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Friction  2022, Vol. 10 Issue (2): 217-231    doi: 10.1007/s40544-020-0419-7
Research Article     
New analytical model of elastic-plastic contact for three- dimensional rough surfaces considering interaction of asperities
Yuqin WEN1,Jinyuan TANG1,*(),Wei ZHOU2,*(),Lin LI1,Caichao ZHU3
1 State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China
2 Hunan Provincial Key Laboratory of High Efficiency and Precision Machining of Difficult-to-Cut Material, Hunan University of Science and Technology, Xiangtan 411201, China
3 State Key Laboratory of Mechanical Transmission, Chongqing University, Xiangtan 400044, China
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The contact calculation of three-dimensional real rough surfaces is the frontier field of tribology and surface science. In this study, we consider the interaction and elastic-plastic deformation characteristics of asperities and further, propose an analytical contact calculation method for rough surfaces considering the interaction of asperities. Based on the watershed algorithm, the rough surface is segmented and the asperities are reconstructed into ellipsoids. According to the height relationship between the asperities, the definition of the deformation reference height of the matrix between each couple of asperities is provided. Subsequently, the calculation formula of the substrate deformation is provided according to the local contact pressure considering the elastic-plastic deformation of the asperity, and the contact state under a specific load is determined using the iterative correction method. The results correspond with those of finite element numerical calculation and the study reveals the following: (1) compared with the results obtained without considering the asperity interaction, contact area, distance, and stiffness will be reduced by 6.6%, 19.6%, and 49.5%, respectively, when the influence of asperity interaction is considered; (2) the interaction of the asperities has the greatest influence on the surface contact distance and stiffness. Under the same load, the existence of asperity interaction will reduce the contact distance, area, and stiffness; (3) considering the interaction of the asperities, the higher asperity will bear more load, but it will simultaneously reduce the contact of the surrounding area and increase that of the distant area. The calculation method proposed in this study has the advantages of high calculation efficiency and accuracy, thus, providing the calculation basis and method for subsequent studies on service performance of rough surfaces, such as the calculation of contact stiffness and fatigue performance analysis of rough surfaces.

Key wordscalculation method      contact analysis      interaction of asperities      rough surface     
Received: 08 March 2020      Published: 17 January 2022
Fund:  National Natural Science Foundation of China(51705142);Key Research and Development Project of Hunan province(2016JC2001);Fundamental Research Funds for the Central Universities of Central South University(2019zzts255)
Corresponding Authors: Jinyuan TANG,Wei ZHOU     E-mail:;
About author: Yuqin WEN. He received his bachelor degree in mechanical engineering from Central South University, Changsha, China, in 2015. Then, he was a Ph.D. student in the State Key Laboratory of High Performance Complex Manufacturing at the same university. His research areas cover tribology and structural fatigue and fracture.|Jinyuan TANG. He received his Ph.D. degree in mechanical engineering from Central South University, Changsha, China. He joined the State Key Laboratory of High Performance Complex Manufac- turing at Central South University since 1982. His research areas cover intelligent manufacturing of high performance devices, and research on design theory of high performance power transmission device.|Wei ZHOU. He received his M.S. and Ph.D. degrees in mechanical engineering from Central South University, China, in 2011 and 2016 respectively. He joined the Hunan Provincial Key Laboratory of High Efficiency and Precision Machining of Difficult-to-Cut Material at Hunan University of Science and Technology since 2016. His research areas cover tribology and structural fatigue and fracture.
Cite this article:

Yuqin WEN,Jinyuan TANG,Wei ZHOU,Lin LI,Caichao ZHU. New analytical model of elastic-plastic contact for three- dimensional rough surfaces considering interaction of asperities. Friction, 2022, 10(2): 217-231.

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Fig. 1 Schematic diagram of watershed division.
Fig. 2 Contact deformation of an ellipsoid asperity.
Fig. 3 Influence of asperity interaction.
Fig. 4 Definition of height of asperity substrate.
Fig. 5 Establishment of finite element model.
Fig. 6 Comparison of interaction of asperities at different substrate heights.
Fig. 7 Surface topography of a grinding workpiece: surface 1, (b) surface 2, and (c) surface 3.
Surfacesσ (mm)R (mm)η (mm2)
Workpiece 15.56×10-41.63×10-22.86×104
Workpiece 24.21×10-48.63×10-34.34×104
Workpiece 31.39×10-38.12×10-32.71×104
Table 1 Topography parameters of a microscopic surface.
Yield strength σs850 MPa
Elastic modulus E209 GPa
Hardness H (2.8σs)2.38 GPa
Poisson's ratio v0.29
Table 2 Mechanical parameters of the surface.
Fig. 8 Correlation between dimensionless load and distance of surface 1.
Fig. 9 Correlation between dimensionless load and distance of surface 2.
Fig. 10 Correlation between dimensionless load and distance of surface 3.
Fig. 11 Influence of interaction of asperities on contact area.
Fig. 12 Influence of interaction of asperities on contact distance.
Fig. 13 Influence of interaction of asperities on contact stiffness.
Fig. 14 Contact stress nephogram without asperity interaction.
Fig. 15 Contact stress nephogram with asperity interaction.
Fig. 16 Contact stress nephogram of finite element model.
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