Conical Frustum Research Articles

Angle-Dependence of the Levitation Force From a Frustum-Shaped Magnet and Recessed Superconducting Bulk

The widespread application of superconducting magnetic levitation bearings is limited by their relatively low stiffness. Recently we investigated a novel thrust bearing geometry comprised of a conical frustum (or truncated cone) shaped permanent magnet levitating inside a matching tapered hole machined into a high-temperature superconductor bulk. This configuration was found to produce superior restoring forces and stiffness compared to the conventional cylindrical magnet and superconductor arrangement. Here, using H-formulation finite-element simulations, we evaluate the angle-dependence of the frustum on the levitation force. We find that the optimal angle is not universal, but depends on the mode of displacement as well as the frustum dimensions. Correlations with the incident magnetic flux are identified for estimating the angle best suited to the operating regime of the bearing.

Monte carlo analysis of various geometrical blankets in a fusion-fission hybrid reactor

• A dense plasma focus device design as a fusion neutron source. • Investigate the neutron diffusion equation in the cylindrical layer, the spherical layer and the frustum cone layer geometries. • Investigate the lowest probability of a neutron returning from the second blanket to the first blanket in the cylindrical layer, the spherical layer and the frustum cone layer geometries. • Investigate the neutron parameters in the One-Blanket Reactor and Two-Blanket Reactorand the ultimate energy of the hybrid reactor by MCNPX code. • To check the safety of staff and reactor facilities, the dose rate of neutrons and photons in the concrete shield is calculated by MCNPX code. Fusion - fission hybrid reactor consists of two main parts. The first part is the Dense Plasma Focus (DPF) where the fusion process is performed and the second part is the blankets which surround the DPF and the fission process is done in the blankets. The most of the fusion neutrons, near the fusion source, are directed upward, so the blanket over the DPF is designed in forms cylindrical, spherical and frustum cone of volumes 183,347 cm 3 , 136,378 cm 3 and 58,223.2 cm 3 respectively at the same effective multiplication factor. Then the thermal neutron diffusion equation, buckling and neutron parameters are studied. After selecting the first blanket, the second blanket is designed in forms cylindrical, spherical and frustum cone of volumes 4.500 × 10 6 cm 3 , 3.689 × 10 6 cm 3 and 6.441 × 10 5 cm 3 respectively. So the frustum cone is chosen for the first and second blanket. The neutron return probability in the frustum cone from the second blanket to the first blanket is low, so the first blanket's effective multiplication factor does not change and the reactor's total effective multiplication factor is stable. Also, MCNPX code has been used to checkout and select neutron multiplier and reflector cells for the most neutron yield.

Mechanical and thermal buckling of functionally graded axisymmetric shells

The buckling analysis of functionally graded materials (FGM) axisymmetric plate-shell type structures under mechanical and termal loading is presented in this work. A numerical solution is obtained by expanding the variables in Fourier series in the circumferential direction and using conical frustum finite elements in the meridional direction. The finite element model, having two nodal circles and ten degrees of freedom per node, is based in the Kirchhoff-Love theory that includes the transverse shear deformations by introducing a penalty function, which corresponds to the first order shear deformation theory (FSDT), is suitable for both thin and thick axisymmetric plate/shell structures. The reduced number of finite elements, which are required to model even complex structures, combined with the use of a small number of discrete layers to model the continuous variation of the mechanical properties through the thickness of the structure, results in an extremely low computational time required for FGM buckling applications. An in-house program has been developed, and applications in a variety of axisymmetric shells are solved, including circular plates. The solutions obtained in mechanical and thermal buckling are discussed and compared with alternative models..

Studying parameters affecting the thinning rate during heat-assisted incremental sheet forming of the lightweight material

ABSTRACT Incremental sheet forming (ISF) is a promising sheet forming process and becomes a worthy alternative to the traditional sheet forming processes. ISF has used in manufacturing small batch or customised sheet components in various industrial sectors. One of the main challenges in this process is how to deals with hard to form materials like lightweight materials. Heat-assisted ISF processes have suggested improving the formability at warm or hot conditions. Among all heat-assisted ISF processes, frictional stir-assisted Single Point Incremental Forming (SPIF) recommended to deform AA6061-T6 sheets. The aim is to investigate the impact of the process parameters on the thinning rate of the final components. A Taguchi technique and varying wall angle conical frustum (VWACF) test have employed to conduct the experiments. Furthermore, analysis of variance (ANOVA) utilised to find the influence of these parameters on the thinning rate. The results show that spindle speed is the main parameter affected the formability of AA6061-T6 sheets in terms of thinning rate. The percentage contribution of this parameter was 90.53%. The maximum thinning is 59.56 % at a rotation speed, feed rate, step size, and tool diameter of 1200 rpm, 500 mm/min., 0.2 mm, and 10 mm, respectively.

Optic Canal Analysis in Syndromic Craniosynostosis: Volumetric and Surface Area Validation Study Using Different Measurement Modalities.

In syndromic craniosynostosis (SC), unlike persistent corneal irritation due to severe exophthalmos and increased intracranial pressure, optic canal (OC) stenosis has been scarcely reported to cause visual impairment. This study aimed to validate the OC volumetric and surface area measurement among SC patients. Sixteen computed tomography scan of SC patients (8 months-6 years old) were imported to Materialise Interactive Medical Image Control System (MIMICS) and Materialise 3-matics software. Three-dimensional (3D) OC models were fabricated, and linear measurements were obtained. Mathematical formulas were used for calculation of OC volume and surface area from the 3D model. The same measurements were obtained from the software and used as ground truth. Data normality was investigated before statistical analyses were performed. Wilcoxon test was used to validate differences of OC volume and surface area between 3D model and software. The mean values for OC surface area for 3D model and MIMICS software were 103.19 mm2 and 31.27 mm2, respectively, whereas the mean for OC volume for 3D model and MIMICS software were 184.37 mm2 and 147.07 mm2, respectively. Significant difference was found between OC volume (P = 0.0681) and surface area (P = 0.0002) between 3D model and software. Optic canal in SC is not a perfect conical frustum thus making 3D model measurement and mathematical formula for surface area and volume estimation not ideal. Computer software remains the best modality to gauge dimensional parameter and is useful to elucidates the relationship of OC and eye function as well as aiding intervention in SC patients.

Transitions between phyllotactic lattice states in curved geometries

Phyllotaxis, the regular arrangement of leaves or other lateral organs in plants including pineapples, sunflowers and some cacti, has attracted scientific interest for centuries. More recently there has been interest in phyllotaxis within physical systems, especially for cylindrical geometry. In this letter, we expand from a cylindrical geometry and investigate transitions between phyllotactic states of soft vortex matter confined to a conical frustum. We show that the ground states of this system are consistent with previous results for cylindrical confinement and discuss the resulting defect structures at the transitions. We then eliminate these defects from the system by introducing a density gradient to create a configuration in a single state. The nature of the density gradient limits this approach to a small parameter range on the conical system. We therefore seek a new surface, the horn, for which a defect-free state can be maintained for a larger range of parameters.

A prognostic analysis on experimental evaluation of thermosyphon using refrigerant R134a and water based on machine learning and optimization techniques

Thermosyphon is an effective heat transfer device which is widely used all over the world for its ease of use, feasible with different environmental challenges. In this research article, the experimentation with different boiling point of working fluids water and R134a has been used in modified thermosyphon. The modified thermosyphon comprises of the cone frustum attached between the condenser and adiabatic section to hold up for high heat inputs. It is noted from the experiment that the working fluids have unique heat transfer capability with regard to thermal properties for applied heat input. The thermal resistance for different fill ratios with water and R134a in thermosyphon was experimented and the optimality in the fill ratio is identified. Due to the modification in the condenser, R134a condenser performs better for both low and high heat inputs but water works well only in high heat inputs. To predict and compare the temperature outputs at the evaporator, adiabatic and condenser sections of the thermosyphon, machine learning algorithm and optimization technique has been deployed and the output is measures for its accuracy, false positive, predictive positive value and effective performance. It is noted both from the experimental and algorithmic approach that the experiment produces less false positive rate which is ≤ 2% and true positive rate which is ≥ 98%, accuracy of the outputs which are ≥ 98%. The optimized outcome also stabilizes the experimental setup strongly and generates an effective performance rate which is ≥ 95%.

Conical frustum gel driven by the Marangoni effect for a motor without a stator

The Marangoni effect has inspired the development of diverse applications such as robots, gel motors, and self-propelled droplets. A major challenge for the developed gel motors is the need for stators, which dampen the rotating velocity and reduce the motor lifetime due to frictional forces from the stators. Therefore, we developed a new type of gel without a stator to realize rotating motions, namely, a conical frustum gel. In this work, we initially studied the principle of the rotated gels driven by the Marangoni effect. For comparison, we designed two types of gels: cylindrical and conical frustum gels. Then we devised mathematic models to estimate the generated torques. The two gels were synthesized. Additionally, both the oil and aqueous fluids were prepared. Next, we investigated the influence of a chemical on the moving duration of the gels. The circular motion trajectories of the gels were compared and analyzed. Finally, we researched the angular velocities and driving torques generated by the two gels. This work should contribute to the development of a non-stator gel motor powered by the Marangoni effect.

Investigation on Snap-Through Buckling Behavior of Dished Shells Under Uniform External Pressure

Abstract Previously, the buckling behavior of several conical and spherical shells have been studied with great rigor. In this paper, snap-through buckling behavior for metallic dished shells under uniform external pressure is investigated. These shells are geometrically complex since they consist of a shallow conical frustum with a flat closed top. Such shells find many engineering applications, for instance as actuator elements in control components in cryogenic engines. Currently, no clear guidelines exist for design performance evaluation of such peculiar shells. This paper aims to establish a valid FE methodology for snap-through buckling and post-buckling analysis of such shells using abaqus in tandem with experiments. A parametric study is carried out to understand the effect of geometrical parameters and imperfection sensitivity of these shells to snap-through buckling. Moreover, experiments were carried out using 3D Digital Image Correlation (3D-DIC) for measuring whole-field deflection and strains. Numerical analysis was carried out, using generalized Eigen value analysis and non-linear analysis using a modified-Riks technique with various material models to correlate with the experimental observations. Non-linear elasto-plastic analysis with a perfectly elastic-plastic material model agrees well with the experimental observations. A comparison of experimental results with that of the numerical study indicates that material plasticity has a major effect on critical buckling pressure.

A novel prediction method of machining accuracy for machine tools based on tolerance

The ongoing research is hard to predict the machining accuracy of machine tools in the preliminary design phase. Hence, a rapid and quantitative prediction method seems very necessary and imperative. In this study, a new machining accuracy prediction strategy for a five-axis machine tool (FAMT) based on tolerance is proposed. Firstly, a characterization model of surface error profiles for key parts of the FAMT is established, and GESP prediction models based on tolerance for a translational axis and a rotary axis are established by utilizing the mapping relationship between tolerance, surface error profiles, and GESPs of key parts for the FAMT. Then, the kinematic equation of the FAMT is established based on GESPs by using the multi-body system (MBS) theory. As a basis, the actual machining position for the cone frustum based on GESPs by considering the tool setting position and the relative NC machining instruction are solved. And, a machining accuracy prediction model for the cone frustum based on tolerance is established. To enhance the prediction efficiency and intuitively evaluate the machining performance of the FAMT, some accuracy indexes of the cone frustum, such as roundness, angularity, and concentricity, are described. Thus, the machining accuracy prediction model based on key parts’ tolerance parameters of the FAMT is established substantially. Finally, a simulation prediction scheme is conducted. Simulation results show that predicted machining accuracy can meet the requirements of accuracy. To further demonstrate the practicability of the method, experimental verification is implemented. Experimental results show measuring values are very close to predictive ones. Therefore, a reasonable conclusion can be drawn that the proposed method can quickly and effectively predict the machining accuracy of machine tools based on tolerance.

Solutions to logistics challenges faced by fishmongers in handling and distributing processed fish. A case study of Anyanui and Keta Districts of Ghana

The study sought simple indigenous logistics solutions to challenges faced by fishmongers with respect to the handling and distribution of processed fish in the Anyanui and Keta Districts of Ghana. It aimed at designing a handling and distribution unit (HADU) to substitute the conical frustum shaped basket (kenten), which is traditionally used for the purpose. This was a follow-up to a research that sort to curtail identified challenges, including improper stowage, perceived overloading, listing of cargo on transport vehicle, crushing and contamination of the processed fish during transit. Observation, simple mathematical calculations, interviews and experimental testing were employed in the study. The researchers’ considered designing a HADU with characteristics similar to the intermodal ISO container. The HADU was to be appropriate for transporting the processed fish by standard tricycles, trucks, and water crafts. Its volume was calculated to be equivalent to that of the kenten, so as to preserve the measurements of products per unit traditionally supplied to customers, thus not complicating the pricing of contents per unit HADU for the traders. With height 40 cm, length 43 cm and width 56 cm, the resultant cuboidal shaped HADU, had handles, corner posts with extensions and corner fitting spaces. The HADU could be loaded in larger numbers on various sizes of trucks and tricycles compared to the kenten. It also solved the in-transit logistics challenges when stacked at a recommended maximum height of three. Upon its acceptance by the fishmongers, the HADU’s concept was recommended to be sold to basket weavers, to try raw materials other than cane, which will lower its production cost.

Study on AlxGa1-xAs nanocones with variable Al composition structures for highly efficient light trapping

In this study, various AlxGa1-xAs nanostructure arrays with variable Al composition are proposed and designed for highly efficient light capture. The optical properties of the proposed nanocone array with variable Al composition have been numerically investigated by COMSOL Multiphysics package based on the finite element method (FEM), and compared with the counterparts of cylinder and conical frustum. The results show that the variable composition AlxGa1-xAs nanocones with uniform sublayer distribution thickness can obtain an ultimate efficiency of 37.3%, which is higher than that of the cylindrical and conical frustum structures under the same conditions. In addition, the effects of geometric parameters of nanostructures on the light absorption of nanoarrays with different shape changing components are studied. Taking the variable component AlxGa1-xAs nanocone structure as an example, increasing the Al component range in the axial direction of the nanocone can significantly improve the absorption of short-wavelength light, which increases the overall absorption efficiency. In addition, for a specific Al composition distribution range, a uniform thickness distribution design of unit sub-layer in nanocone along the z-axis direction can provide optical absorption enhancement of more than 1.8% and 0.9% over than the decreasing and increasing distribution design. The design principles proposed in this work will provide a reference for selecting appropriate parameters in solar cell applications.

Impacts of longitudinal air velocity and fuel flow rate on flame radiative fraction in tunnel

Fires in tunnels have attracted special attention in recent years due to catastrophic fires, which cause huge human and economic losses. For accurate fire modelling and ventilation system design, it is critical to understand the correct radiative fraction (Xr) of the flame. Recent study has proved that Xr decreases with the increase of longitudinal air velocity in heptane pool fires. However, the impacts of longitudinal air velocity and fuel flow rate on Xr in propane or liquefied petroleum gas tunnel fires have not been studied. To fill the gap, this paper conducts two sets of fire experiments in a 1/20 reduced-scale wind tunnel using a porous burner. Unique visible flame shapes are observed and described by the ‘back-to-back conical frustum’. The geometric parameters and their variations with the momentum flux ratio are discussed. In comparison with the experimental results, the radiation model using the proposed flame shape shows an 80 % accuracy. The predictive radiative fractions of the two tests are calculated and compared with other tests from literature. The coupling effects of longitudinal air velocity and fuel flow rate on the flame radiative fraction are studied in detail. And their influences on key parameters of smoke extraction system are analyzed.

Formability Analysis of AA1200 H14 Aluminum Alloy Using Single Point Incremental Forming Process

Single point incremental forming (SPIF) process has the capability to form small/medium-sized part generally used for rapid prototyping applications in automotive and non-automotive industry. Although considerable research has been conducted over the past decades on the formability of various aluminum alloy using SPIF process. This paper presents an investigation on the behavior of AA1200 H14 aluminum alloy by means of SPIF process. The formability of AA1200 H14 in terms of maximum formable wall angle has been evaluated using varying wall angle conical frustum (VWACF) profile. Taguchi method based design of experiment, analysis of variance (ANOVA), signal-to-noise ratio (S/N Ratio) have been employed to identify the significant parameters affecting formability. Utilizing the experimentally acquired results, the S/N ratio (dB) graphs have been drawn and identified the optimal parametric combination for maximizing the wall angle. Further, the formability of the parts has also been evaluated using forming limit curve. The changes in microstructure due to incremental deformation have been studied through scanning electron microscopic analysis.

Volumetric shrinkage estimation of benchmark parts developed by rapid tooling mold insert

This paper estimates the volumetric shrinkage for thermoplastic Polypropylene (PP) injection molded components made using digital Acrylonitrile butadiene styrene (ABS) mold. The parameters affecting volumetric shrinkage for the digital ABS mold are mold temperature and injection temperature, cooling time, hold pressure and injecting speed. Therefore, twelve standard benchmark CAD model were selected with different geometric attributes. Subsequently, simulation analysis was performed on all CAD model using Moldflow® (MFA) simulation software. Additionally, regression analysis is applied to identify the effect of injection molding parameters on the volumetric shrinkage of part made using rapid tooling mold insert of digital ABS material. It is found that maximum volumetric shrinkage (18.75%) is observed for square pyramid frustum, conical frustum, and solid torus. On the contrary, hollow rectangular prism shows minimum shrinkage effect having 12.61% of volumetric shrinkage. This study predicted that shrinkage is the main concern for these three geometric features (i.e., square pyramid frustum, conical frustum, and solid torus) and must be looked for its minimization. The results are experimentally validated, with 3D scanner integrated with COMET plus and Inspect plus softwares. Since shrinkage estimation for digital ABS mold using Rapid Tooling technique has not been attempted before, therefore, this study provides guidance for the optimum parameter selection and assigning suitable shrinkage compensation values for digital ABS mold made using direct rapid tooling.

Vibrations of functionally graded material axisymmetric shells

The free-vibration analysis of functionally graded materials (FGM) axisymmetric plate-shell type structures are presented in this work. A numerical solution is obtained by expanding the variables in Fourier series in the circumferential direction and using conical frustum finite elements in the meridional direction. The finite element model, having two nodal circles and ten degrees of freedom per node, is based in the Kirchhoff-Love theory that include the transverse shear deformations by introducing a penalty function, and using one Gauss point integration scheme which gave excellent results for both thin and thick axisymmetric plate/shells structures. The reduced number of finite elements, which are required to model even complex structures, combined with the use of a small number of discrete layers to model the continuous variation of the mechanical properties through the thickness of the structure, result in an extremely low computational time required for FGM applications. An in-house program has been developed, and applications in a variety of axysimetric shells are solved, including circular plates. The solutions obtained are discussed and compared with solutions obtained by alternative models.

Mechanism for frustum transition over blunt cones at hypersonic speeds

Numerical and experimental studies have demonstrated laminar–turbulent transition in hypersonic boundary layers over sharp cones via the modal growth of planar Mack-mode instabilities. However, due to the strong reduction in Mack-mode growth at higher nose bluntness values, the mechanisms underlying the observed onset of transition over the cone frustum are currently unknown. Linear non-modal growth analysis has shown that both planar and oblique travelling disturbances that peak within the entropy layer experience appreciable energy amplification for moderate to large nose bluntness. However, due to their weak signature within the boundary-layer region, the route to transition onset via non-modal growth of travelling disturbances remains unclear. Nonlinear parabolized stability equations (NPSE) and direct numerical simulations (DNS) are used to identify a potential mechanism for transition over a 7-degree blunt cone that was tested in the AFRL Mach-6 high-Reynolds-number facility. Specifically, computations are conducted to study the nonlinear development of a pair of oblique, unsteady non-modal disturbances in the regime of moderately blunt nose tips. Excellent agreement was demonstrated between the NPSE and DNS predictions. Results reveal that, even though the linear non-modal disturbances are primarily concentrated outside the boundary layer, their nonlinear interaction can generate stationary streaks that penetrate and amplify within the boundary layer, eventually inducing the onset of transition via the breakdown of these streaks. The results indicate that a pair of oblique, controlled non-modal disturbances can produce transition at the location measured in the experiment when their initial amplitude is chosen to be approximately 0.15 % of the free-stream velocity.

Effect of operational parameters on incremental forming of low-alloy sheet metals and its optimisation

ABSTRACT Incremental forming is a method with great forming potential. With this method, especially Low-Alloy Sheet Metals prototypes can be produced. Low-Alloy Sheet DC01, one of the metals, is widely used in the machinery industry. In this study,manufacturability of conical frustum part with circular generatrix form was investigated by “single point incremental forming” method. DC01 sheet was used as the test material. Signal/Noise analysis was performed to investigate the effects of experimental parameters. Later, gray relationship analysis performed. The optimal parameters for the incremental formability of the variable wall angle conical frustum shaped DC01 sheet metal were determined. As the increment and the feedrate decreased, it was observed that both surface roughness and forming force decreased. Surface roughness and forming force are both observed to increase with the growth of the forming tool diameter.

Evaluation of Ground Plane Detection for Estimating Breast Height in Stereo Images

Abstract Diameter at breast height is a standard method for characterizing trees and ultimately forests over large geographical scales. Expressing the cross-section of a tree stem with a diameter measurement has inherent errors, as stems are not perfect conical frustums. Diameter suffices as an approximation, since methods for the exact cross-sectional area of a stem are infeasible in practice. There are other primary sources of error in diameter at breast height measurements: diameter measurement error and breast height measurement error. This paper addresses the latter in the context of an automated measurement system using 3D photography. We consider breast height estimation a fundamental component in such systems, as errors in measurement height can precipitate significant errors in stand-level attribute estimation as diameter changes along the height of the stem because of taper. We evaluate the efficacy of breast height estimation using stereo photogrammetry by fitting a planar surface to the ground and elevating the plane to breast height. Results from a validation test on 560 observations show that breast height can be estimated with a root mean squared error of 10.20 cm within 10 m from the camera and 13.36 cm within 20 m from the camera on flat terrain in varying levels of stem density. Study Implications Increasing the level of automation in forest operations is one approach to address workforce attrition and safety issues in the industry. Automated tree measurement and mapping systems present an opportunity to reduce operational costs by providing machine operators with necessary information to carry out silvicultural prescriptions and eliminate the need for individual tree marking in certain situations. In order to maintain trust between landowners and harvesting contractors, it is imperative that automatic measurement systems are rigorously tested to determine that measurement accuracy is within acceptable limits. Breast height measurement error is often overlooked as a source of error in estimating diameter at breast height. However, accurate breast height estimation is a necessary prerequisite for reliable, consistent, and precise diameter at breast height measurement. The capacity of machine vision systems to automate forest inventory and monitoring tasks is increasing and can help managers achieve sustainable forestry objectives on more acres in less time.

Gradual contraction of pipe cross-section effects on transient behavior of air–water slug flow

The current experimental investigation was aimed at understanding the influence of reducing sections on the transient behavior of slug flow. Experiments were carried out using two concentric area cross-section reducers with 160 mm lengths; the first one was shaped as a conical frustum with a 44 mm inlet diameter reducing to a 30 mm outlet diameter and the second one as a frustum with the same inlet diameter converting to a rectangular cross-section (34 mm × 21 mm). Four different water superficial velocities (0.43, 0.55, 0.72 & 0.84 m s−1) and three different air superficial velocities (2.5, 3.6 & 4.9 m s−1) were applied in the course of the experiments. Visualization studies, as well as frequency distribution analyses, were used to observe flow field changes. The visualization study showed that the gas slug tail, liquid slug, and gas slug subsequent to passing through the reducers converted to non-homogeneous bubbly flow, several small slugs, and pseudo-slugs, respectively. The obtained frequency distributions, which were calculated using a Fourier transform tool, showed that unlike that of the dominant frequency, the power of other frequencies was amplified in the low-frequency range owing to the high formation rate of pseudo-slugs and small slugs. This change indicates that intermittent air–water slug flow with a specified dominant frequency subsequent to passing reducers varies to an uncertain flow with semi-uniform distribution in the low-frequency range. Estimation of Shannon entropy also showed that entropy increased by almost five times downstream of the reducers, which confirms that energy is distributed uniformly in a broad frequency bandwidth. Analyses of the essential bandwidth showed that the reducing section acted as a frequency distribution modifier whose performance decreased with liquid flow rate increments. Based on this achievement, it was found that both the circular and the rectangular reducers were able to generate the named conditions.