Fractal Rough Surface Research Articles

In-situ measurements of contact evolution for fractal rough surfaces under normal compression

The contact interface plays a key role in the overall functionality and stability of structures. Understanding the evolution of the contact interface over time and its dependency on materials and load is crucial for functional integrity and operational safety assessment. In this study, we employ in-situ three-dimensional X-ray computed tomography (3DXRCT) to examine the creep behavior of 3D-printed surfaces exhibiting various roughness under constant normal compression. We observe that the overall contact area enlargement during the contact creep decreases with roughness amplitude and fractal dimension. The variation of interfacial separation distance is found to increase with roughness amplitude and decrease with fractal dimension. Correlation analysis reveals that the microcontact size played a more important role than the asperity shape in determining the microcontact enlargement. By examining the calculated interfacial strains extracted from XRCT measurements, significant deformations are found to occur at the non-contacting zones, indicating strong asperity interactions. This study offers high-resolution experimental measurements and unravels the asperity micromechanics for contact creep on rough surfaces, providing insights into understanding and optimizing the performance of rough interfaces.

A fractal model of rough surfaces based on ellipsoidal asperities

PurposeThis study aims to use fractal theory to investigate the contact mechanics of two bidirectional anisotropic surfaces, taking into account the friction coefficient of the contact interface. This study introduces a model that centers on normal contact load and contact stiffness, providing an extensive framework to elucidate the interactions between these surfaces.Design/methodology/approachThe research adopts the Weierstrass–Mandelbrot (W-M) function for simulating bidirectional surface profiles. Through the application of elastic-plastic contact theory, it evaluates the contact area and load of a singular asperity across elasticity, elastoplasticity and plasticity phases. The contact load and stiffness of the rough surface are determined using a refined asperity density distribution function, and these findings are juxtaposed with extant models to validate their precision and rationality.FindingsThe study delineates the influence of fractal dimension (D), surface roughness (G), ellipse eccentricity (e) and friction coefficient (µ) on the contact area, load and stiffness. It reveals that the contact area enlarges with the fractal dimension (D) yet diminishes with increased eccentricity (e), roughness (G) and friction coefficient (µ). These elements considerably affect the contact load and stiffness, underscoring their significance in comprehending surface interactions.Originality/valueThis study applies fractal theory to analyze the contact mechanics of bidirectional anisotropic surfaces, considering the geometry and mechanics of ellipsoidal asperities on rough surfaces to develop a contact mechanics model. This model clarifies the deformation of an asperity in normal contact, presenting a more rational alternative to current models.

Tangential contact stiffness modeling between fractal rough surfaces with experimental validation

Tangential contact stiffness modeling between fractal rough surfaces with experimental validation

Adhesive Contact of Elastic Solids with Self-Affine Fractal Rough Surfaces

Adhesive Contact of Elastic Solids with Self-Affine Fractal Rough Surfaces

Fractal surface-based three-dimensional modeling to study the role of morphology and physiology in human skin friction

Human skin plays an important role in our perception of contact made throughout the day. In this work, we study the interplay of various morphological and physiological factors that dictate its contact mechanics. A hybrid computational-empirical approach is developed to model skin friction and to understand the role of roughness in contact mechanics of human skin variations in structural properties. A fractal rough surface is considered to model the skin surface. A layered three-dimensional finite element model is generated with stratum corneum, viable epidermis, and dermis which is further used to determine its mechanical response under normal loading. An empirical relationship is then used to predict the coefficient of friction. The effects of varying the Young's modulus, roughness parameters, thickness of stratum corneum and domain size are studied. Simulations are performed for multiple realizations to quantify statistical variations. Our results show that the proposed approach can replicate several experimental findings from the literature such as the decrease in skin friction with humidity and increasing roughness. The study provides qualitative and quantitative insight into the role of roughness in the contact mechanics of human skin while accounting for the effects of micro-level interfacial phenomena.

Theoretical analysis and numerical simulation of methane adsorption behavior on rough surfaces featuring fractal property

This work focuses on the control mechanism of adsorption behavior from rough surfaces featuring fractal property numerically. For that, we develop an equivalent characterization method for rough fractal surfaces, reproduce the adsorption process of methane on the surface by combining molecular dynamics and Grand canonical Monte Carlo (GCMC) simulations, analyze the control mechanisms of complex types of surface geometry on the methane adsorption process, and clarity the ratio of vertical roughness to horizontal complexity as key parameter to describe the adsorption capability. Our numerical results indicate that the adsorption density of methane in fractal and non-fractal slit pores varies with the fractal behavior of surface geometry, while the density of gas phase methane remains unaffected (all distributed around 0.06 g/cm3). And, the complexities of surface geometry process various effects on occurrence mode, adsorption potential energy (ɛ), and adsorption amounts. The surface original complexity will influence the force field, and alter the occurrence mode from monolayer adsorption to pore filling. Meanwhile, the width-to-depth ratio of surface original complexity has a negatively effects the ɛ of methane. The behavioral complexity of the surface reflects the number of small pores on it. For fractal slit pores, the maximum adsorption amounts are 2405.77, 2634.90, and 2749.46 mol/m3, respectively. They are smaller than that of the non-fractal slit pore, which is due to the increase of non-adsorption pores for the small diameter of pores. Above results give a clear explanation to the effects of fractal property on methane adsorption, which will provide a reference to study the adsorption process of methane in Coalbed Methane reservoir.

Prediction of milled surface characteristics of carbon fiber-reinforced polyetheretherketone using an optimized machine learning model by gazelle optimizer

Motivated by the nonlinear behavior of composite materials under different machining operations, this work aims at developing an optimized artificial intelligence model to predict milled surface characteristics of carbon fiber-reinforced polyetheretherketone (CFRPEEK). The milling operations were carried out under high-speed dry-cutting conditions. The developed model was employed to predict fractal dimension and surface roughness as functions of cutting speed, cutting width, feed per tooth, and orientation of fibers. The model is composed of an adaptive network-based fuzzy inference system (ANFIS) optimized by a gazelle optimizer (GO). The performance of the model was compared with five other optimized ANFIS models. ANFIS-GO showed outperformance compared with other models to predict milled surface characteristics. The root-mean-square deviation and determination coefficient of predicted data by ANFIS-GO compared with experimental ones are 0.002 and 0.911 for fractal dimension and 0.129 and 0.998 for surface roughness, respectively.

A statistics view of contact pressure distribution for normal contact of fractal surfaces

Due to inherent nonlinear stiffness and damping characteristics, dry friction interfaces have a significant impact on the dynamics of jointed structures. When two surfaces are brought into purely normal contact, contact pressure distribution is of high concern. This work focused on the statistics of the contact pressure distribution between a rough surface and a smooth rigid plane, which provides new insight into the interface contact behaviour. First, the fractal rough surface is generated using the Weierstrass–Mandelbrot function with measured roughness parameters. With meshed rough surfaces, an elastic–plastic finite element contact analysis is performed to determine the contact pressure distribution. Then, the results of contact pressure are statistically analysed. The effects of roughness and contact load on contact area, contact stiffness and mean contact pressure are thoroughly investigated. The probability distribution of contact pressure is determined by fitting a continuous function using a twofold Weibull mixture model. The proposed probability distribution function is found to be capable of describing contact pressure. The contact pressure distribution is affected by the surface fractal characteristics and evolves with the contact load.

Effect of fractal surface roughness and pressure gradient on the hydraulic behavior of fluid flow through a 3D single rough fracture

This study mainly aimed to numerically investigate the influence of fractal roughness and pressure gradient on the fluid flow through a three-dimensional (3D) single rough fracture with a constant mechanical aperture. To avoid confusion created by the Reynolds number caused by different definitions of characteristic length, the critical pressure gradient was utilized to characterize the onset of non-linear flow in rough fractures. Further, the effect of fractal dimension on the critical pressure gradient was also investigated. The rough fracture surfaces with different fractal dimensions are generated by an open source code SynFrac, and the COMSOL Multiphysics software package based on the finite element method was used to simulate the fluid flow through the generated 3D rough fracture model by solving the Navier-Stokes equations. For each case, Forchheimer’s law was used to describe nonlinear flow and the numerical results show that the critical pressure gradient, ranging from 15.68 kPa/m to 1.50 kPa/m, decreases exponentially with the increase in fractal dimension. The results also show that the relationship between relative effective fracture aperture and pressure gradient can be fitted well by a power function. These results suggest that the non-linear flow appears earlier as the fractal dimension and pressure gradient increase.

Surface morphology in high-speed grinding of TMCs fabricated by selective laser melting

TiC-reinforced titanium matrix composites (TMCs) are typically difficult-to-machine materials. It is prospective to combine the advantages of selective laser melting (SLM) and high-speed grinding to manufacture TMCs parts. This study investigates the surface morphology in high-speed grinding of TMCs fabricated by SLM. Grinding experiments with 28.75–232.66 m/s are conducted. Two surface features are found in the ground surface of TMCs, i.e. smearing at low grinding speeds and scratch at high grinding speeds. Surface morphologies are evaluated based on fractal dimension FD and surface roughness Ra. The results show that the correlations between FD and Ra indicate the ground surface formation mechanisms of TMCs. It is found that submicron TiC generated in SLM cooperating with high grinding speed achieves a good surface quality in terms of reduced surface roughness and subsurface damages for TMCs, which could be beneficial to the fabrication of other metal matrix composites.

Simplified Calculation Model for Contact Resistance Based on Fractal Rough Surfaces Method

Electrical contact resistance (ECR) is critical to evaluate the stability and reliability of electrical connections. In this paper, a simplified contact model is established for rough surfaces based on the fractal theory and Monte Carlo method, which can overcome the difficulty of constructing the resistance networks for traditional contact models. The model reveals the influence of fractal parameters D and G on the surface morphology and contact characteristics. The established surface method can simulate Gaussian and non-Gaussian isotropic surfaces. Then the contact resistance considering a contaminated film is calculated, which provides a quantitative analysis of the change and the influencing factors. The accuracy of the calculation method in this paper is ensured by comparing the existing experimental data and finite element results. The results show that the contact surface with D of 1.5 has the largest real contact area and the smallest contact resistance. The model has accurate calculation results when dimensionless contact load F* is less than 4 × 10−3.

Study on nonlinear dynamic characteristics of gear system with 3D anisotropic rough tooth surface based on fractal theory

Different from the mainstream research, this study fully considers the anisotropic micro-topography of the tooth surface when studying the dynamic characteristics of gears. An anisotropic 3D fractal rough tooth surface model is proposed based on fractal geometry theory. The major advantage of the novel model is that it contains more surface micro details, especially on the tooth width, which are ignored in general studies. The backlash and time-varying meshing stiffness (TVMS) are then revised on the basis of this model. Finally, a 6-degree-of-freedom nonlinear dynamic model considering surface topography is established and the influence of fractal parameters on gear dynamics is investigated. The results show that the fractal parameters change the backlash and TVMS and have an obvious impact on the dynamics and vibration responses of the transmission system. The rough gear system enters chaos earlier and has better stability at high speeds in comparison with the smooth system. As the fractal dimension increases, the dynamic transmission error amplitude gradually decreases and the system tends to stable periodic motion. The characteristic scale coefficient yields a more moderate but opposite effect on the dynamic response of the system compared with the fractal dimension. The finding of this study can provide theoretical guidance for tooth surface machining from the perspective of tooth surface morphology.

Time-Varying Wear Calculation Method for Fractal Rough Surfaces of Friction Pairs

For the wear problem of the real rough surface during sliding friction, based on fractal theory and Hertz contact theory, a 3-D fractal rough surface with random characteristics is constructed, and the relationship between the wear deformation depth of the rough peak and its real contact area during the wear process is derived. Furthermore, considering the peak wear and pit scratch phenomena of rough surfaces in different contact states, the time-varying wear calculation model of the worn surface and the compensation wear calculation model of the unworn surface are established, respectively, and the relationship between the instantaneous wear amount and the dynamic change in the rough surface topography is comprehensively characterized. Combined with image digitization technology, the 3-D rough surface is converted into a 2-D discrete plane with 3-D information. According to the dynamic real-time update of the graph data, the iterative calculation of the wear cycle is completed, the time-varying wear calculation method for fractal rough surfaces of friction pairs is proposed, and the dynamic change in the wear amount and surface topography of the rough surface is simulated. The simulation results are experimentally verified and the influence of friction parameters on the surface topography is analyzed. The results show that after the wear simulation, the profile height of the rough surface is reduced, and the average wear depth is 0.02 mm. Increases in rotational speeds and external loads can exacerbate surface wear, surface topography tends to be flattened, and surface carrying capacity increases. This provides theoretical guidance for the development and manufacture of friction pairs.

Universal Langmuir and Fractal Analysis of High-Resolution Adsorption Isotherms of Argon and Nitrogen on Macroporous Silica.

High-resolution isotherms of argon and nitrogen adsorption on macroporous silica have been simulated with universal Langmuir and fractal models. A four-parameter, fractal universal Langmuir equation is a good fit to the data at low pressures. Standard Gibbs energy changes calculated from equilibrium adsorption coefficients show a series of broad peaks that indicate adsorbate structural transformations as a function of pressure and coverage. The Freundlich equation or mean fractal model is also a good fit to isotherms at low pressures. Pressure-varying fractals are accurate fits to the data. Fractal exponents provide information on adsorbate coverage and surface access. Broad peaks in pressure-varying exponents are indicators of adsorbate structure. From adsorptive gas amounts, mean and pressure-varying fractal exponents provide details of adsorbate fractal dimensions and surface roughness. Both Ar and N2 adsorption cause increases in mean surface roughness when compared with pure silica. Surface roughness fluctuations from pressure-dependent adsorptive gas fractal dimensions are associated with adsorbate structure. At one trough, the surface is smooth and is linked to close-packed Ar or N2. For Ar adsorption at 87 K, this structure is a complete monolayer (1.00(4)), while for Ar (77 K), 1.15(4) layers and for N2 (87 K), 2.02(10) layers. The universal Langmuir specific area of the silica is 10.1(4) m2 g-1. Pressure- and coverage-dependent adsorbate structures range from filling defects and holes on the surface to cluster formation to adsorbed Ar or N2 evenly distributed or packed across the surface. The Ar (87 K) isotherm is most sensitive to adsorbate structural transformations.

Structural and Mechanical Properties of CrN Thin Films Deposited on Si Substrate by Using Magnetron Techniques

Chromium nitride thin films are known for their good mechanical properties. We present the characteristics of ultrathin chromium nitride films under 400 nm thickness deposited on silicon substrates by direct current and high-power impulse magnetron sputtering techniques. The methods of investigation of the CrN films were scanning electron microscopy, atomic force microscopy, and nanoindentation. Qualitative and quantitative analyses were performed using AFM and SEM images by fractal dimension, surface roughness and gray-level co-occurrence matrix methods. Our results show that using magnetron techniques, ultrathin CrN films with excellent mechanical properties were obtained, characterized by values of Young’s modulus between 140 GPa and 250 GPa for the samples obtained using high-power impulse magneton sputtering (HiPIMS) and between 240 GPa and 370 GPa for the samples obtained using direct current sputtering (DC). Stiffness measurements also reveal the excellent mechanical properties of the investigated samples, where the samples obtained using HiPIMS sputtering had stiffness values between 125 N/m and 132 N/m and the samples obtained using DC sputtering had stiffness values between 110 N/m and 119 N/m.

A Generalization of Poiseuille’s Law for the Flow of a Self-Similar (Fractal) Fluid through a Tube Having a Fractal Rough Surface

In this paper, a generalization of Poiseuille’s law for a self-similar fluid flow through a tube having a rough surface is proposed. The originality of this work is to consider, simultaneously, the self-similarity structure of the fluid and the roughness of the tube surface. This study can have a wide range of applications, for example, for fractal fluid dynamics in hydrology. The roughness of the tube surface presents a fractal structure that can be described by the surface fractal noninteger dimensions. Complex fluids that are invariant to changes in scale (self-similar) are modeled as a continuous medium in noninteger dimensional spaces. In this work, the analytical solution of the Navier–Stokes equations for the case of a self-similar fluid flow through a rough “fractal” tube is presented. New expressions of the velocity profiles, the fluid discharge, and the friction factor are determined analytically and plotted numerically. These expressions contain fractal dimensions describing the effects of the fractal aspect of the fluid and of that of the tube surface. This approach reveals some very important results. For the velocity profile to represent a physical solution, the fractal dimension of the fluid ranges between 0.5 and 1. This study also qualitatively demonstrates that self-similar fluids have shear thickening-like behavior. The fractal (self-similarity) nature of the fluid and the roughness of the surface both have a huge impact on the dynamics of the flow. The fractal dimension of the fluid affects the amplitude and the shape of the velocity profile, which loses its parabolic shape for some values of the fluid fractal dimension. By contrast, the roughness of the surface affects only the amplitude of the velocity profile. Nevertheless, both the fluid’s fractal dimension and the surface roughness have a major influence on the behavior of the fluid, and should not be neglected.

Influence of Spray Drying on Encapsulation Efficiencies and Structure of Casein Micelles Loaded with Anthraquinones Extracted from Aloe vera Plant

The encapsulation efficiency (EE%) and structural changes within the Anthraquinones-encapsulated casein micelles (CM) powders were evaluated in this study. For this purpose, the anthraquinone powder extracted from Aloevera, its freeze-dried powder (FDP) and whole leaf Aloe vera gel (WLAG) has been encapsulated in CM through ultrasonication prior to spray dying to produce nanocapsules: CM encapsulated anthraquinone powder (CMAQP), CM encapsulated freeze-dried powder (CMFDP) and CM encapsulated Whole leaf aloe vera gel (CMWLAG). Based on the pH of the solution before drying, CMAQP had the highest EE% following spray drying. However, due to air-interface-related dehydration stresses, SD resulted in a slight decrease in the EE% of anthraquinones (aloin, aloe-emodin, and rhein) in CMAQP. Meanwhile, a significant increase in EE% of CMFDP was observed compared to the aqueous state. According to SEM findings, the particle size of CMAQP was 2.39 µm and ξ-potential of ~−17mV. The CMFDP had a rough fractal surface with large particle sizes and potential of 3.49 µm and ~−11mV respectively. CM deformed, having the least EE% and lowest ξ-potential (−4.5 mV). Spray drying enhances melanoidin formation in CMWLAG, as evidenced by the highest chroma values. The results suggested that EE%, stability, and degree of Maillard reaction are closely linked to the type of anthraquinone encapsulated, the pH of the solution, and the nanostructure of casein micelles during spray drying.

Study on the lubrication state and pitting damage of spur gear using a 3D mixed EHL model with fractal surface roughness

Study on the lubrication state and pitting damage of spur gear using a 3D mixed EHL model with fractal surface roughness

Meshing Characteristics of Spur Gears Considering Three-Dimensional Fractal Rough Surface under Elastohydrodynamic Lubrication

Taking the effect of actual surface topography under elastohydrodynamic lubrication (EHL) conditions on the contact state of gear pairs into consideration, a combination model with the analytical sliced method and two-dimensional (2D) EHL model is proposed to characterize the three-dimensional (3D) meshing characteristics of spur gears. Firstly, the surface topology of gears is tested by a surface profiler, which reflects that the topography of tooth surface accords with fractal characteristics. Thus, by adopting the Weierstrass–Mandelbrot (W-M) fractal function, the gear surface is characterized. Secondly, the numerical 2D EHL model with fractal roughness is established, and distributions of oil film pressure (OFP) and oil film thickness (OFT) at different meshing positions are obtained. Finally, considering the different topography distributions in the direction of face width, time-varying mesh stiffness (TVMS) is calculated based on the analytical sliced method. Thus, the influence of 3D surface topography can be considered. The Hertz contact stiffness is substituted by the time-varying lubricating oil film stiffness (OFS). The influences of tooth surface topography and lubricant film characteristics on meshing characteristics are investigated. The results show that the 3D rough tooth surface may be well characterized by a fractal function with random phase. Moreover, there is a great difference in the distribution of OFP and OFT between rough and smooth surfaces, which certainly influences the gear meshing characteristics.

How can the effect of particle surface roughness on the contact area be predicted?

This paper describes a systematic study of the effect of fractal rough surfaces on the contact area with the aim of advancing contact constitutive laws used in the Discrete Element Method. An in-house Boundary Element code is adopted to investigate the mechanical behaviour of computer-generated surface roughness. Surfaces are generated to have methodically controlled root mean square height (Sq), root mean square gradient (Sdq), short wavevector (q0), large wavevector (q1), Hurst exponent (H) and fractal dimension (Df). The effect of each parameter on the contact area is investigated. Two recently proposed analytical solutions in tribology (i.e. Persson-Tosatti and Pastewka-Robbins) are applied to predict the real contact area. A parameter based on Sq, q0, and H is proposed and its sensitivity for real contact area prediction is demonstrated. Surfaces of natural sand are simulated and their mechanical response shows similar trend as the computer-generated surfaces, albeit more complex.