Research on loading and unloading characteristics of joint surfaces based on ellipsoidal micro⁃asperities

LIU Yulong; LAN Guosheng; SONG Jianguo; LI Yong; LIAO Juntao; KANG Depeng

doi:10.16579/j.issn.1001.9669.2026.07.018

您当前的位置：

首页 >

文章列表页 >

Research on loading and unloading characteristics of joint surfaces based on ellipsoidal micro⁃asperities

·Experimental Research·Testing Technology· | 更新时间：2026-07-17

- Research on loading and unloading characteristics of joint surfaces based on ellipsoidal micro⁃asperities
- Journal of Mechanical Strength Vol. 48, Issue 7, Pages: 156-165(2026)
- 作者机构：
  
  太原科技大学机械工程学院，太原 030024
- 作者简介：
  
  LAN Guosheng, E-mail: languosheng@tyust.edu.cn
- 基金信息：
  
  National Natural Science Foundation of China(51275328)
- DOI：10.16579/j.issn.1001.9669.2026.07.018
  CLC： TH113.1;TH117.1
- Received：22 August 2024，
  
  Revised：2024-12-11，
  
  Online First：17 July 2026，
  
  Published：15 July 2026
- 稿件说明：
移动端阅览
刘宇龙，兰国生，宋建国，等. 基于椭球微凸体的结合面加、卸载特性研究［J］. 机械强度，2026，48（7）：156-165.

LIU Yulong，LAN Guosheng，SONG Jianguo，et al. Research on loading and unloading characteristics of joint surfaces based on ellipsoidal micro⁃asperities［J］. Journal of Mechanical Strength，2026，48（7）：156-165.
刘宇龙，兰国生，宋建国，等. 基于椭球微凸体的结合面加、卸载特性研究［J］. 机械强度，2026，48（7）：156-165. DOI： 10.16579/j.issn.1001.9669.2026.07.018.

LIU Yulong，LAN Guosheng，SONG Jianguo，et al. Research on loading and unloading characteristics of joint surfaces based on ellipsoidal micro⁃asperities［J］. Journal of Mechanical Strength，2026，48（7）：156-165. DOI： 10.16579/j.issn.1001.9669.2026.07.018.

摘要

目的

针对粗糙结合面微凸体几何形貌非单一性导致接触特性模拟不准确的问题，探究不同离心率下椭球微凸体在法向加、卸载过程中的力学响应机制。

方法

首先，基于三维各向异性分形理论与赫兹接触理论，构建了椭球微凸体法向加、卸载动力学模型；然后，分别在微凸体顶端曲率半径取常数、顶端曲率半径随接触面积动态变化（改进模型）两种边界条件下进行了数值仿真；最后，引入灰铸铁磨削结合面的试验数据进行了对比分析，探讨了分形维数与分形粗糙度对接触特性的主导规律。

结果

数值模拟与试验验证表明，结合面粗

糙表面上的微凸体由多重复杂的几何形状共同组成。在引入曲率半径随接触面积动态变化的改进模型中，理论预测值与试验曲线吻合良好，加载阶段误差控制在14%以内，卸载阶段误差控制在22%以内。在弹塑性变形的后半段，试验数据明显向离心率

为0.5~0.7的椭球仿真曲线靠拢，验证了改进椭球接触模型的合理性与工程参考价值。

Abstract

Objective

To address the inaccurate simulation of joint surface contact characteristics caused by the non-uniform geometric shapes of micro-asperities

the mechanical responses and deformation mechanisms of ellipsoidal micro-asperities with varying eccentricities during the normal loading and unloading processes are investigated.

Methods

Firstly

based on the three-dimensional anisotropic fractal theory and Hertzian contact mechanics

a theoretical loading-unloading contact model for ellipsoidal micro-asperities was established. Secondly

numerical simulations were performed under two distinct boundary scenarios: a constant tip curvature radius and a dynamic tip curvature radius varying with the contact area. Finally

test data from a gray cast iron grinding joint surface were introduced to validate the models

and the influences of fractal dimension and fractal roughness on the contact load were analyzed.

Results

The comparative analysis demonstrates that the micro-asperities on rough surfaces are composed of multi-shaped geometries rather than a single profile. For the improved model where the curvature radius varies dynamically with the contact area

the simulated curves exhibit excellent agreement with the test data

restricting errors to within 14% during the loading stage and 22% during the unloading stage. In the late elastoplastic stage

the test trajectory shifts toward the ellipsoidal model with eccentricities between 0.5 and 0.7

confirming the higher bi-directional accuracy and physical feasibility of the improved model.

关键词

Keywords

references

Lin Y Y ， Hui C Y . Mechanics of contact and adhesion between viscoelastic spheres：an analysis of hysteresis during loading and unloading ［J］. Journal of Polymer Science Part B：Polymer Physics ， 2002 ， 40 （ 9 ）： 772 - 793 .

Kadin Y ， Kligerman Y ， Etsion I . Unloading an elastic-plastic contact of rough surfaces ［J］. Journal of the Mechanics and Physics of Solids ， 2006 ， 54 （ 12 ）： 2652 - 2674 .

Ovcharenko A ， Halperin G ， Verberne G ， et al . In situ investigation of the contact area in elastic-plastic spherical contact during loading-unloading ［J］. Tribology Letters ， 2007 ， 25 （ 2 ）： 153 - 160 .

Zait Y ， Kligerman Y ， Etsion I . Unloading of an elastic-plastic spherical contact under stick contact condition ［J］. International Journal of Solids and Structures ， 2010 ， 47 （ 7/8 ）： 990 - 997 .

傅卫平，娄雷亭，高志强，等 . 机械结合面法向接触刚度和阻尼的理论模型［J］. 机械工程学报， 2017 ， 53 （ 9 ）： 73 - 82 .

Fu Weiping ， Lou Leiting ， Gao Zhiqiang ， et al . Theoretical model for the contact stiffness and damping of mechanical joint surface ［J］. Journal of Mechanical Engineering ， 2017 ， 53 （ 9 ）： 73 - 82 . （In Chinese）

高志强，傅卫平，王雯，等 . 弹塑性微凸体侧向接触相互作用能耗［J］. 力学学报， 2017 ， 49 （ 4 ）： 858 - 869 .

Gao Zhiqiang ， Fu Weiping ， Wang Wen ， et al . The contact energy dissipation of the lateral and interactional between the elastic-plastic asperities ［J］. Chinese Journal of Theoretical and Applied Mechanics ， 2017 ， 49 （ 4 ）： 858 - 869 . （In Chinese）

孙万 . 两接触粗糙表面法向接触特性三维分形模型［D］. 太原：太原科技大学， 2021 ： 39 - 58 .

Sun Wan . Three-dimensional fractal model of normal contact characteristics of two contact rough surfaces ［D］. Taiyuan ： Taiyuan University of Science and Technology ， 2021 ： 39 - 58 . （In Chinese）

王颜辉 . 结合面加卸载接触特性多尺度分形理论建模及验证［D］. 太原：太原科技大学， 2021 ： 20 - 25 .

Wang Yanhui . Multi-scale fractal theory modeling and verification of loading and unloading contact characteristics of joint surface ［D］. Taiyuan ： Taiyuan University of Science and Technology ， 2021 ： 20 - 25 . （In Chinese）

殷东华，张学良，温淑花，等 . 结合面首次加载过程的法向接触刚度分形模型［J］. 组合机床与自动化加工技术， 2022 （ 12 ）： 6 - 9 .

Yin Donghua ， Zhang Xueliang ， Wen Shuhua ， et al . A fractal model of normal contact stiffness of fixed joint interface during the first loading ［J］. Modular Machine Tool & Automatic Manufacturing Technique ， 2022 （ 12 ）： 6 - 9 . （In Chinese）

Horng J H . An elliptic elastic-plastic asperity microcontact model for rough surfaces ［J］. Journal of Tribology ， 1998 ， 120 （ 1 ）： 82 - 88 .

Jeng Y R ， Peng S R . Static friction model of elastic-plastic contact behavior of surface with elliptical asperities ［J］. Journal of Tribology ， 2009 ， 131 （ 2 ）： 021403 .

李小彭，牟佳信，潘五九，等 . 具有分形特性的齿侧间隙对齿轮-轴承系统动态特性的影响［J］. 机械工程学报， 2018 ， 54 （ 9 ）： 153 - 160 .

Li Xiaopeng ， Mou Jiaxin ， Pan Wujiu ， et al . Influence of fractal backlash on dynamic behavior of gear-bearing system ［J］. Journal of Mechanical Engineering ， 2018 ， 54 （ 9 ）： 153 - 160 . （In Chinese）

Kogut L ， Etsion I . Elastic-plastic contact analysis of a sphere and a rigid flat ［J］. Journal of Applied Mechanics ， 2002 ， 69 （ 5 ）： 657 - 662 .

Etsion I ， Kligerman Y ， Kadin Y . Unloading of an elastic-plastic loaded spherical contact ［J］. International Journal of Solids and Structures ， 2005 ， 42 （ 13 ）： 3716 - 3729 .

贺林，朱均 . 粗糙表面接触分形模型的提出与发展［J］. 摩擦学学报， 1996 ， 16 （ 4 ）： 375 - 384 .

He Lin ， Zhu Jun . Fractal model for contact of rough surfaces ［J］. Tribology ， 1996 ， 16 （ 4 ）： 375 - 384 . （In Chinese）

张学良 . 机械结合面动态特性及应用［M］. 北京：中国科学技术出版社， 2002 ： 25 - 27 .

Zhang Xueliang . Dynamic characteristics and application of mechanical joint surface ［M］. Beijing ： China Science and Technology Press ， 2002 ： 25 - 27 . （In Chinese）

李声祺，兰国生，李祥，等 . 机械结合面法向接触刚度三维分形理论模型［J］. 组合机床与自动化加工技术， 2023 （ 1 ）： 6 - 10 .

Li Shengqi ， Lan Guosheng ， Li Xiang ， et al . Three dimensional fractal theoretical model of normal contact stiffness of mechanical joint surface ［J］. Modular Machine Tool & Automatic Manufacturing Technique ， 2023 （ 1 ）： 6 - 10 . （In Chinese）

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

METHOD FOR DETERMINING THE CRITICAL POINT OF ELASTIC⁃PLASTIC OF M⁃B MODEL

STUDY ON CONTACT STRESS OF BEVELOID GEAR BASED ON FRACTAL THEORY

STATIC FRICTION COEFFICIENT MODEL OF JOINT SURFACES CONSIDERING ASPERITIES INTERACTION AND SUBSTRATE DEFORMATION (MT)

Study on the mechanical performance and energy absorption characteristics of structures with varying cross-sections and negative Poisson ratio

Research on precision analysis of finite element simplified modeling strategy for turntable framework

Related Author

CAO HongJun

ZHU Min

WANG ShengAo

DENG LiChongYang

MA DeSheng

LIU YongPing

WEI Shuai

DONG ChangBin

Related Institution

College of Nuclear Science and Technology,Naval University of Engineering

Unit 91515

School of Mechanical & Electrical Engineering, Lanzhou University of Technology

College of Mechanical Engineering, Taiyuan University of Science and Technology

⁰