The two-scale model for random rough surface scattering

The problem of electromagnetic scattering from a randomly rough surface is analyzed using the Kirchhoff approximation (stationary phase, scalar approximation), the small perturbation model and the two-scale model. The authors show that physical and geometrical optics approximations can be used for a rough sea surface. A small perturbation model gives a satisfactory solution. Unfortunately, it only applies to a smooth sea surface. Therefore, these methods have been shown to be limited in their regions of validity. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wave number (denoted by k/spl sigma/ and kL, respectively). The two-scale model proposed in this paper is the method which tries to conciliate the two previous aspects. One application is made in the ocean surface case. A set of experimental data, describing simultaneous bistatic radar cross section and forward radar cross section measurements of sea clutter taken with a moderately high resolution X-band scatterometer system operating near grazing incidence for both horizontal and vertical polarizations over a range of low grazing bistatic angles, is used but not presented in this paper to examine the applicability of bistatic scattering models.

There is a need for a solution to the problem of wave scattering from rough surfaces that is accurate when both the classical field perturbation and Kirchhoff approximations are not. In previous work it was shown numerically that the phase perturbation reflection and backscattering coefficients reduce to those of field perturbation theory and the Kirchhoff approximation in the appropriate limits; however, for cases when the classical solutions did not apply, the accuracy of the phase perturbation results could not be determined. In this paper we examine the validity of the phase perturbation technique for a region in parameter space when the two classical solutions fail. Numerical results for the bistatic scattering cross section are compared with exact numerical results for one-dimensional surfaces having a Gaussian roughness spectrum and satisfying a Dirichlet boundary condition. It is found that in the region considered the phase perturbation results agree with the exact results over all scattered angl...

The article focuses on developing a predictive and optimization model for surface roughness in ultra-precision turning (UPT) using a diamond cutter on the spherical surface of Al6061 material. An experimental model with 30 experiments was established, considering three input parameters: spindle speed, feed rate, and depth of cut. The results from this model were collected to create an input dataset for an artificial neural network (ANN) to build a surface roughness prediction model. The ANN structure 3-5-10-1 provided the best prediction results, with Coefficient of Determination ( ) is 0.98, Mean Absolute Percent Error ( ) is 13.36%, Mean Square Error ( ) is 0.68, and Root Mean Square Error ( ) is 0.82. Additionally, the artificial bee colony (ABC) algorithm was employed to determine the optimal cutting parameters that minimize surface roughness. The results indicated that the minimum roughness value achieved was 0.76 nm with the cutting parameters: spindle speed of 823 rev/min, feed rate of 13 mm/min, and depth of cut of 1 µm. Moreover, the effects of different cutting parameter combinations on surface roughness were analyzed and evaluated. The integration of the ANN model with the ABC algorithm enables a reliable prediction model for surface roughness and demonstrates high efficiency in optimizing the objective function. This research contributes valuable insights into surface roughness prediction and optimization in ultra-precision turning of Al6061 material. Furthermore, the proposed modeling and optimization approach can be extended to other materials and the processing of aspherical and diffractive surfaces.

For perfect surface roughness description is not enough to know characteristics of surface profile. It is necessary to use topography methods, so called microtopography. Thereby, surface roughness in microtopographycal understanding must be described with three coordinates, whose in Cartesian coordinates system compose point under consideration height h, abscissa and ordinate, determines point position in the plane. Most efficient methods in irregular surface roughness research are random function theory methods. Therefore, microtopography, analogically to profile, may consider as random function, but two dimensional function, i.e. two variable x and y random field h(x,y). From analogy with random process, random field can be normal – ordinates are distributed by normal (Gaussian) distribution. Moreover, random field can be homogeneous and heterogeneous. Random field is deemed homogeneous if its mean value is discretionary and correlation function depends only from distance between surface points. Important characteristic of random field is correlation function, whose depends of two variables t1 and t2 – orthogonal Cartesian coordinates of vector t. Random field is homogeneous and isotropic when its characteristics are equivalent in any direction. There are three types of surface anisotropy: • General event of surface anisotropy. Characteristics of this event roughness parameters are depend of surface split direction. • Surface roughness with direct anisotropy. Those surfaces are with typical traces of tool and they proper two mutually perpendicular surface roughness directions. • Extended anisotropy area – special event of anisotropy roughness. Of analytical opinion, gainfully anisotropy roughness see as extended occasional isotropy area. This let easy cross from anisotropy surface to isotropy and contrariwise, thereby embrace amount class of surface roughness. Let’s formulate microtopography model of rough surface [1]. Surface roughness is described with homogeneous normal random field h(x,y) that has uninterrupted correlation function and uninterrupted deriviates. We may consider that E{h(x,y)}=0. The mean random field value is plane called mean plane. For describing random field we must know mathematical expectation and field correlation function, what in fact reduces on determining dispersion and rationed correlation function r(t1, t2). Homogeneous random field dispersion D{h} doesn’t depends of direction and can be founded in any surface split. Given model of rough surface let inspect surfaces produced by abrasive instruments and friction surfaces after wear-in period.

A theory of scattering from very rough surfaces is presented. Both the surface rms height and the correlation distance are close to a wavelength and the rms slope is close to unity. The theory is based on the first- and modified second-order Kirchhoff approximations. The second-order scattering includes the incident and scattering shadowing and the angular and propagation tapering shadowing. The angular shadowing limits the angular spectrum of the second-order scattering within those intercepted by the surface, while the propagation shadowing limits the propagation distance within those intercepted by the surface. The calculations are made for the rms height equal to 1.5, 1.0, and 0.5 wavelengths and the correlation distance equal to 1.8 wavelengths and show close agreement with the Monte Carlo simulation of the exact integral equation. The results show that the first-order Kirchhoff scattering is dominant for rms height equal to 0.5 wavelengths, but for rms heights equal to 1.0 and 1.5 wavelengths, the second-order scattering becomes comparable to the first-order and produces the enhanced backscattering. Therefore, this theory provides a possible physical explanation for the enhancement. The range of validity of the theory is also discussed. [Work supported by ARO and NSF.]

Surface roughness that is one of the most important parameters is used to evaluate the quality of a machining process. Improving the accuracy of the surface roughness model will contribute to ensure an accurate assessment of the machining quality. This study aims to improve the accuracy of the surface roughness model in a machnining process. In this study, Johnson and Box-Cox transformations were successfully applied to improve the accuracy of surface roughness model when turning 3X13 steel using TiAlN insert. Four input parameters that were used in experimental process were cutting velocity, feed rate, depth of cut, and insert-nose radius. The experimental matrix was designed using Central Composite Design (CCD) with 29 experiments. By analyzing the experimental data, the influence of input parameters on surface roughness was investigated. A quadratic model was built to explain the relationship of surface roughness and the input parameters. Box-Cox and Johnson transformations were applied to develop two new models of surface roughness. The accuracy of three surface roughness models showed that the surface roughness model using Johnson transformation had the highest accuracy. The second one model of surface roughness is the model using Box-Cox transformation. And surface roughness model without transformation had the smallest accuracy. Using the Johnson transformation, the determination coefficient of surface roughness model increased from 80.43 % to 84.09 %, and mean absolute error reduced from 19.94 % to 16.64 %. Johnson and Box-Cox transformations could be applied to improve the acuaracy of the surface roughness prediction in turning process of 3X13 steel and can be extended with other materials and other machining processes

Purpose – The purpose of this paper is to construct a continuous time series model to study the thermal creep of rough surfaces in contact.Design/methodology/approach – 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.Findings – An asymptotic time series power law is obtained, which associates the creep load, the buck temperature and the creep of the fractal surface.Originality/value – This law is only valid as long as the creep is of the size of the surface roughness. The mo...

A new iterative solution to the problem of sea surface scattering is obtained which has the Kirchhoff approximation as its leading term. This solution is obtained by transforming an integral equation of the first kind for the surface potential to one of the second kind, and applying the method of successive approximations. The advantages of this method are that the conditions under which this solution converges may be readily established and the solution may be iterated to sufficiently high order in the interaction to examine the rate at which it converges. A numerical example of scattering from an echelette grating is considered, and the regime of convergence established. It is found that the new iterative solution converges only for such surfaces on which kσσ′<π><π where k is the wave number of the scattered radiation and σ and σ′ are, respectively, the rms surface height and slope. This finding raises doubts concerning the regime in which the Kirchhoff approximation is traditionally deemed applicable. Finally, numerical studies are presented to illustrate the convergence of the iterative solution.

Modeling and prediction of surface topography and surface roughness in dual-axis wheel polishing of optical glass

A computational technique for the stressed state of a region lying beneath a rough solid surface is proposed. The calculation relies on the solution of a system of Laplace's equations for thin-walled shells and of an energy equation of deformation. Based on experimental data, a Gaussian bearing curve is chosen as a rough surface model. An analytic expression for the dependence of equivalent stresses and strain energy on the shape of the rough surface is derived.

Effects of surface roughness on surface analysis via soft and ultrasoft X-ray fluorescence spectroscopy

A semi-empirical polarimetric scattering model for bare soil surfaces is developed. This scattering model is constructed based on the existing theoretical models in conjunction with an extensive experimental data collected with polarimetric scatterometer systems at microwave frequencies. The backscattering coefficients as well as parameters of phase difference statistics, degree of correlation (/spl alpha/) and polarized phase difference (/spl zeta/), are expressed in terms of both surface parameters (rms height, correlation length, and dielectric constant) and radar parameters (frequency and incidence angle). The semi-empirical model is used as a basis for an inversion algorithm to estimate the surface parameters from the polarimetric backscatter response of a surface when the radar parameters are known. By performing a sensitivity analysis, a set of optimum parameters are chosen for the inversion algorithm. It is shown that the co-polarized ratio (/spl sigma//sup 0/ /sub hv///spl sigma//sup 0/ /sub vv/) the cross-polarized ratio (/spl sigma//sup 0/ /sub hv///spl sigma//sup 0/ /sub vv/), and the degree of correlation for co-polarized phase difference are most sensitive to the surface parameters and least affected by the measurement errors. >

The authors wish to explain the similarity between some figures in the above paper (hereafter called the JPD paper) and in their other publication, Lee S, Jang Y H and Kim W 2008 Effects of nanosized contact spots on thermal contact resistance J. Appl. Phys.103 074308 (hereafter called the JAP paper), and to explain the differences between the two papers, which are not explicitly stated in the JPD paper.The main objective of the JAP paper is to calculate the thermal contact resistance of the nanosized contact spots in multiscale contact. During the process of multiscale analysis, the thermal conductivity varies, especially below the phonon mean free path. The JPD paper deals with the electrical contact resistance in the multiscale contact distribution with an assumption of constant electrical resistivity, which is known as a different kind of physics in a larger characteristic length scale.There are similar figures in the JPD paper and the JAP paper: figures 6, 7 and 8 in the JPD paper and figures 3, 4 and 5 in the JAP paper. Two research works were performed on the basis of a specific microcontact distribution. In the JAP paper, the scale of the contact distribution is in the range of the phonon mean free path of Si, which is a very small size of contact distribution. In the JPD paper, the scale of contact distribution is in the continuum scale, which is larger than the phonon mean free path. In addition, due to the characteristics of a fractal surface which repeatedly generates a similar shape of contact distribution in the different length scales, the shape of contact distribution looks similar, but the total sizes of domain in the JPD and JAP figures are different. The projected areas L × L of fractal surface of the JAP paper and JPD paper are 10 μm × 10 μm and 10 mm × 10 mm, respectively. The length scale is already stated in the JAP paper, but not in the JPD paper. Thus, we have to state that the figures were adapted from the JAP paper without clear attribution and that credit should be given to the original source of the images. Most significantly, the two most important features of the two works are based on totally different physics and the calculation methods for contact resistance.The text of section 4.3 of the JPD paper should be modified. The left column of page 5 and the first two lines of the right column should be replaced by the following text.The projected area of a self-affine fractal surface is plotted in figure 6. In order to find the microcontact spot distribution from the fractal surface, numerical simulations are applied to the model of multiscale rough surface. Several contact models are constructed according to the resolution of 1/24 to 1/28. Figure 7 shows a typical finite element model in which the rough elastic surface is in contact with a perfectly flat rigid surface. Due to the fine meshes in the contact interface, strong mesh gradations are required. The contact simulation enforcing the impenetrability constraint on the mating surfaces is performed by a commercial finite element package, Abaqus/HKS ([22] of the JPD paper). The resulting microcontact spot distributions for different resolution of the rough surface are obtained in figure 8. As reported by Borri-Brunetto et al ([23] of the JPD paper), the actual contact area decreases and the number of contact spots increases as the resolution of the discretization escalates.A more detailed description for the model can be obtained in the JAP paper.

This paper presents the characteristics of radio wave scattering from rough sea surfaces in Ka-band. The physical optics method, which is one of the high frequency approximation algorithm, is employed to calculate radar cross section of electromagnetic simulation models of rough sea surfaces with Ship-EDF software. Rough sea surfaces are divided into six levels according to the wind speed over them. The simulation results show the effection that wind speed, the grazinng angle and frequency of radio wave have on the monostatic radar cross section of rough sea surfaces under the conditions of both horizontal and vertical polarization. With the increase of the roughness of sea surfaces and grazing angle of radio wave, the radar cross section value of rough sea surfaces increase. The frequencies of Ka-band have little contribution to the radar cross section value.

This paper presents the surface roughness model which is proposed and developed to predict the surface roughness in the CNC turning of the carbon steel with the coated carbide tool under various cutting conditions by using the response surface analysis with the Box-Behnken design based on the experimental results. The in-process monitoring of the cutting force and the cutting temperature is utilized to analyze the relation between the surface roughness and the cutting condition. The tool dynamometer and the infrared pyrometer are employed and installed on the turret of CNC turning machine to measure the in-process cutting force and cutting temperature. The models of cutting force ratio and cutting temperature are also developed based on the experimental data. The optimum cutting condition is determined referring to the minimum surface roughness of the surface plot, which is obtained from the developed surface roughness model. The experimental results show that the higher cutting speed gives the better surface roughness due to the higher cutting temperature, however the tool life becomes shorter. The feed rate is the most significant factor which affects the surface roughness, while a small depth of cut helps to improve the surface roughness. The effectiveness of the surface roughness prediction model has been proved by utilizing an analysis of variance (ANOVA) at 95% confident level. Hence, the surface roughness can be predicted and obtained easily referring to the developed surface roughness model.