Conical Frustum Research Articles

GA-based optimization to control the thickness distribution in components manufactured via superplastic forming

Superplastic forming (SPF) is a net-thinning sheet metal forming process that allows to achieve very complex geometries; nevertheless, due to its deformation mechanics, it is difficult to achieve a uniform thickness distribution in the final component since the most stretched regions of the blank are contemporarily characterized by the most severe thinning. With the aim of proposing a robust approach, a new methodology able to optimize the thickness distribution in components produced by SPF is proposed. Although two different titanium-based (Ti-6Al-4 V ELI) axisymmetric components – i.e., a hemisphere and a frustum of cone – were chosen as case studies, the methodology can be extended to any material and to any geometry, even considering more than one objective function. The superplastic forming was numerically simulated, and the Finite Element (FE) model was embedded into an automatic procedure managed by the multi-objective genetic algorithm MOGA-II. The blank's initial thickness distribution was modelled using a second-order polynomial function and its coefficients were determined to get, at the end of the SPF process, a uniform thickness in the formed part irrespective of the specific geometry. Titanium blanks were machined on a 5-axis milling machine to obtain the calculated optimal initial thickness distribution; subsequently, such blanks were superplastically formed and inspected in order to measure the thickness distribution. Tests showed a very good fitting with the numerical prediction thus confirming the robustness and the effectiveness of the proposed methodology.

A New Approach for Estimation of Physical Properties of Irregular Shape Fruit

Dimensions, volume, and mass of agricultural goods are essential physical features to build sizing, grading, and packaging systems. Manual property measurements are time-consuming, costly, and labor-intensive due to traditional technologies while various devices need to be installed to adapt process requirements. Furthermore, it is very challenging to accurately measure product with irregular or specific shapes, such as starfruit (Averrhoa carambola). Recently, there have been several research results on estimating features of the irregularly shaped object, they are either get inaccurate results or need repeated captures, computational resources, and time to rebuild the three-dimensional representation of the goods. The starfruit has not been studied completely in this size and weight measurements. This paper focuses on new techniques which exhibit simple installation to generate multiple functions for estimating the dimensions, volume, and mass with high accuracy. In this proposed method, we separated the process into two main phases. In the first phase, a camera is used to capture a top-view image of a starfruit, then image processing and machine vision techniques are applied to process the acquisition image before the process slices numerically the starfruit into several pieces along the longitudinal axis and estimates the physical attributes of each pieces using disc method and conical frustum method. Its volume is the summation of the volume of each partial slice. In the next phase, the density is used to estimate the mass of starfruit since the correlation coefficient (R-squared) between the volume and mass of starfruit is nearly linear with 0.9205. The validated results are highly competitive with accuracy of about 99% for the volume and mass in 300 testing samples.

Accuracy of Various Methods to Estimate Volume and Weight of Symmetrical and Non-Symmetrical Fruits using Computer Vision

Many researchers have used images to measure the volume and weight of fruits so that the measurement can be done remotely and non-contact. There are various methods for fruit volume estimation based on images, i.e., Basic Shape, Solid of Revolution, Conical Frustum, and Regression. The weight estimation generally uses Regression. This study analyzed the accuracy of these methods. Tests were done by taking images of symmetrical fruits (represented by tangerines) and non-symmetrical fruits (represented by strawberries). The images were processed using segmentation in saturation color space to get binary images. The Regression method used Diameter, Projection Area, and Perimeter as features that were extracted from the binary images. For symmetrical fruits, the best accuracy was obtained with the Linear Regression based on Diameter (LDD), which gave the highest R2 (0.96 for volume and 0.93 for weight) and the lowest RMSE (5.7 mm3 for volume and 5.3 gram for volume). For non-symmetrical fruits, the highest accuracy for non-symmetric fruits was given by the Linear Regression based on Diameter (LRD) and Linear Regression based on Area (LRA) with an R2 of 0.8 for volume and weight. The RMSE for LRD and LRA for strawberries was 3.3 mm3 for volume and 1.4 grams for weight.

Temporal variation in the depth of the magma surface at Aso volcano in 2014–2015

Monitoring the depth of the magma surface at open-vent volcanoes can be a practical tool to infer temporal variations in the magma supply during an eruption. We focus on the magmatic eruption of Aso volcano in 2014–2015 to estimate the temporal change in the depth of the magma surface, and show that this needs to be coupled with an understanding of the shallow conduit geometry if it is to be done in a representative manner. The eruption lasted 5 months from November 2014 and ending with a crater floor collapse in May 2015. During the eruption, we recorded seismo-acoustic waveforms related to frequent Strombolian explosions. The infrasound signals show several distinct peak frequencies derived from acoustic resonance inside the vent. We estimate the depth of the magma surface using the time delay of seismo-acoustic signals and the peak frequency of infrasound signals. In addition, the temporal variation in the shape of the conduit is constrained by the overtone frequency of the acoustic resonance. From the beginning of the eruption to early-January 2015, the magma surface was located at a depth of sim 200 m, and the conduit was a cylindrical pipe. Later, between January and February, the magma surface rose to sim 120 m, and the shape of the conduit changed to a conical frustum flaring inside. This finding indicates that the magma was injected into the shallow conduit and that it heated and weakened the conduit wall near the magma surface. Before the cessation of the magmatic eruption, the magma surface dropped by approximately 70 m. This magma drainage and, primarily, the instability of the conduit shape caused the crater floor to collapse. We show the possibility of tracking and assessing the depth of the magma surface and the shallow conduit geometry even with limited seismo-acoustic observations.

Shadowed Type-2 Fuzzy Sets in Dynamic Parameter Adaption in Cuckoo Search and Flower Pollination Algorithms for Optimal Design of Fuzzy Fault-Tolerant Controllers

In recent, various metaheuristic algorithms have shown significant results in control engineering problems; moreover, fuzzy sets (FSs) and theories were frequently used for dynamic parameter adaption in metaheuristic algorithms. The primary reason for this is that fuzzy inference system (FISs) can be designed using human knowledge, allowing for intelligent dynamic adaptations of metaheuristic parameters. To accomplish these tasks, we proposed shadowed type-2 fuzzy inference systems (ST2FISs) for two metaheuristic algorithms, namely cuckoo search (CS) and flower pollination (FP). Furthermore, with the advent of shadowed type-2 fuzzy logic, the abilities of uncertainty handling offer an appealing improved performance for dynamic parameter adaptation in metaheuristic methods; moreover, the use of ST2FISs has been shown in recent works to provide better results than type-1 fuzzy inference systems (T1FISs). As a result, ST2FISs are proposed for adjusting the Lèvy flight (P) and switching probability (P′) parameters in the original cuckoo search (CS) and flower pollination (FP) algorithms, respectively. Our approach investigated trapezoidal types of membership functions (MFs), such as ST2FSs. The proposed method was used to optimize the precursors and implications of a two-tank non-interacting conical frustum tank level (TTNCFTL) process using an interval type-2 fuzzy controller (IT2FLC). To ensure that the implementation is efficient compared with the original CS and FP algorithms, simulation results were obtained without and then with uncertainty in the main actuator (CV1) and system component (leak) at the bottom of frustum tank two of the TTNCFLT process. In addition, the statistical z-test and non-parametric Friedman test are performed to analyze and deliver the findings for the best metaheuristic algorithm. The reported findings highlight the benefits of employing this approach over traditional general type-2 fuzzy inference systems since we get superior performance in the majority of cases while using minimal computational resources.

"Conical" Frustum Multi-Beam Phased Arrays for Air Traffic Control Radars.

The design of conical frustum phased array antennas for air traffic control (ATC) radar systems is addressed. The array architecture, which is controlled by a fully digital beam-forming (DBF) network, is composed by a set of equal vertical modules. Each module consists of a linear sparse array that generates on receive multiple instantaneous beams pointing along different directions in elevation. To reach the best trade-off between the antenna complexity (i.e., minimum number of array elements and/or radio frequency components) and radiation performance (i.e., matching a set of reference patterns), the synthesis problem is formulated in the Compressive Sampling (CS) framework. Then, the positions of the array elements and the complex excitations for generating each single beam are jointly determined through a customized version of the Bayesian CS (BCS) tool. Representative numerical results, concerned with ideal as well as real antenna models, are reported both to validate the proposed design strategy and to assess the effectiveness of the synthesized modular sparse array architecture also in comparison with conventional arrays with uniformly-spaced elements.

Crashworthiness performance of thin-walled hollow and foam-filled prismatic frusta, Part 2: Experimental study

Prismatic or conical frusta are used as crash boxes, absorbing the energy of impact loads in collision, due to their advantages in comparison with circular or parallelepiped tubes (decrease of peak crushing force and stabilization of crushing process). The paper presents results of experimental research into crashworthiness performance and energy absorption effectiveness of thin-walled prismatic frusta of square base, produced from two face to face steel channel sections, joint using the riveting technique. Hollow and filled with polypropylene foam specimens were tested on drop hammer tower. On the basis of impact tests load–deformation characteristics were determined, represented by load-shortening diagrams. Selected crashworthiness indicators (Peak Crushing Force, Crash Load Efficiency, Stroke Efficiency and Total Efficiency) were calculated. Experimental load-shortening diagrams and experimental values of crashworthiness indicators were compared with the results of numerical FE simulations. Validation of the FE model was performed, which was the main objective of the study. FE model and results of the parametric analysis into energy absorption effectiveness of examined frusta was presented in Part 1 of this study: Crashworthiness performance of thin-walled hollow and foam-filled prismatic frusta — FEM parametric study.

Highly Sensitive Bending Sensor Based on Multicore Optical Fiber With Diagonal Cores Reflector at the Fiber Tip

A high-sensitivity bending sensor based on multi-core fiber Bragg gratings (MCFBGs) is presented and demonstrated. The bending sensor is based on FBGs fabricated on the symmetric distribution cores of seven-core fiber (SCF), where a 45-degree reflective cone frustum (RCF) is fabricated at the fiber end. The optical paths of two symmetric cores are connected by the 45-degree RCF. The wavelength drifts of the two FBGs on the symmetric cores caused by bending were similar in magnitude and opposite in direction, while the wavelength drifts of the two FBGs caused by temperature were similar in magnitude and direction. Therefore, the influence of temperature change on the curvature measurement can be automatically eliminated, and the bending sensitivity can be doubled by calculating the difference between the reflected wavelengths of the two FBGs. The sensor's spectral responses to the curvature at different bending directions are experimentally investigated. The maximum curvature sensitivity of the sensor is 225.9 pm/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> , within the curvature range from 0 to 6.9 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> .

Configuration-based Optimization for Virtual Hand Haptic Simulation.

Interacting with virtual objects via haptic feedback using the user's hand directly (virtual hand haptic interaction) provides a natural and immersive way to explore the virtual world. It remains a challenging topic to achieve 1 kHz stable virtual hand haptic simulation with no penetration amid hundreds of hand-object contacts. In this paper, we advocate decoupling the high-dimensional optimization problem of computing the graphic-hand configuration, and progressively optimizing the configuration of the graphic palm and fingers, yielding a decoupled-and-progressive optimization framework. We also introduce a method for accurate and efficient hand-object contact simulation, which constructs a virtual hand consisting of a sphere-tree model and five articulated cone frustums, and adopts a configuration-based optimization algorithm to compute the graphic-hand configuration under non-penetration contact constraints. Experimental results show both high update rate and stability for a variety of manipulation behaviors. Non-penetration between the graphic hand and complex-shaped objects can be maintained under diverse contact distributions, and even for frequent contact switches. The update rate of the haptic simulation loop exceeds 1 kHz for the whole-hand interaction with about 250 contacts.

Improvement of scarf repair patch shape for composite aircraft structures

ABSTRACT Scarf patching is the preferred technique for repairing physically damaged aircraft composite structures. The commonly used patch design is a circular conical frustum with a 3°optimized scarf angle. However, for this repair patch design the volume of material removed from the repaired composite panel can be quite large. This paper examines the effects of the different parameters on the stress state in the patch adhesive, such as ply orientation, stacking sequence, ply thickness and scarf angle. It explores an adaptive design of the repair patch for orthotropic materials and composite laminates, using 3D Finite Element Analysis. The design optimization approach is based on the evaluation of a Failure Criterion Index (FCI) and the minimization of its Relative Standard Deviation (RSD). An optimized scarf shape, which takes into account biaxial tensile loading conditions, fiber direction, and stacking sequence, is an elliptical conical frustum that induces a variable scarf angle along the sweeping angle. This design showed that less parent material is removed than that of the circular shape (decreased by up to 41%) and that the shear stress dispersion in the adhesive was significantly reduced (RSD decreased by up to 18%). The optimization method and the improved shapes are presented and discussed with respect to the influencing parameters.

Evaluation of uncoupled ductile damage models for fracture prediction in incremental sheet metal forming

The formability limit in a typical incremental sheet forming (ISF) far exceeds the conventional estimate assuming necking failure. The material subjected to incremental forming fails by fracture. Although damage models have been used to correlate the failure in incremental forming, a detailed understanding of the failure mechanism spanning strain paths is not clear yet. In this work, three parts with varied shapes (hybrid five lobe, pyramid and variable wall angle conical frustum (VWACF)) were developed using ISF to cover a range of possible strain paths. The failure is predicted using established uncoupled phenomenological damage models. Damage models were calibrated for AA1050 aluminium sheet by the method of inverse approach using carefully designed tensile tests and FE simulations. Three different damage models were implemented as user subroutine in commercial software code, ABAQUS/Explicit and the results predicted were compared. The linear damage accumulation used to develop fracture locus under monotonic loading could not predict the failure limit in a benchmark single groove test. Therefore a non linear damage accumulation rule (NLDA) is implemented to simulate ISF. The parameters of the NLDA were calibrated from the single groove test. The fracture forming limits during ISF was established using circular grid analysis near the failure zone of the formed part. A good agreement can be found between the experimental observations and numerical predictions for fracture location and part height. It was observed that the overall predictive capability of Hosford Coulomb (HC) damage model is better among three damage models investigated for the given range of loading conditions. However all the three models under-predicted the experimental fracture strain measured in ISF. The possible explanation for the discrepancy is explored.

Galileo Galilei and the centers of gravity of solids: a reconstruction based on a newly discovered version of the conical frustum contained in manuscript UCLA 170/624

The manuscript UCLA 170/624 (ff. 75–76) contains Galileo’s proof of the center of gravity of the frustum of a cone, which was ultimately published as Theoremata circa centrum gravitatis solidorum in Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Leiden 1638). The UCLA copy opens the possibility of giving a fuller account of Theoremata dating and development, and it can shed light on the origins of this research by the young Galileo. A comparison of the UCLA manuscript with the other extant copies is carried out to propose a new dating for the composition of the Theoremata. This dating will then be reconsidered in light of the mathematical content. The paper ends with a complete description of the content of the UCLA manuscript and the edition of Galileo’s text there contained.

Stress Detection of Conical Frustum Windows in Submersibles Based on Polarization Imaging.

Stress detection of the conical frustum window is a very important issue to ensure the safety of deep manned submersibles. In this paper, we propose a method based on polarization imaging to evaluate the stress accumulation and recovery in the conical frustum window. An experimental setup of Mueller matrix polarimetry is built, and the samples are made by referring to the typical conical frustum windows in submersibles. By pressurizing different pressures on the samples, we can find the changes of their Mueller matrix images and further derived polarization parameters. The results show that the polarization parameters can characterize the stress transfer process and the elastic–plastic transformation process of the window under different pressurization pressures. We also use a two-layered wave plate model to simulate the stress distribution in the window, which reveals different performances of the former and latter layers of the window under pressurization. Finally, we use a finite element model to simulate and understand some of the above experimental results. This proposed method is expected to provide new possibilities for monitoring the window stress and further ensure the safety of deep manned submersibles.

Impact of Residual Limb Volume Loss on Socket Internal Pressures: A Preliminary Study

ABSTRACT Introduction Daily volume loss of residual limb is a condition that most prosthetic users face, negatively affecting their life. One of the consequences is the loss of contact between the residual limb and the socket, which modifies internal pressures. Objective The aim of this study was to study how the loss of volume of the residual limb affects socket adjustment through measuring pressures inside the socket. Study design The study design is prospective longitudinal. Materials and Methods Four subjects with unilateral transtibial amputation, with at least 1 year of prosthetic use, and walking with a comfortable prosthesis participated in this study. The pressure between the socket and the subject's residual limb was measured with an FSocket System (Tekscan). Residual limb volume was measured before and after each test with two different methods: optical scanning (Structure Sensor, Occipital) and conical frustum model. Sanders' protocol for volume loss was followed (Sanders et al. J Rehabil Res Dev. 2012;49:1467–1478). Volume changes in the residual limb and socket internal pressures were analyzed. Results/Discussion The pressure graph obtained is consistent with Sanders' volume graphs. The pressure distribution inside the socket is lost after 5 hours of use of the prosthetic device; this can be related to volume loss and alignment. The only area where the pressure increases is in the distal zone, given that once the prosthetic fit is lost, weight bearing is transferred to the socket's distal section (mean volume loss, intrasession −3%; mean pressure loss, intrasession −39%). Conclusions The study suggests that a small change in the volume can cause a change in the distribution of pressures inside the socket, indicating that the prosthetic fit may be compromised. For patient follow-up, measuring pressure inside the socket could be a useful indicator of socket misfit. Clinical Relevance Daily volume changes in the prosthesis can produce pressures that lead to pain, injuries, an inefficient gait, and prosthesis abandonment. Consequently, it is important to understand the behavior of the pressures inside the socket and the influence of the daily changes of volume on the socket adjustment to design better strategies and techniques of daily volume changes management.

Testing the performance of secondary anvils shaped with focused ion beam from the single-crystal diamond for use in double-stage diamond anvil cells.

The success of high-pressure research relies on the inventive design of pressure-generating instruments and materials used for their construction. In this study, the anvils of conical frustum or disk shapes with flat or modified culet profiles (toroidal or beveled) were prepared by milling an Ia-type diamond plate made of a (100)-oriented single crystal using the focused ion beam. Raman spectroscopy and synchrotron x-ray diffraction were applied to evaluate the efficiency of the anvils for pressure multiplication in different modes of operation: as single indenters forced against the primary anvil in diamond anvil cells (DACs) or as pairs of anvils forced together in double-stage DACs (dsDACs). All types of secondary anvils performed well up to about 250GPa. The pressure multiplication factor of single indenters appeared to be insignificantly dependent on the shape of the anvils and their culets' profiles. The enhanced pressure multiplication factor found for pairs of toroidally shaped secondary anvils makes this design very promising for ultrahigh-pressure experiments in dsDACs.

An Interference Inspection Algorithm of Limb and Hexapod Frame in the Treatment of Lower Limb Deformity

Pre-operative correction trajectory planning is one of the important aspects of deformity correction. Avoidance of limb-frame interference is essential to verify the implementability of the preplanned correction trajectory, as well as to maintain the continuity and security of the correction strategy. In this study, a novel interference inspection algorithm is developed to investigate the interaction of the limb and hexapod frame in the treatment of lower limb deformities. The algorithm is built on a minimum distance model of the cone frustum busbar and cylindrical axis using vector analysis. A predefined trajectory is generated by Cartesian coordinate path control. Subsequently, an interference case is performed through numerical simulation and motion simulation. The results show that the conclusion of numerical simulation and motion simulation is consistent, which prove the feasibility of the algorithm. The results also show that it is possible to identify the riskiest struts, which are prone to interfere with the limb, and the riskiest positions. The proposed algorithm can support the clinician in selecting the suitable frame configuration to avoid interference. The algorithm solves the problem that the interference can only be judged by clinical observation in the clinic.

Free vibrations analysis of composite and hybrid axisymmetric shells

The free vibration of laminated composite (C) and hybrid axisymmetric shell structures, consisting of a composite laminated material sandwiched between two functionally graded material laminas (F1/C/F2), is analysed in the present work. The numerical solutions are obtained by expanding the variables in Fourier series in the circumferential direction and using conical frustum finite elements in the meridional direction. The implemented finite element is a simple conical frustum with two nodal circles, with ten degrees of freedom per nodal circle. This model requires only a reduced number of finite elements to model the geometry of axisymmetric structures, the integration procedures use one Gauss point, and the through the thickness properties variation in FGM laminas is modelled by a small number of virtual layers, resulting a very high computational efficiency. The in-house developed code presents very good solutions when compared with results obtained by alternative available models.

Split-Plot I-Optimal Design Optimisation of Combined Oil-Based and Friction Stir Rotation-Assisted Heating in SPIF of Ti-6Al-4V Titanium Alloy Sheet under Variable Oil Pressure

The aim of this paper is to determine the optimal input parameters for the process in order to ensure the maximum formable wall angle is obtained in a conical frustum with a varying wall angle fabricated using Single Point Incremental Forming (SPIF). The test material was 0.8-mm-thick Ti-6Al-4V titanium alloy sheets, and the test used a tungsten carbide tool with a rounded tip with a radius of 4 mm. Complete workpieces were heated using hot oil with a temperature of about 200 °C, and in addition, the high rotation speed of the forming tool generated an amount of friction heat. The input parameters were tool rotational speed, feed rate, step size, and tool rotation direction. Various oil pressures were used to improve both the accuracy of the components formed and the friction heating process. On the basis of calculations performed by means of the response surface methodology, split-plot I-optimal design responses were obtained by means of polynomial regression models. Models were fitted using REstricted Maximum Likelihood (REML), and p-values are derived using the Kenward–Roger approximation. Observation of the fracture surface of Ti-6Al-4V drawpieces showed that the destruction is as a result of ductile fracture mode. Tool rotational speed and step size are the most significant factors that affect the axial force, followed by feed rate. It was also found that step size is the most significant factor that affects the in-plane SPIF force.

Mip-NeRF RGB-D: Depth Assisted Fast Neural Radiance Fields

Neural scene representations, such as Neural Radiance Fields (NeRF), are based on training a multilayer perceptron (MLP) using a set of color images with known poses. An increasing number of devices now produce RGB-D(color + depth) information, which has been shown to be very important for a wide range of tasks. Therefore, the aim of this paper is to investigate what improvements can be made to these promising implicit representations by incorporating depth information with the color images. In particular, the recently proposed Mip-NeRF approach, which uses conical frustums instead of rays for volume rendering, allows one to account for the varying area of a pixel with distance from the camera center. The proposed method additionally models depth uncertainty. This allows to address major limitations of NeRF-based approaches including improving the accuracy of geometry, reduced artifacts, faster training time, and shortened prediction time. Experiments are performed on well-known benchmark scenes, and comparisons show improved accuracy in scene geometry and photometric reconstruction, while reducing the training time by 3 - 5 times.

Shape Accuracy in Single Point Incremental Forming of Conical Frustums from Titanium CP2 Sheets

This paper presents frustum cone drawpiece analysis made of titanium CP2 sheet by a single incremental sheet forming. Central composite design has been adopted to carry out an experiment containing 20 runs, then multi-criteria parameter optimization has been done. Optimal parameters have been validated and responses deviations do not exceed 4% compared to created models. For the drawpiece formed with optimal parameters, AGRUS optical measurement and X-ray tomography has been applied to check the obtained of the part wall thickness and general deviations compared to the CAD model. The wall angle discrepancy of the cone generatrix has also been analyzed. No gaps or ruptures have been confirmed by X-ray. The blank rolling direction has a significant effect on the drawpiece deviations. The measurement results showed deviations of the drawpiece wall angle +0.27°/- 0.06°, sheet thickness on the cone +0.012/-0.04 mm and +0.151/-0.096 mm from the reference CAD geometry.