A Parametric Study on the Sub-surface Stresses in Spur Gears under Mixed-lubrication Regime using Load-sharing and Finite Element Simulation

Mohammad Danesh, Saleh Akbarzadeh, Peiman Mosaddegh, Morteza Parsa


Gears as key elements in power transmission systems are widely used in industry. Based on the manufacturing process, the surface of gears compared to other mechanical components such as roller bearings might be rougher and thus the effect of surface roughness in their performance should be given full consideration. One of the most important parameters in the gears' performance is the maximum shear stress that occurs below the surface, which is believed to be the key factor in surface fatigue and pitting. In this research, a model that employs the load-sharing concept to predict the friction coefficient and film thickness for each point along the line of action is developed. The sub-surface stress field that is generated below the tooth surface is calculated based on the friction coefficient. The predicted sub-surface stresses are compared to the results obtained from the commercial finite element software ABAQUS. An acceptable agreement is observed in comparing the results from the two methods. Finally, a parametric study has been conducted to study the effect of load, velocity, viscosity and surface hardness on the calculated maximum sub-surface shear stress and its location.


Sub-surface Stresses; ABAQUS; Spur Gear; Load-sharing Concept, Finite Element Simulation

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Kannel, J.W., and Tevaarwerk, J.L., "Stress Evaluation under Rolling/ Sliding Contacts", NASA CR-165561, Oct. 1981.

Beheshti, A., and Khonsari, M.M., "On the prediction of fatigue crack initiation in rolling/sliding contacts with provision for loading sequence effect", Tribology International, pp. 1620-1628, 2011.

Fernandens, P.J.L., and Mcduling, C., "Surface contact fatigue failures in gears", Engineering Failure Analysis. vol. 4, pp. 99–107, 1997.

Mihailidis, A., Bakolas, V., and Balkan, J., "Numerical simulation of real 3-D rough surfaces", J. Balkan Tribol. Assoc. 5 pp. 247–255, 1999.

Majumdar, B.C., and Hamrock, B. J., "Effect of Surface-Roughness on Elastohydrodynamic Line Contact", J Lubric. Tech-T ASME. Vol. 104(3), pp. 401-409, 1982.

Patir, N., and Cheng, H. S., "An Average Flow Model for Determining Effects of Three-Dimensional Roughness On Partial Hydrodynamic Lubrication", ASME J. Lubr. Technol., Vol. 100, pp. 8–14, 1978.

Greenwood, J.A., Johnson, K.L., and Matsubara, E., "A surface roughness parameter in Hertz contact", wear. vol. 100, pp. 47-57, 1984.

Johnson, K.L., Greenwood, J. A., and Poon, S. Y., "A Simple Theory of Asperity Contact in Elastohydrodynamic Lubrication", Wear. vol. 19, pp. 91-108, 1972.

Gelinck, E.R.M., and Schipper, D. J., "Calculation of Stribeck Curves for Line Contacts", Tribol. vol. 33, pp. 175–181, 2000.

Lu, X., Khonsari, M. M., and Gelinck, E. R. M. , "The Stribeck Curve:Experimental Results and Theoretical Prediction", ASME J. Tribol. vol. 128, pp. 789–794, 2006.

Akbarzadeh, S., and Khonsari, M.M., "Performance of Spur Gears Considering Surface Roughness and Shear Thinning Lubricant ", Journal of Tribology. vol. 130(2), p. 021503, 2008.

Akbarzadeh, S., and Khonsari, M.M., "Thermoelastohydrodynamic analysis of spur gears with consideration of surface roughness", Tribology Letters. vol. 32, pp. 129–141, 2008.

Ebrahimi sererst, A., Akbarzadeh, S., "Mixed Elastohydrodynamic Analysis of Helical Gears Using Load-Sharing Concept," Journal of Engineering Tribology, 228, pp.320-331, 2014.

Bahrami Ghahnavieh, A., Akbarzadeh, S., Mosaddegh, P.,"A Numerical Study on the Performance of Straight Bevel Gears Operating Under Mixed Lubrication Regime," Mechanism and Machine Theory, 75, pp. 27-40, 2014.

Masjedi, M., and Khonsari, M. M., "Film Thickness and Asperity Load Formulas for Line-Contact EHL with Provision for Surface Roughness", Journal of Tribology. vol. 134,011503, 2012

Masjedi, M., and Khonsari, M. M., "Theoretical and experimental investigation of traction coefficient in line-contact EHL of rough surfaces", Tribology International . vol. 70, pp.179-189, 2014.

Zhao, Y., Maietta, D.M., and Chang, L., "An asperity microcontact model incorporating the transition from elastic deformation to fully plastic flow", Tribology. vol. 122, pp. 86-93, 2000.

Moes, H., "Optimum similarity analysis with applications to elastohydrodynamic lubrication", Wear. vol. 159, pp. 57-66, 1992.

Greenwood, J.A., and Williamson, J.B.P., "Contact of nominally flat surfaces", Proc. R. Soc., vol. 295, pp.300-319, 1966.

Johnson, K.L., Contact mechanics, Cambridge University Press, UK, 1985.

M. Parsa and S. Akbarzadeh, “A new load-sharing-based approach to model mixed-lubrication contact of spur gears,” Proc. Inst. Mech. Eng. Part J J. Eng. Tribol., 2014.


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