International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
Comparison of bending stresses for different number
of teeth of spur gear obtained using MATLAB
Simulink with AGMA and ANSYS
Ishan Patel1 , Dr. M.S. Murthy2
1
PG Scholar, Mechanical Engineering, Indore Institute of Science and technology, Indore, India
Professor, Mechanical Engineering, Indore Institute of Science and technology, Indore, India
2
Abstract— Spur gears are normally used in every field of
engineering where the power transmission is required at
moderate speed. The study in this paper shows that the complex
design problem of spur gear which requires fine software skill
for modelling and also for analysing. The above problem can be
resolved by using MATLAB Simulink which provide equivalent
results to the AGMA and also to the ANSYS. In this paper we
first modelled spur gear in Pro engineer wildfire 5.0 and then
calculated the stresses on ANSYS work bench. After that we
create a Simulink model using curve fitting equation. The results
are compared with both AGMA and ANSYS.
Keywords— Spur gear, Modelling, AGMA, curve fitting,
simulink.
I. INTRODUCTION
The overall efficiency of any kind of power transmission
machine depends on the amount of power loss in the process.
The best way of transmitting power between the shafts is
gears. Gears are mostly used to transmit torque and angular
velocity. The design of gear is a complex process generally it
needs large number of iteration and data sets. In many cases
gear design is traditional and specified by different types of
standards [1], [2]. Involute shaped gears found to be almost
everywhere because of the contact forces act along a straight
line.
The Simulink model in this work was created for two main
reasons. First of all, the MATLAB Simulink model was
constructed to allow Ansys users to theoretically predict the
response of the analysis Software whatever that may be.
Instead of going through number of iterations and various
typical design processes of the gear analysis the Simulink
program allows the user to predict the response of the system
without actually doing the Analysis on the intend gear.
Senthil Kumar, Muni, and Muthuveerappan [3] carried
out work on optimization of asymmetric spur gear drives to
improve the bending load capacity. Yong Wang [4] in his
work optimized tooth profile based on identified gear
dynamic model has suggested a method to determine the
dynamic model of a practical gear system. Costopoulos and
Spitas [5] in their research studied the reduction of gear fillet
stresses by using one-sided involute asymmetric teeth. Li[6]
ISSN: 2231-5381
in his work effect of addendum on contact strength, bending
strength and basic performance parameters of a pair of spur
gears obtained basic performance parameters, effect of
addendum on tooth contact strength and bending strength of
the spur gear. S. T.Yusuf et.al [7] in their work simplified
model of a DC rotating machine for mechanical energy
generation using MATLAB/Simulink presents a study of a
simplified model of MATLAB/Simulink on DC rotating
machine on the place of complex mathematical model. They
have discussed in detailed simulation results and analysis.
A A Ansari, D M Deshpande [8] in their work
mathematical model of asynchronous machine in MATLAB
Simulink exhibit the steady state performance of induction
motor in MATLAB program. They have modelled and also
simulated with SIMULINK model.
II. MODELLING OF GEAR
In total 15 numbers of gears are modelled in
Pro/ENGINEER Wildfire [9], which are having the following
parameters. Material of gear is taken structural steel
TABLE I
Description
No . of teeth (Z)
Module(m)
Pitch Circle Diameter(D)
Gear face width (b)
Pressure angle(α)
Helix angle (β)
Addendum (ha)
Dedendum (hf)
Specifications
20
10 mm
200 mm
50 mm
20
0
10 mm
1.157*m
Modulus of Elasticity
2E+05 MPa
Poisson’s ratio
0.3
the procedure to model the gear of 20 number of teeth
with the parameters above mentioned in the Pro-E Wildfire,
other set of gears are modelled in the same way. Part
parameters are the basic parameters which defining the gear,
http://www.ijettjournal.org
Page 3141
International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
these part parameters determine all the other parameters that
define the gear tooth profile by using the Tools/Relation menu.
Figure 1 show the part parameters.
Geometry Factor (yj)
= 0.4
Tangential force calculation:
Power (P) = 15 HP=11.190 Kw
Speed
= 750 R.P.M
Torque (Tp ) =
. × (
(
)
)
= 142.47 N-m
×
Tangential Force (Ft) =
σ Agma =
.
× × . × .
× . × .
× .
=1424.75 N
=13.35 MPa
B: Static structural Analysis
The structural analysis of the spur gear tooth model is
carried out using the finite element analysis in ANSYS 14.5.
The load applied at the highest point of single tooth contact.
The Mess is generated with tetrahedron nodes. Figure 2, is
showing mesh generation. Maximum element size of 5 mm is
selected for the Mess Control. By applying the analysis over
the tooth which is facing the load we get the stress
distribution in the numeric as well as in the form of colour
scheme. By varying the number of teeth and keeping the other
parameters constant various models of the spur gear are
created. Various models created by varying number of teeth
are shown in Figure 3 and figure 4, and these figures also
show the finite element analysis.
Fig. 1 Tools / Relation Menu
III. STRESS CALCULATION
All the calculations are carried out of Eq. (1) on the basis
of AGMA standards.
A. AGMA Stress calculation [10]
Bending stress (σ) =
×
×
×
×
×
(1)
×
Where
Diametral pitch (Pd) =
Application Factor (Ka)
Size Factor (Ks)
Pd =
(Pd)= 0.1
= 1.2
(2)
= 1
Load distribution Factor (Km) = 1.2
Dynamic Factor (Kv)
Normal tangential Load (Ft)
ISSN: 2231-5381
Fig. 2 Meshed 3-D Model of Spur gear
= 0.8
= 1424.75 N
http://www.ijettjournal.org
Page 3142
International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
Fig. 3 Static analysis of gear having 15 teeth
Fig. 5 GUI Interface of MATLAB Simulink
IV. RESULT & DISCUSSION
TABLE III
Bending Stress in MPa
Fig. 4 Static analysis of gear having 20 teeth
C: Bending Stress calculation over Simulink:
For calculation of bending stresses in MATLAB-Simulink
a equation of curve fitting is formed by the data of ANSYS.
By making program coding on MATLAB then the solution is
done and results are shown in TABLE II. Figure 5 shows the
Simulink GUI window which give bending stress data.
ISSN: 2231-5381
S. No
No. Of
Teeth
1
15
10.77
10.017
10.49
2
16
10.49
10.68
10.95
3
17
11.53
11.35
11.46
4
18
12.23
12.02
12
5
19
12.38
12.68
12.59
6
20
13.445
13.35
13.22
7
21
13.4991
14.02
13.89
8
22
14.7
14.69
14.6
9
23
15.407
15.36
15.35
10
24
16.028
16.14
11
25
16.69
16.98
ANSYS
16.59
16.637
AGMA
Simulink
Table II clearly shows the results of changing the number of
teeth from 15 to 25, the stress is continuously increasing. For
constant load and speed the minimum number of teeth gears
are suitable. The result table shows that the results of AGMA
http://www.ijettjournal.org
Page 3143
International Journal of Engineering Trends and Technology (IJETT) - Volume4 Issue7- July 2013
and Simulink are much closer than results of ANSYS. Figure
6 shows the relation between number of teeth and bending
stress and also it shows the comparison of results obtained
through AGMA and ANSYS.
17
ANSYS
AGMA
Simulink
16
17
15
AGMA
ANSYS
14
Stress
16
Stress
15
13
14
12
13
11
12
10
11
9
14
16
10
18
20
22
24
26
No of Teeth
9
14
16
18
20
22
24
26
Fig. 8 Bending stress AGMA-ANSYS-Simulink
No of Teeth
IV: Conclusions:
Fig. 6 Bending stress AGMA- ANSYS
. Figure 7 is discussed the relation between number of teeth
and bending stress and also it shows the comparison of results
obtained through AGMA and Simulink.
The trend results obtained from both ANSYS and Simulink
are close to the results of AGMA. Which concludes that
simulink is also an equivalent tool if modeled properly by
using curve fitting.
REFERENCES
17
AGMA
Simulink
Stress
16
[1]
15
[2]
14
[3]
13
[4]
12
11
[5]
10
[6]
9
14
16
18
20
22
24
26
No of Teeth
[7]
Fig. 7 Bending stress AGMA-Simulink
Figure 8 is discussed the relation between number of teeth
and bending stress and also it shows the comparison of results
obtained through AGMA-Simulink and ANSYS.
ISSN: 2231-5381
[8]
[9]
[10]
Vasilios Spitas, et.al,” Fast modelling of conjugate gear tooth profiles
using discrete presentation by involute segments”, Mechanism and
Machine Theory 42 (2007) 751–762.
V. B. Math, Satish Chand, “An Approach to the Determination of Spur
Gear Tooth Root Fillet”, ASME 340 Vol. 126, MARCH 2004.
Senthil Kumar, D.V.Muni,G.Muthuveerappan, “Profile modification, a
design approach for increasing the tooth strength in spur gear”,
Mechanism and Machine Theory 43 (2008) 829–858.
Yong Wang, “Optimized tooth profile based on identified gear
dynamic model”, Mechanism and Machine Theory 42 (2007) 1058–
1068.
Th. Costopoulos, V. Spitas, “Reduction of gear fillet stresses by using
one-sided involute asymmetric teeth”, Int Mechanism and Machine
Theory 44 (2009) 1524–1534.
Shuting Li, “Effect of addendum on contact strength, bending strength
and basic performance parameters of a pair of spur gears”,
Mechanism and Machine Theory 43 (2008) 1557–1584.
T.Yusuf et.al, “Simplified model of a DC rotating machine for
mechanical energy generation using MATLAB/SIMULINK,
International Journal of Engineering and Innovative Technology” Vol.
2, Issue 6, Dec 2012.
A A Ansari, D M Deshpande, “Mathematical Model of Asynchronous
Machine in MATLAB Simulink”, International Journal of Engineering
Science and Technology Vol. 2(5), 2010, 1260-1267.
Pro/ENGINEER Wildfire 5.0
Dudley’s, “Gear hand book” 2nd ed, pp. 6.15-6.22
http://www.ijettjournal.org
Page 3144