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The friction coefficient is one of the key parameters in the tribological performance of mechanical systems. In the condition of light normal load and low rotation speed, the friction coefficients of ball-on-disc with rough surface in dry sliding contact are experimentally investigated. Friction tests are carried out under normal load 2–9 N, rotation speed 20–48 rpm at room temperature, and surface roughness 0.245–1.010 μm produced by grinding, milling, and turning. Results show that the friction coefficient increases first and then becomes stable, in which the running-in and steady-state periods are included. With the growth of normal load and rotation speed, or the decline of surface roughness, the duration and fluctuation of the running-in period verge to reduce. The whole rising slope of the friction coefficient in the running-in period goes up more quickly with the increment of rotation speed, and it ascends more slowly as normal load enlarges. In terms of the steady-state period, the deviation of the friction coefficient shows a dwindling trend when normal load or rotation speed grows, or surface roughness descends. As normal load or rotation speed rises, the value of the friction coefficient rises first and then drops. Additionally, the mean value of the friction coefficient in steady-state is approximately independent of surface roughness. [ABSTRACT FROM AUTHOR]

• Multi-stage contact model of interface as variation of contact degree is proposed. • Asperity deformation depends on contact force and shows nonlinearity at length scale. • Each contact stage is distinct as various deformation modes of multi-scale asperities. • Inherent critical contact force between two stages of surface is decided by morphology. A novel multi-stage contact model of fractal rough surfaces is proposed in this paper. Actual asperity deformation depending on contact degree is derived at length scale, based on which, the actual deformation mode of asperity is analyzed. In accordance with deformation modes of multi-scale asperities, the contact behavior of the whole surface is distinguished into five stages as the increment of contact force. A complete model of contact characteristics across multi-stage is established, and the corresponding mathematical analytical solution of each stage is provided. Accordingly, the relationship between contact force, normal stiffness, and real contact area are analyzed under the effects of fractal factors. The simulation results of the developed model are also compared with that of available models and experimental data. [ABSTRACT FROM AUTHOR]

In this work, the normal contact stiffness of lubricated rough interface is evaluated theoretically by describing the lubricated rough interface as an equivalent thin layer. Layer parameters, including equivalent thickness and effective Young's modulus, are used to characterize the normal contact stiffness by incorporating the contributions of asperity contact and lubricant contact simultaneously. On the basis of layer parameters, the normal contact stiffness of lubricated rough interface is obtained as a function of interfacial separation, surface topography, and properties of contacting solids and lubricants. Effects of surface topographies and lubricant types on the normal contact stiffness are investigated at varying interfacial separations and contact area fractions. The proportion of solid stiffness and lubricant stiffness from the total normal stiffness is also discussed. Numerical solutions reveal that the normal contact stiffness depends sensitively on the lubricant property at initial contact, whereas the influences of surface topographies become obvious with the decrement of interfacial separation or increment of contact area fraction. Comparisons between the predicted values of normal contact stiffness and experimental data for both dry interface and lubricated interface are presented to validate the rationality of the developed model. [ABSTRACT FROM AUTHOR]

In this paper, a method for evaluating the contact stiffness ratio of the elastic rough interface is proposed. The rough contact interface subjected to normal load is replaced by an equivalent thin layer with isotropic material. The interfacial stiffness ratio is characterized using the material parameters of the thin layer. The shear modulus and Young's modulus of the thin layer are determined by introducing the stuck length coefficient combined with the micro-contact analysis of the deformed asperity. The derived stiffness ratio is related to the surface topography, interfacial separation, material properties of the contacting bodies, and the stuck length coefficient. The implicit solution of the stuck length coefficient is also obtained. Variations of the stiffness ratio with the interfacial separation and the normal force are analyzed for different surface topographies and stuck length coefficients. Comparisons between the interfacial stiffness ratio of the proposed method and the experimental results as well as the calculated values of existing models are performed. [ABSTRACT FROM AUTHOR]

Contact stiffness is an important parameter for describing the interface characteristics in many engineering applications. In this paper, five different statistical micro-models including the Greenwood-Williamson (GW), Zhao-Maietta-Chang (ZMC), Kogut-Etsion (KE), Jackson-Green (JG) and Brake are employed to predict the normal contact stiffness for rough surface contact. It is found that the expressions of contact stiffness obtained using the statistical micro-models are very complex and the direct relationship between the contact stiffness and normal load is not available. Accordingly, an explicit approximated expression for contact stiffness is established in terms of normal load based on the results of numerical simulations. The normal contact stiffness as a function of normal load can be approximated using a power law, in which the coefficient and power are related to surface roughness parameters, material properties as well as nominal contact area. The close agreement between the predicted results and full numerical simulations verify the accuracy of the established explicit expression. The contact stiffness calculated using the predictive expressions are also compared with available experimental results from both ultrasonic method and contact resonance method. Further, the explicit expression of contact resonance frequency for rough surface contact with respect to the normal load is also provided, which can be used to evaluate the contact resonance frequency. The predicted contact resonance frequency is also validated through comparing with experimental results. • Five different statistical micro-models are employed to predict the normal contact stiffness for rough surface contact. • Direct relationship between contact stiffness and normal load is not available using the statistical micro-models. • An explicit approximated expression for contact stiffness is established in terms of normal load. • Predictive contact stiffness values are verified using available experimental results. [ABSTRACT FROM AUTHOR]

Based on the continuity of length scale for asperities, a complete model of normal stiffness between curved fractal surfaces considering friction factor is proposed. Through the coupling of critical base diameter and contact area, deformation modes of all asperities are determined, and contact stiffness of the whole rough surface is derived by double integral. Accordingly, effects of contact load, surface topography, friction factor, size parameters and material properties on the contact stiffness are investigated. Results show that contact stiffness depends sensitively on the fractal dimension, and exhibits nonmonotonic characteristics as fractal roughness varies across scales. Finally, predicted values of normal stiffness are compared with existing contact models as well as experimental data. [Display omitted] • A revised contact model between curved friction surfaces is proposed based on continuous length scales. • The proposed critical length scales are inherent properties of fractal surfaces. • Deformation modes of asperities are determined by incorporating the critical length scale and contact area simultaneously. • The relationship of stiffness and fractal roughness shows nonmonotonic across scales and the turning point is affected by the fractal dimension. [ABSTRACT FROM AUTHOR]

• An analytical model is developed to evaluate the interfacial stiffness ratio theoretically considering the interface as an equivalent thin layer. • Effective moduli of the thin layer are derived by a homogenization process of the deformed asperities over the whole rough surface. • The interfacial stiffness ratio depends on surface topographies, interfacial separations, and material properties of contacting bodies. • The interfacial stiffness ratios predicted by the proposed model are basically consistent with experimental results. This work presents a semi-analytical model to evaluate the interfacial stiffness ratio of stationary contacts between rough surfaces. The rough contact interface is described as a homogenized thin layer with effective moduli, which are employed to characterize the ratio of the tangential to normal contact stiffness. In conjunction with the micro-contact analysis of the deformed asperity, effective moduli of the homogenized layer are determined by an ensemble average process of the moduli produced by deformed asperities made over the rough interface. Results show that the sought ratio is related to the surface topography, interfacial separation, and material properties of contacting bodies. Variations of the interfacial stiffness ratio with the applied load for different surface topographies are presented. The proposed model of the stiffness ratio is verified by comparing with the previous models and experimental results eventually. [ABSTRACT FROM AUTHOR]