30291546.cs.en.pdf

TECHNICAL UNIVERSITY BRNO
BRNO UNIVERSITY OF TECHNOLOGY
FACULTY OF MECHANICAL ENGINEERING
INSTITUTE OF MECHANICAL TECHNOLOGY
FACULTY OF MECHANICAL ENGINEERING INSTITUTE
OF MANUFACTURING TECHNOLOGY
METHODS OF MANUFACTURING GEARS
Method of the production of part with tooth system
BACHELOR THESIS
BACHELOR THESIS
AUTHOR OF THE WORK DALIBOR KUBLA
AUTHOR
WORK MANAGER Ing. MILAN KALIVODA
SUPERVISOR
Brno 2010
Translated from Czech to English - www.onlinedoctranslator.com

FSI BUT BACHELOR THESIS Sheet 4
ABSTRACT
The aim of the bachelor's thesis is to clarify the methods of manufacturing
gears, machines and tools. The practical part compares the production methods for
the selected gears; the rolling method of milling and the splitting method of milling.
Keywords
gears,
way, machining, workpiece, cutting movement.
milling rolling way, milling I divide
ABSTRACT
The purpose of this bachelor thesis is to clarify the methods of production
of gear, machinery and tools. The practical part compares the methods for the
production of gears; method of hobbing milling and method of separating
milling.
Key words
Gear, hobbing milling, separating milling, machining, workpiece, cutting
movement.
BIBLIOGRAPHICAL CITATION
KUBLA, D.Gear manufacturing methods. Brno: University of Technology in Brno,
Faculty of Mechanical Engineering, 2010. p. 41, appendices 8. Supervisor Ing. Milan
Kalivoda.

Declaration
I declare that I am a bachelor's thesis on the topicGear manufacturing methods
developed independently with the use of professional literature and sources, listed in the
list that forms an appendix to this work.
28/05/2010 ……………………………….
Bachelor's name and surname

Thanks
I thank the supervisor of my bachelor's thesis, Ing. Milan Kalivod, for his professional
guidance during the creation of the work and for valuable comments and advice. And I would
also like to thank my parents, my brother and, last but not least, my grandfather, who
supported me and helped me during my studies.

CONTENT
Abstract
Declaration
Thanks
Content
Introduction
1. MANUFACTURE OF GEAR WHEELS
1.1 Machining of front wheel teeth
1.1.1 Basic concepts and gear relationships
1.1.2 Milling by splitting method
1.1.3 Rolling milling
1.1.4 Reversing with a comb knife
1.1.5 Turning with a disc knife
1.1.6 Stretching
1.2 Machining of bevel wheels with straight and bevel teeth
1.2.1 Imaging gearing
1.2.2 Gear milling
1.2.3 Gear stretching
1.3 Machining of bevel gear teeth with curved teeth
1.3.1 Gleason method
1.3.2 The Oerlikon method
1.3.3 The Klingenber method
1.4 Production of screws and screw wheels
1.5 Gear Finishing
1.5.1 Sheving
1.5.2 Honing
1.5.3 Grinding
1.5.4 Lapping
1.5.5 The achieved quantity Randand accuracy
2. MACHINES FOR MANUFACTURING GEARS
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40
41
3. COMPARISON OF METHODS ON SELECTED GEAR MANUFACTURERS
3.1 Calculation of a real gear
3.2 Calculation of an imaginary wheel with fewer teeth
3.3 Calculation of an imaginary wheel with more teeth
3.4 Graphical evaluation
Conclusion
List of used sources List of used
abbreviations and symbols List of
attachments

INTRODUCTION
Formulation of the problem
The production of gears clearly belongs to one of the most interesting
machining processes in the engineering industry as such.
The gears themselves are the basic element by which the transmission and
transformation of mechanical energy and movement is realized in machines. Gear wheels are
among the most complex machine components, both in terms of theory and construction, as
well as production.
Rapid development in the field of design, calculation and production of spur
gears with involute gearing took place in the context of the development of modern
technologies. It is about the constant expansion and improvement of computer
technology, which offered the use of perfect programs for optimized designs of gear
geometry. Furthermore, the development and expansion of numerically controlled
machine tools (CNC), which led not only to greater productivity and more accurate
production, but above all enabled the production of gears with various non-standard
tooth shapes.
The aim of the bachelor thesis
The aim of the bachelor's thesis is to clarify the methods of gear production, machines
and tools needed for the given type of production. The practical part of the bachelor's thesis is
a comparison of two methods of gear production on selected gear products.
Giant. 1 Demonstration of the working area of the machine during gear machining8

1 MANUFACTURE OF GEARS
Gear machining is one of the most demanding processes in engineering
production. This process requires powerful, precise machines and tools, highly
qualified workers and technicians. When machining gears, it is important to
maintain high precision, durability, efficiency and also noiselessness, as gears are
part of the movement mechanisms of most machines, means of transport and
equipment.
Gear wheels are produced in many variants according to the way the teeth are designed:
- machining front wheel gears,
- machining bevel gear teeth with straight and bevel teeth,
- machining bevel gear teeth with curved teeth.
When it comes to the production of precise gearing, the use of finishing
methods is necessary. These methods are detailed in subsection 1.5.
1.1 Machining of front wheel teeth
Spur gears are machined in different ways depending on the availability of
technology, especially machines, and the required accuracy - see table 1
Tab.1.1 Achieved accuracy of gear teeth for given machining methods

1.1.1 Basic concepts and gear relationships
The following relationships are necessary for the production and construction of gears:
- pitch circle
d = m.of
wherem is the modulus of aof is the number of teeth
Spur gear modules are standardized according to ČSN 01 4608.
- tooth pitch
(1.1)
p = π.m (1.2)
- tooth height
h = 2.25.m (1.3)
- head circle
dand= d + 2.m (1.4)
- heel ring
dF= d – 2.5.m
Tooth widthb is chosen according to the calculation of the gear strength according to ČSN 01 4686.
(1.5)
Giant. 1.1 Basic gear values
The side profile of the tooth is most often formed by an involute curve. This
curve is created by rolling a straight line along a fixed base circle.

Giant. 1.2 Formation of an involute curve
It is also possible to produce tooth profiles other than involute ones. They are, for
example, cycloid gears. A cycloid is created as a curve described by the point of the circle (the
so-called forming point) when it is rolled along a straight line. The external cycloid gearing has
an epicycloid outline. Epicycloid (epi-has the meaning above, on the surface) is a curve
described by a point forming a circle when it is rolled outwards along another, basic circle.
When rolling the forming circle along the base circle from the inside describes the point
forming the hypocycloid circle (hypo -has the meaning under, lower).
Giant. 1.3 Formation of a cycloidal curve Giant. 1.4 Formation of epicycloid and hypocycloid
1.1.2 Milling by splitting method
Milling of the teeth in a dividing manner is carried out with cutters
whose profile corresponds to the shape of the tooth gap. Disc or pin cutters
are used.
Giant. 1.5 The principle of machining with a disc shaped cutter

Giant. 1.6 Disc cutter for
involute gearing
Giant. 1.7 Pin cutter for involute
gearing
During milling, after machining one tooth gap with a dividing device, the workpiece
is rotated by one pitch and another tooth gap is milled. Disc module cutters are produced
for modules m = 0.2 to 16 mm. For roughing the gearing of larger modules (m > 20 mm)
roughing disk cutters with a graduated profile are used. Pin milling cutters for roughing
with module m > 30 mm have a trapezoidal profile and blades in a helix, which enables
the use of larger feeds. When milling oblique teeth with a disk module milling cutter, the
working table of the machine with the workpiece is rotated relative to the axis of the
spindle by the tooth inclination angle βto. Slanted teeth are created by a combination of
the longitudinal movement of the table and the rotational movement of the workpiece.
Milling bevel gear with a pin cutter is the same, but the work table does not rotate.
1.1.3 Rolling milling
This method of manufacturing gearing is more widespread due to its
high work productivity and good gearing accuracy. The tool is a rolling mill
that has the shape of an involute worm and whose profile in the normal plane
is formed by a basic ridge. Spur gears and worm gears can be produced by
rolling milling.
and)Milling straight teeth
Giant. 1.8 Principle of the milling method
straight teeth by rolling
Giant. 1.9 Demonstration of gear milling
roll away3

The main cutting movement is carried out by a milling cutter that rotates around its axis.
The workpiece is moved to the milling cutter so that its rolling ring rolls along the rolling line of the
milling cutter ridge during its rotation. With each revolution of the workpiece, the milling cutter
makes as many revolutions as the milled wheel has teeth. The cutter axis must be inclined relative
to the workpiece by an angle β, which is the same as the pitch angle of the helix on the pitch
cylinder. We determine the inclination of the cutter according to the right or left inclination of the
teeth.
Giant. 1.10 Position of the tool when milling direct gears
Many older milling machines will machine the workpieceinconsistentway. The new
rolling mills are already modified forconsecutivemilling, where the cutter is in the initial
position under the workpiece and has a feed direction from bottom to top. This method of
machining enables an increase in cutting speed and feed rate.
Giant. 1.11 Consecutive milling of gears and radial approach to depth
b)Milling of oblique teeth
The method of milling oblique teeth is almost the same as milling straight teeth,
with the difference in the setting of the hobbing cutter relative to the workpiece. For
teeth that have a right inclination, it is recommended to use a cutter with a right helix,
and for teeth with a left inclination, a cutter with a left helix, where the axis of the cutter
bends to an angle β - λ. This leads to better milling and eliminates the possibility of tool
jamming.

Giant. 1.12 Milling of oblique gearing with a left inclination with a left-hand milling cutter
and with a right bevel right-hand cutter
In the case when the right-hand pitch of the gearing is machined with the left-hand helix and vice
versa, then it is necessary to set the axis of the cutter to the angle β + λ.
Giant. 1.13 Milling of bevel gears with a left inclination with a right-hand cutter
and with a right-handed left-handed cutter
1.1.4 Imaging with a comb knife
This method works on the principle of engagement of the tool with the workpiece.
The tool for turning the teeth of front gears with a comb knife is a toothed comb that has
a trapezoidal profile. The cutting motion is performed by the tool and is reciprocating.
The tool is set to the depth of the tooth and machining is done by cutting into the
workpiece. After machining a few tooth gaps, the feed and rotation stops, then the
workpiece moves back to the starting position. The number of tooth gaps produced is
determined by the length of the tool.
The mentioned method of machining gears is also calledthe way of Maag.

Giant. 1.14 Reversing with a comb knife
1.1.5 Imaging with a disc knife
Turning with a disc knife works on the principle of engagement of two
gears without backlash. The tool and the workpiece roll off each other as if two
spur gears mesh together. It is possible to produce wheels with external as well
as internal gearing. With this method, it is possible to produce several bikes at
once. The bevel gear is turned in the same way, which is then rotated during the
working thread at the angle of inclination of the teeth by means of screw guides.
Turning with a disc knife is also known by the namethe Fellows way.
Giant. 1.15 Turning with a disc knife

1.1.6 Stretching
Stretching is used in large-scale and mass production, as the costs of producing
the tool are high. Machining is carried out with a set of graduated knives folded into
a block of a drawing mandrel - a tool. The gradation of the knives is done depending
on the type of material of the wheel, the thickness of the chips removed and the
cutting speed. Stretching gears is an economical process, as the removed layer of
material is divided into a large number of edges, i.e. that the durability and service
life of the tool are relatively long.
Giant. 1.16 Gear stretching
1.2 Machining of bevel gear teeth with straight and bevel
teeth
Machining of bevel gears is one of the most demanding methods of
engineering production. Bevel gears have straight, bevel and curved teeth. Bevel
gear teeth are machined by turning, milling and stretching.
The flanks of the teeth are made either by copying, rolling, or shape cutters.
The rolling method is one of the most accurate and is carried out using a dividing
method or continuous rolling.
1.2.1 Representation of gearing
and)Rendering according to the template
A pulley moves along the template, the shape of which corresponds to the shape of the side
of the tooth, which controls the mechanism with the turning knives. The knives are fixed on the
pulley slides. It turns with two knives and thanks to this, both flanks of the tooth are machined at
the same time. In this way, a high quality surface is achieved, as it is machined only with the tips of
the knives. The shape of the template depends on the shape of the tooth, and one template is
enough for the same number of teeth of bevel wheels with different modules.

Giant. 1.17 Mapping of bevel gear teeth by copying
b)Reversal with two knives
In the machine, two trapezoidal knives are clamped in the knife holders of the rotating knife
head. The knives make a cutting movement in the direction of the surface lines of the flanks of the
teeth and at the same time rotate with the knife head around its axis. The bevel wheel is clamped
in the headstock, which is set in a position corresponding to the apex angle of the machined wheel.
The edges of the knives are formed by the flanks of the teeth in the shape of an involute when the
knife head and the working wheel are rotated simultaneously. At the same time, the right side of
the tooth is machined with one knife and the left side with the other knife. After that, both the knife
head and the workpiece return to the initial position, and the workpiece is rotated by one pitch with
the dividing device.
Giant. 1.18 Reversal of bevel gear teeth with two knives1

1.2.2 Gear milling
Straight and bevel gears are milled with form cutters using a dividing
method, or with two disk knife heads.
and)Milling with shaped cutters
Milling with shaped cutters is used for the production of bevel wheels that do not
require great precision and also for the production of wheels of large modules and
diameters. The tool is a shaped disc or pin cutter. The tooth gap is machined gradually,
first the center is roughened, then the wheel is turned and one side of the tooth is milled,
and the same is repeated for the other side of the tooth.
Giant. 1.19 Milling of bevel gear teeth with a shaped disk cutter
b)Milling with two disc knife heads
The tool consists of two disc heads with mutual edges that overlap in the
tooth gap. The workpiece performs a radial feed to the depth of the tooth.
The gearing is milled using a rolling method.

Giant. 1.20 Milling bevel gear teeth with two disc knives
heads
1.2.3 Gear stretching
The production of bevel wheels in mass and serial production is most
productive by drawing with a large-diameter (up to 600 mm) disk draw, which has
graduated edges with the shape of a tooth gap on its circumference. The tool
performs a rotational movement and moves along the tooth from a smaller profile to
a larger one. Stretching one tooth gap takes approximately 4 to 6 seconds, so this
process is fast and productive.
Giant. 1.21 Stretching of bevel gears1

1.3 Machining of bevel gears with curved teeth
Machining of curved teeth of bevel gears is carried out by roller milling
in the following ways:
- Gleason – the teeth are circular spiral,
- Oerlikon – teeth curved according to the cycloid,
- Klingenber – the teeth are curved according to the involute.
1.3.1 Gleason method
This production method is characterized as milling bevel wheels by dividing the
front knife head. The principle consists in the engagement of the machined wheel
and the base wheel. The front knife head rotates independently of other movements
of the mechanism. The cutting movement is created by the rotary movement of the
workpiece and the rotation of the drive plate with the knife head. The workpiece is
moved to the depth of the tooth gap and the tooth gap is milled again. After that, the
workpiece is moved away, the knife head is moved to the initial position, and thus
the division into the next tooth takes place, and the process repeats.
Giant. 1.22 The Gleason method1
1.3.2 The Oerlikon method
Gearing is produced by three movements:
1. rotary movement of the knife head
2. turning the workpiece
3. by turning the cradle – here the clamped front knife head is located
The blades with a straight edge are arranged in such a way that parts of separate
spirals are formed.

Giant. 1.23 The Oerlikon method1
1.3.3 The Klingenberg method
Gearing is produced by three movements:
1. rotary motion
2. turning the workpiece
3. rolling of the cutter on the drifting board
This method is used for piece and small batch production.
Giant. 1.24 The Klingenberg method1

1.4 Production of screws and screw wheels
The production of augers is carried out either by turning with the help of a shaping knife,
similar to the production of threads, or by a disc milling machine in a rolling method on universal
milling machines.
Giant. 1.25 Example of screw milling3
Worm gears are usually produced with a hobbing mill that has a worm profile. The axis of the
cutter is perpendicular to the axis of the machined wheel and lies exactly in half the thickness of the
wheel.
Giant. 1.26 Worm gears

Worm gears can transmit large powers, usually 50 to 100 kW. Another
advantage is small dimensions and thus also lower weight. Worm gears have
high transmission ratios i = 5 to 100, they are self-locking, i.e. there is no
spinning. They are characterized by calm and quiet operation.
The disadvantage is relatively large frictional forces during transmission, worm wheels are
made of different materials. The production of gearing is more demanding, more expensive, and
its service life is usually lower than that of rolling gears due to wear.
1.5 Gear Finishing
Precision wheels classified in the 1st to 4th degree of accuracy. Heat-
treated wheels are finished by shaving, grinding and lapping.
1.5.1 Sheving
This method of gear finishing is used for unhardened wheels, or after
cementing before hardening, produced by roll milling or turning. The shaving tool is
a corrected gear wheel with straight or slanted teeth, which have grooves on the
sides, and these grooves form edges and a space for the removal of chips. The
finishing allowance for hemming is very small, 0.1 to 0.15 mm. The axes of the tool
and the workpiece are crossed at an angle of 5 to 15°. The tool moves along the
entire width of the tooth. The finishing wheel makes a reciprocating sliding
movement in the direction of its axis. In chamfering, the direction of rotation of both
the tool and the workpiece changes at the extreme dead ends.
Giant. 1.27 Sheving of spur gears

Giant. 1.28 The shape of the tooth of the shaving wheel
1.5.2 Honing
It is a very similar method of hemming. The difference is that the shaving wheel
is replaced by a wheel made of a mixture of plastic and abrasive. Honing is used to
improve the geometric properties and surface roughness of hardened gears.
1.5.3 Grinding
Grinding removes inaccuracies after machining and deformations after
heat treatment of gears. Grinding of gears is carried out by a dividing method
with shaped discs, a dividing method with rolling of the side of the tooth, and
a rolling method.
and)Grinding in a dividing way with shaped discs
In the splitting method, the sides of the teeth are ground with a one-sided or
double-sided shaped grinding wheel. The shape of the profile of the grinding wheel
corresponds to the shape of the side of the tooth. Either grinding with one or two
discs is used. When grinding with two tools, each tool grinds one side of the tooth.
Split grinding is less accurate and its other disadvantage is the difficulty of matching
the grinding wheels to the exact shape.
Giant. 1.29 Shape grinding of teeth
disc
Giant. 1.30 Grinding with two shapes
discs

b)Grinding in a dividing way with a roll-off of the side of the tooth
Depending on the arrangement of the grinders, this method is
implemented for the case when the ground tooth rolls along one or two grinding
wheels. Grinding in this way has negative effects.
Giant. 1.31 Grinding in a splitting method with rolling of the side of the
tooth a) with one grinding wheel
b) two disc grinding wheels
C)Rolling grinding
Rolling grinding is more accurate than splitting grinding. A ground gear
performs a rolling motion along an imaginary toothed rack. Part of that ridge
can be formed by a trapezoidal grinding wheel or two disc wheels. The most
efficient method is grinding with a disc in the shape of an involute worm,
which works on the same principle as in the rolling method of milling.
Giant. 1.32 Rolling method of grinding with an involute-shaped grinding wheel
snail
1.5.4 Lapping
Lapping removes the last surface irregularities on the sides of the teeth.
Lapping is often used to finish bevel gears with curved teeth that cannot be
ground. The lapped wheel is engaged with a cast-iron wheel of the same
module. Lapping paste or a mixture of oil and abrasive is added to the wheel
engagement. Lapping allowances are around 0.02 to 0.05 mm.

1.5.5 The achieved quantity Randand accuracy
Since great demands are placed on gears, we distinguish 8 degrees of accuracy. In order to
achieve a certain degree of accuracy, it is necessary to choose a certain type of production, but at
the same time it is necessary to observe the average arithmetic deviation of the profile of the side
of the teeth.
Tab. 1.2 Achieved hardness and R valuesandduring production
IT Way
production
Greatness
Rand[µm]
Grinding on the most precise roller grinders
1. and lapping
2. Grinding on the most precise roller grinders
0.1 to 0.2
0.2
Grinding on very precise roller grinders,
3. milling on special rolling mills designed for milling
precision wheels
Grinding on precision roller grinders,
4. milling on special rolling milling machines
Grinding on precise rolling and profile machines
5. grinders, turning, shaving, milling on precision
milling machines
Milling and turning on regular, carefully
6. Adjusted machines, non-hardened wheels
On ordinary machines in the rolling method. For
7. machining teeth can be heat treated
8. By milling or turning with shape machines
0.2 to 0.4
0.2 to 0.4
0.2 to 0.8
0.8 to 1.6
1.6 to 6.3
6.3 to 12.5
2 GEAR MANUFACTURING MACHINES
Machines on which the production of gears is carried out:
a) cutters for front gears, rolling method,
b) cutters for bevel gears, dividing and rolling method,
c) milling machines for face, screw and worm wheels, rolling method,
d) milling machines for bevel wheels with spiral gearing, dividing and rolling
method,
e) machines for spur and bevel wheels with straight teeth, various methods,
f) universal milling machines for face and bevel wheels, working with a shank milling cutter -
dividing,
g) gear grinders,
h) special gearing machines.
Machines for the production of gears are universal or with CNC control. Universal
machines are still often used nowadays, but from the point of view of the possibilities of
designing the shape of the teeth, machines with CNC control, which can work in a multi-
axis system, are preferred. Examples of some types of CNC machines see appendix 6,7
and 8.

and)Turning tools for front gears, rolling method
- vertical, working with a comb knife (Maag), one slide:
- ∅wheels up to 500 mm,
- ∅wheels over 1000 to 2000 mm,
- ∅wheels over 2000 mm.
- vertical, working with a comb knife (Maag), two sliders (e.g. Maag
shapers type DSH 20)
- vertical, working with a wheel knife (Fellows):
- horizontal on straight teeth, working with one knife
b)Bevel gear cutters, dividing and rolling method
- rolling method, straight and inclined teeth:
- ∅wheels over 315 mm to 630 mm,
C)Milling machines for face, screw and worm wheels, rolling method
- without differential (only straight teeth)∅wheels up to 400 mm
- with differential (straight screw and worm teeth):
d)Milling machines for bevel wheels with spiral gearing, dividing and rolling
method
- rolling method special, for roughing the pinion
- rolling method special, for finishing the pinion
- special dividing method, for roughing disc wheels
- dividing method special, for finishing disc wheels
- rolling method of all constructions (Gleason, Klingenberg, Spiromatic,
FM):
E)Machines for spur and bevel gears with straight teeth, different style

F)Universal milling machines for face and bevel wheels, working with a shank cutter - dividing
G)Gear grinders
- working with rolling arc, straight and helical teeth:
- without rolling arc, straight and helical teeth:
- grinders for internal gears
h)Special gearing machines
- milling machines for rounding teeth
- milling machines for chamfering the edges of teeth
- lapping and running-in machines for front wheels
- lapping and running-in machines for bevel wheels
- shaving machines:
- ∅wheels up to 315 mm (e.g. USSR machine type "571"),
- ∅wheels over 315 mm (e.g. USSR machine type "5715").
Specific types of machines:
Milling machines–FO 6, FO 8, FO 10, OFA 16A, OFA 71, 5B 312, 5K 324 A, 53 A 20,
RA 300, CNC Höffler HF900
Pictures–OH 6, OHA 16B, OHA 50, OHA 50A, OHO 20, OHO 50, DSH 20,
MAAG SH 75, FELLOWS 10-5 CNC, K4a, S526
Note : Illustrations of some types of machines in Annexes 2, 3, 4 and 5.

3 COMPARISON OF METHODS AT SELECTED DENTAL
MANUFACTURERS
The practical part of the bachelor's thesis is a comparison of methods for the
production of spur gears. This is a method of rolling milling and milling with a dividing
method.
The comparison will take place in such a way that the machine production times of a
real gear wheel and two imaginary wheels that differ in the number of teeth are determined.
This is how the machine times will be determined for both selected methods of gear
production. There will be the same tools for all three wheels, i.e. a hobbing cutter and a disc
cutter. Milling of the wheel will be done on a rolling milling machine FO 10.
The actual gear comes from COK Farm, where it was part of the scraper
drum of an American New Holland NH 648 round baler and due to heavy
wear had to be taken out of service and replaced with a new gear.
Giant. 3.1 A real gear with straight teeth
Wheel parameters:
- material 14220 (manganese chrome steel for cementing and refining with large
core strength)
- 24 teeth
- module 8
- engagement angle of the side of the teeth 20°

3.1 Calculation of a real gear
Calculation of wheel dimensions:
Giant. 3.2 Basic dimensions of the gear wheel
Tooth pitch
= ∙
= ∙ 8 = 28.133
(3.1)
Basic spacing
= ∙
= 28.133 ∙ 20° = 23.617
(3.2)
Pitch circle diameter
= ∙
= 8 ∙ 24 = 192
(3.3)
The diameter of the base circle
= ∙ ∙
= 8 ∙ 24 ∙ 20° = 180.421
(3.4)
Diameter of head circumference
= + 2 ∙
= 192 + 2 ∙ 8 = 208
(3.5)
Head clearance
= 0.25 ∙
= 0.25 ∙ 8 = 2
(3.6)
Unit clearance
∗=
2
(3.7)
∗= = 0.25
8
Heel circle diameter
= − 2 ∙ ∙ 1 + ∗
= 192 − 2 ∙ 8 ∙ 1 + 0.25
(3.8)
= 172

Tooth thickness
= 0.5 ∙ ∙
= 0.5 ∙ ∙ 8 = 12.566
(3.9)
Tooth gap width
= 0.5 ∙ ∙
= 0.5 ∙ ∙ 8 = 12.566
(3.10)
Tooth head height
ℎ =
ℎ = 8
(3.11)
Tooth heel height
ℎ = 1.25 ∙
ℎ = 1.25 ∙ 8 = 10
(3.12)
Tooth height
ℎ = ℎ + ℎ
ℎ = 8 + 10 = 18
(3.13)
a) Rolling milling Tool:
- milling cutter for involute gearing KHSS-E, PM, ČSN 22 2551, viz.
Giant. 3.3
Giant. 3.3 Rolling mill4
Cutter parameters :
∅Dand= 125 mm
∅d = 40 mm
LF= 132 mm
x = 5 mm
m = 8
α = 20°
number of tooth grooves = 10 f
of= 0.96 mm
inC= 20.6 mm∙min-1

Total machine time :
= ∙ ∙
∙ ∙
(3.14)
L…… total milling length z……
number of workpiece teeth
and……. number of machining chips per clamping fof….
cutter feed nw….. number of revolutions of the cutter uw
...number of milling operations (1)
= + + + (3.15)
b…… tooth width of the workpiece ln
….. ramp up
lMr……course
lof……safety distance for β = 0 to 5°
Giant. 3.4 Graphic representation of the total pathL tools in AutoCad
2009
= 29.5 + (37.6 + 3) + 2.6 + 3.5 = 76.2
Note : rise length lnand the course lMris given by the dimension of the concrete
gearing tools.
Cutter speed :
=1000 ∙
∙
(3.16)
1000 ∙
∙
1000 ∙ 20.6
∙ 125
= = = 52.4 −1
The total time will be :
76.2 ∙ 24 ∙ 2
0.96 ∙ 52.4 ∙ 1
3657.6
50.3
= = = 72.7

b) Milling by splitting method
Since a real gear has 24 teeth, the direct division method is used. A
universal dividing device can be used for direct division. For this purpose, a
dividing disc with 24 holes is mounted on the head of the dividing spindle of the
device instead of the dividing disc with notches, which is used in the manual
dividing device. It can therefore be divided directly by removing the 1 : 40 worm
gears from the engagement and without using three interchangeable dividing
discs with holes at 2, 3, 4, 6, 8, 12 and 24 equal pitches.5
Giant. 3.5 Universal dividing device with three replaceable and one non-replaceable
dividing disc with 24 holes5
Calculation of the dividing device :
=24=24= 1 -The dividing handle is turned once by 360°.
24
Tool:
- disc shaped cutter for involute gearing m8 x 20, ČSN 22 2510, viz. Giant.
3.6
Giant. 3.6 Disc shaped cutter6
Cutter parameters :
∅Dand= 112 mm
∅d = 32 mm
s = 28 mm
z = 12

Fof= 0.05 mm
inC= 20.6 mm∙min-1
Total machine time :
=
∙
∙ ∙ ∙
(3.17)
L…… total milling length z…… number
of workpiece teeth zF……number of
cutter teeth fof…. cutter feed nw…..
number of revolutions of the cutter u
w...number of milling operations (1)
= + + (3.18)
b……tooth width of the workpiece ln
….. ramp up
lMr……course
Giant. 3.7 Graphic representation of the total pathL tools in AutoCad
2009
= 29.5 + (42.5 + 3) + 3.5 = 78.5
The cutter speed is determined according to relation 3.16 :
1000 ∙
∙
=
1000 ∙ 20.6
∙ 112
= = 58.5 −1
The total time will be :
78.5 ∙ 24
0.05 ∙ 58.5 ∙ 12 ∙ 1
1884
35.1
= = = 53.7

3.2 Calculation of an imaginary wheel with fewer teeth
Since it is a gear wheel with the same module, it is obvious that the different
values from the real wheel will only be in the diameter of the pitch circle, the
diameter of the base circle, the diameter of the head circle and the diameter of the
heel circle. Formulas 3.3, 3.4, 3.5 and 3.8 are used to calculate dimensions.
Pitch circle diameter = 8
∙ 18 = 144
= 8 ∙ 18 ∙ 20° = 135.316
= 144 + 2 ∙ 8 = 160
= 144 − 2 ∙ 8 ∙ 1 + 0.25 = 124
a) Rolling milling
The cutting conditions of the tools are the same as in subsection 3.1 and also
the total machined length will remain the same, the only value that differs from the
real gear is the number of teeth.
Determination of machine time according to relation 3.14 :
∙ ∙
∙ ∙
=
76.2 ∙ 18 ∙ 2
0.96 ∙ 52.4 ∙ 1
2743.2
50.3
= = = 54.5
b) Milling by splitting method
The indirect division method is used here. We divide indirectly by
including the transmission gear. Such a gear consists of a worm and a worm
wheel, the ratio of which is usually 1:40.
The worm gear splitter works as follows:
The dividing movement is achieved by the dividing crank, which is connected to the
screw shaft. At the same time, a pin located in the handle of the dividing handle fits into the
holes of the dividing disc, which ensures the correct setting of the spacing. The dividing disc is
held in position by a locking pin. The circular spacing of the holes of the three dividing discs
usually has the following number of holes:5

1.
2.
3.
15, 16, 17, 18, 19, 20
21, 23, 27, 29, 31, 33
37, 39, 41, 43, 47, 49
40 40
18
4
18
= = = 2 +
Giant. 3.8 Dividing disc5
∙
∙ ∙ ∙
=
78.5 ∙ 18
0.05 ∙ 58.5 ∙ 12 ∙ 1
1413
35.1
= = = 40.3
3.3 Calculation of an imaginary wheel with more teeth
The procedure for determining wheel dimensions and machine production times is the same
as in subsection 3.2.
Pitch circle diameter = 8
∙ 26 = 208
= 8 ∙ 18 ∙ 20° = 195.456
= 208 + 2 ∙ 8 = 224
= 208 − 2 ∙ 8 ∙ 1 + 0.25 = 188
a) Rolling milling
∙ ∙
∙ ∙
=
76.2 ∙ 26 ∙ 2
0.96 ∙ 52.4 ∙ 1
3962.4
50.3
= = = 78.8

b) Milling by dividing method
In this case, the indirect division method is again used here.
40 40
26
14
26
= = = 1 +
∙
∙ ∙ ∙
=
78.5 ∙ 26
0.05 ∙ 58.5 ∙ 12 ∙ 1
2041
35.1
= = = 58.1
3.4 Graphical evaluation
It follows from the formulas that the course of the graphic expression is linear, since the
only variable here is the number of teeth. That is, the total machine time is directly proportional to
the number of milled teeth of the workpiece.
Tab. 3.1 Calculated machine times
Number of teeth
wheels
Rolling method
tAS[minutes]
Divisive method
tAS[minutes]
18
24
26
54.5
72.7
78.8
40.3
53.7
58.1
Graphic expression:
Time dependence on the number of teeth
85
80
75
70
65
60
55
50
45
40
35
30
rolling milling
way
milling with dividers
way
18 19 20 21 22 23 24 25 26
number of teeth
Giant. 3.9 Graphic dependence of machine time on the number of machined teeth
machine
time
t
AS
[minutes]

CONCLUSION
This bachelor's thesis gives a comprehensive overview of the manufacturing
methods and calculations of the dimensions of gears. The entire issue is divided into
subchapters according to the type of gearing (spur gears with straight and bevel
teeth, bevel gears with straight, bevel and curved teeth).
The practical part of the work was a comparison of the production methods
for the typed gear wheel by rolling milling and splitting milling. It was a wheel of
a relatively large module (8) with 24 teeth and two imaginary wheels that differed
only in the number of teeth (one imaginary gear wheel had fewer and the other
more teeth, compared to the real wheel).
After calculating the dimensions of the wheels and the total machine times of production,
the course of these machine times was graphically shown depending on the number of teeth of the
wheel. It follows that it is a linear course, the result of only changes in the number of teeth on the
given wheels. This is due to the fact that the same cutting conditions of the tools can be used up to
a certain number of teeth (30). If the number of wheel teeth differed by larger differences, then the
cutting conditions such as feed per tooth fofand cutter speed nwwere different. In practice, it is
known that the greater the number of machined teeth, the lower the revolutions of the cutter.

LIST OF SOURCES USED
1. KOCMAN, K. and PROKOP, J.Machining technology. Brno: Akademické
nakladatelství CERM, 2005. 270 pp. ISBN 80-214-3068-0.
2. Gear machining.NATIONAL STANDARDS AND NORMS - Uniform norms.
Edition I. Prague 1964. 209 pp. CNN 10-25-0-0/1
3.S800/1200/1600/2000[online]. 2010 [cit. 2010-05-26]. SAMPUTENSILI.
Available of WWW:
<http://www.samputensili.com/media/SU/Machines/S900-
2000/S_800_S_1200_S_1600_S_2000_en.pdf >.
4.Custom production of gearing tools, both special and standard [online].
2010 [cit. 2010-05-26]. KASIKTOOLS. Available from WWW: <http://
www.kasiktools.cz/files/katalog.pdf >.
5.Division of the circumference of a circle[online]. 2001 [cit. 2010-05-26]. PAICHL, J.
Available from WWW: <http://www.paichl.cz/paichl/knihy/Schulze_10.htm >.
6.E-shop of milling tools[online]. 2010 [cit. 2010-05-26]. MT Tools. Available
from WWW: <http://www.i-frezy.cz/i-frezy/eshop/11-1-Tvarovekotoucove-
frezy/48-3-Na-evolventni-ozubeni-kol/5/1069-CSN22-2510-modulova-
freza- m8x20-c1 >.
7.Machine tools[online]. 2010 [cit. 2010-05-26]. TOS as a member of the
CTYGROUP group. Access WWW:
<http://www.tosas.cz/lang/produkty/ozubarenske-stroje >.
8.HG series gear centers[online]. 2006 [cit. 2010-05-26]. SAMPUTENSILI.
Available of WWW:
<http://www.samputensili.com/nqcontent.cfm?a_id=12980&lang=uk >.

LIST OF ABBREVIATIONS AND SYMBOLS USED
Abbreviation/Symbol
b
C
C*
d
dand
db
dF
Fof
h
hand
hF
and
ln
lMr
lof
m
nO
nw
with
witht
t
Unit
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
-
mm
mm
mm
-
min-1
min-1
mm
mm
mm
min
-
mm∙min-1
Description
the width of the wheel teeth
head clearance
unit clearance
pitch circle diameter
head circle diameter
base circle diameter heel
circle diameter
feed per tooth
tooth height
tooth head height
tooth heel height
number of chips per run-up
clamping
overrun
safety distance module
workpiece speed
cutter speed
feed direction
tooth thickness
tooth height
machine time
number of milling operations
cutting speed
the number of teeth of the workpiece
the number of cutter teeth
computer numerical control
cutter diameter
total machined length
length of the milling cutter
tooth pitch
radius
angle of engagement
tool position adjustment angle
tool position deflection angle
Ludolf number
tAS
atw
inC
of
ofF
CNC
Dand
L
LF
P
R
a
β
λ
π
-
-
mm
mm
mm
mm
mm
°
°
°
-
-
-
-
-
-
-

LIST OF ATTACHMENTS
Attachment 1
Appendix 2
Appendix 3
Appendix 4
Appendix 5
Appendix 6
Appendix 7
Appendix 8
Wiper drum assembly Gear milling machine TOS
FO 6 Gear milling machine TOS OH 4 Gear milling
machine TOS OH 6 Gear milling machine MAAG
SH 75 Gear milling machine OFA 75 CNC 6 Gear
milling machine OFA 32 CNC 6 Gear milling
machine OHA 50 CNC 5

Attachment 1
Wiper drum assembly

Appendix 2 (1/3)
Gear milling machine TOS FO 62

Appendix 2 (2/3)
Technical data of TOS FO6 and FO 8 machines2

Appendix 2 (3/3)
Technical data of the TOS FO 10 machine2

Appendix 3
Gear changer TOS OH 42

Appendix 4 (1/2)
Gear changer TOS OH 62

Appendix 4 (2/2)
Technical data of TOS OH 4 and OH 6 machines2

Appendix 5 (1/2)
Gear turning machine MAAG SH 752

Appendix 5 (2/2)
Technical data of MAAG SH 45 and MAAG SH 75 machines2

Appendix 6
Gear milling machine OFA 75 CNC 67

Appendix 7
Gear milling machine OFA 32 CNC 67

Appendix 8
OHA 50 CNC gear rolling lathe 57

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