Rough Cylindrical Surfaces Research Articles

Maple-модель руху частинки по евольвентному циліндру

In grain harvesters there is an interaction of a moving particle with a rough surface of enclosing casings of various cylindrical forms. Establishing the patterns of particle motion on the rough surface of the cylinder allows you to calculate the structural and kinematic parameters of the enclosing casings. In order to rationally move or separate bulk material, it is necessary to take into account a significant number of design and technological factors, which is extremely difficult to do without computer analysis. Computer technology allows to solve the problem of modeling the motion of a particle on a rough cylindrical surface, completely eliminate time-consuming analytical transformations to form the law of its motion, and leave only the interactive computational experiment. The purpose of the study is to develop a Maple-model of particle motion in an involute cylinder. The parametric equation of the uv-coordinate grid of a horizontal cylinder with an orthogonal cross section of the involute of a circle with an upward convexity is obtained. This made it possible to obtain the laws of motion of the particle in the projections on the horts. As a result of modeling, the trajectory-kinematic properties of particle motion on a fixed rough surface of an involute cylinder are established. Computational experiments have shown that to reduce crop losses, the upper casings of the combing reapers in the form of an involute cylinder must be divided into separate sections, because the grains thrown by the combing beater at an angle to the rectilinear cylindrical surfaces can break away from them.

Calculation of the statistical characteristics of the light reflected by a rough random cylindrical homogeneous Gaussian surface

ABSTRACTStatistical characteristics of light reflected by a rough random cylindrical homogeneous Gaussian surface are investigated using a modified method of specular points, as developed by Gardashov. In this proposed method, a special procedure for determining the light intensity near the caustics has been formulated. The probability distribution of the intensity of reflected light is expressed in terms of a special function, which is determined by the characteristic function of distribution of radii of curvature at the specular points and the distribution density of the number of specular points. The distribution of radii of curvature, derived by Gardashov, and expressed in terms of dimensionless radii of curvature, has a simple expression which does not contain any parameter of the surface (as a surface rms deviation, etc.). Consequently, it is universally valid and applicable to any cylindrical homogeneous Gaussian surface. After modification, the infinite dispersion of the reflected light intensity turns into a finite. The relationship between the distributions of reflected light intensity and the number of specular points, in the form of a Fredholm integral equation of the first kind is obtained. The kernel of the integral equation is expressed in terms of a characteristic function of the radii of curvature at specular points. The validity of formulae and relationships, thus derived, is tested by numerical simulations.

A solution considering elastic-plastic deformation of asperities for contact between rough cylindrical surfaces

PurposeThis paper aims to study the contact between rough cylindrical surfaces considering the elastic-plastic deformation of asperities.Design/methodology/approachThe elastic deformation of the nominal surface of the curved surface is considered, the contact area is discretized by the calculus thought and then the nominal distance between two surfaces is obtained by iteration after the pressure distribution is assumed. On the basis of the Zhao, Maietta and Chang elastic-plastic model, the contact area and the contact pressure of the rough cylindrical surfaces are calculated by the integral method, and then the solution for the contact between rough cylindrical surfaces is obtained.FindingsThe contact characteristic parameters of smooth surface Hertz contact, elastic contact and elastic-plastic contact between rough cylindrical surfaces are calculated under different plastic indexes and loads, and the calculation results are compared and analyzed. The analysis shows that the solution considering the elastic-plastic deformation of asperities for the contact between rough cylindrical surfaces is scientific and rational.Originality/valueThis paper provides a new effective method for the calculation of the contact between rough cylindrical surfaces.

Deformation and Heating of an Elastoviscoplastic Cylindrical Layer Moving Owing to a Varying Pressure Drop

Within the framework of the theory of large elastoplastic deformations generalized to the case of viscous and thermophysical properties of materials, we give a solution of a sequence of coupled problems on the onset and development of a flow in a material layer filling the gap between two rigid coaxial cylindrical surfaces under increasing pressure drop and on the subsequent flow deceleration under decreasing pressure gradient. Here the thermophysical and deformation processes are coupled, and the yield stress depends on temperature. Heat production due to the layer material friction against the rough cylindrical boundary surfaces is taken for an additional heat source.

Statistical Properties of FMCW Radar Altimeter Signals Scattered From a Rough Cylindrical Surface

Statistical parameters of the beat signal of the frequency-modulated continuous-wave (FMCW) radar altimeter in case of scattering from cylindrical rough surface are determined in the Kirchhoff approximation. A concept of the double dimensionality of the beat signal is formulated in this paper. Results of this paper can be used to construct a simple simulation model to assess signal processing algorithms implemented in an FMCW radar altimeter.

Tangential Contact Stiffness of Rough Cylindrical Faying Surfaces Based on the Fractal Theory

The tangential contact stiffness of cylindrical asperities is investigated using macro- and micro-mechanisms in this study. A microanalysis model is developed and the tangential contact stiffness of elliptically parabolic asperities on the contact surface is determined. The shape influence coefficient of the cylindrical contact is defined, and its rationality is evaluated. The influence of asperity distribution on the rough surface is determined, and the tangential contact stiffness macroanalysis model is constructed based on fractal theory. The mathematical expression to determine the tangential contact stiffness of the macroscopically cylindrical contact is generated, and the effects of influential factors on tangential contact stiffness are explicitly evaluated. Numerical results show that the tangential contact stiffness of asperities is determined by several factors, such as material properties, applied loads, fractal dimension, and surface shape.

Determination of the distribution of the number of specular points of a random cylindrical homogeneous Gaussian surface

Statistical characteristics of light reflected by the rough random cylindrical homogeneous Gaussian surface are being investigated by using the method of specular points. The inverse problem, in the form of a Fredholm integral equation of the first kind for determining the distribution of the number of specular points from the known reflected radiance distribution, is formulated. The kernel of this equation is determined by the characteristic function of the distribution of radii of curvature in specular points, derived by Gardashov. The validity of the obtained original formulas is controlled by numerical simulations.

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long “rough” capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson–Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.

Speckle size of light scattered from slightly rough cylindrical surfaces.

This research is an extension of the optical method of quality control presented in a previous paper [Appl. Opt. 39, 5811 (2000)] to the case of slightly rough cylindrical surfaces. Applying the Kirchhoff scalar diffraction theory yields an analytical expression of the autocorrelation function of the intensity scattered from slightly rough cylindrical surfaces. This function, which is related to speckle size and shape, is shown to depend on the surface correlation length, unlike for plane surfaces for which the speckle depends on the illuminated area only. The theoretical expression is compared with that for the speckle produced by the light scattered from a cylindrical bearing and from various high-quality wires, showing that the method allows the correlation lengths of high-quality cylindrical surfaces to be determined.

Anisotropic speckle patterns in the light scattered by rough cylindrical surfaces

Speckle patterns in the light field scattered from the rough surface of a cylindrical object are experimentally studied. The light speckles are elongated in the direction normal to the cylinder axis. A theoretical model explains the main features of the scattered light field. The dimensions of light speckles depend on both the surface roughness and the surface curvature.

Development of an Optical Hole-Diameter Measuring Instrument

An optical hole-diameter measuring instrument has been developed. The instrument, which consists of two laser diodes, a photo sensitive detector, two condenser lenses and some mirrors, is intended to measure, based on trigonometry, the distances to the hole wall on two sides alternately. The fundamental analysis and experiment showed that it was possible to measure the distances to the object having not only a mirror-like plane surface but also a rough cylindrical surface. Using the instrument, which was manufactured on trial, it was found that the hole-diameter between 9.5 and 11.0 mm could be measured within accuracy of 23 μm.

Light scattering from periodic rough cylindrical surfaces

Light scattering from rough cylindrical surfaces at near-zero grazing angle is investigated by applying Beckmann's scalar scattering model to the surface's tangential planes and superimposing the individual intensities to form the scattering pattern. A solution for sinusoidal surface-roughness profiles is derived and numerical results are obtained to study the influences of surface wavelength and amplitude on the far-field scattering pattern. The spatial and intensity distributions of the fringe (across and along thefringe) are found to be related to the surface wavelength and amplitude, respectively. Scattering intensity-distribution measurements are carried out on turned surfaces, and the results obtained are in agreement with the model's prediction. As a direct application, a technique to estimate the surface broughness of turned surfaces is proposed. This technique offers an absolute measurement in which the roughness amplitude and wavelength of the surface are defined relative to the illumination wavel gth.

Scattering of waves from a random cylindrical surface

The stochastic theory combined with a group-theoretic consideration developed by the authors for the scattering from a planar and a spherical random surface is applied to the case of a cylindrical random surface, which is assumed to be a homogeneous Gaussian random field, homogeneous with respect to the group of motions on the cylinder, translations along the axis and rotations around the axis. An operator acting on a random field is introduced, which keeps a homogeneous random field invariant, and which gives a representation of the motion-group on the cylinder. As an irreducible representation, i.e., an eigenfunction of the operator, the random wave field is obtained for the mth cylindrical wave injection on the random rough cylinder, and is represented as a stochastic functional of the cylindrical random surface in terms of a Wiener-Ito expansion. The random wave field for a plane-wave injection is decomposed into a sum over m of such random wave fields for the mth cylindrical wave injection. Various statistical characteristics of the scattered wave are calculated from the stochastic wave field so obtained; such as coherent scattering amplitude, coherent power flow, incoherent power flow, angular distributions for the coherent and incoherent scattering, and the power conservation law, especially, a stochastic version of the optical theorem stating that the total scattering cross-section consisting of the coherent and incoherent power flow equals the imaginary part of the coherent forward-scattering amplitude. Approximate solutions are obtained for a slightly rough cylindrical surface with Dirichlet and Neumann boundary conditions. Anomalous scattering does not take place in the case of a cylindrical Neumann surface, contrary to the case of a planar random surface, so that a single scattering approximation could be used for every small roughness. Some numerical calculations are shown of the angular distributions for coherent and incoherent scattering.

On the Exact Solution of Boundary Value Problems with Non-separable Geometries, Like a Rough Surface

A Dirichlet problem is considered for the Helmholtz equation and for a class of geometries for which the Helmholts operator does not separate (e.g. a rough surface). It is shown that, contrary to the widely held view, it is possible to obtain the solution of this problem in a closed form which resembles closely the solutions obtained for separable geometries—expansions generated by Sturm-Liouville theory. As with separable geometries, we show in particular that the expansion coefficients can be written explicitly as integrals containing a priori known functions—that matrix inversion is not required for the determination of the expansion coefficients. The problem includes as a special case the scattering of electromagnetic waves from a rough cylindrical surface which is the boundary of a perfect conductor. The method is very general and can be used for much more complicated boundary value problems, such as scattering by dielectric interface.