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This paper aims to propose a semi-analytical model to investigate the elastic-plastic contact between fractal rough surfaces. Parametric studies have been performed to analyze the dependencies between the contact properties and the scale-independent fractal parameters.

A modified two-variable Weierstrass-Mandelbrot function has been used to build the geometrical model of rough surfaces. The computation program was developed using software MATLAB R2015a. The results have been qualitatively validated by the existing theoretical and experimental results in the literature.

In most cases, a nonlinear relation between the load and the displacement of the rigid plane is found. Only under the condition of larger loads, an approximate linear relation can be seen for great D and small G values. (D: fractal dimension and G: fractal roughness).

The contact model of the cylindrical joints (conformal contact) with radial clearance is constructed by using the fractal theory and the Kogut-Etsion elastic-plastic contact model, which includes purely elastic, elastic-plastic and fully plastic contacts. The present method can generate a more reliable calculation result as compared with the Hertz contact model and a higher calculation efficiency as compared with the finite element method for the conformal contact problem.

The purpose of this paper is to calculate the meshing stiffness of nutation face gear considering the roughness, establish the calculation method of time-varying meshing stiffness of rough tooth surface and analyze the influence of roughness, load and other factors on the meshing stiffness of tooth surface.

The Weierstrass–Mandelbrot (W-M) function in the Majumdar–Bhushan model is used to characterize the rough contact line of the tooth surface, the normal height and radius of the micro convex body are calculated and the contact flexibility of the contact point of the tooth surface is obtained. The contact flexibility and the bending shear deformation flexibility obtained previously are substituted into the improved deformation compatibility equation for iterative calculation, and the time-varying meshing stiffness of the nutation face gear considering the roughness is obtained.

Compared with ABAQUS finite element simulation results, it is found that the meshing stiffness curve of rough tooth surface is more gentle than that of smooth tooth surface, the meshing stiffness value is smaller and the meshing stiffness change is smaller at the position where the number of gear teeth coincide changes.

In the process of calculating contact deformation, the fractal theory W-M function is used to characterize the contact line of the rough nutation face gear, and the deformation coordination condition considering roughness is improved. Therefore, the method of time-varying meshing stiffness considering roughness can obtain more accurate results, which provides theory and data for the subsequent dynamics analysis of the nutation face gear transmission.

The purpose of this paper is to explore the effect of surface roughness characterized by fractal geometry on squeeze film damping characteristics in damper of the linear rolling guide, which has not been studied so far.

The stochastic model of film thickness between rail and damper is established by using the two-variable Weierstrass–Mandelbrot function defining multi-scale and self-affinity properties of the rough surface topography. The stochastically averaged Reynolds equation is solved by using the variables separation method to further derive the film pressure distribution, the damping coefficient, the damping force and squeeze film time. The effect of surface roughness on squeeze film damping characteristics of the damper is analyzed and discussed through simulation.

By comparing cases of the rough surface for different fractal parameters and the smooth surface, it is shown that for the isotropic roughness structure, the presence of surface roughness of the damper decreases the squeeze film damping characteristics. It is found that roughness effect on the damping coefficient is associated with the film thickness. In addition, the vibration amplitude effect is negligible for the damper of the linear rolling guide.

To investigate the random surface roughness effect, the rough surface topography of damper of the linear rolling guide is characterized by using the fractal method instead of the traditional mathematical statistics method.

This study aims to investigate the influence of surface texture distribution in respect to the procedure of pavement surface wear on friction performance.

The Weierstrass–Mandelbrot (W-M) equation is used to appropriate pavement surface profile. Through this approximation, artificial rough profiles by combining fractal parameters and conventional statistical parameters for different macro-texture are created to simulate the procedure of pavement surface wear. Those artificial profiles are then imported into discrete element model to calculate the interaction forces and friction coefficient between rolling tire and road. Furthermore, wavelet theory is used to decompose the profiles into different scales and explore the correlation between the profiles of each scale and pavement friction.

The influence of tire vertical displacement (TVD) on friction coefficient is greater than fractal dimension of road surface texture. When TVD decreases, the profiles can provide higher friction, but the rolling stability of tire is poor. The optimal fractal dimension of road surface is about 1.5 when considering friction performance. The pavement friction performance improves with wavelength from 0.4 to 6.4mm and decreases with wavelength from 12.8 to 51.2mm.

Artificial fractal curves are generated and analyzed by combining W-M function with traditional parameter, which can also be used to analyze the influence of texture distribution on other pavement performance. The preliminary research provides a potential approach for the evaluation of pavement friction performance.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2019-0499/

Hydro-viscous drive (HVD) clutches are widely used in equipment requiring soft start, such as fans and pumps, to transmit torque and adjust speed by changing the gap distance between friction pairs. This paper aims to propose a novel two-parameter evaluation method for HVD during the mixed lubrication stage. The objective is to develop an effective model that establishes the relationship between these parameters and the actual surface topography.

In the presented methods, the fractal features of the real manufacturing surface are calculated based on the power spectrum function by the ultra-depth three-dimensional microscope. After that, the hybrid friction model of the friction plate is established based on mixed elasto-hydrodynamic lubrication theory, boundary friction model and fractal theory. Then the torque and load bearing characteristics of the clutch are obtained, and the influences of the surface fractal features are investigated and discussed. Finally, the Weierstrass–Mandelbrot function is adopted for the surface topography characterization and evaluation.

The results indicate that the proposed method exhibits good accuracy, while the speed difference between the friction pair exceeds 2,500 rpm. It is concluded that this paper proposed a way to evaluate the torque and loading capacity of HVD considering the real manufacturing surface topography and is helpful for surface optimization.

The originality and value of this study lie in its development of a novel torque and load bearing capacity evaluation method for HVD in mixed lubrication stage, considering manufacturing surface topography and describing the real manufacturing surface.

The purpose of this paper is to study the effects of surface roughness on the lubrication performances of the linear rolling guide, which provides theoretical guidance for its lubrication design.

The two-variable Weierstrass–Mandelbrot function is used to represent the random and multi-scale characteristics of the rough surface topography. The elastohydrodynamic lubrication (EHL) model of contact between the steel ball and raceway is built. The full numerical solutions of the pressure and film thickness are obtained by using the multi-grid technique.

The presence of surface roughness can cause the random fluctuations of the pressure and film thickness, and the fluctuations can become more dramatic for the rougher surfaces. It is also found that the film characteristics can be influenced significantly by the working conditions, such as the load, velocity and ambient viscosity of lubricants.

Characterization of surface topographies regarding EHL problems in the past studies cannot reflect random and multi-scale characteristics. In this paper, the fractal-based method is introduced to analysis of the point-contact micro-EHL. It reveals the mechanism and law of contact lubrication influenced by the fractal surface roughness and enriches the lubrication principle and method of the linear rolling guide.

This paper aims to study the relationship between normal contact stiffness and contact load. It purpose a new calculation model of the normal contact stiffness of joint surfaces by considering the elastic–plastic critical deformation change of asperities contact.

The paper described the surface topography of joint surfaces based on fractal geometry, and fractal parameters and of fractal function derived from measurement data. According to the plastic–elastic contact theory, the contact deformation characteristic of asperities was analyzed; the critical deformation estimation model was presented, which expressed critical deformation as the function of fractal parameters and contact deformation; the contact stiffness calculation model of single asperity was brought forward by considering critical deformation change.

The paper combined the surface topography description function, analyzed the asperity contact states by considering the critical deformation change, and calculated normal contact stiffness based on fractal theory and contact deformation analysis. The comparison between theoretical contact stiffness and experimental data indicated that the theoretical normal contact stiffness agreed with the experimental data, and the estimation model for normal contact stiffness was appropriate.

Owing to the possibility of plastic deformation during the loading process, the experimental curve between the contact stiffness and the contact load is nonlinear, resulting in an error between the experimental results and the theoretical calculation results.

The paper established the relationship between critical deformation and fractal surface topography by constructing asperity distribution function. The paper proposed a new normal contact stiffness calculation model of joint surfaces by considering the variation of critical deformation in contact process.

The purpose of this paper is to reveal the dynamic contact characteristics of the slip ring. Dynamic contact resistance models considering wear and self-excited were established based on fractal theory.

The effects of tangential velocity, stiffness and damping coefficient on dynamic contact resistance are studied. The relationships between fractal parameters, wear time and contact parameters are revealed.

The results show that the total contact area decreases with the friction coefficient and fractal roughness under the same load. Self-excited vibration occurs at a low speed (less than 0.6 m/s). It transforms from stick-slip motion at 0.4 m/s to pure sliding at 0.5 m/s. A high stiffness makes contact resistance fluctuate violently, while increasing the damping coefficient can suppress the self-excited vibration and reduce the dynamic contact resistance. The fractal contact resistance model considering wear is established based on the fractal parameters models. The validity of the model is verified by the wear tests.

The results have a great significance to study the electrical contact behavior of conductive slip ring.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-09-2023-0300/

Micro-texture is processed on the surface to reduce the friction of the contact surface, and its application is more and more extensive. The purpose of this paper is to create a texture function model to study the influence of surface parameters on the accuracy of the simulated surface so that it can more accurately reflect the characteristics of the real micro-textured surface.

The microstructure function model of rough surfaces is established based on fractal geometry and polar coordinate theory. The offset angle θ is introduced into the fractal geometry function to make the surface asperity normal perpendicular to the tangent of the surface. The 2D and 3D contour surfaces of the surface groove texture are analyzed by MATLAB simulation. The effects of fractal parameters (D and G) and texture parameter h on the curvature of the surface micro-texture model were studied.

This paper more accurately characterizes the textured 3D curved surface, especially the surface curvature. The scale coefficient G significantly affects curvature, and the influence of fractal dimension D and texture parameters on curvature can be ignored.

The micro-texture model of the rough surface was successfully established, and the range of fractal parameters was determined. It provides a new method for the study of surface micro-texture tribology.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-09-2023-0298/

The objective of the present work is to find an alternative approach for gearbox condition monitoring using wear particle characterization incorporated with image vision systems.

It is a quite well‐known phenomenon that wear generates whenever two metallic bodies have contact with each; other hence the present work tries to investigate the effect of improper lubrication in the gearbox due to wear particle generation between gear wheels. Since the identification of wear for machine condition monitoring needs much expertise knowledge and is time‐consuming using the conventional process, fractal mathematics with image morphological analysis has been utilized to overcome this situation in the present work.

The type of wear has been found for the present method by utilizing the lubricant used in the system ferrographically and a great deal of image processing has been done to characterize the type of particle so that the proper maintenance strategy can be undertaken.

Wear particle characterization is a quite common method in maintenance engineering, especially when fault diagnosis of any equipment is concerned. In the present work, the CCD acquisition of the images has been done for different particles, but one analysis amongst them has been shown in this paper. Among all other methodologies, the new technique of fractal mathematics has been used in the present work to minimize the imaging hazards and to make the system more user‐friendly.