Fractal Prediction Model of Thermal Contact Conductance of Rough Surfaces

The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces, which has been widely studied since last few decades, and for predicting which many theoretical models have been established. However, the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity. In this paper, a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes： elastic, elastoplastic and fully plastic. Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model. The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area. The larger the fractal dimension, or the smaller the fractal roughness, the larger the thermal contact conductance is. The thermal contact conductance increases with decreasing the ratio of Young＇s elastic modulus to the microhardness. The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface, which provide certain reference to the further study on the issue of heat transfer between contact surfaces.

Elastoplastic Contact Mechanics Model of Rough Surface Based on Fractal Theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ~b, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.

An Elastic-plastic Adhesion Model for Contacting Fractal Rough Surface and Perfectly Wetted Plane with Meniscus

The strong stiction of adjacent surfaces with meniscus is a major design concern in the devices with a micro-sized interface. Today, more and more research works are devoted to understand the adhesion mechanism. This paper concerns the elastic-plastic adhesion of a fractal rough surface contacting with a perfectly wetted rigid plane. The topography of rough surface is modeled with a two-variable Weierstrass-Mandelbrot fractal function. The Laplace pressure is dealt with the Dugdale approximation. Then the adhesion model of the plastically deformed asperities with meniscus can be established with the fractal microcontact model. According to the plastic flow criterion, the elastic-plastic adhesion model of the contacting rough surfaces with meniscus can be solved by combining the Maugis-Dugdale （MD） model and its extension with the Morrow method. The necessity for considering the asperities＇ plastic deformation has been validated by comparing the simulation result of the presented model with that of the elastic adhesion model. The stiction mechanism of rough surfaces with meniscus is also discussed.

Hybrid method for investigation of electromagnetic scattering from conducting target above the randomly rough surface

A current based hybrid method （HM） is proposed which combines the method of moment （MOM） with the Kirchhoff approximation （KA） for the analysis of scattering interaction between a two-dimensional （2D） infinitely long conducting target with arbitrary cross section and a one-dimensional （1D） Gaussian rough surface. The electromagnetic scattering region in the HM is split into KA region and MOM region. The electric field integral equation （EFIE） in MOM region （target） is derived, the computational time of the HM depends mainly on the number of unknowns of the target. The bistatic scattering coefficient for the infinitely long cylinder above the rough surface with Gaussian roughness spectrum is calculated, and the numerical results are compared and verified with those obtained by the conventional MOM, which shows the high efficiency of the HM. Finally, the influence of the size, location of the target, the rms height and correlation length of the rough surface on the bistatic scattering coefficient with different polarizations is discussed in detail.

Solution of scattering from rough surface with a 2D target above it by a hybrid method based on the reciprocity theorem and the forward-backward method

This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments （MOM）. Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.

Bidirectional reflectance distribution function modeling of one-dimensional rough surface in the microwave band

An efficiently iterative analytical-numerical method is proposed for two-dimensional （2D） electromagnetic scattering from a perfectly electric conducting （PEC） target buried under a dielectric rough surface. The basic idea is to employ the Kirchhoff approximation （KA） to accelerate the boundary integral method （BIM）. Below the rough surface, an iterative system is designed between the rough surface and the target. The KA is used to simulate the initial field on the rough surface based on the Fresnel theory, while the target is analyzed by the boundary integral method to obtain a precise result. The fields between the rough surface and the target can be linked by the boundary integral equations below the rough surface. The technique presented here is highly efficient in terms of computational memory, time, and versatility. Numerical simulations of two typical models are carried out to validate the method.

Fractal characteristics investigation on electromagnetic scattering from 2-D Weierstrass fractal dielectric rough surface

A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing.

Wear Resistance of 3Cr2W8V Rough Surfaces

Three types of rough surface were processed by laser irradiation on the 3Cr2W8V material hot-work die steel surface. The wear experiments with smooth surface and rough surface samples were repeated on the pin-tray wear machine. According to the wear results, we studied the regularity of wear resistance of different rough surface samples. The results indicated that bionic rough surface can improve the wear resistance of the material and the wear resistance can be increased 1-2 times, compared with the smooth surface. Also, the wear resistance of the rough surface was affected by laser current and duration of impulse. The bigger the laser current or the impulse duration, the better is the wear resistance. When the distance between the same kind of units which are distributed on the surfaces is changed, the wear resistance changes. The wear resistance of a bionic rough surface on which the grid units were distributed at spacing of 1 mm was the best. And we designed the wear models.

Preload-responsive adhesion of microfibre arrays to rough surfaces

Adhesion of bio-inspired microfibre arrays to a rough surface is studied theoretically. The array consists of vertical elastic rods fixed on a rigid backing layer, and the surface is modeled by rigid steps with a normally distributed height. Analytical expressions are obtained for the adhesion forces in both the approach and retraction processes. It is shown that, with the increasing preload, the pull-off force increases at first and then attains a plateau value. The results agree with the previous experiments and are expected helpful in adhesion control of the array in practical applications.

Study of MPI based on parallel MOM on PC clusters for EM-beam scattering by 2-D PEC rough surfaces

This paper firstly applies the finite impulse response filter （FIR） theory combined with the fast Fourier transform （FFT） method to generate two-dimensional Gaussian rough surface. Using the electric field integral equation （EFIE）, it introduces the method of moment （MOM） with RWG vector basis function and Galerkin＇s method to investigate the electromagnetic beam scattering by a two-dimensional PEC Gaussian rough surface on personal computer （PC） clusters. The details of the parallel conjugate gradient method （CGM） for solving the matrix equation are also presented and the numerical simulations are obtained through the message passing interface （MPI） platform on the PC clusters. It finds significantly that the parallel MOM supplies a novel technique for solving a two-dimensional rough surface electromagnetic-scattering problem. The influences of the root-mean-square height, the correlation length and the polarization on the beam scattering characteristics by two-dimensional PEC Gaussian rough surfaces are finally discussed.

Application of a multiregion model to the EM scattering from a rough surface with or without a target above it

An efficient multiregion model is introduced to calculate the electromagnetic scattering from a perfectly electrical conducting （PEC） rough surface with or without a PEC target above it. In the multiregion model, the rough surface is split into multiple regions depending on their position along the rough surface. Two intermediate regions are chosen as the dominant region. If a target is located above the rough surface, the target will also be included in the dominant region. The method of moments （MOM） is only adopted on the dominant region to ensure validity. Hence, the new model can greatly reduce the number of unknowns associated with full MOM analysis. The induced electric currents on the other regions are obtained by approximately considering the mutual coupling between different regions along the rough surface. Compared with the published hybrid method, this new model is not only suitable for EM scattering from a target above a rough surface but also applicable for just rough surfaces. Several numerical simulations are presented to show the validity and efficiency of the multiregion model.

Reliable approach for bistatic scattering of three-dimensional targets from underlying rough surface based on parabolic equation

A parabolic equation （PE） based method for analyzing composite scattering under an electromagnetic wave incidence at low grazing angle, which composes of three-dimensional （3-D） electrically large targets and rough surface, is presented and discussed. A superior high-order PE version is used to improve the accuracy at wider paraxial angles, and along with the alternating direction implicit （ADI） differential technique, the computational efficiency is further improved. The formula of bistatic normalized radar cross section is derived by definition and near-far field transformation. Numerical examples are given to show the validity and accuracy of the proposed approach, in which the results are compared with those of Kirchhoff approximation （KA） and moment of method （MoM）. Furthermore, the bistatic scattering properties of composite model in which the 3-D PEC targets on or above the two-dimensional Gaussian rough surfaces under the tapered wave incidence are analyzed.

Scattering from Rough Surfaces Using the"Shooting and Bouncing Rays" Technique

The “shooting and bouncing rays” (SBR) technique is used to analyze the electromagnetic scattering characters of ocean rough surfaces varying with time. Some numerical results are presented and compared with the method of moments, and some factors, such as the incident angle, polarization and frequency are investigated which influence on electromagnetic scattering characters of ocean rough surfaces.

Variational Approach to Scattering by Inhomogeneous Layers Above Rough Surfaces

In this paper, we study, via variational methods, the problem of scattering of time harmonic acoustic waves by unbounded inhomogeneous layers above a sound soft rough surface. We first propose a variational formulation and exploit it as a theoretical tool to prove the well-posedness of this problem when the media is non-absorbing for arbitrary wave number and obtain an estimate about the solution, which exhibit explicitly dependence of bound on the wave number and on the geometry of the domain. Then, based on the non-absorbing results, we show that the variational problem remains uniquely solvable when the layer is absorbing by means of a priori estimate of the solution. Finally, we consider the finite element approximation of the problem and give an error estimate.

Carpet Cloak Design for Rough Surfaces

Conventional carpet cloak structures have been utilized to conceal the objects located on a planar perfect electric conductor surface. We systematically investigate hiding arbitrarily shaped objects on a rough surface, as a more general and practical scenario. In addition, the required cloak is designed considering different boundary conditions for the surface beneath the object, despite the previous studies. To achieve an invisibility cloak, taking advantage of linear coordinate transformation, a simple homogeneous material is obtained to realize the cloak structure, facilitating the fabrication processes. Numerical simulations validate the performance of the proposed cloaking method. Therefore, the proposed structure is capable of cloaking in more general and complicated scenarios.

Research on synthetic aperture radar imaging technology of one-dimensional layered rough surfaces

A quick and exact imaging method for one-dimensional layered rough surfaces is proposed in this paper to study the scattering characteristics of a layered medium that exists widely in nature.The boundary integral equations of layered rough surfaces are solved by using the propagation-inside-layer expansion combined with the forward and backward spectral acceleration method（PILE＋FB-SA）,and the back scattering data are obtained.Then,a conventional synthetic aperture radar（SAR） imaging procedure called back projection method is used to generate a two-dimensional（2D） image of the layered rough surfaces.Combined with the relative dielectric permittivity of realistic soil,the random rough surfaces with Gauss spectrum are used to simulate the layered medium with rough interfaces.Since the back scattering data are computed by using the fast numerical method,this method can be used to study layered rough surfaces with any parameter,which has a great application value in the detection and remote sensing areas.

VIBRATION OF CANTILEVERS WITH ROUGH SURFACES

We study the effect of surface roughness on the resonance frequency of micro-cantilever sensors. The analysis demonstrates that surface roughness can enhance, decrease or even annul the effect of surface stress on the resonance frequency, depending on the surface inclination angle and the Poisson ratio of the coating film on the cantilever.

A new 3D plastoelastohydrodynamic lubrication model for rough surfaces

Plastoelastohydrodynamic lubrication of rough surfaces(R-PEHL)is a cutting-edge area of research in interface fluid-structure coupling analysis.The existing R-PEHL model calculates the elastic-plastic deformation of rough surface by the Love equation in a semi-infinite space smooth surface,which deviates from the actual surface.Therefore,it is an innovative work to study the exact solution of elastic-plastic deformation of rough surface and its influence on the solution results of R-PEHL model.In this paper,a new contact calculation model of plastoelastohydrodynamic lubrication(PEHL)with three-dimensional(3D)rough surface is proposed by integrating numerical method of EHL and finite element method.The new model eliminates an original error introduced by the assumption of semi-infinite space in contact calculation,providing wide applicability and high accuracy.Under the given rough surfaces and working conditions,the study reveals that:(1)the oil film pressure calculated by the new model is lower than that of the smooth surface in semi-infinite space by 200–800 MPa;(2)the Mises stress of the new model is 2.5%–26.6%higher than that of the smooth surface in semi-infinite space;(3)compared with the semi-infinite space assumption,the rough surface plastic deformation of the new model is increased by 71%–173%,and the local plastic deformation singularity may appear under the semi-infinite space assumption;(4)the plastic deformation caused by the first contact cycle on the rough surface of the new model accounts for 66.7%–92.9%of the total plastic deformation,and the plastic deformation of the semi-infinite space accounts for 50%–83.3%.This study resolves the contradiction between the smooth surface assumption and the rough surface in the existing R-PEHL model,establishing a solid logic foundation for the accurate solution of R-PEHL model.

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

The elastic adhesive contact of self-affine fractal rough surfaces against a rigid flat is simulated using the finite element method. An array of nonlinear springs, of which the force-separation law obeys the Lennard–Jones potential, is introduced to account for the interfacial adhesion. For fractal rough surfaces, the interfacial interaction is generally attractive for large mean gaps, but turns repulsive as the gap continuously shrinks. The interfacial interactions at the turning point corresponding to the spontaneous contact are shown for various surfaces. For relatively smooth surfaces, the probability density distributions of repulsion and attraction are nearly symmetric. However, for rougher surfaces, the simulation results suggest a uniform distribution for attraction but a monotonously decreasing distribution with a long tail for repulsion. The pull-off force rises with increasing ratio of the work of adhesion to the equilibrium distance, whereas decreases for solids with a higher elastic modulus and a larger surface roughness. The current study will be helpful for understanding the adhesion of various types of rough solids.

High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.