Elliptic Cone Research Articles

A Model of Diameter Measurement Based on the Machine Vision

If the shaft diameter can be measured in-situ during the finishing process, the closed-loop control of the shaft diameter processing process can be realized and the machining accuracy can be improved. Present work studies the measurement of shaft diameter with the structured light system composed of a laser linear light source and a camera. The shaft is a kind of part with rotationally symmetric structure. When the linear structured light irradiates the surface of the shaft, a light stripe will be formed, and the light stripe is a part of the ellipse. Therefore, the in-situ measurement of the shaft diameter can be realized by the light stripe and the rotational symmetry of the shaft. The measurement model of shaft diameter is established by the ellipse formed by the intersection of the light plane and the measured shaft surface. Firstly, in the camera coordinate system, normal vector of the light plane and the coordinates of the ellipse center are obtained by the calibration; then, the equation of oblique elliptic cone is established by taking the ellipse as the bottom and the optical center of the camera as the top. Next, the measurement model of shaft diameter is obtained by the established oblique elliptic cone equation and theoretical image plane equation. Finally, the accuracy of the measurement model of shaft diameter is tested by the checkerboard calibration plate and a lathe. The test results show that the measurement model of shaft diameter is correct, and when the shaft diameter is 36.162mm, the speed is 1250r/min, the maximum average measurement error is 0.019mm. The measurement accuracy meets the engineering requirement.

HIFiRE-5b Boundary-Layer Transition Length and Turbulent Overshoot

Hypersonic International Flight Research Experimentation 5 (HIFiRE-5) is a hypersonic flight-test experiment designed to investigate the aerothermodynamics of a 3-D geometry. The vehicle is an elliptic cone with a 2:1 aspect ratio and 2.5 mm nose radius. The HIFiRE-5b achieved a Mach number of 7.7–7.9 and freestream unit Reynolds number of to during descent. Heat flux was calculated from thermocouple pairs and boundary-layer transition locations were identified from these heating rates. A multilobed transition front was observed; it is suspected that a different mechanism is responsible for each of these lobes. The vehicle’s attitude oscillated, which has been exploited to assess the sensitivity of heat flux to yaw angle along the leading edges and ascertain the appropriateness of the filtering applied to the thermocouple signals. Spatial heat-flux profiles have been constructed for constant freestream unit Reynolds numbers. The heat-flux rate at the end of transition is examined; turbulent overshoot was present along some azimuths, but not others. This flight-test result indicates the phenomenon is not specific to ground test, freestream noise level, or wall-to-stagnation-temperature ratio. Finally, transition length (its end location normalized by its onset location) is reported and connected to turbulent spot generation rates.

Experimental research on crossflow instability for a hypersonic 4∶1 elliptic cone

In this work, the cross-flow instability on the surface of a blunt elliptical cone with a long-short-axis ratio of 4∶1 is studied experimentally in the Mach 6 hypersonic quiet wind tunnel. Comprehensive use of temperature sensitive paint (TSP) technology, nano-tracer-based planar laser scattering (NPLS) technology and Kulite sensor pressure test to measure the temperature distribution in the cross-flow area on the surface of the model, boundary layer flow structure and model surface pressure are tested. The mechanism of boundary layer transition in the cross-flow control area on the surface of the elliptical cone is studied, and the influence law of incoming flow unit Reynolds number and angle of attack on boundary layer transition is obtained, and some conclusions are obtained below. In the wind tunnel noise mode, the transition of the boundary layer in the cross-flow area between the surface center line and the leading edge of the elliptical cone model with a length-to-short-axis ratio of 4∶1 is controlled by the traveling waves, and no footprint of the steady vortex is found. The characteristic frequency of the traveling wave is about 20 kHz. When the unit Reynolds number of the incoming flow increases, the transition position will be advanced, and the frequency and amplitude of the traveling wave will increase. Within a certain angle of attack, the transition position of the upwind boundary layer is delayed, and the characteristic frequency of the traveling wave does not change much but the energy is weakened. When the angle of attack continues to increase, the transition phenomenon disappears.

A robotic grasping approach with elliptical cone-based potential fields under disturbed scenes

Vision-based grasping plays an important role in the robot providing better services. It is still challenging under disturbed scenes, where the target object cannot be directly grasped constrained by the interferences from other objects. In this article, a robotic grasping approach with firstly moving the interference objects is proposed based on elliptical cone-based potential fields. Single-shot multibox detector (SSD) is adopted to detect objects, and considering the scene complexity, Euclidean cluster is also employed to obtain the objects without being trained by SSD. And then, we acquire the vertical projection of the point cloud for each object. Considering that different objects have different shapes with respective orientation, the vertical projection is executed along its major axis acquired by the principal component analysis. On this basis, the minimum projected envelope rectangle of each object is obtained. To construct continuous potential field functions, an elliptical-based functional representation is introduced due to the better matching degree of the ellipse with the envelope rectangle among continuous closed convex curves. Guided by the design principles, including continuity, same-eccentricity equivalence, and monotonicity, the potential fields based on elliptical cone are designed. The current interference object to be grasped generates an attractive field, whereas other objects correspond to repulsive ones, and their resultant field is used to solve the best placement of the current interference object. The effectiveness of the proposed approach is verified by experiments.

Fractional characterization of fluid and synergistic effects of free convective flow in circular pipe through Hankel transform

Although heat transfer by transient free convection has been investigated with different cross sections such as elliptical cones, rectangular or square ducts, and triangular plates, none of the analytical study of a circular cylinder in free space via fractional calculus approaches with sinusoidal conditions is explored. This manuscript presents fractional modeling of a circular cylinder to observe the heat transfer by transient free convection flow subject to the sinusoidal boundary conditions. The fractionalized mathematical model is solved via Hankel and Laplace transforms through two types of fractional calculus approaches called Atangana–Baleanu and Caputo–Fabrizio differential operators. The governing equations of the circular cylinder have been coupled for the sake of thermally interacting effects for knowing the hidden role of a particular geometry, viz., circular cylinder. In the literature, the analytic solutions for concentration, temperature, and velocity have been explored by means of Mittage–Leffler functions. The comparative investigation of heat transfer based on embedded rheological parameters such as the Prandtl number (Pr), Schmidt number (Sc), thermal Grashof number (Gr), and mass Grashof number (Gc) has been depicted as graphs via Atangana–Baleanu and Caputo–Fabrizio differential operators.

Determination of the structural efficiency of quadric and cylindrical surfaces when used as reinforced concrete roof structures

Modern architecture of civil engineering structures made of reinforced concrete is demanding solutions to problems related to design and construction of roofs shaped as creative forms which require an adequate combination of arts and physical-mathematical models. In that sense, the quadric and cylindrical surfaces offer an attractive based on their volumetric expression, historicity, and mathematical feasibility. In this work, seven cylindrical and quadric surfaces named elliptic cylinder, parabolic cylinder, elliptic cone, elliptic paraboloid, hyperbolic paraboloid, ellipsoid and hyperboloid of two sheets have been analysed to find out which of them show to be more efficient when used as reinforced concrete roof structures. To do so, the configuration of each structure hase been adjusted in terms of similar stiffness, strength parameters and enclosed volume. The structural efficiency was computed using the results of weight/load ratio, available strength, material consumption and relative stiffness. The solution of the model has been achieved using a combination of exact solutions and numerical methods. To compute the model results a Matlab® code was written and validated using the structural software SAP2000®. The best structural efficiency in terms of stiffness, strength, and materials consumption was obtained for roofs configurated using surfaces built from parabolas, i.e., elliptic paraboloid, hyperbolic paraboloid, and parabolic cylinder. The results of this work can be used in future studies and applications related to arhitectural comfort, structural behaviour and material consumption in construction of roofs.

Numerical Simulation of Characteristics of Spray Flow Field on the Conical Surface

Aiming at the gas-liquid two-phase flow process in the spray flow field on the conical outer surface, based on Euler-Euler method a spray film forming model is proposed. A polyhedral mesh was utilized to divide the fluid computing domain and the coupled SIMPLE algorithm was adopted to solve the model. The results of show that the spray shape on the outer surface of the cone is similar to that on the outer surface of the arc, and both are in the shape of an elliptical cone; in the area far away from the wall surface, the difference ofsurface has almost no effect on the spray cone angle. In terms of the spraying speeds of the two spraying methods within the area close to the outer surface of the cone, for the circumferential spraying, the spray normal speed is higher than that of spraying along the busbar, and the maximum tangential speed is lower. Meanwhile, both the two speeds are almost equal to that of spraying the arc surface; for spraying along the busbar, the spray normal speed is higher than that of the arc outer surface, and the maximum tangential speed is lower.

Boundary Value Problems for Elliptic Pseudodifferential Equations in a Multidimensional Cone

We consider model boundary value problems for elliptic pseudodifferential equations in multidimensional cones. A result on the unique solvability and representation of solutions of some boundary value problems in suitable Sobolev–Slobodetskii spaces is obtained. A priori estimates of solutions are given.

Forced vibration analysis of composite-geometrically exact elliptical cone helices via mixed FEM

In this pioneering study, the cross-sectional warping included transient response and normal/shear stress components of composite elliptical and elliptical cone helices over exact axis geometry are investigated using a mixed FEM. The transient analysis is performed using the Newmark time integration algorithm with or without the amplitude decay factor. The constitutive equations of composite curved rods are derived from three-dimensional elasticity theory. A displacement-type finite element formulation computing the warping-included torsional rigidity is incorporated with the mixed finite element formulation. The curvatures and displacement-type finite elements are used to estimate the normal and shear stress distributions on the respective cross-sections. The maximum normal/shear stresses of a composite straight beam are compared with the literature. An excellent agreement is obtained for the results of an exact elliptical cone helix under dynamic loads compared to the results of 3D solid finite elements. During the implementation of the time integration scheme, the first and second time derivatives of forces and moments are preserved, and their time histories are discussed. Finally, the influences of helix geometry, lamination, and the ratios of material constants on the transient response besides the stresses are investigated. All the numerical examples in this paper are original for the literature.

On the symmetry of induced norm cones

ABSTRACT Several authors have studied the problem of making an asymmetric cone symmetric through a change of inner product, and one set of positive results pertains to the class of elliptic cones. We demonstrate that the class of elliptic cones is equal to the class of induced-norm cones that arise through Jordan-isomorphism with the second-order cone, thereby showing that this symmetry result was essentially known.

Real-Time Size and Mass Estimation of Slender Axi-Symmetric Fruit/Vegetable Using a Single Top View Image.

Among the physical attributes of agricultural materials, mass, volume, and sizes have always been important quality parameters. Previous research focused mostly on volume estimation using stereo-based approaches, which rely on manual intervention or require a multiple-cameras set up or multiple-frames captures from different viewing angles to reconstruct the three-dimensional point-cloud information. These approaches are tedious and not suitable for practical machine vision systems. In this work, we only use a single camera mounted on the ceiling of the imaging chamber, which is directly above the fruit/vegetable to capture its top-view, two-dimensional image. We developed a method to estimate the mass/volume of agricultural products with axi-symmetrical shapes such as a carrot or a cucumber. The mass/volume is estimated as the sum of smaller standard blocks, such as chopped pyramids, an elliptical cone, or a conical cone. The computed mass/volume showed good agreement with analytical and experimental results. The weight estimation error is 95% for the case of the carrot and 96.7% for the cucumber. The method proved to be sufficiently accurate, easy to use, and rotationally invariant.

CHoCC: Convex Hull of Cospherical Circles and Applications to Lattices

We discuss the properties and computation of the boundary B of a CHoCC (Convex Hulls of Cospherical Circles), which we define as the curved convex hullH (C) of a set C of n oriented and cospherical circles{Ci} that bound disjoint spherical caps of possibly different radii. The faces of B comprise: ndisks, each bounded by an input circle, t=2n−4triangles, each having vertices on different circles, and 3t∕2 developable surfaces, which we call corridors. The connectivity of B and the vertices of its triangles may be obtained by computing the Apollonius diagram of a flattening of the caps via a stereographic projection. As a more direct alternative, we propose a construction that works directly in 3D. The corridors are each a subset of an elliptic cone and their four vertices are coplanar. We define a beam as the convex hull of two balls (on which it is incident) and a lattice as the union of beams that are incident each on a pair of balls of a given set. We say that a lattice is clean when its beams are disjoint, unless they are incident upon the same ball. To simplify the structure of a clean lattice, one may union it with copies of the balls that are each enlarged so that it includes all intersections of its incident beams. But doing so may increase the total volume of the lattice significantly. To reduce this side-effect, we propose to replace each enlarged ball by a CHoCC and to approximate the lattice by an ACHoCC, which is an assembly of non-interfering CHoCCs for which the contact-faces are disks. We also discuss polyhedral approximations of CHoCCs and of ACHoCCs and advocate their use for processing and printing lattices.

Convective Heat Transfer Enhancement through Laser-Etched Heat Sinks: Elliptic Scale-Roughened and Cones Patterns

The efficient dissipation of localized heat flux by convection is a key request in several engineering applications, especially electronic ones. The recent advancements in manufacturing processes are unlocking the design and industrialization of heat exchangers with unprecedented geometric characteristics and, thus, performance. In this work, laser etching manufacturing technique is employed to develop metal surfaces with designed microstructured surface patterns. Such precise control of the solid-air interface (artificial roughness) allows to manufacture metal heat sinks with enhanced thermal transmittance with respect to traditional flat surfaces. Here, the thermal performance of these laser-etched devices is experimentally assessed by means of a wind tunnel in a fully turbulent regime. At the highest Reynolds number tested in the experiments ( R e L ≈ 16 , 500 ), elliptic scale-roughened surfaces show thermal transmittances improved by up to 81% with respect to heat sinks with flat surface. At similar testing conditions, cones patterns provide an enhancement in Nusselt number and thermal transmittance of up to 102% and 357%, respectively. The latter results are correlated with the main geometric and thermal fluid dynamics descriptors of the convective heat transfer process in order to achieve a predictive model of their performance. The experimental evidence shown in this work may encourage and guide a broader use of micro-patterned surfaces for enhancing convective heat transfer in heat exchangers.

Three-dimensional roof collapse analysis in circular tunnels in rock

Collapse of a roof in circular cross-section tunnels is analyzed. The kinematic approach of limit analysis is utilized, with strength of the rock described by the Hoek-Brown failure criterion. The parametric form of the Hoek-Brown function is used to avoid introduction of an alternative explicit form of the shear strength criterion. Three measures of safety are considered: stability number, the factor of safety, and the support pressure needed to assure roof stability. The shape of the rock block in the failure mechanism consists of a right elliptic cone with a piece-wise linear generatrix and a prismatic section inserted between the two halves of the cone. The complexity of the cross-section of the block with the tunnel makes for an intricate integration of the rates of the dissipated work and the work of external forces. All three measures of safety are strongly dependent on the quality of rock described in the Geological Strength Index, whereas the dependence on the rock type captured in coefficient mi is less distinct. The length of the roof failure mechanism is subject to a constraint dependent on the spacing of the supporting ribs in the tunnel. All measures of safety (or stability) are distinctly dependent on the length constraint; the shorter the spacing between the ribs, the safer the tunnel against roof collapse. The 2D analysis yields the most conservative outcome.

Hypersonic Flow Past Over an Elliptic Nose Cone Configurations: International Conference on Recent Trends in Artificial Intelligence, IOT, Smart Cities & Applications (ICAISC-2020)

The present work provides a detailed study of the hypersonic flow over elliptical nose cones at a Mach number of 5.8, numerically. The main focus of the paper is to determine parameters of the nose cones which provide minimum aerodynamic drag and heating. The conjugate heat transfer method is used to examine aerodynamic heat transfer between gas and surface accommodations for different fineness ratios at zero angle of attack. It is observed that for higher fineness ratio provide minimum drag. It also shows the detailed comparison of the flow/shock features in the vicinity of the elliptical nose cones for different fineness ratios in order to determine its influence on aerodynamic drag and heating. It is also noticed that the aerodynamic heating is almost same for all fineness ratios. In general, the present study reveals that at higher fineness ratios are preferred for achieving aerodynamic characteristics in hypervelocity vehicles.

The influence of the water injection method on two-well-horizontal salt cavern construction

With high construction efficiency and large usable volumes, underground TWH caverns in rock salt formations provide optimal storage for large-scale compressed natural gas. Previous studies of SWV cavern construction indicate that different water injection methods will result in different leaching rates and will therefore form different cavern geometries. Therefore the influence of the water injection method on the TWH cavern construction process and geometries were thoroughly evaluated in this study. Based on the leaching numerical simulation code TWHSMC V2.0, we conducted a series of simulation experiments. The results illustrate that under the same water injection rate, the cavern construction speed of the alternate injection method is faster than the unidirectional injection method. Using the unidirectional method will form asymmetrical triangular pyramidal caverns. In contrast, using the alternate method will form symmetrical elliptical cone caverns. Under repeated alternating “Injection” and “Withdrawal” operations, the larger the flow rate, the shorter the cavern construction time, and the smaller the H/L ratio coefficient, as well as the closer the cavern geometry is to the horizontal cavern. Thus, during construction of a TWH-cavern in thinly-bedded rock salt (halite) deposits, repeated and alternating injections and withdrawals with high flow rates are necessary.

Underwater Laser Scanner: Ray-Based Model and Calibration

Underwater 3-D perception is crucial for autonomous manipulation and mapping. Using a mirror-galvanometer system to steer a laser line projector and using triangulation with a camera it is possible to produce full 3-D perception, while avoiding moving the sensor with respect to the scene. This paper presents a ray-based model of a laser scanner and a calibration method for such a model. The model takes into account the distortion introduced to the system by the flat viewports used for both the laser and the camera. The paper also introduces the computation of elliptical cones as a way to synthesize the ray-based model and speed up the triangulation computation. The present study reports results obtained using the real sensor in a water tank to reconstruct objects and planes to assess the sensor's accuracy, as well as a comparison between the two triangulation methods (ray-based and elliptical cone).

Curvature distribution and autocorrelations in elliptic cylinders and cones

Not all micro-vessels (MV) are traditionally circular and there are examples of elliptic cylindrical MVs in life sciences, particularly if projected with a slant. Similarly, certain biological structures, ferroelectric liquid crystals, aluminum oxide clusters and witherite crystallites’ cross-section appear to be elliptical cones. We studied the mean curvature (H) distribution of these elliptic morphological structures with geometric parameter such as eccentricity; e (ratio of semi-minor to semi-major axes) and a measure of how much diagonal section deviates from circularity and height (h) in case of cones. By means of topographical cues, we defined the curvature-curvature autocorrelation function (gk) and applied this notion to mean curvature (H) of circular and elliptical cylinders and cones. The Fourier transform of correlation function, i.e. “curvature factor” is analogous to “structure factor (or Patterson function)” in X-ray and neutron scattering intensity. It elucidates critically important information related to surface curvature fluctuation relevant to shape (geometry), network and phase transformation. The latter is induced by cells under mechanical stress, occurring in many soft systems (polymeric liquid crystals, foams, bubbles) and biological tissues, particularly cell walls of primary and branched vessels bed in microvasculature that distributes blood within tissue during hypertension and migraines. This perspective is useful in a sustained release of angiogenic/vasculogenic factors and relevant for precision medicine and engineered microvessels and tissues in vitro and in vivo extended cellular processes. The quantitative analysis carried out in this work facilitates our understanding of the mechanical mechanisms associated with thrombosis during surgery that typically occur in bent or stretched MVs due to microenvironment such as localized shear stresses and biochemical factors.

Generalizing the entanglement entropy of singular regions in conformal field theories

We study the structure of divergences and universal terms of the entanglement and Rényi entropies for singular regions. First, we show that for (3 + 1)-dimensional free conformal field theories (CFTs), entangling regions emanating from vertices give rise to a universal contribution {S}_n^{mathrm{univ}}=-frac{1}{8pi }{f}_b(n){int}_{gamma }{k}^2{log}^2left(R/delta right) , where γ is the curve formed by the intersection of the entangling surface with a unit sphere centered at the vertex, and k the trace of its extrinsic curvature. While for circular and elliptic cones this term reproduces the general-CFT result, it vanishes for polyhedral corners. For those, we argue that the universal contribution, which is logarithmic, is not controlled by a local integral, but rather it depends on details of the CFT in a complicated way. We also study the angle dependence for the entanglement entropy of wedge singularities in 3+1 dimensions. This is done for general CFTs in the smooth limit, and using free and holographic CFTs at generic angles. In the latter case, we show that the wedge contribution is not proportional to the entanglement entropy of a corner region in the (2 + 1)-dimensional holographic CFT. Finally, we show that the mutual information of two regions that touch at a point is not necessarily divergent, as long as the contact is through a sufficiently sharp corner. Similarly, we provide examples of singular entangling regions which do not modify the structure of divergences of the entanglement entropy compared with smooth surfaces.

Modified TIG Welding Joint Process: An Approach to Improve Microstructure and Fracto-Mechanical Behavior by MWCNTs Inducement in Al-Mg-Si Alloy.

This work provides a comprehensive investigation of multi-walled carbon nanotubes (MWCNTs) inducement in weldment and their apparent effect on the microstructure, %elongation and ultimate fracture behavior of Al-Mg-Si alloy referring modified tungsten inert gas (TIG) welding joints. Serious experimental work is carried out at 1 wt%, 1.5 wt%, and 2 wt% of MWCNTs to provide a gradually increasing heterogeneous nucleation. The behavior of grain morphology showed the pure field of epitaxial growth without MWCNTs, and the forestry type morphology for 1 wt% MWCNTs at low welding currents (160 A), though there was a noticeable conversion into equiaxed (EQZ) grains filled with inter-dendritic particles at high welding currents (180 A and 200 A) for 1.5 wt% and 2 wt% of MWCNTs. Moreover, the formation of a cellular type network above the fusion line predominated initially at all parameters. Conversely, fine EQZ grains were formed as they moved upward into the welded zone (WZ) explicitly at a high heat input. A conceptual pictorial model is presented in the study which summarized the behavior of morphological changes at the utilized parameters. The welded joints have demonstrated an increasing trend of strength and %elongation in contrast to joints without added MWCNTs. Comparative results have shown an exceptional increment of 71 to 76% and 67 to 75% of elongation up to ultimate tensile strength (UTS), and a fracture point that was clinched for 1 wt% and 1.5 wt% MWCNTs at 180A. From macro to micro-examination of the fracture surfaces, pure ductile modes constituting elliptical cup and cone type isotropic flow was evident in all specimens. Detailed confirmation of the pull-out fracture mode of MWCNTs has highlighted in the scanning electron microscope (SEM) images that intimated a methodical contribution in load-transfer from matrix to the fiber under axial load. Overall, a concise en-route for MWCNTs inducement is well-appointed through tube fillers along with an activating facilitator (TiO2) in contrast to stereotype fillers for improved behavior termed as modified TIG welding joint process in study.