Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model

Chu Hongyan; An Ran; Cai Ligang

doi:doi:10.11648/j.ijmea.20160406.15

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Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model

Chu Hongyan, An Ran, Cai Ligang

Published in International Journal of Mechanical Engineering and Applications (Volume 4, Issue 6)

Received: 24 December 2016 Accepted: Published: 28 December 2016

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Abstract

Hertz contact theory (HCT) is a study of contact stress and deformation which is widely used in many engineering fields. However, there are many limiting conditions for the applications of the HCT, in this paper, the contact model between a plastic cylinder and a rubber cylinder does not fit two limiting conditions: Small deformation and no rigid body motion. By applying three-dimensional finite element models, the deformation and the maximum contact stress of two rotating cylinders have been analyzed. Comparing the simulation results and the theoretical results, the applicability of Hertz contact theory to this model has been discussed. The results show that: In the condition of large deformation, the theoretical results of maximum contact stress fit the actual situation, but the half-width of the contact area does not fit. Under the rolling condition, the theoretical maximum contact stress has a large deviation to simulation result.

Published in	International Journal of Mechanical Engineering and Applications (Volume 4, Issue 6)
DOI	10.11648/j.ijmea.20160406.15
Page(s)	242-248
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Hertz Contact Theory, Large Deformation, Contact Stress, Elastic Cylinder

References

[1]	Tian Hongliang, Zhu Dalin, Fang Zifan, Qin Hongling. Hertz contact for 129 years [J]. Journal of China Three Gorges University (NATURAL SCIENCE EDITION), 2011, 06: 61-71. J. Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vol. 2. Oxford: Clarendon, 1892, pp.68–73.
[2]	Sun Shulei, Ding Junjun, Li Fei, Huang Yunhua, Zhou Zhang Yi. Research on the wheel / rail contact problem of metro vehicles [J]. urban rail transit research, 2013, 08: 39-43.
[3]	Mingyong Liu. Study on thermo elastic hydrodynamic lubrication of helical gears based on finite line contact [D]. Chongqing University, 2013
[4]	Wang Zubing, Fang Zongde, Su Jin. Study on meshing characteristics of profile modification spur gear [J]; mechanical transmission; 12 phase of 2011.
[5]	S.-H. Gao, G. Meng, X.-H. Long. Study of milling stability with Hertz contact stiffness of ball bearings [J]. Archive of Applied Mechanics, 2011, 818.
[6]	Ma Wen. Calculation and finite element analysis of rolling bearing contact problem [J]. mechanical engineering and automation, 2011, 06: 51-53.
[7]	W. Yan, F. D. Fischer. Applicability of the Hertz contact theory to rail-wheel contact problems [J]. Archive of Applied Mechanics, 2000, 704.
[8]	V. G. Vil’ke, I. I. Kosenko, E. B. Aleksandrov. On computer implementation of the Hertz elastic contact model and its simplifications [J]. Regular and Chaotic Dynamics, 2009, 146.
[9]	Xu Kai, Su Jianxin, Zhou Yongdan, Qiu Ming, Wang Weisheng. Finite element analysis of line contact and point contact of gears [J]. mechanical transmission, 2014, 08: 77-81.
[10]	Xiaoyong Li, Shilong Wang, Jie Zhou. Analysis of elliptical Hertz contact of steel wires of stranded-wire helical spring [J]. Journal of Mechanical Science and Technology, 2014, 287.
[11]	Wan Fei, Li Guo-xi, Gong Jing-zhong, Wu Bao-zhong. Dynamic study of anti-backlash gears and angle-contact ball bearing based on a simplification of the Hertz contact theory [J]. Proceedings of the Institution of Mechanical Engineers, 2016, 2301.

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APA Style

Chu Hongyan, An Ran, Cai Ligang. (2016). Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model. International Journal of Mechanical Engineering and Applications, 4(6), 242-248. https://doi.org/10.11648/j.ijmea.20160406.15

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ACS Style

Chu Hongyan; An Ran; Cai Ligang. Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model. Int. J. Mech. Eng. Appl. 2016, 4(6), 242-248. doi: 10.11648/j.ijmea.20160406.15

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AMA Style

Chu Hongyan, An Ran, Cai Ligang. Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model. Int J Mech Eng Appl. 2016;4(6):242-248. doi: 10.11648/j.ijmea.20160406.15

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@article{10.11648/j.ijmea.20160406.15,
  author = {Chu Hongyan and An Ran and Cai Ligang},
  title = {Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model},
  journal = {International Journal of Mechanical Engineering and Applications},
  volume = {4},
  number = {6},
  pages = {242-248},
  doi = {10.11648/j.ijmea.20160406.15},
  url = {https://doi.org/10.11648/j.ijmea.20160406.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20160406.15},
  abstract = {Hertz contact theory (HCT) is a study of contact stress and deformation which is widely used in many engineering fields. However, there are many limiting conditions for the applications of the HCT, in this paper, the contact model between a plastic cylinder and a rubber cylinder does not fit two limiting conditions: Small deformation and no rigid body motion. By applying three-dimensional finite element models, the deformation and the maximum contact stress of two rotating cylinders have been analyzed. Comparing the simulation results and the theoretical results, the applicability of Hertz contact theory to this model has been discussed. The results show that: In the condition of large deformation, the theoretical results of maximum contact stress fit the actual situation, but the half-width of the contact area does not fit. Under the rolling condition, the theoretical maximum contact stress has a large deviation to simulation result.},
 year = {2016}
}

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TY  - JOUR
T1  - Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model
AU  - Chu Hongyan
AU  - An Ran
AU  - Cai Ligang
Y1  - 2016/12/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ijmea.20160406.15
DO  - 10.11648/j.ijmea.20160406.15
T2  - International Journal of Mechanical Engineering and Applications
JF  - International Journal of Mechanical Engineering and Applications
JO  - International Journal of Mechanical Engineering and Applications
SP  - 242
EP  - 248
PB  - Science Publishing Group
SN  - 2330-0248
UR  - https://doi.org/10.11648/j.ijmea.20160406.15
AB  - Hertz contact theory (HCT) is a study of contact stress and deformation which is widely used in many engineering fields. However, there are many limiting conditions for the applications of the HCT, in this paper, the contact model between a plastic cylinder and a rubber cylinder does not fit two limiting conditions: Small deformation and no rigid body motion. By applying three-dimensional finite element models, the deformation and the maximum contact stress of two rotating cylinders have been analyzed. Comparing the simulation results and the theoretical results, the applicability of Hertz contact theory to this model has been discussed. The results show that: In the condition of large deformation, the theoretical results of maximum contact stress fit the actual situation, but the half-width of the contact area does not fit. Under the rolling condition, the theoretical maximum contact stress has a large deviation to simulation result.
VL  - 4
IS  - 6
ER  -

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Author Information

Chu Hongyan

Mechanical Engineering, Beijing University of Technology, Beijing, China
An Ran

Mechanical Engineering, Beijing University of Technology, Beijing, China
Cai Ligang

Mechanical Engineering, Beijing University of Technology, Beijing, China

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APA Style

Chu Hongyan, An Ran, Cai Ligang. (2016). Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model. International Journal of Mechanical Engineering and Applications, 4(6), 242-248. https://doi.org/10.11648/j.ijmea.20160406.15

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ACS Style

Chu Hongyan; An Ran; Cai Ligang. Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model. Int. J. Mech. Eng. Appl. 2016, 4(6), 242-248. doi: 10.11648/j.ijmea.20160406.15

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AMA Style

Chu Hongyan, An Ran, Cai Ligang. Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model. Int J Mech Eng Appl. 2016;4(6):242-248. doi: 10.11648/j.ijmea.20160406.15

Copy | Download

@article{10.11648/j.ijmea.20160406.15,
  author = {Chu Hongyan and An Ran and Cai Ligang},
  title = {Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model},
  journal = {International Journal of Mechanical Engineering and Applications},
  volume = {4},
  number = {6},
  pages = {242-248},
  doi = {10.11648/j.ijmea.20160406.15},
  url = {https://doi.org/10.11648/j.ijmea.20160406.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20160406.15},
  abstract = {Hertz contact theory (HCT) is a study of contact stress and deformation which is widely used in many engineering fields. However, there are many limiting conditions for the applications of the HCT, in this paper, the contact model between a plastic cylinder and a rubber cylinder does not fit two limiting conditions: Small deformation and no rigid body motion. By applying three-dimensional finite element models, the deformation and the maximum contact stress of two rotating cylinders have been analyzed. Comparing the simulation results and the theoretical results, the applicability of Hertz contact theory to this model has been discussed. The results show that: In the condition of large deformation, the theoretical results of maximum contact stress fit the actual situation, but the half-width of the contact area does not fit. Under the rolling condition, the theoretical maximum contact stress has a large deviation to simulation result.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model
AU  - Chu Hongyan
AU  - An Ran
AU  - Cai Ligang
Y1  - 2016/12/28
PY  - 2016
N1  - https://doi.org/10.11648/j.ijmea.20160406.15
DO  - 10.11648/j.ijmea.20160406.15
T2  - International Journal of Mechanical Engineering and Applications
JF  - International Journal of Mechanical Engineering and Applications
JO  - International Journal of Mechanical Engineering and Applications
SP  - 242
EP  - 248
PB  - Science Publishing Group
SN  - 2330-0248
UR  - https://doi.org/10.11648/j.ijmea.20160406.15
AB  - Hertz contact theory (HCT) is a study of contact stress and deformation which is widely used in many engineering fields. However, there are many limiting conditions for the applications of the HCT, in this paper, the contact model between a plastic cylinder and a rubber cylinder does not fit two limiting conditions: Small deformation and no rigid body motion. By applying three-dimensional finite element models, the deformation and the maximum contact stress of two rotating cylinders have been analyzed. Comparing the simulation results and the theoretical results, the applicability of Hertz contact theory to this model has been discussed. The results show that: In the condition of large deformation, the theoretical results of maximum contact stress fit the actual situation, but the half-width of the contact area does not fit. Under the rolling condition, the theoretical maximum contact stress has a large deviation to simulation result.
VL  - 4
IS  - 6
ER  -

Copy | Download