Cone Element Research Articles

Numerical Simulation of Plasma Spraying Performance Index

In recent years, there has been an increasing interest in plasma jet numerical simulation. Speed and temperature propagation in axial and radial direction in plasma jet significantly influences on speed and temperature of sprayed material and therefore on coating quality. However, there are few studies concerning plasma jet numerical simulation in modern software systems and they describe a specific problem. It is a wellknown fact that using simple structural components such as plasmatron heads for plasma thermal spraying allows us to increase the quality of zirconium oxide coatings by increasing the speed of spraying particles and decreasing their spread value and allows to increase economic efficiency of the process by increasing the operation factor of spraying material. However, scientists have not studied well the influence of the plasmatron head, which looks like a cone element, and the simulation of a high temperature flow along the channel is not mentioned in publications. Therefore, it is necessary to research the flow of a high temperature current along the channel of the head.

ЭКСПЕРИМЕНТАЛЬНОЕ ОПРЕДЕЛЕНИЕ ТОЧНОСТИ БАЗИРОВАНИЯ И ЗАКРЕПЛЕНИЯ ИНСТРУМЕНТА

There are presented results of experimental investigations allowing the definition of factors (parameters) influencing the accuracy of basing and fastening a tool in a machine spindle. 
 The plant design developed allows modeling the work of elements and mechanisms of a spindle unit of a jig-boring machine (JBM) at the moment of tool changing. 
 The series of experiments carried out allowed drawing the following conclusions: 
 - the accuracy of a tool installation in a machine spindle depends upon its angular position in a spindle taper; 
 - angular errors of a tool cone element decrease a rigidity of a “spindle-tool” subsystem by 10…15%; 
 - elastic movements in the area of a contact increase by 2-2.5 times at the presence of ovality in the cross-section of a holder (at ovality 18mkm); 
 - the accuracy of tool location in a spindle increases with the increase of an axial tightening force (recommended tightening force – 3 ≤ Ptight. ≤ 5kN); 
 - the holder operation results in the rigidity decrease of a tool system by 10…15% (operation term – 5 years).

Shape optimization of the cone body for the improved performance of the V-cone flowmeter: A numerical study

The present study has been carried out to optimize the shape of the cone body by providing a curved surface (the radius of curvature (R)) at the base of the cone element for improving the performance of the V-cone flowmeter using CFD. Radii of curvature of 20 mm (hemispherical, R/d = 0.5), 22 mm (R/d = 0.55) 25 mm (R/d = 0.625) and 27.62 mm (R/d = 0.6905) are taken in order to gradually reduce the arc length keeping the chord length constant. In addition a semi-elliptical based cone with 20 mm semi-major axis and10 mm semi-minor axis has also been investigated in the present study. The centre of the spheres and ellipse lie on the axis either in the frustum or cylindrical part of the cone. The equivalent diameter ratio (β) has been taken as 0.6 while three different fore-vertex angles (φ) namely 60°, 75° and 90° have been investigated. The Reynolds number has been varied in the range of 1 × 103 to 1 × 106. The results have been compared with the slant surface based cone. It is seen that introduction of a curved surface at the cone base has profound effect on the coefficient of discharge of the V-cone flowmeter. The coefficient of discharge is dependent on Reynolds number for the flowmeter with hemispherical and semi-elliptical based cone element. The coefficient of discharge is seen to be a weak function of Reynolds number for Re = 4000 and beyond for the other three curvatures. The cone flowmeter with a curved base cone of R/d equals to 0.55 has higher coefficient of discharge and smaller standard deviation compared to a device with an aft vertex cone.

Effect of vertex angle and vertex tip radius on the performance of V-cone flow meter using CFD

The aim of the present systematic study is to establish the effect of vertex angle and vertex tip radius on the performance of the V-cone flowmeter. Three different cone arrangements namely without support, front and rear supported cone element have been undertaken for a fixed beta value (β) of 0.6 with different vertex angles (φ). Shear Stress Transport k-ω (SST k-ω) turbulence model has been adopted for the closure solution. The performance evaluation is done on the basis of coefficient of discharge (Cd) and the extent of uncertainty (UCd) present in predictions within the range of Reynolds number (Re) investigated (Re = 103 to 106). This study is in the back drop of ISO 5167-5(2016) which has identified the vertex angle in the range of 52°±10°. From the study, it is revealed that in all the three mode of the cone arrangements, the cone element with vertex angle of 75° results in a discharge coefficient which is nearly constant for Reynolds number greater than 1000 with minimum uncertainty. An additional investigation has also been carried out for three vertex angles (φ) namely 60°,75° and 90° to analyze the effect of cone tip radius at Re = 5 × 105 on the performance of the V-cone flowmeter. It is seen that vertex tip radius has no effect on the performance.

Performance measurement analysis of various cone flow meters with various beta edge types and flow field parameters

The beta edge, as one part of the cone element in cone flow meters, has several types. Cone flow meters with different beta edges have different applications and measurement performance. The sharp angle, corner cut and arc are the most common forms of beta edges used in cone flow meters. Their structures are analyzed without changing other parameters. Through theoretical analysis of their hydromechanics, a conclusion can be drawn that the discharge coefficient linearity error and permanent pressure loss in cone flow meters can be predicted based on the consistency in the recirculation quantity and the dissipation function value. The research objects are cone flow meters with different beta edge forms whose inner tube diameter is 100mm and whose β values are 0.45, 0.55 and 0.65. The cone wake flow field characteristics were obtained and analyzed using the CFD method. Different beta edges cause different changes to the recirculation quantity and the dissipation in the cone wake flow region. Based on the theoretical prediction, the corner cut beta edge has the best discharge coefficient linearity error and relatively small permanent pressure loss. The accuracy of this prediction was experimentally verified. The experimental results demonstrate that the sharp-angle beta edge achieves the best performance in mechanical processing consistency, while the arc beta edge is the worst.

Experimental and numerical design of a long-waist cone flow meter

A long-waist cone flow meter is designed for steady differential pressure measurement and relatively small overall pressure drop. A constant-diameter annular flow channel is formed between cone element and pipe wall. The flow field of water flows through cone element is studied with 3-D CFD simulations. The constant-diameter annular channel is found being able to adjust the incoming fluid, and small rear angle of cone element could reduce flow separation and overall pressure difference. An optimized structure of long-waist cone flow meters, referred as LWC, is proposed based on the investigations on flow field analysis. A steady contracting differential pressure and an overall differential pressure can be tapped from a LWC. A set of LWCs was fabricated with diameter ratio β ranging from 0.55 to 0.75, and waist length L from 20 to 60mm when β=0.65 for experimental tests and CFD verifications. A decreasing trend of dimensionless differential pressure Δp* and δp* and an increasing trend of discharge coefficient Cd of LWCs under different Reynolds number are observed and analyzed, and flow rate prediction of different Newtonian single phase flow is experimentally studied. A case study of oil–water two-phase flow is then presented with a selected LWC and an average error below 5% is achieved when treating the mixture a homogeneous flow.

Optimization of Face Cone Element for Spiral Bevel and Hypoid Gears

In the blank design of spiral bevel and hypoid gears, the face cone is defined as an imaginary cone tangent to the tops of the teeth. Traditionally, the face cone element or generatrix is a straight line. On the other hand, the tooth root lines, which are traced by the blade tips, are normally not straight lines. As a result, the tooth top geometry generally does not fit the mating member’s real root shape, providing an uneven tooth root-tip clearance; additionally, in some cases root-tip interference between the tooth tip and the root tooth surfaces of the mating gear members may be observed. To address this issue, this paper describes a method of determining an optimized face cone element for spiral bevel and hypoid gears. The method is based on the incorporation of calculation of tooth surface and root geometries, the conjugate relationship of the mating gear members, the ease-off topography, and the tooth contact analysis. The resulting face cone element may not be a straight line but generally an optimized curve that, in addition, to avoidance of the interference, offers maximized contact ratio and even tooth root-tip clearance. Manufacturing of bevel gear blanks with a curved face cone element can be implemented by using computer numerically controlled machines.

Experimental and CFD investigation of 100 mm size cone flow elements

This paper presents performance characteristics of 100 mm line size cone flow elements having beta ratios of 0.4, 0.5, 0.6, 0.7 and 0.8. A magnetic flow meter is used as a reference standard for flow measurement in vertical test section. A series of experiments have been conducted using water at in-house Flow Calibration Facility (FCF) to cover the Reynolds number ranging from 20,000 to 200,000. The performance characteristics of 100 mm line size cone flow elements with different beta values have been evaluated experimentally. It is found that the discharge coefficient of the cone flow element is nearly independent of the specified range of Reynolds number. Testing of the cone flow element in accordance with new API 5.7 is carried out at flow calibration facility. The testing requirements in the standard explain the conditioning effect of the cone flow element having gate valve disturbance upstream of the cone at various locations. The effect of the upstream velocity profile has been investigated by placing a gate valve upstream of the cone flow element at a distance of 0D and 28D and performing experiments at 25%, 50% and 100% opening of gate valve. The value of the discharge coefficient is not affected when the cone is placed at a distance of 0D and for 100% opening of gate valve. The uncertainty results of the cone testing are discussed. For studying pressure and velocity distributions, cone elements are modeled using computational fluid dynamics (CFD) code PHOENICS. Pressure and velocity profiles for different sizes of cone elements are plotted. From the pressure profile, it can be seen that the pressure recovery downstream of the cone is within a distance of 3D. The velocity profile downstream of the cone signifies the use of flow element as a signal conditioner. For measurement of flow through a 100 mm line, differential pressure across the cone is measured using a Differential Pressure Transmitter (DPT). Experiments were repeated by replacing the cone element for obtaining different β values.

Evidence for a new optical element in insect visual systems

We present a model of the cone element in insect ommatidia based on recent developments in the theory of tapering graded-index media. A comparison with experimental results for a butterfly indicates that light-guiding graded-index tapers may be a component of insect visual systems.

Static analysis of thin rotational shells

The purpose of the research presented here was to determine the elastic stresses induced in a thin shell of revolution. The method adopted was that of finite elements. A curved cone element was therefore developed which could predict the static response in thin loaded shells of revolution. The imposed loading can be axisymmetric or asymmetric. The element which is of isoparametric formulation is thought to have the salient advantages of having true nodal slope conformity, variable thickness, optional degrees of freedom within each element and ability to respond to lateral as well as inplane loads. Some of the numerical results using the present element have been included. The new formulation should be of special interest to engineers who have access to small computers since almost all the examples listed were solved on such a machine. It is hoped that, a moderate variety of engineering problems could now be solved more economically.

ANALYSIS OF AXISYMMETRICAL SHELLS BY THE DIRECT STIFFNESS METHOD

A method for the structural analysis of shells of revolution, composed of materials with orthotropic properties, is discussed. The development is based on the direct stiffness method. A truncated cone element is introduced to take advantage of symmetry. Derivations of the stiffness and stress matrices for the truncated cone element are given. Several examples are solved on the digital computing machine using a program that is based on the truncated cone element. The results are compared to other theoretical results, and the correlation is excellent. Extension of the technique to handle linear unsymmetric deformation and nonlinear symmetric deformation is discussed.