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The purpose of this paper is to develop a general mathematic approach to model the microstructures of porous structures produced by additive manufacturing (AM), which will result in fractal surface topography and higher roughness that have greater influence on the performance of porous structures.

The overall shapes of pores were modeled by triply periodic minimal surface (TPMS), and the micro-roughness details attached to the overall pore shapes were represented by Weierstrass–Mandelbrot (W-M) fractal representation, which was integrated with TPMS along its normal vectors. An index roughly reflecting the irregularity of fractal TPMS was proposed, based on which the influence of the fractal parameters on the fractal TPMS was qualitatively analyzed. Two complex samples of real porous structures were given to demonstrate the feasibility of the model.

The fractal surface topography should not be neglected at a micro-scale level. In addition, a decrease in the fractal dimension D_s may exponentially make the topography rougher; an increase in the height-scaling parameter G may linearly increase the roughness; and the number of the superposed ridges has no distinct influence on the topography. Furthermore, the synthesis method is general for all implicit surfaces.

The method provides an alternative way to shift the posteriori design paradigm of porous media to priori design mode through numeric simulation. Therefore, the optimization of AM process parameters, as well as the porous structure, can be potentially realized according to specific functional requirement.

The synthesis of TPMS and W-M fractal geometry was accomplished efficiently and was general for all implicit freeform surfaces, and the influence of the fractal parameters on the fractal TPMS was analyzed more systematically.

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 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.

The purpose of this paper is to provide a static friction coefficient prediction model of rough contact surfaces based on the contact mechanics analysis of elastic-plastic fractal surfaces.

In this paper, the continuous deformation stage of the multi-scale asperity is considered, i.e. asperities on joint surfaces go through three deformation stages in succession, the elastic deformation, the elastic-plastic deformation (the first elastic-plastic region and the second elastic-plastic region) and the plastic deformation, rather than the direct transition from the elastic deformation to the plastic deformation. In addition, the contact between rough metal surfaces should be the contact of three-dimensional topography, which corresponds to the fractal dimension D (2 < D < 3), not two-dimensional curves. So, in consideration of the elastic-plastic deformation mechanism of asperities and the three-dimensional topography, the contact mechanics of the elastic-plastic fractal surface is analyzed, and the static friction coefficient nonlinear prediction model of the surface is further established.

There is a boundary value between the normal load and the fractal dimension. In the range smaller than the boundary value, the normal load decreases with fractal dimension; in the range larger than the boundary value, the normal load increases with fractal dimension. Considering the elastic-plastic deformation of the asperity on the contact surface, the total normal contact load is larger than that of ignoring the elastic-plastic deformation of the asperity. There is a proper fractal dimension, which can make the static friction of the contact surface maximum; there is a negative correlation between the static friction coefficient and the fractal scale coefficient.

In the mechanical structure, the research and prediction of the static friction coefficient characteristics of the interface will lay a foundation for the understanding of the mechanism of friction and wear and the interaction relationship between contact surfaces from the micro asperity-scale level, which has an important engineering application value.

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.

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 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.

The purpose of this paper is to construct a continuous time series model to study the thermal creep of rough surfaces in contact.

For normal loading, the contact between rough surfaces can often be modeled as the contact of an effective surface with a rigid fiat surface. A solution for the deformation of such equivalent surface, generated using fractal geometry, can be modified. However, in this study only the case of a single rough surface in contact with a rigid flat surface is considered. In the interface, the material is assumed to follow the idealized constitutive viscoelastic standard linear solid (SLS) model. Fractal geometry, through Cantor set theory, is utilized to model the roughness of the surface.

An asymptotic time series power law is obtained, which associates the creep load, the buck temperature and the creep of the fractal surface.

This law is only valid as long as the creep is of the size of the surface roughness. The modified model admits an analytical solution for the case when the behavior is linear viscoelastic. The proposed model shows a good agreement when compared with experimental results available in the literature.

In this paper, the influence of fractal interface geometry to the evolution of the friction mechanism is studied. The paper is based on fractal approaches for the modeling of the multiscale self‐affine topography of these interfaces. More specifically, these approaches are based on scale‐independent parameters such as the fractal dimension. Here, friction between rough surfaces is assumed to be the result of the gradual plastification of the fractal interface asperities. In order to study the resulting highly nonlinear problem a variational formulation is used in order to describe contact between the interfaces. The numerical method used here leads to the successive solution of quadratic optimization problems. Finally, structures with different fractal interfaces are analyzed in order to obtain results for the relation between the fractal dimension and the overall response of the structures.

The purpose of this paper is to propose a fractal model of thermal contact conductance (TCC) of rough surfaces based on cone asperity.

A detailed numerical study is conducted to examine the effects of contact load, fractal dimensional, fractal roughness and material properties on the TCC of rough surfaces.

The results indicate that when the fractal dimension D is less than 2.5, the TCC of rough surfaces increases nonlinearly with the increase of the contact load. However, when the fractal dimension D is greater than or equal to 2.5, the TCC of rough surfaces increases linearly with the increase of the contact load; the TCC of the rough surfaces increases with the increase of the fractal dimension D and the decrease of the fractal roughness G; the material parameters also have an influence on the TCC of the rough surfaces, and the extent of the effect on the TCC is related to the fractal dimension D.

A fractal model of TCC of rough surfaces based on cone asperity is established in this paper. Some new results and conclusions are obtained from this work, which provides important theoretical guidance for further study of TCC of rough surfaces.