Statistical Model and Experimental Validation of Normal Contact Stiffness for Hard-Coated Rough Surfaces Considering Substrate Deformation

ZHANG Xueliang; ZHANG Shengxian; SU Xiaoyuan; CHEN Yonghui; WANG Nanshan

doi:10.7652/xjtuxb202603020

您当前的位置：

首页 >

文章列表页 >

Statistical Model and Experimental Validation of Normal Contact Stiffness for Hard-Coated Rough Surfaces Considering Substrate Deformation

更新时间：2026-03-09

- Statistical Model and Experimental Validation of Normal Contact Stiffness for Hard-Coated Rough Surfaces Considering Substrate Deformation
- Journal of Xi'an Jiaotong University Vol. 60, Issue 3, Pages: 210-219(2026)
- 作者机构：
  
  太原科技大学机械工程学院，030024，太原
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202603020
  CLC： TH113
- Received：30 June 2025，
  
  Published：10 March 2026
- 稿件说明：
移动端阅览
ZHANG Xueliang, ZHANG Shengxian, SU Xiaoyuan, et al. Statistical Model and Experimental Validation of Normal Contact Stiffness for Hard-Coated Rough Surfaces Considering Substrate Deformation[J]. Journal of Xi'an Jiaotong University, 2026, 60(3): 210-219.
DOI：

ZHANG Xueliang, ZHANG Shengxian, SU Xiaoyuan, et al. Statistical Model and Experimental Validation of Normal Contact Stiffness for Hard-Coated Rough Surfaces Considering Substrate Deformation[J]. Journal of Xi'an Jiaotong University, 2026, 60(3): 210-219. DOI： 10.7652/xjtuxb202603020.

摘要

为了更准确地预测硬涂层粗糙表面的接触刚度，建立了考虑基体变形的硬涂层粗糙表面法向接触刚度统计模型，并进行了实验验证。首先，推导建立了单个硬涂层微凸体弹性和弹塑性法向接触刚度模型，在此基础上，建立了考虑基体变形影响的硬涂层微凸体法向接触刚度模型，及考虑基体变形的硬涂层粗糙表面法向接触刚度统计模型。然后，对所建模型进行了仿真分析，研究了涂层厚度比、涂层与基体材料性能、基体表面塑性指数等对硬涂层粗糙表面法向接触刚度及接触载荷的影响规律。最后，进行了实验验证。结果表明：当考虑基体变形时，具有较厚且较硬涂层的粗糙表面，其法向接触刚度和接触载荷较大；当涂层粗糙表面的接触载荷不变时，随着基体表面塑性指数的增大，硬涂层粗糙表面的法向接触刚度随之增大；实验获取了基体材料为45钢、涂层材料为TiN的涂层粗糙表面法向接触刚度，其模型仿真计算结果较好吻合了实验数据，二者平均相对误差小于7%，说明了所建模型的正确性。

Abstract

To more accurately predict the contact stiffness of hard-coated rough surfaces

a statistical model for normal contact stiffness considering substrate deformation is established and experimentally validated.First

elastic and elastoplastic normal contact stiffness models for a single hard-coated asperity are derived and developed.Based on these

normal contact stiffness model for a hardcoated asperity accounting for substrate deformation effects is established

leading to a statistical model for normal contact stiffness of hard-coated rough surfaces incorporating substrate deformation. Next

simulation analyses are performed on the established models to investigate the effects of coating thickness ratio

material properties of the coating and substrate

and substrate surface plasticity index on the normal contact stiffness and contact load of hard-coated rough surfaces. Finally

experimental validation is conducted.The results show that when substrate deformation is considered

rough surfaces with thicker and harder coatings exhibit greater normal contact stiffness and higher contact loads.Under constant contact load

as the substrate surface plasticity index increases

the normal contact stiffness of hard-coated rough surfaces also increases.Experimental normal contact stiffness data are obtained for coated rough surfaces with a 45 steel substrate and TiN coating material.The simulation results of the model are in good agreement with the experimental data

with an average relative error of less than 7%

demonstrating the validity of the established model.

关键词

Keywords

references

IIDA K, ONO K.Design consideration of contact/nearcontact sliders based on a rough surface contact model[J]. Journal of Tribology, 2003, 125(3)：562-570.

HOGMARK S, JACOBSON S, LARSSON M.Design and evaluation of tribological coatings[J].Wear, 2000, 246(1/2)：20-33 .

杜建融，陶冠羽，曾路，等.TiAlSiN纳米复合涂层的研究进展[J].表面技术，2024，53(18)：31-54.

DU Jianrong，TAO Guanyu，ZENG Lu，et al. Research progress on TiAlSiN nanocomposite coatings[J].Surface Technology，2024，53(18)：31-54.

王恩泽，鲍崇高，邢建东.涂层对氧化铝/耐热钢基复合材料磨料磨损性能的影响[J].西安交通大学学报，2003，37(9)：945-948.

WANG Enze，BAO Chonggao，XING Jiandong. Effects of particle coatings on abrasive resistance of alumina/heat-resistant steel matrix composite at high temperature[J].Journal of Xi’an Jiaotong University，2003，37(9)：945-948.

王浩，张镕驿，席柯楠，等.耐热钢表面Cr 2 O 3 涂层原子掺杂后的抗氢脆性能与阻氢机理[J ] .西安交通大学学报，2025，59(10)：189-199.

WANG Hao，ZHANG Rongyi，XI Kenan，et al. Hydrogen embrittlement resistance and hydrogen barrier mechanism of atomically doped Cr 2 O 3 coatings on heatresistant steel[J ] .Journal of Xi’an Jiaotong University，2025，59(10)：189-199.

赵新波，屈治国，张剑飞，等.膨胀石墨和碳纳米管涂层对相变材料性能的影响[J].西安交通大学学报，2025，59(6)：63-72.ZHAO Xinbo，QU Zhiguo，ZHANG Jianfei，et al.

Effect of expanded graphite and carbon nanotubes coating on phase change materials properties[J].Journal of Xi’an Jiaotong University，2025，59(6)：63-72.

刘彦庆，宋余九.几种表面涂层组织和耐蚀性的研究[J].西安交通大学学报，1990(6)：129-130.

LIU Yanqing，SONG Yujiu.Study on microstructure and corrosion resistance of several surface coatings[J].Journal of Xi’an Jiaotong University，1990(6)：129-130.

HOLMBERG K, RONKAINEN H, LAUKKANEN A, et al. Friction and wear of coated surfaces：scales, modelling and simulation of tribomechanisms[J].Surface and Coatings Technology, 2007, 202(4/7)：1034-1049.

CHEN Z, ETSION I.The elastic-plastic contact behavior of rough surfaces with hard coatings[J].Tribology International, 2019, 134：435-442.

BELL T, MAO K, SUN Y.Surface engineering design：modelling surface engineering systems for improved tribological performance[J].Surface and Coatings Technology, 1998, 108-109：360-368.

COLE S J, SAYLES R S.Anumerical model for the contact of layered elastic bodies with real rough surfaces[J]. Journal of Tribology, 1992, 114(2)：334-340.

RAMACHANDRA S, OVAERT T C.Effect of coating geometry on contact stresses in two-dimensional discontinuous coatings[J].Journal of Tribology, 2000, 122(4)：665-671 .

BHUSHAN B, VENKATESAN S.Effective mechanical properties of layered rough surfaces[J].Thin Solid Films, 2005, 473(2)：278-295.

CHEN Zhou, GOLTSBERG R, ETSION I.Plasticity evolution in a coated sphere compressed by a rigid flat[J].Tribology International, 2016, 98：116-124.

WANG Tingjian, WANG Liqin, GU Le, et al. Stress analysis of elastic coated solids in point contact[J]. Tribology International, 2015, 86：52-61.

GOLTSBERG R, ETSION I, DAVIDI G.The onset of plastic yielding in a coated sphere compressed by a rigid flat[J].Wear, 2011, 271(11/12)：2968-2977.

GREENWOOD J A, WILLIAMSON J B P.Contact of nominally flat surfaces[J].Proceedings of the Royal Society of London：A Mathematical and Physical Sciences, 1966, 295(1442)：300-319.

廖山钧，张学良，廉义章.硬涂层粗糙表面接触刚度统计建模研究[J].润滑与密封，2025，50(6)：52-59.

LIAO Shanjun，ZHANG Xueliang，LIAN Yizhang. Research on statistical model of contact stiffness of hard-coated rough surfaces[J].Lubrication Engineering，2025，50(6)：52-59.

YEO C D, KATTA R R, POLYCARPOU A A.Improved elastic contact model accounting for asperity and bulk substrate deformation[J].Tribology Letters, 2009, 35(3)：191-203.

李玲，李治强，张健，等.含硬涂层结构的表面微观接触新模型[J].振动与冲击，2018，37(3)：195-201.

LI Ling，LI Zhiqiang，ZHANG Jian，et al. A new microcontact model for rough surface with a hard-coating[J]. Journal of Vibration and Shock，2018，37(3)：195-201.

李玲，王晶晶，史小辉，等.考虑基体变形的结合面连续光滑接触刚度模型[J].工程力学，2021，38 (12)：223-231 .

LI Ling，WANG Jingjing，SHI Xiaohui，et al. A continuous smooth contact stiffness model for joint surface considering substrate deformation[J]. Engineering Mechanics，2021，38(12)：223-231.

张伟，张学良，温淑花，等.考虑微凸体基体变形和相互作用的结合面法向接触刚度模型[J].西安交通大学学报，2020，54(6)：115-121.

ZHANG Wei，ZHANG Xueliang，WEN Shuhua，et al. A normal contact stiffness model of joint surfaces considering interaction of deformations of substrate and asperity[J].Journal of Xi’an Jiaotong University，2020，54(6)：115-121.

王晶晶，李玲，孙立泰，等.耦合基体变形与微凸体相互作用的结合面刚度模型[J].机械工程学报，2022，58(9)：190-199.

WANG Jingjing，LI Ling，SUN Litai，et al. Stiffness model of joint surface based on coupling of substrate deformation and asperity interaction[J].Journal of Mechanical Engineering，2022，58(9)：190-199.

CHEN Z, GOLTSBERG R, ETSION I.Auniversal model for a frictionless elastic-plastic coated spherical normal contact with moderate to large coating thicknesses[J].Tribology International, 2017, 114：485-493.

GOLTSBERG R, ETSION I.Auniversal model for the load-displacement relation in an elastic coated spherical contact[J].Wear, 2015, 322-323：126-132.

LI Ling, WANG Jingjing, SHI Xiaohui, et al. A modified elastoplastic contact stiffness model considering continuous smooth contact characteristics and substrate deformation[J].Acta Mechanica Solida Sinica, 2021 , 34(5)：754-765.

MCCOOL J I.Relating profile instrument measurements to the functional performance of rough surfaces[J]. Journal of Tribology, 1987, 109(2)：264-270.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Application of Conical Asperity in Contact Analysis of Rough Surfaces

Numerical Simulation of Heat-Moisture Barrier Performance of a Horizontal Air Curtain in Cold Storage

Mechanism and Optimal Control Strategy for Hysteresis in Rapid Dehumidification Response of Indirect Thermal Systems in Electric Vehicles

Electrothermal Coupling Research on the Evolutionary Law of Anti-Corona Performance for High-Altitude Air-Cooled Generators

A Fast Calculation Method for Thermal Flow Fields in Transformer Windings Based on PI-DeepONet

Related Author

田红亮

董元发

钟先友

王骁鹏

郤能

郑金华

Related Institution

College of Mechanical and Power Engineering, China Three Gorges University

⁰