Technical Brief

Contact Stress Evaluation of Involute Gear Pairs, Including the Effects of Friction and Helix Angle

[+] Author and Article Information
Santosh S. Patil

Department of Mechanical Engineering,
Universiti Teknologi PETRONAS,
Bandar Seri Iskandar,
Tronoh 31750, Perak, Malaysia
e-mail: santosh045@gmail.com

Saravanan Karuppanan

Department of Mechanical Engineering,
Universiti Teknologi PETRONAS,
Bandar Seri Iskandar,
Tronoh 31750, Perak, Malaysia
e-mail: saravanan_karuppanan@petronas.com.my

Ivana Atanasovska

Innovation Center of Faculty of Mechanical Engineering,
University of Belgrade,
Belgrade 11000, Serbia
e-mail: iatanasovska@mas.bg.ac.rs

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received December 20, 2014; final manuscript received March 24, 2015; published online May 11, 2015. Assoc. Editor: Jordan Liu.

J. Tribol 137(4), 044501 (Oct 01, 2015) (5 pages) Paper No: TRIB-14-1311; doi: 10.1115/1.4030242 History: Received December 20, 2014; Revised March 24, 2015; Online May 11, 2015

The aim of this technical brief is to provide a new viewpoint of friction factor for contact stress calculations of gears. The idea of friction factor has been coined, for the calculation of contact stresses along the tooth contact for different helical gear pairs. Friction factors were developed by evaluating contact stresses with and without friction for different gear pairs. In this paper, three-dimensional (3D) finite element method (FEM) and Lagrange multiplier algorithm have been used to evaluate the contact stresses. Initially, a spur gear finite element (FE) model was validated with the theoretical analysis under frictionless condition, which is based on Hertz's contact theory. Then, similar FE models were constructed for 5 deg, 15 deg, 25 deg, and 35 deg helical gear pairs. The contact stresses of these models were evaluated for different coefficients of friction. These results were employed for the development of friction factor.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Vijayarangan, S., and Ganesan, N., 1994, “Static Contact Stress Analysis of a Spur Gear Tooth Using the Finite Element Method, Including Frictional Effects,” Comput. Struct., 51(6), pp. 765–770. [CrossRef]
Ristivojević, M., Lazović, T., and Vencl, A., 2013, “Studying the Load Carrying Capacity of Spur Gear Tooth Flanks,” Mech. Mach. Theory, 59, pp. 125–137. [CrossRef]
Patil, S., Karuppanan, S., Atanasovska, I., and Wahab, A. A., 2014, “Frictional Tooth Contact Analysis Along Line of Action of a Spur Gear Using Finite Element Method,” Proc. Mater. Sci., 5, pp. 1801–1809. [CrossRef]
Nikolic, V., and Atanasovska, I., 2003, “The Analysis of Contact Stress on Meshed Teeth's Flanks Along the Path of Contact for a Tooth Pair,” Facta Univ., Ser.: Mech. Autom. Control Rob., 3(15), pp. 1055–1066.
Velex, P., and Cahouet, V., 2000, “Experimental and Numerical Investigations on the Influence of Tooth Friction in Spur and Helical Gear Dynamics,” ASME J. Mech. Des., 122(4), pp. 515–522. [CrossRef]
Rao, C. R. M., and Muthuveerappan, G., 1993, “Finite Element Modelling and Stress Analysis of Helical Gear Teeth,” Comput. Struct., 49(6), pp. 1095–1106. [CrossRef]
Vijayarangan, S., and Ganesan, N., 1993, “Stress Analysis of Composite Spur Gear Using the Finite Element Approach,” Comput. Struct., 46(5), pp. 869–875. [CrossRef]
Hwang, S., Lee, J., Lee, D., Han, S., and Lee, K., 2013, “Contact Stress Analysis for a Pair of Mating Gears,” Math. Comput. Modell., 57(1–2), pp. 40–49. [CrossRef]
Patil, S., Karuppanan, S., and Wahab, A. A., 2013, “Contact Pressure Evaluation of a Gear Pair Along the Line of Action Using Finite Element Analysis,” Appl. Mech. Mater., 393, pp. 403–408. [CrossRef]
Karpat, F., Ekwaro-Osire, S., Cavdar, K., and Babalik, F. C., 2008, “Dynamic Analysis of Involute Spur Gears With Asymmetric Teeth,” Int. J. Mech. Sci., 50(12), pp. 1598–1610. [CrossRef]
Kawalec, A., Wiktor, J., and Ceglarek, D., 2006, “Comparative Analysis of Tooth-Root Strength Using ISO and AGMA Standards in Spur and Helical Gears With FEM-Based Verification,” ASME J. Mech. Des., 128(5), pp. 1141–1158. [CrossRef]
Patil, S. S., and Karuppanan, S., Atanasovska, I., and Wahab, A. A., 2014, “Contact Stress Analysis of Helical Gear Pairs, Including Frictional Coefficients,” Int. J. Mech. Sci., 85, pp. 205–211. [CrossRef]
Hertz, H., 1896, “On the Contact of Elastic Bodies,” J. Pure Appl. Math., i, pp. 146–162. [CrossRef]
ANSYS Release 12.0, 2009, Structural Analysis Guide, ANSYS, Canonsburg, PA.
ANSI/AGMA, 2001, Fundamental Rating Factors Calculation Methods for Invoule Spur and Helical Gear Teeth, American National Standard/American Gear Manufacturers Association, Alexandria, VA.
Gopinath, K., and Mayuram, M. M., 2013, “Helical Gears, Machine Design II, IIT-Madras, Module 2, Lecture 11,” http://nptel.ac.in/courses/IIT-MADRAS/Machine_Design_II/pdf/2_11.pdf


Grahic Jump Location
Fig. 1

Meshed spur gear model along with the boundary conditions: (a) point A, (b) point B, (c) point C, (d) point D, and (e) point E

Grahic Jump Location
Fig. 2

von Mises equivalent contact stress distribution along the characteristic contact points: (a) point A, (b) point C, and (c) point E

Grahic Jump Location
Fig. 3

Validation plot of active contact stresses along the path of contact

Grahic Jump Location
Fig. 4

Sample of von Mises stress distributions at pitch point contact for: (a) μ = 0.0 case and (b) μ = 0.3 case

Grahic Jump Location
Fig. 5

Friction factor at pitch point contact for a spur gear pair

Grahic Jump Location
Fig. 6

Friction factor for different gear sets with varying coefficients of friction



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In