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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (9): 1674-1680    DOI: 10.3785/j.issn.1008-973X.2019.09.005
Mechanical Engineering     
Analysis and improvement on elastic-plastic micro-contact modelof rough surface
Jian CHEN1(),Jin-hua ZHANG1,Lin-bo ZHU2,*(),Jun HONG1
1. Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System, Xi’an Jiaotong University , Xi’an 710049, China
2. School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an 710049, China
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Abstract  

The shortcomings of existing interpolation polynomial and power-exponential micro-contact models were compared and analyzed, in order to accurately describe the micro-contact characteristics of rough surfaces. An improved elastic-plastic micro-contact model considering the material properties was proposed using a normalization method. Compared with the existing models, the improved model has good continuity and smoothness at the yield critical and full plastic critical points, also taking into account the influence of material’s Poisson’s ratio on the maximum contact pressure factor. Results show that the proposed model can describe the micro-contact characteristics more continuously, smoothly and monotonously, compared with the classical KE model and Lin model; the contact area of asperity is independent of the Poisson's ratio of the material, and is not affected by the maximum contact pressure factor; and the average contact pressure, contact load and contact stiffness of asperity are related to the Poisson's ratio, which are also proportional to the maximum contact pressure factor.

Key words： micro-contact      elastic-plastic deformation      interpolation polynomial      power exponential function      material properties      rough surface     
Received: 30 November 2018      Published: 12 September 2019
CLC:  O 343  
Corresponding Authors: Lin-bo ZHU     E-mail: jxfb0602@163.com;linbozhu@mail.xjtu.edu.cn
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Jian CHEN
Jin-hua ZHANG
Lin-bo ZHU
Jun HONG
Cite this article:

Jian CHEN,Jin-hua ZHANG,Lin-bo ZHU,Jun HONG. Analysis and improvement on elastic-plastic micro-contact modelof rough surface. Journal of ZheJiang University (Engineering Science), 2019, 53(9): 1674-1680.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.09.005     OR     http://www.zjujournals.com/eng/Y2019/V53/I9/1674


粗糙表面弹塑性微接触模型分析与改进

为了准确描述粗糙表面微接触特性，对比分析现有插值多项式类和幂指函数类微接触模型存在的不足，采用量纲归一化方法，提出一种考虑材料属性的弹塑性微接触改进模型. 与现有模型相比，改进后的微接触模型在屈服临界点和全塑性临界点处具有良好的连续性和光滑性，且考虑了材料泊松比对最大接触压力因子的影响. 结果表明：较经典的KE模型和Lin模型，提出的模型能够连续、光滑和单调地描述微接触特性；微凸体接触面积与材料泊松比无关，且不受最大接触压力因子取值的影响；微凸体的平均接触压力、接触载荷和接触刚度与材料泊松比相关，且与最大接触压力因子成正比.


关键词： 微接触,  弹塑性变形,  插值多项式,  幂指函数,  材料属性,  粗糙表面 
Fig.1 Diagram for contact between asperity and rigid smooth plane
模型 微凸体接触特性 临界点
接触面积 平均接触压力 接触载荷 屈服 全塑性
ZMC[7] 4次多项式 对数多项式 接触面积和
平均接触压力的乘积 		${\delta _{{\rm{ec}}}}$ $54{\delta _{{\rm{ec}}}}$
Zhao[8] ZMC模型 3.5次多项式 $110{\delta _{{\rm{ec}}}}$
Brake[9] 3次多项式 3次多项式 $110{\delta _{{\rm{ec}}}}$
Xu[10] Brake模型 椭圆曲线 $110{\delta _{{\rm{ec}}}}$
Li[11] 3次多项式 ZMC模型 $110{\delta _{{\rm{ec}}}}$
Tab.1 Comparisons for micro-contact model of interpolation polynomial
Fig.2 Comparison of contact area predicted different template functions
Fig.3 Comparison of contact characteristics predicteddifferent models
幂指表达式 KE模型[12] Lin模型[13] Wang模型[14]
α β α β α β
注：KE 模型有 2 个弹塑性变形区间（弹塑性区间Ⅰ： $1 \leqslant \delta /{\delta _{{\rm{ec}}}} \leqslant 6$；弹塑性区间Ⅱ： $6 \leqslant \delta /{\delta _{{\rm{ec}}}} \leqslant 110$），Lin 模型和 Wang 模型只有 1 个弹塑性变形区间.
$\frac{{{A_{{\rm{ep}}}}}}{{{A_{{\rm{ec}}}}}} = \alpha {\left( {\displaystyle\frac{\delta }{{{\delta _{{\rm{ec}}}}}}} \right)^\beta }$ 0.93 1.136 1.00 1.159 7 1.00 1.158 1
0.94 1.146
$\displaystyle\frac{{{p_{{\rm{ep}}}}}}{{\sigma }} = \alpha {\left( {\displaystyle\frac{\delta }{{{\delta _{{\text{ec}}}}}}} \right)^\beta }$ 1.19 0.289 1.08 0.220 4 1.00 0.209 1
1.61 0.117
$\frac{{{F_{{\rm{ep}}}}}}{{{F_{{\rm{ec}}}}}} = \alpha {\left( {\displaystyle\frac{\delta }{{{\delta _{{\rm{ec}}}}}}} \right)^\beta }$ 1.03 1.425 1.00 1.380 1 1.00 1.367 3
1.40 1.263
全塑性临界点 $\delta _{\rm pc2}^{\rm KE} = 110{\delta _{{\rm{ec}}}}$ $\delta _{\rm pc}^{\rm Lin} = 76.8{\delta _{{\rm{ec}}}}$ $\delta _{\rm pc}^{\rm Wang} = 80{\delta _{{\rm{ec}}}}$
Tab.2 Comparison of coefficient and exponent in power exponential function models
Fig.4 Change of dimensionless average contact pressure with dimensionless deformation
Fig.5 Change of maximum contact pressure factor withPoisson's ratio
Fig.6 Change of dimensionless contact load with dimensionless deformation
Fig.7 Change of dimensionless contact stiffness with dimensionless deformation
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