1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME
10
THE ANALYSIS OF SOME FACTORS FOR THE OPTIMIZATION OF
CYLINDRICAL GEAR TRANSMITTERS
Dr. sc. NIJAZI IBRAHIMI1
, Dr. sc. SADULLAH AVDIU2
, Msc. RIAD RAMADANI3
,
Dr. sc. FATIH KARPAT4
1,2,3
Faculty of Mechanical Engineering, University of Prishtina “Hasan Prishtina”, Prishtina, Kosovo
4
Faculty of Mechanical Engineering, Uludag University, Bursa, Turkey
ABSTRACT
On the phase of dimensioning of the gear transmitters have influence center distance, gear
ratio, material, thermal processing etc. The purpose of this paper is analysis of factors that have
influence on the optimization of cylindrical gear transmitters. It is analyzed safety factor for pitting
and safety factor for bending for gear transmitters on the dependence of center distance and gear
ratio, than it is analyzed safety factor for pitting on dependence on safety factor for bending, gear
ratio and material. Through analysis of these factors are defined limits of size that have influence on
the optimization of gear transmitters.
Keywords: Cylindrical Gear Transmitters, Optimization, Gear Optimization.
1.0 INTRODUCTION
Gear power transmitters are part of mechanical group of high importance, which need to
fulfill criterion for required performance criteria as: center distance, dimensions, safety factor,
efficiency factor, contact ratio etc.
Gear power transmitter with multi-stage, represents complex mechanical system that they
need to fulfill technical requirement for:
- compact design,
- gear ratio,
- efficiency,
- factor of safety
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 5, Issue 4, April (2014), pp. 10-15
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME
11
Choosing the best model, which needs to fulfill certain requirements of desired performance,
imposes some limitation in the aspect of: assembling of gears pair, gears mesh, roughness of face and
flank of gears, surface and volume durability, and other limitations [1].
2.0 THE ANALYSIS OF FACTORS THAT INFLUENCE ON THE OPTIMIZATION GEAR
TRANSMITTERS
Many factors influence on the dimensioning of gear power transmitters, therefore it is very
important to make the analysis of factors that influence in their optimization.
Factors that influence on the optimization of gear transmitters are: center distance, gear radio,
contact ration, module of gears, material, safety factors, volume, etc [2].
In order to achieve optimization of each factor mentioned above, a gear pair was analyzed
with the following parameters:
- Pinion material: steel, type Č.4732, for improvement,
- Gear material: steel, type Č.1731 for improvement,
- Standard module: mn12
=4.5 mm,
- Number of teeth of pinion: z1
=19,
- Number of teeth of gear: z2
=80,
- Face width: b12
=100 mm,
- Helix angle: β12
=14
o
,
- Center distance a12
=230 mm,
- Torque of pinion: T1
=387.324 N· mm,
2.1. Safety factor for pitting on dependence of center distance
Factor of safety from Pitting [3]:
[ ]
H
H
HS
σ
σ
= (2.1)
Where are:
Critical contact stress of teeth face
[ ] xwVRLNTHH ZZZZZZ⋅= limσσ (2.2)
Working stress of teeth face
βαβεσ HHvA
t
EHH KKKK
u
u
bd
F
ZZZZ ⋅⋅⋅⋅
+
⋅
⋅
=
1
(2.3)
If in the expression (2.1), we substitute expressions (2.2) and (2.3) and expressions below:
1
1
1
2
d
T
Ft
⋅
= and
1
2
1
+
⋅
=
u
a
d

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME
12
It is obtained expression for calculation of safety factor for pitting on dependency of center
distance.
βαβε
σ
HHvABEH
xwVRLNTH
H
KKKK
u
u
ba
T
ZZZZZ
ZZZZZZ
S
⋅⋅⋅⋅
+
⋅
⋅⋅
⋅⋅
=
3
2
3
1
11lim
1
)1(
4
102
)(
(2.4)
In the fig. 2.1., are represented curves of safety factor for pitting on dependency of center
distance, for some values of gear radio.
220 222 224 226 228 230 232 234 236 238 240
1.05
1.08
1.11
1.14
1.17
1.2
1.23
1.26
1.29
1.32
1.35
SH1 a( )
SH2 a( )
SH3 a( )
SH4 a( )
SH5 a( )
a
Fig. 2.1: Safety factor for pitting on dependency of center distance, for some values of gear radio:
SH1(a) – u=3.8; SH2(a) – u=4; SH3(a) – u=4.2; SH4(a) – u=4.4; SH5(a) – u=4.6
From the fig. 2.1., it can be seen that with the increase of center distance, for constant gear
radio, we have increase of safety factor for pitting.
Also, with the increase of gear radio, we have decrease of safety factor for pitting.
2.2. Safety factor for bending on the dependence of center distance
Safety factor for bending [3]
[ ]
F
F
FS
σ
σ
= (2.5)
Where are:
Critical stress for bending
[ ] xRrelTrelTSTNTFF YYYYY δσσ ⋅= lim (2.6)
Working stress for bending
βαβεσ FFvA
n
t
saFaF KKKK
mb
F
YYYY ⋅⋅⋅⋅
⋅
= (2.7)

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME
13
If in the expression (2.5), we substitute expressions (2.6) and (2.7) and expressions below:
1
1
1
2
d
T
Ft
⋅
= and
1
2
1
+
⋅
=
u
a
d
It is obtained expression for calculation of safety factor for bending on the dependency of the
center distance
βαβε
δσ
FFvA
n
saFa
xRrelTrelTSTNTF
F
KKKK
amb
uT
YYYY
YYYYY
S
⋅⋅⋅⋅
⋅⋅
⋅+⋅
= 3
1
11lim
1
10)1(
)(
(2.8)
In the fig. 2.2., are represented curves of safety factor for bending on the dependency of
center distance, for some values of gear radio
220 222 224 226 228 230 232 234 236 238 240
4.5
4.65
4.8
4.95
5.1
5.25
5.4
5.55
5.7
5.85
6
SF1 a( )
SF2 a( )
SF3 a( )
SF4 a( )
SF5 a( )
a
Fig. 2.2: Safety factor for bending on dependency of center distance, for some values of gear radio:
SF1(a) – u=3.8; SF2(a) – u=4; SF3(a) – u=4.2; SF4(a) – u=4.4; SF5(a) – u=4.6
From the fig. 2.2., it can be seen that with the increase of center distance, for constant gear
ratio, we have increase of the safety factor for bending.
Also, with the increase of gear ratio, we have decrease of safety factor for bending.
2.3. Safety factor for pitting on dependency of safety factor of bending
From the expressions (2.4) and (2.8), center distance on the dependency of safety factor for
pitting and safety factor for bending is:
( )
xwVRLNTH
HHvAHBEH
ZZZZZZub
KKKKuTSZZZZZ
a
1lim
33
11
2
1102
σ
βαβε
⋅⋅⋅
⋅⋅⋅⋅+⋅⋅⋅⋅⋅
= (2.9)

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME
14
( )
xRrelTrelTSTNTFn
FFFvAsaFa
YYYYYmb
SKKKKuTYYYY
a
δ
βαβε
σ 1lim
1
3
1 101
⋅⋅
⋅⋅⋅⋅⋅⋅+⋅⋅
= (2.10)
From equalization of center distance aa = , it is obtained expression of safety factor for
pitting on dependency of safety factor of bending:
( )
( ) 11lim
33
1
111lim
3
1
1
)(1102
)(2101
xRrelTrelTSTNTFnHHvABEH
FxwVRLNTHFFvAsaFa
H
YYYYYmbKKKKuTZZZZZ
SZZZZZZubKKKKuTYYYY
S
δβαβε
βαβε
σ
σ
⋅⋅⋅⋅⋅⋅⋅+⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅+⋅⋅
= (2.11)
In the fig. 2.3., are represented curves of safety factor for pitting on dependency of safety
factor for bending, for some values of gear ratio and material steel for improvement.
5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6
1.1
1.13
1.16
1.19
1.22
1.25
1.28
1.31
1.34
1.37
1.4
SH1SF( )
SH2SF( )
SH3SF( )
SH4SF( )
SH5SF( )
SF
Fig. 2.3: Safety factor for pitting on dependency of safety factor for bending, for some values of
gear ratio and material steel for improvement: SH1(SF) – u=3.8; SH2(SF) – u=4;
SH3(SF) – u=4.2; SH4(SF) – u=4.4; SH5(SF)– u=4.6;
From the fig. 2.3., it can be seen that with the increase of safety factor for bending, for
constant gear ratio, we have increase of safety factor for pitting. With the increase of gear ratio, we
have increase of safety factor for pitting.
Also, for the material steel for case-harden it is assigned safety factor for pitting on
dependency of safety factor for bending.
In the fig. 2.4., are represented curves of safety factor for pitting on dependency of safety
factor for bending, for some values of gear ratio and material steel case-harden.

6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 4, April (2014), pp. 10-15 © IAEME
15
3.46 3.56 3.66 3.76 3.87 3.97 4.07 4.18 4.28 4.38 4.49 4.59 4.69 4.79 4.9 5
1.1
1.15
1.19
1.24
1.29
1.33
1.38
1.43
1.47
1.52
1.57
1.61
1.66
1.71
1.75
1.8
SH1SF( )
SH2SF( )
SH3SF( )
SH4SF( )
SH5SF( )
SF
Fig. 2.4: Safety factor for pitting on dependency of safety factor for bending, for some values of
gear ratio and material steel for case-harden: SH1(SF) – u=3.8; SH2(SF) – u=4;
SH3(SF) – u=4.2; SH4(SF) – u=4.4; SH5(SF)– u=4.6;
From the fig. 2.4., it can be seen that with the increase of safety factor for bending, for
constant gear ratio, we have increase of safety factor for pitting.
Also, with the increase of gear ratio, we have increase of safety factor for pitting. For the
material steel for case-harden the limit of safety factor for bending is 3.46 against it 5 for material
steel for improvement.
3. CONCLUSION
Based on the analysis of safety factor on dependency of center distance and gear ration we
can conclude:
- With the increase of center distance, increases safety factors for pitting and bending.
- With the increase of gear ratio, increases safety factor for pitting and bending.
- Material of gear has influence on safety factor for pitting and bending.
REFERENCES
[1] Riad Ramadani: Analiza e faktorëve që ndikojnë në optimizimin e transmetuesve me
dhëmbëzorë, Master Work, Prishtinë, 2009.
[2] Johannes Jahn: Introduction to the theory of nonlinear optimization, Universität Erlangen-
Nürnberg, Germany, 2007.
[3] Nijazi Ibrahimi, Detalaet e Makinave II - Libri 1 dhe 2, Prishtinë, 2006.
[4] Singiresu Rao: Engineering optimization, theory and practice, Purdue University, West
Lafayette, Indiana 2006.
[5] P. Alexander, T. Sudha and M. Omamageswari, “Automatic Gear Transmission in Two
Wheelers using Embedded System”, International Journal of Advanced Research in
Engineering & Technology (IJARET), Volume 3, Issue 2, 2012, pp. 164 - 175, ISSN Print:
0976-6480, ISSN Online: 0976-6499.