IRJET- Error Identification and Comparison with Agma Standard in Gears using Finite Element Analysis

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 07 | July 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1416
ERROR IDENTIFICATION AND COMPARISON WITH AGMA STANDARD IN
GEARS USING FINITE ELEMENT ANALYSIS
Dr. N. Nandakumar1, T. Allwin Raja2
1Associate Professor, Department of mechanical Engineering, Government College of Technology, Coimbatore,
Tamilnadu, India.
2PG Scholar, Department of Engineering Design, Government College of Technology Coimbatore, Tamilnadu, India
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Abstract - The objectives of this thesis are to use a
algebraical style to progress theoretic replicas of thebehavior
of helical gears and rack and pinion in mesh, to help to predict
the effect of gear contact stresses and bending stress error.
The core attention of the existing study as established to
govern proper representations of contact rudiments, to
analyze bending stresses and contact stressofhelicalgear and
rack and pinion respectively by ANSYS and equate the
outcomes with AGMA theoretic standards.
Key Words: Helical gear, rack and pinion, contact stress
analysis, bending stress analysis
1. INTRODUCTION
Gearing is one of the most critical components in a
mechanical power transmission system, and in most
industrial rotating machinery. It is possible that gears will
predominate as the most effective means of transmitting
power in future machines due to their high degree of
reliability and compactness. In addition,the rapidshiftinthe
industry from heavy industries such as shipbuilding to
industries such as automobile manufacture and office
automation tools will necessitate a refined application of
gear technology. The increasing demand for quiet power
transmissioninmachines,vehicles,elevatorsandgenerators,
has created a growing demand for a more precise analysisof
the characteristics of gear systems. In the automobile
industry, the largest manufacturerofgears,higherreliability
and lighter weight gears are necessary as lighter
automobiles continue to be in demand. In addition, the
success in engine noise reduction promotes the production
of quieter gear pairs for further noise reduction. Noise
reduction in gear pairs is especially critical in the rapidly
growing field of office-automation equipment as the office
environment is adversely affected by noise, and machines
are playing widening role in that environment.
The finite element method is very often used to analyze the
stress state of an elastic body with complicated geometry,
such as a gear. In this thesis, first, the finite element models
and solution methods needed for the accurate calculation of
two dimensional Rack and pinion contact stresses and
Helical gear bending stresses were determined. Then, the
contact and bending stresses calculated using ANSYS 19.2
were equated to the outcomes gained from present
approaches. The purpose of this thesis is to develop a model
to learning and forecast the typical counting the connection
stresses and the Bending stress of gears in mesh by the
ANSYS 19.2 Tool packagegroundedonmathematical system.
The aim is to find the amount of stress error inthegears,and
thereby reduce the amount of failure rate generated.
2. CONTACT STRESS
2.1. IMPORTANCE OF CONTACT STRESS
Despite the importance of contact in the mechanics of solids
and its engineering applications, contact effects are rarely
seriously taken into account in conventional engineering
analysis, because of the extreme complexity involved.
Mechanical problems involving contacts are inherently
nonlinear .Usually the loading causes significant changes in
stiffness, which results in a structure that is nonlinear.
Nonlinear structural behavior arises for a number of
reasons, which can be reduced to three main categories (1)
Geometric Nonlinearities, (2) Material Nonlinearities, (3)
Change in Status Nonlinearities, Throughthe quick change of
computational mechanism, but, excessive advancement has
been finished in geometric study of the tricky. Using the
finite element way, several connection glitches, oscillating
after moderately humble ones to quite difficult ones, can be
resolved with high precision. TheFiniteElementMethodcan
be restrained the desired technique to treat interaction
problems, since of its confirmed achievement in giving a
extensive variety of engineering delinquent in zones of solid
mechanics, fluid flow, heat transfer, and for electromagnetic
field and coupled field problems.
2.2. CONTACT PROBLEM OF RACK AND PINION
The fig 1 shows Rack and pinion are hard-pressedcounter to
each other. This prototype was constructedgroundedonthe
Hertz contact stress theoretic delinquent. The ranges were
premeditated beginning from the pitch diameters of the
pinion and gear .The contact stress of this prototype should
characterize the contact stress amongtwogears.Intheinput
file, first, the geometry of Rack andpinionmustbedescribed.
Then the geometry areas were meshed. In contact areas a
fine mesh was built. The boundary conditions were applied
in this model. The loads also were applied .In eachstepthere
are a lot of sub-steps. In each sub-step the number of
equilibrium iterations was set.

Fig.1. RACK AND PINION
2.3 . CONTACT STRESS ANALYSIS
The fig 2 shows the usual connection stress laterally on the
interaction parts. The similar process is ended for dissimilar
materials and the outcomesareequatedwithAGMAordinary
outcome and discourse around the stress difference.
FIG.2.CONTACT STRESS ANALYSIS
3. BENDING STRESS
When one investigates actual gears inservice,theconditions
of the surface and bending failure are two of the most
important features to be considered. The finite element
method is very often used to analyze the stress states of
elastic bodies with complicated geometries, such as gears.
There are published papers, which have calculated the
elastic stress distributions in gears. In these works, various
calculation methods for the analysis of elastic contact
problems have been presented. The finite element method
for two-dimensional analysis is used very often. It is
essential to use a three-dimensional analysisifgearpairs are
under partial and non uniform contact. However, in the
three-dimensional calculation, a problem is created due to
the large computer memory space that is necessary. In the
technique for producing a FEM typical for bending stress
analyses, the calculations secondhand to produce the gear
tooth shape curve. When meshing the teeth in ANSYS, if
“SMART SIZE” is used the number of elementsneartheroots
of the teeth are automatically much greater than in other
places. It also indicates that only one tooth is enough for the
bending stress analysis for the 3-D model.
FIG.3.HELICAL GEAR
3.1. BENDING STRESS ANALYSIS
The Figure 4 displays how to mesh the 3D model and how to
place happening the load on the sample. Here are internal
side nodes on the individually side of apiece part. So a great
number of degrees of free movement in this 3D model take a
lengthier period to enclose running.It similarlyspecifiesthat
only one tooth is sufficient for the bending stress study for
the 3-D model. The investigation displays one tooth FEM
prototype and display how abundant Von Mises stress is on
the base of tooth when the number of teeth is 37 forthegear.
FIG.4.BENDING STRESS ANALYSIS
In this unit the tooth base stressesand thetoothdeflectionof
one tooth of helical gear is designed using an ANSYS model.
4. AGMA ANALYSIS
In this section, a comparison of the tooth root stresses
obtained in the three dimensional model and in the two

dimensional model using ANSYS with the results given by
the standards of the AGMA is carried out. is recommended
by the AGMA and the other coefficients, such as the dynamic
factor, are set at 1.2.
Where σ(c) and σ(f) are contact and bending stress
respectively.
5. BENDING STRESS COMPARISON
The Von Mises stresses on the root of tooth were carried out
in order to know if they match the results from ANSYS.
The above calculations of the Von Mises stresses on the root
of tooth were carried out in order to know if they match the
results from ANSYS In this Table 1 the maximum values of
the tooth root stress obtained by the ANSYS method.
TABLE.1.BENDING STRESS ANALYSIS
5.2. CONTACT STRESS COMPARISON
TABLE.2.CONTACT STRESS ANALYSIS
NUMBER
OF TEETH
AGMA
(MPa)
ANSYS
(MPa)
% ERROR
33 85.050 84.429 0.74
35 91.129 91.770 0.69
37 115.126 110.78 3.97
40 116.86 113.79 2.63
42 128.86 124.80 2.93
44 141.97 132.15 7.43
These changes are supposed to be produced by aspects such
as the mesh design and the limited circumstances on the
finite element analysis, and the supposed location of the
dangerous unit in the values are shown in Table 2.
6. CONCLUSION
It was exposed that an FEA prototype could be helped to
analyze the interaction among two physiques exactly by
confirmation of contact stresses among two cylinders in
contact and comparison with the Hertzian equations. Active
approaches to approximation the tooth interaction stress
using a 3D interaction stress prototype and to guesstheroot
bending stresses via 3D FEA prototype are anticipated. The
expansion of a innovative mathematical way for FEA
showing of the full gear figure which can alternate in mesh
together with the contact problem is offered.Themotionless
stress fault was too attained after running the replicas in
ANSYS.
REFERENCES
[1] Norton, R. L., “MachineDesign:AnIntegratedApproach”,
New Jersey: Prentice-Hall Inc.
[2] Hamrock, B. J., Jacobson, S.R., “FundamentalsofMachine
Elements”.
[3] Buckingham, E., 1949, “Analytical Mechanics of Gears”,
McGraw-Hill, New York.
[4] Coy, J. J., Chao, C. H. S., 1982, “A method of selecting grid
size to account for Hertz deformation in finite element
analysis of spur gears”, Trans. ASME,J.Mech.Design104
759-766.
[5] Gatcombe, E.K., Prowell, R.W., 1960, “Rocket motorgear
tooth analysis”, (Hertzian contact stresses and times)
Trans. ASMA, J. Engng Industry.
[6] Umezawa, K., 1988, “Recent Trends in Gearing
Technology”, JSME International Journal Series III
Vol.31, No. 2, pp 357-362.
[7] Klenz, S. R., 1999, “Finite Element Analyses of A Spur
Gear Set”, M.Sc. Thesis, Dept. of Mechanical Engineering,
University of Saskatchewan.
[8] Smith, J. O. Liu, C. K., “Stresses Due to Tangential and
Normal Loads on an Elastic Solid with Applications to
Some Contact Stress Problems”, Journal of Applied
Mechanics
[9] Wang, J., 2003, “Survey of Nonlinear Vibration of Gear
Transmission Systems” Appl Mech Rev vol 56, No 3.
[10] Chong, T. H., Bar, I., 2001,“Multiobjectiveoptimal Design
of Cylindrical Gear Pairs for the Reduction of Gear Size
NUMBER
OF
TEETH
AGMA
(MPa)
ANSYS
(MPa)
% ERROR
28 650.43 671.24 3.2
30 670.32 690.43 3
34 732.65 757.12 3.34
37 745.59 771.69 3.5
40 765.76 797.92 4.2
42 788.77 820.32 4

and Meshing Vibration”, JSME International Journal,Vol.
44, No. 1, pp 291-292
[11] B.Bloomfield, Designing facegears,
Mach.Design19(1947) 129134.
[12] G.F. Heath, R.B. BosslerJr., Advanced rotorcraft
transmission (ART) program final report, NASA
Contractor Report 191057, January 1993.
[13] G.F.Heath,R.R.Filler,J.Tan,Developmentoffacegeartechnol
ogyforindustrialandaerospacepowertransmission,NASA
/CR2002211320,May2002.
[14] R.R.Filler, G.F.Heath, S.C.Slaughter, D.G.Lewicki, Torque
Splitting By a Concentric Face Gear Transmission, the
American Helicopter Society 58th Annual Forum,
Montreal, 2002June1113.
[15] G.F. Heath, S.C. Slaughter, M.T.Morris, J.Fetty, D.G.
Lewicki, D.J. Fisher, Face Gear Development under the
Rotor craft Drive System for the 21st Century Program,
the American Helicopter Society 65th Annual Forum,
2009 May 27-29.

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