47-49
Cincinnati Standard Plate
One side 24-25-28-30-34-37-38-39-41-42-43
Other side 46-47-49-51-53-54-57-58-59-62-66

The procedures for cutting seven flutes would be as follows:

1. Mount the proper index plate on the dividing head.
2. Loosen the index crank nut and set the index pin into a hole on the
21-hole circle.
3. Tighten the index crank nut and check to see that the pin enters the
hole easily.
4. Loosen the set screw on the sector arms.
5. Place the narrow edge of the left arms against the index pin.
6. Count 15 holes the 21-hole circle. Do not include the hole in which the
index crank pin is engaged.
7. Move the right sector arms slightly beyond the 15th hole and tighten
the sector arm setscrew.
8. Align the cutter with the work piece.
9. Start the machine and set the cutter to the top of the work by using a
paper feeler ( Fig. 3.15 ).
10. Move the table so that the cutter clears the ends of the work.
11. Tighten the friction lock on the dividing head before making each cut
and loosen the lock when indexing for spaces.
12. Set the depth of cut and take the first cut.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/27
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

13. After the first flute has been cut, return the table to the original
starting position.
14. Withdraw the index pin and turn the crank clockwise five full turns
plus the 15 holes indicated by the right sector arm. Release the index
pin between the 14th and 15th holes, and gently tap it until it drops
into the 15th hole.
15. Turn the sector arm farthest from the pin clockwise until it is against
the index pin.

NOTE: It is important that the arm farthest from the pin be held and
turned. If the arm next to the pin were held and turned, the spacing between
both sector arms could be increased when the other arm hit the pin. This
could result in an indexing error which would not be noticeable until the
work was completed.

16. Lock the dividing head; then continue machining and indexing for the
remaining flutes. Whenever the crank pin is moved past the required
hole, remove the backlash between the worm and worm wheel by
turning the crank counterclockwise approximately one-half turn and
then carefully clockwise until the pin engages the proper hole.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/28
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

3.10. TO CUT A SPUR GEAR
The procedure for machining a spur gear is outlined in the following:

Procedure:
3.1.1. Calculate the necessary gear data, refer to Table 3.1
Two identical gears in mesh have a CD of 120 mm. Each gear has
24 teeth. Calculate;

i. Pitch diameter
ii. Modul
iii. Outside diameter
iv. Whole depth
v. Circular pitch
vi. Chordal thickness

2xCD
3.1.1.i. PD = ( equal gears )
2
2x120
=
2
240
=
2
= 120 mm

PD
ii M =
N
120
=
24
= 5

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/29
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

iii. OD = (N + 2 ) x M
= 26 x 5
= 130 mm

iv WD = M x 2.166
= 5 x 2.166
= 10.83 mm

v. CP = MxP
= 5 x 3.1416
= 15.708 mm

MxÕ
vi. CT =
2
5x3.1416
=
2
=7.85 mm

2. Turn the gear blank to proper outside diameter
3. Press the gear blank firmly onto the mandrel.

NOTE: If the blank was turned on a mandrel, be sure that it is tight because
the heat caused by turning might have expanded the blank slightly.

4. Mount the index head and footstock, and check the alignment of
the index centers ( Fig. 3.13. ).

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/30
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Figure 3.13. Checking the alignment of index centers with a dial indicator

5. Set the dividing head so that the index pin fits into a hole on the
39- hole circle and the sector arms are set for 30 holes.

NOTE: Do not count the hole in which the pin is engaged.

6. Mount the mandrel (and work piece), with the large end toward
the indexing head, between the index centers.

NOTE:
a. The footstock centre should be adjusted up tightly into
the mandrel and lock in position.
b. The dog should be tightened properly on the mandrel
and the tail of the dog should not blind in the slot.
c. The tail of the dog should then be locked in the driving
fork of the dividing head by means of the sets screws.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/31
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

d. This will ensure that there will be no play between the
dividing head and the mandrel.
e. The dog should be far enough from the gear blank to
ensure that the cutter will not hit the dog when the
gear is being cut.

7. Move the table close to the column to keep the setup as rigid as
possible.
8. Mount a cutter on the milling machine arbor over the approximate
centre of the gear. Be sure to have the cutter rotating in the
direction of the indexing head.
9. Centre the gear blank with the cutter by either of the following
methods:
a. Place a square against the outside diameter of the gear
(Fig 2.23). With a pair of inside calipers or a rule,
check the distance between the square and the side of
the cutter. Adjust the table until the distances from
both sides of the gear blank to the sides of the cutter
are the same.

Figure 3.10.. Centering a gear cutter and the work piece

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/32
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

b. A more accurate method of centralizing the cutter is to
use gauge blocks instead of the inside calipers or rule.
10. LOCK THE CROSSLIDE.
11. Start the milling cutter and run the work under the cutter.
12. Raise the table until the cutter just touches the work. This can be
done by using a chalk mark on the gear blank or a piece of paper
between the gear blank and the cutter to indicate when the
cutter just touching the work ( Fig. 3.15 ).

Figure 3.15. Setting a gear cutter to the diameter of the work piece

13. Set the graduated feed collar on the vertical feed to zero (0).
Move the work clear of the cutter by means of the longitudinal
feed handle and raise the table to about two-thirds the depth of
the tooth (4.572 mm); then lock the knee clamp.

NOTE: A special stocking cutter is sometimes used to rough out the teeth.

14. Slightly notch all gear teeth on the end of the work to check for
correct indexing ( Fig. 3.16 ).

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/33
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

Figure 3.16. Notching all gear teeth eliminates errors

15. Rough out the first tooth and set the automatic feed trip dog after
the cutter is clear of the work.
16. Return the table to starting position.

NOTE: Clear the end of the work with a cutter.

17. Cut the remaining teeth and return the table to the starting
position.
18. Loosen the knee clamp, raise the table to the full depth of 0.270
in., and lock the knee clamp.

NOTE: It is advisable to remove the crank from the knee elevating shaft
so that it will not be moved accidentally and change the setting.

19. Finish-cut all teeth.

NOTE: After each tooth has been cut, the cutter should be stopped before the
table is returned to prevent marring the finish on the gear 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
J3103/3/34
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

ACTIVITY 3B

3.3. What direct indexing is necessary to mill 8 flutes on a reamer blank ?

3.4. Explain how the ratio 40:1 is determined on a standard dividing head.
3.5. What procedure should you follow in order to set the sector arms for 12
holes on an 18-hole circle ?
3.6. With the aid of a labelled diagram, list down the procedures to align
the index centers.

3.7. How would you center the gear blank with the cutter ?

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/35
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

FEEDBACK ON ACTIVITY 3B

24
3.3. Indexing =
8
= 3 holes in a 24-holes circle
NOTE: Never count the hole/slot in which the index pin is engaged.

3.4. The index head spindle carries a 40-tooth worm wheel, which meshes
with a worm. The worm ( at right angle to the spindle ) is connected to the
index crank, the pin of is engaged in the index plate. Since there are 40 teeth
on the worm wheel, one complete turn of the index crank will cause the
spindle and the work to rotate 1/40th of a turn. Similarly 40 turns will
revolve the spindle and the work one turn. Thus there is a ratio of 40:1
between the turns of the index crank and the dividing head spindle.

3.5. Index plate and sector arms
The index plate is a circular plate provided with a series of equally spaced
holes into which the index crank pin engages. The sector arms fit on the
front of this plate and may be set to any portions of a complete turn.
To get 12 holes in an 18-hole circle choose plate no. 1 of Brown and Sharpe
index plate. Follow these procedures:
1. Mount the index plate no. 1 on the dividing head.
2. Loosen the index crank nut and set the index pin into a hole on
the 18-hole circle.
3. Tighten the index crank nut and check to see that the pin enters
the hole easily.
4. Loosen the set screw on the sector arms.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/36
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

5. Place the narrow edge of the left arms against the index pin.
6. Count 12 holes the 18-hole circle. Do not include the hole in
which the index crank pin is engaged.
7. Move the right sector arms slightly beyond the 12th hole and
tighten the sector arm setscrew.

3.6.
1. Mount the index head and footstock, and check the alignment of
the index centers.

Checking the alignment of index centers with a dial indicator

2. Set the dividing head so that the index pin fits into a hole on the
39- hole circle and the sector arms are set for 30 holes.

NOTE: Do not count the hole in which the pin is engaged.

3. Mount the mandrel (and work piece), with the large end toward
the indexing head, between the index centers.

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/37
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

NOTE:
a. The footstock centre should be adjusted up tightly into the
mandrel and lock in position.
b. The dog should be tightened properly on the mandrel and the
tail of the dog should not blind in the slot.
c. The tail of the dog should then be locked in the driving fork of
the dividing head by means of the sets screws.
d. This will ensure that there will be no play between the dividing
head and the mandrel.
e. The dog should be far enough from the gear blank to ensure that
the cutter will not hit the dog when the gear is being cut.

3.7. Centre the gear blank with the cutter by either of the following methods:
a. Place a square against the outside diameter of the gear. With a
pair of inside calipers or a rule, check the distance between the
square and the side of the cutter. Adjust the table until the
distances from both sides of the gear blank to the sides of the
cutter are the same.

.. Centering a gear cutter and the work piece

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/38
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

SELF-ASSESSMENT 3

1. Calculate the tooth caliper settings for measuring the following gears.
(a) 37T, 6 mm module; (b) 40T 20 mm circular pitch.

2. The figure below shows two (2) gears in mesh. Gear A has 66 teeth and
modul 2.5. The gear ratio is 3:2. Calculate the following:

(a). Outside diameter of gear and pinion
(b). Number of teeth of pinion
(c). Centre distance of gear and pinion
(d). Whole depth of gear

66T

A

B

PD rm PD rm
Y Y
Y

Y
er

er
ABB

ABB
y

y
bu

bu
2.0

2.0
to

to
re

re
J3103/3/39
he

he
k

k
lic

lic
GEAR
C

C
w om w om
w

w
w. w.

FEEDBACK OF SELF-ASSESSMENT 3

1. (a) 9.4128 mm, 6.111 mm
(b) 9.995 mm, 6.4923 mm.

2. (a) 170 mm, 115 mm.
(b) 44, 165 mm, 110 mm
(c) 137.50 mm
(d) 5.415 mm

Unit3 Gear

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