Conical Surface Research Articles

On constant-ratio surfaces of rotation in Euclidean 4-space

The general rotational surfaces of [Formula: see text] were first studied by Moore. The Vranceanu surfaces are special examples of this kind of surfaces. These constant-ratio surfaces are surfaces for which the ratio of the norms of the tangent and normal components of the position vector fields is constant. However, spherical surfaces and conical surfaces are also trivial examples of constant-ratio surfaces. Thus, if the norms of the tangent or normal components of the position vector fields are constant, then the given surface is called [Formula: see text]-constant or [Formula: see text]-constant, respectively. In this paper, we considered three types of rotational surfaces lying in [Formula: see text]-dimensional Euclidean space [Formula: see text]. We have obtained the necessary and sufficient conditions for these surfaces to satisfy the [Formula: see text]-constant, [Formula: see text]-constant or constant-ratio conditions. With the help of these results, we characterized the meridian curves of the surfaces. Further, we also give some examples to support the results obtained.

The influence of cone structure and wettability on vaporization nucleation

Surface wettability and surface structure are critical factors that affect vaporization nucleation. However, their coupling effects on nucleation have yet to be thoroughly studied. This study employs molecular dynamics (MD) techniques to investigate the impact of nanostructures and walls with varying wettability on vaporization nucleation. Theoretical analysis verification demonstrate that increasing the hydrophobic ratio of the hybrid wall or adding a cone structure to the wall reduces the vaporization nucleation time.Previous studies did not separate the “surface area” and “cone height” factors when examining the relationship between cone surface structure and boiling. In this work, we analyzed the factors that affect vaporization nucleation. We found that increased surface area shortens nucleation time, and when the surface area is the same, higher cone heights lead to shorter nucleation times. Additionally, we examined the coupling effect of surface structure and wettability on nucleation. The results indicate that an increased proportion of hydrophobic walls with identical surface structures enhances the likelihood of nucleation. Furthermore, hydrophilic wall-hydrophobic cones with the same hydrophilic-hydrophobic ratio are more prone to nucleation than hydrophobic wall-hydrophilic cones. These findings provide insights into the design of nanostructures to enhance heat transfer involving boiling.

CENTRIFUGAL PUMP ROTOR NUT

A centrifugal pump rotor is proposed with the impeller mounted on the shaft using two nuts of fixed interacting reciprocal conical surfaces. The scientific work relates to the field of pump engineering, namely, to one of the methods of locking the rotor nut used in the design of centrifugal pumps, various self-locking devices of mechanisms and structural elements of fasteners that prevent self-unscrewing. The self-locking nut includes a nut, a solid crown with an inner conical surface interacting with the annular groove of the nut itself and with an annular conical groove on the outer surface and, moreover, on one side of the annular groove of the nut itself with a conical outer surface, and the inner conical surface of solid crown is conjugated with the outer conical surface of the nut itself. The inner conical surfaces of the solid crown are connected to the outer ones – the nut with tension.

Characterization of a pyritized fossil pollen cone from Clarkia, Idaho

The Miocene Lake deposit in Clarkia, Idaho is composed of highly fossiliferous silty clays. These rocks were formed in an anoxic and likely toxic deep lacustrine environment which facilitated the fossilization of plant material with a high amount of morphological detail. Many of the plant compression fossils exhibit exceptional preservation, including the preservation of original biomolecules. Pyritized plant specimens are much less common and the details of plant pyritization at this site are not yet fully understood. Pyritized male pollen cones from Taxodium dubium provide an opportunity to explore the processes of pyrite preservation in the Clarkia deposit.One specimen was examined using scanning electron microscopy (SEM) and energy-dispersive x-ray analysis (EDS). The only pyrite textures observed on this specimen were framboids and framboidal microcrystals. Pyrite was found in abundance on the surface of the pollen cones and to a much lesser extent on the surface of the stem. Underneath the pyrite coating, both the cones and stem were carbon-rich, indicating organic preservation. Some pyrite crystals were found in the interior of the stem, but likely originated from the exterior and developed through cracks or tears in the fossil. Pyrite crystals did not form inside the cell walls of the stem. The decaying specimen likely provided a scaffold that could facilitate the formation of pyrite upon the specimen surface. Gypsum crystals found in close association with pyrite likely formed as a product of oxidation after the specimens were taken from the rock.

Large Amplitude Vibration of FG-GPL Reinforced Conical Shell Panels on Elastic Foundation.

Functionally graded (FG) composite structures reinforced by graphene platelets (GPL) have been widely adopted as a state-of-the-art structural element due to their preeminent properties and functional designability. However, most studies are confined to beams, plates, and cylindrical panels, relying on the numerical differential quadrature method (DQM) and the finite element numerical method. In this context, the current study intends to investigate the nonlinear free vibration of FG-GPL-reinforced composite (RC) conical panels resting on an elastic medium by developing a 2-D planar meshfree method-based nonlinear numerical method. The nonlinear free vibration problem is expressed by the first-order shell deformation theory and the von-Kármán nonlinearity. The complex conical neutral surface of the panel is transformed into a 2-D rectangular plane to avoid painstaking mathematical manipulation. The troublesome shear-membrane locking is suppressed by employing the MITC3+shell element, and the derived nonlinear modal equations are solved by introducing a three-step direct iterative scheme. The present method is compared with the DQM through the benchmark experiment, from which a good agreement between the two methods is observed. And, the nonlinear free vibration characteristics of FG-GPLRC conical panels on an elastic foundation are profoundly investigated, and it is found that those are significantly influenced by the foundation stiffness, the amount and dispersion pattern of GPLs, the panel geometry sizes, and the boundary condition.

AN OBSERVER MOVING ALONG A CONE IN <span class="inline-formula"><span class="math">\({{\mathbb{R}}^{{\mathbf{3}}}}\)</span></span> UNDER CONDITIONS OF OPPOSITION FROM THE OBJECT

The paper presents two models of motion of a corporeal observer along a conical surface in \({{\mathbb{R}}^{3}}\), when the observed moving object has a set of high-speed hitting mini-objects.

Cross-Diffusion and Higher-Order Chemical Reaction Effects on Hydromagnetic Copper–Water Nanofluid Flow Over a Rotating Cone in a Porous Medium

Spin coating of engineering components with advanced functional nanomaterials which respond to magnetic fields is growing. Motivated by exploring the fluid dynamics of such processes, a mathematical model is developed for chemically reactive Cu–H2O magnetohydrodynamic (MHD) nanofluid swirl coating flow on a revolving vertical electrically insulated cone adjacent to a porous medium under a radial static magnetic field. Heat and mass transfer is included and Dufour and Soret cross-diffusion effects are also incorporated in the model. Thermal and solutal buoyancy forces are additionally included. To simulate chemical reaction of the diffusing species encountered in manufacturing processes, a higher-order chemical reaction formulation is also featured. Via suitable scaling transformations, the governing nonlinear coupled partial differential conservation equations and associated boundary conditions are reformulated as a nonlinear ordinary differential boundary value problem. MATLAB-based shooting quadrature with a Runge–Kutta method is deployed to solve the emerging system. Concentration, temperature and velocity variations for various nondimensional flow parameters have been visualized and analyzed. In addition, key wall characteristics, i.e., radial and circumferential skin friction, Nusselt number and Sherwood number, have also been computed. Validation with earlier studies is also included. The simulations indicate that when compared to a lower-order chemical reaction, a higher-order chemical reaction allows a greater rate of heat and mass transfer at the cone surface. Increasing Dufour (diffuso-thermal) and Soret numbers generally reduces radial and circumferential skin friction and also Nusselt number, whereas it elevates the Sherwood number. Both skin friction components are also suppressed with increasing Richardson number. Strong deceleration in the tangential and circumferential velocity components is induced with greater magnetic field.

Influence of nozzle external geometry on the emission of screech tones

The effect of external nozzle geometry on the emission of screech tones was studied experimentally. Four conical reflector surfaces, with half-angles ranging from 60° to 90°, were installed around the exit of a round convergent nozzle. The investigation focused on two closely spaced fully-expanded Mach numbers, M j = 1.32 and 1.34. The acoustic far-field was surveyed by a microphone phased array that included a continuously-scanning microphone, the latter enabling high spatial resolution. The isolated jets contained well-known screech mode B and its harmonics. Addition of the reflectors caused significant changes in the modal emission pattern, with tones traditionally linked to mode C occurring at M j = 1.34 but not at M j = 1.32. Tonal components associated with new modes E and F emerge at both Mach numbers when the cone half-angle is 60° or 70°. The noise source distribution generally elongates with decreasing cone angle. Some modes show clear scattering from the reflectors, while others do not. The study underscores the complexity that initial conditions can impart on the modal structure of screech and demonstrates the capability of the continuous-scan beamforming technique in resolving fine features of the source.

Использование способов начертательной геометрии для графического исследования параметров режущей части спирального сверла

The article presents examples of practical application of descriptive geometry methods for solving engineering problems of determining and studying the parameters of the cutting part of a spiral drill. The necessity of graphical constructions is noted, which is due to the fact that it is impossible to measure the rear angle by a direct measurement method using a universal measuring instrument due to the complex geometric shape of the measuring object. The analysis of the geometric shape of the working part of the spiral drill, which includes the main rear conical surface of the drill tooth, the front screw surface of the drill groove, the cylindrical surface of the tooth back, the main and transverse cutting edges are presented. Using the double contact theorem, a projection of the tooth profile of a spiral drill is constructed on a plane parallel to the drill axis with a given profile projection on a plane perpendicular to the drill axis. The tooth profile is determined by the lines of intersection of the conical surface with the cylindrical surface and with the helical surface of the drill groove. The shape of the drill groove is considered to be set. Projections of the transverse cutting edge of the drill are constructed as lines of intersection of two conical surfaces with intersecting axes. The problem is solved using a bundle of auxiliary planes. The tendency of an increase in the angle of inclination of the transverse cutting edge to the drill axis with a decrease in the distance between the intersecting axes of conical surfaces is shown. Graphically, at an arbitrary point of the drill blade, the value of one of the main geometric parameters of the drill - the rear angle is determined. It is shown that the closer the point of the blade is to the center of the drill, the greater the value of the rear angle. The constructions are made in the 2D Compass-Graph design system. The paper used alternative methods for solving geometric problems, which, unlike traditional ones, provide a simpler and more visual graphical solution.

An Analysis Model for Predicting Windage Power Loss of Aviation Spiral Bevel Gears Under Optimal Injection Jet Layout

With the increasing rotating speed of aviation spiral bevel gears, the load-independent windage power loss caused by hydrodynamic behavior has a greater impact on transmission efficiency. An analytical model is established to predict the windage power loss of spiral bevel gears with oil injection lubrication. The improved model regards the total windage losses as the sum of oil–gas dragging effects on the tooth flank, toe/heel, circular cone surface, circumference of the teeth, and tooth root. Then the numerical method and analytical method are combined to calculate windage losses. A multi-objective NSGA-II optimization algorithm is used to optimize the jet layout parameters. The rationality and accuracy of this model are verified by comparing the calculation results of an example with data sets of existing experimental findings and computational fluid dynamics (CFD) simulation results. The calculation results show that compared with the tooth profile assumption method in the existing literature, the improved calculation formula of windage dragging effect on tooth flank can better reflect the influence of oil injection lubrication layout parameters on windage loss and make the windage loss calculation more accurate. Finally, the influence of gear body parameters, working conditions parameters, geometric parameters, and injection lubrication layout parameters on the windage loss is examined. This research provides a theoretical basis and methodological guidance for optimization design of reducing windage power loss.

Electroosmotic flow, ionic current rectification, and selectivity of a conical nanopore modified with a pH-regulated polyelectrolyte layer: Influence of functional groups profile

Nanopores functionalized with polyelectrolyte (PE) brushes on their surface are widely used to improve the performance of solid-state nanopore-based devices. Since the profile of the functional groups, and therefore, fixed charge density, inside PE layer can be influenced by surrounding conditions and the way a nanopore is modified, it is usually nonuniformly distributed. However, a theoretical model taking account of the presence of a PE layer on the nanopore surface assumes that its functional groups are uniformly distributed. In this study we consider a conical nanopore surface modified with a pH-regulated PE layer. Two types of PE layer are considered: the functional groups are clustered near the PE-liquid interface (type 1), and near the nanopore surface (type 2). We theoretically study the influence of pH, types of PE layer, and bulk salt concentration on the ion transport behavior of the nanopore, and the associated mechanisms are discussed. The dependence of the average electroosmotic flow on relevant driving force and resistive force, including shear stress and drag, is analyzed. The influence of the types of PE layer on the I−V, rectification, and selectivity behaviors of the nanopore depends highly on the levels of pH and applied potential. The larger diffusion flux of type2 polyelectrolyte layer is the most important factor affecting current performance. Knowing the rectification behavior of a nanopore is helpful for estimating the solution pH and understanding the profile of the functional groups in PE. A reversal in selectivity is observed when both pH and bulk salt concentration are low, which can be attributed to that the ionic flux is dominated by H+.

Free convection flow from a heated cone with a downward tip submerged in Newtonian fluids employing a finite volume technique

Computational fluid dynamics technique have been employed to capture the plain convective flow past from a heated cone with a tip downward in various stagnant Newtonian fluids. Using detailed isotherm patterns around the cone under steady-state conditions examine the heat transfer characteristics that have been reported. The findings illustrate the distribution of the friction factor, average Nusselt number and local Nusselt number around the cone surface over a wide range of dimensionless values such as Grashof and Prandtl numbers. The guiding PDEs such as conservation of mass, momentum and energy are solved by finite volume method using commercial software of ANSYSCFX16.0. To simplify the governing equations while capturing the natural convection, Boussinesq approximation has been adopted to coupling the flow and temperature fields.This study reveals the contribution of various angles (φ = 15°,300and45°), diverse Prandtl numbers (Pr = 0.71,5,10,20,50) and distinct Grashof numbers (GrL = 104, 105, 106) for the efficacy of them over the slant surface of the cone. The heat transmission and parametric features of these processes have been discussed for how heat can be transferred from a heated cone when it is submerged in a liquid. Visualization of the effects of different parameters for different cone apex angles was done by displaying the results graphically. The present simulations are in a near match to the numeric values appeared in the literature.

Concircular helices and concircular surfaces in Euclidean 3-space $\mathbb{R}^{3}$

In this paper we characterize concircular helices in $\mathbb{R}^{3}$ by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in $\mathbb{R}^{3}$ as a special family of ruled surfaces, and we show that $M\subset\mathbb{R}^{3}$ is a proper concircular surface if and only if either $M$ is parallel to a conical surface or $M$ is the normal surface to a spherical curve. Finally, we characterize the concircular helices as geodesics of concircular surfaces.

Research on the calculation method of windage power loss of aviation spiral bevel gear and experiment verification

This paper proposes a method for calculating windage power losses of spiral bevel gears by dividing the losses into the sum of windage effects on tooth surface, toe/heel, conical surface, and circumferential surface, according to the gear structure. A calculation model for each component of windage losses is established based on the basic equation of fluid dynamics. Subsequently, a windage loss measurement test bench is developed, and a windage moment measurement method is proposed for experimental spiral bevel gears. The individual contributions of each windage loss component are calculated. The results of the calculations indicate that the gear speed is the primary factor that impacts windage losses, with the windage power loss being proportional to the 2.96th power of gear speed. Gear geometry parameters and the jet flow impacting the tooth surface are also significant factors, followed by the hub and spoke values in the wheel body parameters. The findings also show that an increase in lubricating oil content in oil-gas two-phase flow can significantly increase windage losses. Finally, a comparison between the dimensionless windage calculation values and the experimental measurement values demonstrates good agreement. This paper provides theoretical guidance for future research aimed at reducing windage power loss and improving the efficiency of aviation gear transmission.

Construction of the Stable Lubricant Film on One-Dimensional Cone-Structured Surfaces for Directional Liquid Transport.

Directional liquid transport along one-dimensional structures finds vast applications in fog harvest, liquid separation, sensing, chemical synthesis, and numerous other scenarios. Dynamically, the liquid transport speed is boosted by the driving force and retarded by the hysteresis from the liquid/substrate interface. A capillary force-relied lubricant film or a covalently attached polymer brush on the surface could increase liquid mobility temporarily by reducing the interfacial hysteresis. However, the easy depletion of the lubricant film and the stringent restriction of the substrate severely hamper droplet's directional transport in a long run. Herein, we report a feasible and durable hysteresis reduction design with the polymer-brush stabilized lubricating surface (PBSLS). The PBSLS is achieved through incorporating liquid-like polydimethylsiloxane brushes (b-PDMS) and the liquid PDMS oligomer (o-PDMS). The covalent attached b-PDMS "locks" the lubricant oil o-PDMS to the cone surface via strong intermolecular van der Waals force in between. The PBSLS on the cone surface can be sustained under constant shearing force from liquid transport for at least 6 h. A cone with such PBSLS shows increased ability of droplet transport and enhanced fog collection performance in the long run. This design supplies an effective way toward regulating macro-level interfacial performance through surface design on the molecular level.

WITHDRAWN: Enhancing industrial applicability of aluminum alloys chips recycling through Friction Stir Extrusion: Thin wires production process

Friction Stir Extrusion is one of the most promising solid-state chip recycling techniques because of its relative simplicity and high efficiency. One of the most straightforward applications for the process is the production of recycled wires to be used as filler material in welding or welding-based additive manufacturing processes, in order to create an industrial symbiosis link, fostering a circular economy and enhancing the Technology Readiness Level (TRL) of the process. The scalability of the process to the thin wires needed for such applications has not been investigated so far. In this paper, an experimental and numerical analysis was developed. A dedicated numerical model was first validated and then used to design the tool geometry. The effect of tool rotation and tool force on both “standard” mechanical properties, as UTS and microhardness, and specific properties for the envisaged application, as the wrapping around reels with different radii, was investigated. The numerical model results were used to explain the influence of the process parameters on the distribution of the main field variables, i.e., temperature, strain, and strain rate, as well as on material flow. It was found that a conical shoulder surface favors the conditions for effective solid bonding. Low values of the extrusion force have detrimental effects on the wires properties as they result either in insufficient strain, or hot cracking defects.

Wave Diffraction from a Bicone Conjoined with an Open-Ended Conical Cavity

The problem of axially symmetric TM-wave diffraction from a bicone conjoined with an open-ended conical cavity is analysed rigorously. The scatterer is formed by the perfectly conducting semi-infinite and truncated semi-infinite conical surfaces; the spherical termination of an internal area of the truncated cone creates the open-ended cavity. In this paper the certain physical aspects of diffraction which are known to cause mathematical difficulties are considered. It includes an accurate analysis of the wave-mode transformation phenomena at the open end of the cavity, as well as a study of wave radiation from the cavity into the biconical waveguide. The primary outcome of this paper is a precise treatment of the wave diffraction problem mentioned above using new techniques and establishing new properties of resonance modes’ penetration into the biconical waveguide region.

Developable Surfaces Foliated by General Ellipses in Euclidean Space R3

In this article, we classify the developable surfaces in three-dimensional Euclidean space R3 that are foliated by general ellipses. We show that the surface has constant Gaussian curvature (CGC) and is foliated by general ellipses if and only if the surface is developable, i.e., the Gaussian curvature G vanishes everywhere. We characterize all developable surfaces foliated by general ellipses. Some of these surfaces are conical surfaces, and the others are surfaces generated by some special base curves.

Study regarding the influence of process conditions on the surface topography during ultra-precision turning

During ultra-precision turning, the turned surface “copies” a large amount of turning process condition information. In this study, the path equations were combined with the turned surface topography equations, and the condition parameters were superimposed to develop theoretical surface topography models for ultra-precision turned end face, cylindrical, conical, and spherical surfaces influenced by turning condition parameters. The models were validated through a series of experiments. The turned surfaces were analyzed in the spatial frequency domain, and the corresponding relationship between the frequency information in the time domain and the spatial domain was obtained. The corresponding area power values were calculated to determine the quantitative impact of condition parameters on surface roughness. According to the calculation results, the surface roughness under the influence of process conditions was positively correlated with the amplitude of turning process condition parameters. The topography of the simulated surfaces was consistent with that of the experimental surfaces, and the trend of area power values corresponding to different turning process condition parameters in the simulated surface topography was consistent with the experimental results. It was proved that the established relational model, which determined the qualitative and quantitative influence of machining conditions on the machined surface, is tenable. This study established a mapping relationship between the machining condition parameters and their impact on surface topography, and also further provided a foundation for the digitization of ultra-precision machine tools.

Sequence variants contributing to dysregulated inflammatory responses across keratoconic cone surface in adolescent patients with keratoconus.

Keratoconus (KTCN) is the most common corneal ectasia resulting in a conical shape of the cornea. Here, genomic variation in the corneal epithelium (CE) across the keratoconic cone surface in patients with KTCN and its relevance in the functioning of the immune system were assessed. Samples from four unrelated adolescent patients with KTCN and two control individuals were obtained during the CXL and PRK procedures, respectively. Three topographic regions, central, middle, and peripheral, were separated towards the whole-genome sequencing (WGS) study embracing a total of 18 experimental samples. The coding and non-coding sequence variation, including structural variation, was assessed and then evaluated together with the previously reported transcriptomic outcomes for the same CE samples and full-thickness corneas. First, pathway enrichment analysis of genes with identified coding variants pointed to "Antigen presentation" and "Interferon alpha/beta signaling" as the most overrepresented pathways, indicating the involvement of inflammatory responses in KTCN. Both coding and non-coding sequence variants were found in genes (or in their close proximity) linked to the previously revealed KTCN-specific cellular components, namely, "Actin cytoskeleton", "Extracellular matrix", "Collagen-containing extracellular matrix", "Focal adhesion", "Hippo signaling pathway", and "Wnt signaling" pathways. No genomic heterogeneity across the corneal surface was found comparing the assessed topographic regions. Thirty-five chromosomal regions enriched in both coding and non-coding KTCN-specific sequence variants were revealed, with a most representative 5q locus previously recognized as involved in KTCN. The identified genomic features indicate the involvement of innate and adaptive immune system responses in KTCN pathogenesis.