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Analysis and numerical simulation of rolling contact between sphere and cone

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Abstract

In non-conforming rolling contact, the contact stress is highly concentrated in the contact area. However, there are some limitations of the special contact model and stress model used for the theoretical study of the phenomenon, and this has prevented in-depth analysis of the associated friction, wear, and failure. This paper is particularly aimed at investigating the area of rolling contact between a sphere and a cone, for which purpose the boundary is determined by the Hertz theory and the geometries of the non-conforming surfaces. The phenomenon of stick-slip contact is observed to occur in the contact area under the condition of no-full-slip (Q < μ · P). Using the two-dimensional rolling contact theory developed by CARTER, the relative positions of the stick and slip regions and the distribution of the tangential force over the contact area are analyzed. Furthermore, each stress component is calculated based on the McEwen theory and the idea of narrow band. The stress equations for the three-dimensional rolling contact between the sphere and the cone are obtained by the principle of superposition, and are used to perform some numerical simulations. The results show that the stress components have a large gradient along the boundary between the stick and slip regions, and that the maximum stress is inversely proportional to the contact coefficient and proportional to the friction coefficient. A new method for investigating the stress during non-classical three-dimensional rolling contact is proposed as a theoretical foundation for the analysis of the associated friction, wear, and failure.

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, Harbin University of Science and Technology, Harbin, 150080, China

    Yanling Zhao, Chengtao Xia, Jingzhong Xiang, Xianli Liu & Xiangguo Su

  2. Shenyang Aerospace Mitsubishi Motors Engine Manufacturing Co., Ltd, Shenyang, 110000, China

    Hongbo Wang & Jiaping Xuan

Authors
  1. Yanling Zhao
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  2. Chengtao Xia
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  3. Hongbo Wang
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  4. Jiaping Xuan
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  5. Jingzhong Xiang
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  6. Xianli Liu
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  7. Xiangguo Su
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Corresponding author

Correspondence to Yanling Zhao.

Additional information

Supported by National Natural Science Foundation of China(Grant No. 51275140)

ZHAO Yanling, born in 1963, is currently a professor at School of Mechanical and Power Engineering, Harbin University of Science and Technology, China. She received her bachelor degree from Harbin Institude of Technology, China, in 1986 and received her master degree and PhD degree from Harbin University of Science and Technology, China, in 1989 and 2008, respectively. Her current research interests include friction and wear study, mechanical structure design and system dynamics.

XIA Chengtao, born in 1988, is currently a master candidate at School of Mechanical and Power Engineering, Harbin University of Science and Technology, China. He received his bachelor degree from Shandong University of Technology, China, in 2012. His research interests include elastic mechanics and contact theory.

WANG Hongbo, born in 1988, is a technologist at Shenyang Aerospace Mitsubishi Motors Engine Manufacturing Co., Ltd, China. She received her master degree from Harbin University of Science and Technology, China, in 2015. Her research interests include elastic mechanics and contact theory.

XUAN Jiaping, is currently a technologist at Shenyang Aerospace Mitsubishi Motors Engine Manufacturing Co., Ltd, China. He recieve his master degree from Harbin University of Science and Technology, China, in 2014. His research interests include dynamics simulation and numerical analysis.

XIANG Jingzhong, born in 1962, is currently a professor at School of Mechanical and Power Engineering, Harbin University of Science and Technology, China and a vice president of Mechanical Design Teaching Research Association of Heilongjiang Province, China. He received his master degree from Harbin University of Science and Technology, China, in 2003. His research interests include mechanical and electrical integration and motion control technology.

LIU Xianli, born in 1961, is currently a professor and the president at School of Mechanical and Power Engineering, Harbin University of Science and Technology, China. He received his PhD degree from Harbin Institude of Technology, China, in 1999. His research interests include clean cutting, multimedia cutting database technology and image technology.

SU Xiangguo, born in 1977, is currently an associate professor at School of Mechanical and Power Engineering, Harbin University of Science and Technology, China. He received his master degree from Harbin Institude of Technology, China, in 2000. His research interests include fatigue and failure analysis.

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Zhao, Y., Xia, C., Wang, H. et al. Analysis and numerical simulation of rolling contact between sphere and cone. Chin. J. Mech. Eng. 28, 521–529 (2015). https://doi.org/10.3901/CJME.2015.0302.022

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  • DOI: https://doi.org/10.3901/CJME.2015.0302.022

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