Parabolic Grooves Research Articles

Design of Parabola-Shaped Planar Lossy Magnetic Surface for Improved Isolation Characteristic Between GPS Array Elements With Circular Polarization Property

This letter proposes the design of a parabola-shaped planar lossy magnetic (PLM) surface for improving the isolation characteristic of Global Positioning System (GPS) arrays. The proposed surface consists of multiple parabolic grooves that are filled with lossy magnetic material that allows the resulting surface to serve as an artificial magnetic conductor. A four-element GPS array with and without the proposed surface is fabricated and measured in a full-anechoic chamber to demonstrate the feasibility of the parabola-shaped PLM surface. The results confirm that the developed surface is suitable for improving the isolation characteristic for GPS arrays while minimizing array pattern gain reduction at increased steering angles.

Diffractive–refractive optics: X-ray focusing splitter

The sagittally focusing X-ray crystal monochromator based on diffractive–refractive optics (IDL—inclined diffraction lens) is the Bartel monochromator with longitudinal parabolic grooves fabricated to its diffraction surface. It is proposed to modify the groove profile in such a way that it will be composed of two laterally displaced parabolic surfaces. This kind of monochromator generates two, slightly laterally displaced focused beams. The pulses prolongation by this kind of optics is also discussed.

V-groove and parabolic array for enlarging the acceptance angle of a side-absorption concentrated photovoltaic system

Conventional planar solar concentrators own the merit of compactness but usually with some issues, such as complicated fabrication, complex assembly, low efficiency, etc. Our previous work investigated a kind of planar solar concentrators, the concentrator of the side-absorption concentrated photovoltaic system (SCPV) which consists of the single concentrating element and is rather compact, feasible for fabrication and assembly, as well as efficient. Since the angular acceptance is essential for concentrating photovoltaics, this study proposes two schemes to increase the acceptance angle of a SCPV. The first scheme optimizes the v-groove array reflector at the bottom of the concentrator by means of tracing the angular subtense of the sun, while the second scheme replaces the v-groove array with the parabolic groove by investigating a sacrifice region. The design principles and the numerical evaluations of the two schemes are reported, while the experimental results and the causes of efficiency loss are systematically analysed and discussed. The simulated results show that the acceptance angles of the first and the second schemes are enlarged by factors of 2.2 and 3.1, respectively, while the theoretical optical-efficiency of concentrator are 85.5% and 94.2%, respectively. Experimentally, the acceptance angle for the first scheme was measured as ±4.4°, equivalent to an enlargement by a factor of 2.2 and agreeing with the simulation. From comparisons between modelling and experimental results, the causes of efficiency loss are thoroughly explored, and the approaches for further efficiency enhancement are presented. Moreover, since enlarging the acceptance angle of the concentrating photovoltaics eases the maintenance and reduces the expenses of the tracker, this work highlights the potential of the reported schemes for benefitting cost reduction, maintenance, compactness and weather endurance of the concentrated photovoltaic system.

Hydrodynamic Lubrication of Micro-Grooved Gas Parallel Slider Bearings with Parabolic Grooves

The hydrodynamic lubrication performance of micro-grooved gas parallel slider bearings with parabolic grooves is investigated in this paper. By using the multi-grid finite element method, the pressure distribution between a micro-grooved slider and a smooth slider is obtained. The geometric parameters of the parabolic grooves are optimized to maximize the average pressure under a given sliding speed. The numerical results show that geometric parameters such as groove depth, width, spacing, and orientation angle have an important influence on hydrodynamic pressure. Furthermore, the effect of sliding speed on hydrodynamic pressure is investigated under a given set of groove depths. It is observed that there is an optimum value of sliding speed to maximize the average pressure for any given groove depth and that the optimum value is dependent of the groove depth. The results of this study indicate that the average pressure could be improved by employing the optimized groove depth according to the practical sliding speed. DOI: http://dx.doi.org/10.5755/j01.mech.23.6.19850

High transmission Ni compound refractive lens for high energy X-rays.

We present a new planar Ni compound refractive lens for high energy X-rays (116 keV). The lens is composed of identical plano-concave elements with longitudinal parabolic grooves manufactured by a punch technique. In order to increase the lens transmission, the thickness of the single lens at the parabolic groove vertex was reduced to less than 5 μm and the radius of curvature was reduced to about 20 μm. The small radius of curvature allowed us to reduce the number of single elements needed to get the focal length of 3 m to 54 single lenses. The gain parameter has been significantly improved compared to the previous lenses due to higher transmission, but the focused beam size and its gain are not as good as expected, mostly due to the aberrations caused by the lens shape imperfections.

Justification of design and parameters of seeding unit for fertilizers

The paper deals with the choice and justification of seeding unit for mineral fertilizers. The original analysis showed that the existing seeding units for fertilizers do not provide application of high doses of fertilizers. The standard grooved-coil unit is required to provide stable and reliable dosing of high doses of fertilizers. The objective of this research is to study the construction design and parameters of the seeding unit used for mineral fertilizers. Theoretical study of the grooved-coil unit for mineral fertilizers revealed that improving groove forms can improve their performance. Thus, grooves having parabolic shape can raise the efficiency of a circle shape by 80 % or more and the elliptic shape by 1.5 times. To provide seeding of the increased doses of mineral fertilizers, the authors recommended keeping operating mode of the serial coil operation, using parabolic grooves.

Load performance analysis of three‐pad fixing pad aerodynamic journal bearings with parabolic grooves

AbstractThree‐pad fixing pad aerodynamic journal bearings (TPFPAJBs) have been widely used in precision instruments due to their low friction, high stability and non‐pollution. In order to improve the load performance of TPFPAJBs, parabolic grooves are opened in the bearing pad surfaces. By opening parabolic grooves in various bearing pad surfaces, the effects of the orientation angle, distance, width and depth of the grooves on the load performance of micro‐grooved TPFPAJBs can be investigated. The numerical results show that the location of the micro‐grooved bearing pads can greatly affect the load performance of micro‐grooved TPFPAJBs. When the given bearing pad surface is grooved, the effects of the bearing number and width‐to‐diameter ratio on the load performance of micro‐grooved TPFPAJBs can be studied. The bearing number and width‐to‐diameter ratio are observed to have significant influences on the load performance of micro‐grooved TPFPAJBs. Copyright © 2015 John Wiley & Sons, Ltd.

Identification of Plasmonic Modes in Parabolic Cylinder Geometry by Quasi-Separation of Variables.

This paper describes the plasmonic modes in the parabolic cylinder geometry as a theoretical complement to the previous paper (J Phys A 42:185401) that considered the modes in the circular paraboloidal geometry. In order to identify the plasmonic modes in the parabolic cylinder geometry, analytic solutions for surface plasmon polaritons are examined by solving the wave equation for the magnetic field in parabolic cylindrical coordinates using quasi-separation of variables in combination with perturbation methods. The examination of the zeroth-order perturbation equations showed that solutions cannot exist for the parabolic metal wedge but can be obtained for the parabolic metal groove as standing wave solutions indicated by the even and odd symmetries.

Influence of Geometric Shapes on the Hydrodynamic Lubrication of a Partially Textured Slider With Micro-Grooves

The effect of partial surface texturing in the form of parabolic grooves, rectangular grooves, and triangular grooves on the hydrodynamic pressure is investigated in the present work. The dimensionless hydrodynamic pressure generated by the partial surface texturing is obtained by the multigrid method. The effect of the texturing parameters on the dimensionless average pressure is analyzed for a given set of operating parameters. The results indicate that the geometric shape, area density, groove depth, and orientation of the grooves have an obvious influence on the hydrodynamic pressure. However, the groove width has little effect on the dimensionless average pressure. The results of the present work demonstrate that surface texturing design is very important to generate additional hydrodynamic pressure according to the operating parameters of the mechanical components.

A planar parabolic refractive nickel lens for high-energy X-rays

A compound refractive lens made of nickel and designed for focusing high-energy synchrotron X-rays is presented. The lens consists of 600 parabolic grooves and focuses X-rays in one plane only (planar lens). The lenses made and investigated by us earlier exhibited low transmission and irregularities in the focused beam profile. Since then, improvements in lens manufacturing technology have been made. The present lens gives an almost Gaussian profile and produces four times higher intensity at its maximum compared with the intensity of primary X-ray beams of 174 keV.

The Influence of Partially Textured Slider with Oriented Parabolic Grooves on the Behavior of Hydrodynamic Lubrication

An analytical model is developed to investigate a partially textured slider of infinite width with orientation parabolic grooves. The generating mechanism for hydrodynamic lubrication of the partial surface texturing in the sliding surface is similar to that of a step slider. By using the multigrid method, the hydrodynamic pressure generated by the partial surface texturing is obtained. The surface texturing parameters are numerically optimized to obtain maximum hydrodynamic effect in terms of the dimensionless average pressure for a given set of operating parameters. The results indicate that parameters such as groove orientation angle, depth, area density, and textured fraction have an obvious influence on the hydrodynamic pressure for partial surface texturing. However, the groove width has little or no effect on the dimensionless average pressure. The results of the study show that the hydrodynamic lubrication performance can be ameliorated by optimizing the surface texturing according to the operating parameters of the mechanical components.

Hydrodynamic Lubrication of Conformal Contacting Surfaces With Parabolic Grooves

The effect of surface texturing in the form of parabolic grooves on the hydrodynamic lubrication properties is investigated in this paper. Numerical simulation of the pressure distribution of lubricant between a textured slider and a smooth, moving slider has been performed. The evaluation criterion of hydrodynamic effect of dimensionless average pressure is calculated and presented with the variation of minimum film thickness, groove width, groove depth, spacing and orientation angle. Optimum values of geometrical parameters such as the dimensionless groove depth, spacing and orientation angle are obtained which correspond to maximum average pressure. It is also noted that the average pressure increases monotonically with increasing groove width. The results show that the hydrodynamic effect can be improved by employing optimized surface texturing design.

Diffractive-refractive optics: X-ray collimator

Diffractive-refractive optics are x-ray focusing monochromators based on the diffraction on profiled crystal surface. Diffraction on longitudinal parabolic groove machined in crystal surface forms a sagittaly focused synchrotron radiation beam. Such kind of monochromator may be realized as a crystal with parabolic hole, where the beam is diffracted on the inner wall of the hole. Two such asymmetrically cut crystals set into antiparallel position, creating a dispersive (+,-,-,+) arrangement, form a sagittaly focusing x-ray monochromator which should be practically aberration-free. The focusing properties of such kind of monochromator are discussed in detail and it is shown for the first time that it can be used not only for focusing but also for creating highly parallel monochromatic beam in the broad region of the Bragg angles. This device with parabolic hole has not been tested experimentally yet.

DPSM Modeling for Studying Interaction Between Bounded Ultrasonic Beams and Corrugated Plates with Experimental Verification

Periodically corrugated structures play an important role in the field of vibration control and for designing structures with desired acoustic band gaps. Analytical solutions for corrugated plates are available for well-defined, smooth corrugations, such as sinusoidal corrugations that are not very common in the real world. Often corrugated plates are fabricated by cutting grooves at regular intervals in a flat plate. No analytical solution is available to predict the wave propagation behavior in such a periodically corrugated plate in which the equation of the plate surface changes periodically between a planar fiat surface and a nonplanar parabolic groove. This problem is solved here for steady-state case by a newly developed semianalytical technique called distributed point source method (DPSM), and the theoretical predictions are compared with the experimental results generated by reflecting a bounded 2.25 MHz ultrasonic beam by a fabricated corrugated plate. The main difference that is observed in the reflected beam profile from a flat plate and a corrugated plate is that the back-scattering effect is much stronger for the corrugated plate, and the forward reflection is stronger for the flat plate. The energy distribution inside the corrugated plate also shows backward propagation of the ultrasonic energy.

Complete wetting of pits and grooves

For one-component volatile fluids governed by dispersion forces an effective interface Hamiltonian, derived from a microscopic density functional theory, is used to study complete wetting of geometrically structured substrates. Also the long range of substrate potentials is explicitly taken into account. Four types of geometrical patterns are considered: i) one-dimensional periodic arrays of rectangular or parabolic grooves and ii) two-dimensional lattices of cylindrical or parabolic pits. We present numerical evidence that at the centers of the cavity regions the thicknesses of the adsorbed films obey precisely the same geometrical covariance relation, which has been recently reported for complete cone and wedge filling. However, this covariance does not hold for the laterally averaged wetting film thicknesses. For sufficiently deep cavities with vertical walls and close to liquid-gas phase coexistence in the bulk, the film thicknesses exhibit an effective planar scaling regime, which as a function of undersaturation is characterized by a power law with the common critical exponent -1/3 as for a flat substrate, but with the amplitude depending on the geometrical features.

Complete Wetting of Nanosculptured Substrates

Complete wetting of geometrically structured substrates by one-component fluids with long-ranged interactions is studied theoretically. We consider periodic arrays of rectangular or parabolic grooves and lattices of cylindrical or parabolic pits. We show that the midpoint interfacial heights within grooves and pits are related in the same way as for complete wedge and cone filling. For sufficiently deep cavities with vertical walls and small undersaturation, an effective planar scaling regime emerges. The scaling exponent is -1/3 in all cases studied, and only the amplitudes depend on the geometrical features. We find quantitative agreement with recent experimental data for such systems.

Aberrations of diffractive–refractive optics: Bragg-case sagittal focusing of multiple parabolic elements

The diffractive–refractive optical device consisting of four crystals in (+, −, −, +) setting with longitudinal parabolic grooves has a geometrical aberration which influences the achievable focus size. This aberration is discussed analytically by using a new, more precise formula for the calculation of focusing distance, which respects the finite distance between optical elements. The calculation of the intensity distribution surrounding the focus is illustrated by a ray-tracing method based on the dynamical theory of diffraction. It demonstrates an achievable focus size. Finally we discuss that this aberration may be suppressed by the slight narrowing of the groove profile. In particular, the parameter a in the equation of parabola has to slightly grow with x. A practical application may require an ultra-precise fabrication of the grooves.

Linear focusing by a plane grating with curved grooves

We study the field diffracted by a plane grating with curved (parabolic) grooves. We will demonstrate that when a monochromatic plane wave is incident on a grating with parabolic grooves the diffracted field has a focal line whose position depends on the curvature radius of the parabolas and the incidence angle of the light onto the grating. The effect described has potential applications in grating-based devices for focusing light without requiring any additional optics.

X-ray Inclined Lens

As defined here, the term ;inclined lens' means a longitudinal parabolic groove fabricated into a crystal monochromator. If properly designed, it should provide the horizontal (sagittal) focusing of an X-ray beam. The focusing is based on the sagittal deviation of the beam diffracted on the wall of the groove. This effect follows from the dynamical theory of inclined diffraction. The focusing efficiency is limited compared with other methods. On the other hand, the simplicity is the main advantage of this device. The exact shape of the groove is calculated and several methods of keeping the vertical dimension of the beam small are proposed.

Diffraction efficiency of reflection gratings with a parabolic section profile

Diffraction properties of reflection gratings with a parabolic groove profile are analyzed. It is shown that these structures produce a large number of diffracted waves with similar intensities. Theoretical and experimental results at the wavelength of 780 nm are shown. These gratings are made from holographic diffraction gratings recorded in a photoresist.