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Shakedown Analysis of Evolving Non-Hertzian Rolling Contact Using a Semi-analytical Numerical Model


The non-conforming rolling contact under high loads results in considerable plastic deformation of the surface. This surface plastic flow is studied using a twin-disk tribometer, and the observed deformation as a function of the number of rolling cycles is classified into three distinct stages. Substantial geometric changes are observed in the initial stage and during this process, the contact type changed from Hertzian to non-Hertzian in the first few cycles, and then it changed from non-Hertzian back to near Hertzian by the end of this stage. A semi-analytical model is hence used to perform the contact analysis. Special traction elements are employed near the surface discontinuities within the contact area to resolve singularities. The contact area is observed to change from elliptic to a near-rectangular shape and the evolution of the contact parameters during this process is reported. Shakedown limits are obtained at different instants of the deformation process using Melan’s theorem. It is observed that the high stresses near the surface discontinuities greatly affect the shakedown limits. The actual stress state is observed to move on a shakedown map until it goes below the shakedown limit but above the elastic limit as predicted.

Graphic Abstract

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Figure reproduced with permission by authors from M.S. thesis by P. Balasubramanian, University of Illinois, 2018 [22]

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Data Availability

All data are shown clearly in plots, and will be available upon request.

Code Availability

Custom code was developed for the simulations, but techniques used are clearly detailed in the paper to be able to replicate.


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This research was supported by Transportation Technology Center, Inc. (TTCI), Pueblo, Colorado. We thank Prabhakaran Balasubramanian and Hao Richie Fu for their prior work on this project. We also thank Professors Q. Jane Wang, D. Taylor, G.B. Sinclair, and H. Sehitoglu for their helpful comments and suggestions.


This research was supported by Transportation Technology Center, Inc. (TTCI), Pueblo, Colorado.

Author information




YSJ: Conceptualization, Formal analysis, Investigation, Writing—original draft. ACD: Conceptualization, Methodology, Supervision, Writing—review & editing.

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Correspondence to Alison C. Dunn.

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Jetti, Y.S., Dunn, A.C. Shakedown Analysis of Evolving Non-Hertzian Rolling Contact Using a Semi-analytical Numerical Model. Tribol Lett 69, 137 (2021).

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  • Rolling contact
  • Contact mechanics
  • Stress analysis
  • Twin-disk testing

Mathematics Subject Classification

  • 74A10
  • 74A55