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Elastohydrodynamic Lubrication Interface Stiffness and Damping Considering Asperity Lateral Contact

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Abstract

Elastohydrodynamic lubrication (EHL) point contact occurs between two rough surfaces at the mesoscopic level, while the interaction of rough surfaces involves contact between asperities at the microscale level. In most cases, the contact between asperities within an interface takes the form of lateral contact rather than peak contact. Regions devoid of contact asperities are filled with lubricating oil. However, conventional models often oversimplify lateral contact forms as interactions between asperities and a smooth, rigid plane. These simplifications fail to accurately represent the true contact conditions and can lead to inaccuracies in the analysis of EHL’s contact performance. To address this issue, we have developed a novel EHL interface model comprising two rough surfaces. This model allows us to explore the influence of asperity height, contact angle, and contact azimuth angle on EHL interface performance.

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Data Availability

Data will be made available on request.

Abbreviations

\(A_{n}\) :

The nominal contact area

\(W\) :

The normal load

\(R\) :

The radius of asperity

\(z\) :

The height of asperity

\(h\) :

The average gap (the mean film thickness)

\(\varphi\) :

The asperity contact angle

\(\theta\) :

The contact azimuth angle

\(F_{in}\) :

The normal force on asperity

\(n_{i}\) :

The normal component force

\(\tau_{i}\) :

The tangential component force

\(h_{i}\) :

The horizontal component force

\(\delta\) :

The asperity deformation

\(\delta_{c}\) :

The critical deformation

\(\delta_{m}\) :

The amplitude of the deformation

\(S_{k}\) :

The hardness coefficient

\(\nu\) :

The equivalent Poisson’s ratio

\(E\) :

The composite Young’s modulus

\(G\) :

The shear modulus

\(\omega\) :

The angular frequency

\(t\) :

The time

\(T\) :

The period

\(k_{in}\) :

The asperity contact stiffness

\(k_{idn}^{{}}\) :

The average contact stiffness

\(e_{in}^{{}}\) :

The asperity contact energy dissipation

\(\delta^{*}\) :

The asperity deformation (The superscript asterisk (*) denotes dimensionless quantities.)

\(\zeta^{*}\) :

The asperity displacement

\(\zeta_{m}^{*}\) :

The displacement amplitude

\(\mu_{s}\) :

The friction coefficient

\(c_{i\tau }^{*}\) :

The tangential contact damping

\(k_{i\tau }^{*}\) :

The tangential contact stiffness

\(\phi (z)\) :

The distribution of asperity heights

\(\sigma_{z}\) :

The standard deviation of the asperity height distribution

\(\eta_{a}\) :

The density of asperities

\(\Gamma (\varphi ,\theta )\) :

The joint probability density function of asperity contact angles and contact azimuth angles

\(M\) :

The asperity number

\(m\) :

The number of contacting asperities

\(\sigma_{\varphi }\) :

The standard deviations of asperity contact angles

\(\sigma_{\theta }\) :

The standard deviations of asperity contact azimuth angle

\(\Delta^{*}\) :

The normal deformation of the interface

\(F_{s}^{*}\) :

The solid asperity contact force

\(K_{s}^{*}\) :

The solid contact stiffness

\(C_{s}^{*}\) :

The solid contact damping

\(A_{l}\) :

The total area of the closed oil pits

\(p_{l}\) :

The normal dynamic force of the squeeze oil film

\(p_{l}\) :

The normal dynamic force of the squeeze oil film

\(\overline{{p_{l} }}\) :

The mean pressure

\(B\) :

The width of contact area

\(\eta_{l}\) :

The lubricating oil viscosity

\(\phi_{x} ,\phi_{y}\) :

Two pressure flow factors

\(\phi_{c}\) :

The contact factor

\(\overline{h}_{T}^{*}\) :

The expectation of dimensionless local film thickness

\(\chi\) :

The end leak coefficient

\(F_{l}^{*}\) :

The dimensionless liquid contact force

\(K_{l}^{*}\) :

The liquid contact stiffness

\(C_{l}^{*}\) :

The liquid contact damping

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Funding

This research is supported by the National Natural Science Foundation of China (No. 52005401, No. 52375127), the Cultivation Scientific Research Project of Panzhihua University (2021PY001), the Opening Project of Material Corrosion and Protection Key Laboratory of Sichuan province (2022CL15), and the Project for Science and Technology Plan of Henan Province (212102210445).

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Authors and Affiliations

  1. School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Zhiqiang Gao, Yu Zhang, Lixia Peng, Weiping Fu & Wen Wang

  2. School of Intelligent Manufacturing, Panzhihua University, Panzhihua, 617000, China

    Xian Wei

  3. Material Corrosion and Protection Key Laboratory of Sichuan Province, Sichuan University of Light Chemical Technology, Yibin, 644002, China

    Xian Wei

  4. School of Mechanical Engineering, Anyang Institute of Technology, Anyang, 455099, China

    Yanfang Zhu

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  1. Zhiqiang Gao
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  2. Yu Zhang
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Contributions

ZG: Formal analysis, Writing original draft, Funding acquisition, Writing review & editing; YZ: Investigation; XW: Software, Visualization, Funding acquisition. YZ: Conceptualization, Methodology; WF: Validation, Visualization, Supervision; WW: Project administration.

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Correspondence to Weiping Fu.

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Gao, Z., Zhang, Y., Wei, X. et al. Elastohydrodynamic Lubrication Interface Stiffness and Damping Considering Asperity Lateral Contact. Acta Mech. Solida Sin. 37, 109–123 (2024). https://doi.org/10.1007/s10338-023-00441-9

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