A Comparison of Bending Stress and Contact Stress of a Helical Gear as Calculated by AGMA Standards and FEA

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459,ISO 9001:2008 Certified Journal, Volume 4, Issue 5, May 2014)

38

A Comparison of Bending Stress and Contact Stress of a Helical

Gear as Calculated by AGMA Standards and FEA

A.Sathyanarayana Achari

1

, R.P.Chaitanya

2

, Srinivas Prabhu

3

1

M.Tech Scholar, 3Assistant Professor, Department of Mechanical Engineering, NMAMIT, Nitte, Karnataka, India 2_{Junior Manager, CRS, JSW Steel Limited, Vidya Nagar, Toranagallu, Bellary, Karnataka, India}

Abstract—In the gear design, the surface strength and tooth root strength of the gears are assumed to be one of the major contributors for the gear failures in a gear pair. Therefore, the analysis of stresses in a gear has become a more popular as an area of research to reduce or to minimize the failures and for optimal design of gear pairs. In this paper, bending stress at the root of the helical gear tooth and surface contact stresses are computed by using theoretical method as well as FEA. To estimate the bending stress at the tooth root Lewis beam strength method was applied. NX CAD 8.5 modeling software package is used to create the 3D solid model of helical gear pairs. NX Nastran 8.5 software package is used to analyze the gear tooth root bending stress. Contact stresses are calculated by AGMA standards. In this also NX CAD 8.5 modeling software package is used to generate helical gear tooth contact models. NX Nastran 8.5 software package is used to analyze the surface contact stress. Ultimately, these two methods, tooth root bending stress and contact stress results are compared with respect to each other.

Keywords— Helical gear, FEA, AGMA, Bending stress, Contact stress.

I. INTRODUCTION

Gears are needful to the modern global economy and are used in almost all applications where power transmission is required, such as industrial equipments, automobiles helicopters, marine vessels and airplanes. Frequency of product pattern change and the vast amounts of cost and time required to make a change over, and also called time-based competition, has become a characteristic factor of current global manufacturing and new product development in aerospace industries, aircraft industries, automotive industries and other industries [3].

Helical gears are important transmission parts. Their tooth root bending stress and surface contact stress had always been one of the research focuses and many scholars have done a lot of work on it.

The design of a helical gear pair is a complex process. Generally it needs a large number of iterations and datasets. Andrnj. K and Jerzy. W [3] presented the comparison study of tooth root strength by using ISO and AGMA standards. Wei SUN, etc. [4] presented a new method to calculate bending deformation of an involute helical gear. M.R.Lias etc.[5] investigated the stress distribution of gear tooth due to axial misalignment conditions. B.Venkatesh etc.[6] has done the modeling and analysis of aluminum helical gear for marine applications. J.Venkatesh etc.[7] focused on investigating the stresses of the different helix angle of the helical gear.

The helical gears can fail due to excessive bending stress at the root of gear tooth or surface contact stresses. This can be avoided only by minimizing bending stresses and contact stress or by modifying the geometry or parameters of the gear tooth. In this paper real involute gear pair with transmission ratio analyzed.

The major steps are involved to obtain the results are explained as follows

a)Modeling of the helical gear without losing its tooth

geometry in NX CAD 8.5 software.

b)Generating the profile of single tooth of the helical

gear to determine bending stress at the tooth root and compare the results with modified Lewis beam strength method.

c)To determine the surface contact stress NX Nastran

8.5 software package is used and compared with an AGMA standard equation.

II. CREATION OF 3D SOLID MODELS OF GEARS

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International Journal of Emerging Technology and Advanced Engineering

39 2.1Pinion geometry parameters

Name of the Parameters Value

Number of teeth 30

Pitch circle diameter (in mm) 315.9

Normal module 10

Helix angle (in degrees) 15

Face width (in mm) 165

Pressure angle (in degrees) 20

Addendum circle diameter (in mm) 335.78

Dedendum circle diameter (in mm) 290.78

Fig.1. 3D solid model of Pinion

2.2 Gear profile parameters

Name of the Parameters Value

Number of teeth 55

Pitch circle diameter (in mm) 568.20

Normal module 10

Helix angle (in degrees) 15

Face width (in mm) 150

Pressure angle (in degrees) 20

Addendum circle diameter (in mm) 588.20

Dedendum circle diameter (in mm) 543.20

Fig.2. 3D solid model of Gear

Fig.3. 3D solid model of Contact gear pairs

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International Journal of Emerging Technology and Advanced Engineering

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III. CALCULATION OF BENDING STRESS AND CONTACT

STRESS BY AGMA METHOD

Wilfred Lewis introduced an equation for finding the bending stress in gear tooth in which the tooth form entered into the formulation. The equation, announce in 1892, still remains as the basic equation for most gear designs today.

To derive the Lewis equation, referred fig. 5, which shows a cantilever of cross sectional dimensions F and t, length l and the transmitted tangential load across the face width. Therefore the bending stress is,

Fig.5. Gear tooth considered as a cantilever beam[2].

The fundamental equation for bending stress is [2]

The fundamental equation for Pitting resistance (contact stress) is [2]

For Steel,

All the calculations are executed on the basis of fundamental formulae recommended by AGMA standards.

3.1 Bending stress calculation of Pinion.

3.2 Bending stress calculation of Gear.

3.3 Contact stress calculation of pinion..

3.4 Contact stress calculation of Gear

IV. DETERMINATION OF BENDING STRESS AND CONTACT

STRESS BY FINITE ELEMENT ANALYSIS

Finite element analysis is the numerical solution of the behavior mechanical components that are acquired by discretizing the mechanical components into a small finite number of building blocks (known as elements) and by

analyzing those mechanical components for their

acceptability and reliability.

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International Journal of Emerging Technology and Advanced Engineering

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For over 40 years, Nastran has been the choicest analysis solution in every leading major industry, including medical, heavy machinery, shipbuilding, automotive, defense, automotive and aerospace industries.

The helical gears contact model generated in NX CAD 8.5 software package as shown in fig.3 and the fig.4 shows the finite element model of the helical gear pairs with applied boundary conditions. 3D tetrahedral mesh with element size 5 to 6 mm is used for mesh generation of the gear models. NX Nastran 8.5 software package is used for the analysis.

4.1 Bending stress determination for pinion by using FEA

Fig.6. Bending stress of the pinion

The boundary condition was applied to the FEM model of gear tooth as per the Lewis beam strength method for the determination of bending stress. Fig.6 shows that the maximum Von-mises stress is developed at the root of the

pinion tooth of 541.61 N/mm2. Thus, the maximum

Von-mises stress developed by FEA is almost nearer to the bending stress as calculated by AGMA standards.

Fig.7. Bending stresses of pinion by specifying ranges from 300 N/mm2

to maximum Von-mises stress (541.61 N/mm2)

4.2 Bending stress determination for gear by using FEA

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International Journal of Emerging Technology and Advanced Engineering

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Fig.8 shows that the maximum Von-mises stress is

developed at the root of the gear tooth of 520.51 N/mm2.

Overall, the bending stresses were similar when compared to the two calculated methods.

Fig.9. Bending stress of gear by specifying ranges from 350 N/mm2_to

maximum Von-mises stress (520.51 N/mm2₎

In fig.7 and fig.9, some suitable specified range has taken in finding the stress only at the root of the gear tooth.

4.3Contact stress determination by using FEA

The boundary condition was applied for determination of contact stress as shown in fig.4. The gear was fixed and applied an input torque to the pinion with a pinned constraint.

Fig.10. Contact stress of the helical gear pair

Fig.10 shows that, the maximum Von-mises stress of

1008.70 N/mm2 is developed at surface contact point of the

teeth. The closer view of the contact stress at the contact point can be seen in fig.11.

Fig.11. Contact stress of helical gear pair of the teeth.

V. CONCLUSIONS

The work done primarily focused on validation of the Lewis bending strength and AGMA theory using Finite Element approach. The geometric modeling of the helical gear tooth profile was done with proper boundary conditions applied to the finite element model of the helical gear pair. The FEA results obtained are very close to the AGMA standards results.

Comparison of Bending stress results:- Teeth

numbers

Bending stress by AGMA Std. (N/mm2)

Bending stress by NX Natran 8.5 (N/mm2)

Difference (In %)

30 539.23 541.61 0.4 %

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International Journal of Emerging Technology and Advanced Engineering

43 Comparison of Surface Contact stress results:-

Contact stress by AGMA (N/mm2)

Contact stress by NX Natran 8.5 (N/mm2)

Difference (In %)

1041.46 1008.70 3.1 %

By observing the theoretical and FEA results, error percentage is very less i.e, from 0.4 to 2.1 % in bending stress and about 3% error in surface contact stress. So, Finite Element Analysis is an easy method of finding the bending stresses at the root of the gear tooth and surface contact stresses of an involute helical gear with less time consuming. The accuracy of this study is better than the theoretical/empirical solution.

Good results are obtained as well as good understanding of the bending stress and contact stress of the helical gear. The understanding is viewed as just as important as the results it is this knowledge which will allow an engineer to improve a design. As a future work, finding the surface contact stress under dynamic loading condition along with temperature variances can be performed.

Acknowledgment

The author would like to thank Mayank Pande (Junior Manager), Ankith Jain (Junior Manager), JSW Steel limited, Bellary, Karnataka, India and Aprameya C.R, Government polytechnic college, kampli for their continuous support and guidance.

In addition, author gives special thanks to Arindam Roy Chowdary (General Manager), JSW Steel Limited, Bellary and Karnataka for providing the opportunity to do the project work. The blessing of the family and my mother is the main cause behind the successful completion of this paper. I wish to acknowledge great moral support given by NMAM Institute of Technology, Nitte, Karnataka, India.

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[3] Andrzej Kawalec, Jerzy Wiktor and D.Ceglarek, “Comparative

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[4] Wei Sun, Tao Chen and Xu Zhang “A New Method to Calculate

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[5] M.R.Lias, T.V.V.L.N.Rao, M.Awang and M.A.Khan,. “The Stress

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