1. 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.

2. 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
J3103/3/2
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
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-

3. 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
J3103/3/3
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
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withdrawn, the gear blank is rotated (indexed), and the cutter proceeds to cut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

4. 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
J3103/3/4
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
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.

5. 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
J3103/3/5
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
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.

6. 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
J3103/3/6
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
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

7. 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
J3103/3/7
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
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).

8. 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
J3103/3/8
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
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

9. 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
J3103/3/9
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
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.

10. 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
J3103/3/10
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
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.

11. 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
J3103/3/11
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
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.

12. 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
J3103/3/12
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
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

13. 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
J3103/3/13
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
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

14. 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
J3103/3/14
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
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

15. 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
J3103/3/15
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
(f) Working depth = Modul × 2.166
= 3 × 2.166
= 6.498 mm
(g). Cutter number ( see Table 3.2 ) = 3

16. 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
J3103/3/16
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
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.

17. 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
J3103/3/17
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
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

18. 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
J3103/3/18
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
(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