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浙江大学学报(工学版)
浙江大学学报(工学版)  2019, Vol. 53 Issue (9): 1674-1680    DOI: 10.3785/j.issn.1008-973X.2019.09.005
机械工程     
粗糙表面弹塑性微接触模型分析与改进
陈剑1(),张进华1,朱林波2,*(),洪军1
1. 西安交通大学 现代设计及转子轴承系统教育部重点实验室，陕西 西安，710049
2. 西安交通大学 化学工程与技术学院，陕西 西安，710049
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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摘要：

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    
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
收稿日期: 2018-11-30 出版日期: 2019-09-12
CLC:  O 343  
通讯作者: 朱林波     E-mail: jxfb0602@163.com;linbozhu@mail.xjtu.edu.cn
作者简介: 陈剑（1985—），男，博士生，从事装配连接研究. orcid.org/0000-0002-8369-6597. E-mail： jxfb0602@163.com
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陈剑
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引用本文:

陈剑,张进华,朱林波,洪军. 粗糙表面弹塑性微接触模型分析与改进[J]. 浙江大学学报(工学版), 2019, 53(9): 1674-1680.

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.

链接本文:

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

图 1  单微凸体与刚性光滑平面接触示意图
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 $110{\delta _{{\rm{ec}}}}$
表 1  插值多项式类微接触模型比较
图 2  不同样板函数预测接触面积的比较
图 3  不同模型预测接触特性的比较
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 $\delta _{\rm pc2}^{\rm KE} = 110{\delta _{{\rm{ec}}}}$ $\delta _{\rm pc}^{\rm Lin} = 76.8{\delta _{{\rm{ec}}}}$ $\delta _{\rm pc}^{\rm Wang} = 80{\delta _{{\rm{ec}}}}$
表 2  幂指函数类模型中系数和指数比较
图 4  无量纲平均接触压力随无量纲变形的变化
图 5  最大接触压力因子随泊松比的变化
图 6  无量纲接触载荷随无量纲变形的变化
图 7  无量纲接触刚度随无量纲变形的变化
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