In this work, a new formulation of elastic–plastic contact model for the normal contact between rough surfaces is proposed based on the fractal theory. The surface topography is described using the modified one-variable Weierstrass–Mandelbrot fractal function. A new elastoplastic asperity contact model is developed based on the contact mechanics combined with the continuity and smoothness of mean contact pressure and contact load across different deformation regimes from elastic to elastoplastic, and from elastoplastic to fully plastic. The contact stiffness of a single asperity in the three deformation regimes of fully plastic, elastoplastic and elastic is derived, which changes smoothly at transit points between different deformation modes and overcomes the shortcoming of discontinuity derived from previous model. The contact stiffness and contact load of the whole surface in the three deformation regimes are formulated by integrating the micro-asperity contact. The difference between contact stiffness calculated from the plastic–elastoplastic–elastic three contact regimes and plastic–elastic two contact regimes is not obvious for surface with rougher topograph; however, for surface with smoother topograph, the two contact regimes predict a much smaller contact stiffness. The relationship of the normal contact stiffness and the normal contact force follows a power law function for the fractal surface contact considering three deformation regimes. The power exponent is nonlinearly dependent on the fractal dimension, which is different from the linear relationship for the purely elastic contact.
This is a preview of subscription content, log in to check access.
This work was supported by the National Natural Science Foundation of China [Grant Number 51775037] and Open Project Foundation of the State Key Laboratory of Traction Power in Southwest Jiaotong University [Grant Number TPL1713].
Gonzalez-Valadez M, Baltazar A, Dwyer-Joyce RS (2010) Study of interfacial stiffness ratio of a rough surface in contact using a spring model. Wear 268:373–379CrossRefGoogle Scholar
Du F, Hong J, Xu Y (2014) An acoustic model for stiffness measurement of tribological interface using ultrasound. Tribol Int 73:70–77CrossRefGoogle Scholar
Bazrafshan M, Ahmadian H, Jalali H (2014) Modeling the interaction between contact mechanisms in normal and tangential directions. Int J Non Linear Mech 58:111–119CrossRefGoogle Scholar
Zou HT, Wang BL (2015) Investigation of the contact stiffness variation of linear rolling guides due to the effects of friction and wear during operation. Tribol Int 92:472–484CrossRefGoogle Scholar
Oskar EL, Nordborg A, Arteaga IL (2016) The influence of surface roughness on the contact stiffness and the contact filter effect in nonlinear wheel-track interaction. J Sound Vib 366:429–446CrossRefGoogle Scholar
Greenwood JA (1966) Williamson JBP (1966) Contact of nominally flat surfaces. Proc R Soc Lond Ser A 295:300–319CrossRefGoogle Scholar
Nayak PR (1971) Random process model of rough surfaces. Trans ASME J Lubr Technol 93:398–407CrossRefGoogle Scholar
Xiao HF, Shao YM, Brennan MJ (2015) On the contact stiffness and nonlinear vibration of an elastic body with a rough surface in contact with a rigid flat surface. Eur J Mech A Solids 49:321–328CrossRefGoogle Scholar
Zhao YS, Song XL, Cai LG et al (2016) Surface fractal topography-based contact stiffness determination of spindle-toolholder joint. Proc Inst Mech Eng Part C J Mech Eng Sci 230(4):602–610CrossRefGoogle Scholar
Liou JL, Lin JF (2010) A modified fractal microcontact model developed for asperity heights with variable morphology parameters. Wear 268:133–144CrossRefGoogle Scholar
Kogut L, Etsion I (2002) Elastic-plastic contact analysis of a sphere and rigid flat. J Appl Mech 69:657–662CrossRefGoogle Scholar
Mandelbrot BB (1975) Stochastic models for the Earth’s relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. Proc Natl Acad Sci 72(10):3825–3828MathSciNetCrossRefGoogle Scholar
Majumdar A, Bhushan B (1991) Fractal model of elastic-plastic contact between rough surfaces. J Tribol 113(1):1–11CrossRefGoogle Scholar
Yan W, Komvopoulos K (1998) Contact analysis of elastic-plastic fractal surfaces. J Appl Phys 84(7):3617–3624CrossRefGoogle Scholar