Simple Analytical Calculation Research Articles

Development of a Novel Lightweight Utility Pole Using a New Hybrid Reinforced Composite—Part 1: Fabrication and Experimental Investigation

This paper is the first part of a two-part paper that discusses the development of a novel lightweight and cost-effective hybrid 3D composite material and its and utilization for constructing utility poles. The main objective was to generate a material/pole with a comparable performance to the commercially available poles made of 2D fiber-reinforced polymer (FRP) and examine its feasibility. The novel hybrid composite was configured using a recently developed and marketed 3D E-glass fabric–epoxy composite reinforced with wood dowels, referred to as 3D dowel-reinforced FRPs (3D-drFRPs) hereafter. Firstly, the compressive and flexural properties of the 3D-drFRPs are evaluated. Then, the development of the 3D pole is discussed followed by the fabrication details of two 3D-drFRPs using the standard test method, and their responses are compared. For the second part, robust finite element (FE) models were developed in an LS-DYNA environment and calibrated based on the experimental results. A sophisticated nonlinear FE model was used to simulate the performances of ASTM standard-size compression and three-point bending specimens and tapered 2D and prismatic 3D poles. Moreover, the responses of equivalent 2D and 3D poles were simulated numerically, as the task could not be accommodated experimentally due to our laboratory’s deficiencies. The integrity of the numerical simulation results was validated against experimental results, confirming the accuracy of the developed model. As an example, the stiffness values for the 3-pt bending specimens and the 3D poles obtained through the simulations were very close to the experimentally obtained results, with small margins of errors of 3.2% and 0.89%, respectively. Finally, a simplified analytical calculation method was developed so practicing engineers can determine the stiffnesses of 3D-DrFRP poles very accurately and quickly.

D-Q Axis Inductance Analytical Calculation for Fractional-Slot Distributed Winding IPM Motor Based on Big-Small Pole Space Method

The d-q axis inductance is the crucial parameter for the interior permanent magnet (IPM) motor. In order to facilitate the design, analysis, and optimization of IPM motors, it is of great significance to develop an accurate and simplified inductance analytical calculation method. Among the existing calculation methods, the magnetic equivalent circuit (MEC) has advantages in the inductance calculation of the IPM motor due to the simple modeling, the fine processing of the saturation region and the visualization of the magnetic field distribution. However, the traditional MEC method is only applicable to the IPM motor with integer-slot distributed winding (ISDW) or fractional-slot concentrated winding (FSCW), while lacking of in-depth research on fractional-slot distributed winding (FSDW). The magnetic circuit topology of FSDW IPM motors is not as single as that of FSCW/ISDW IPM motors. It leads to problems in the traditional MEC method when dividing the d/q axis flux path in FSDW motors. To solve this problem and expand the applications of MEC method, a big-small pole space (BSPS) method is proposed after fully considering the common characteristics of MMF distribution and reluctance distribution in FSDW motors, which fills the gap of MEC method applied to FSDW motors. The BSPS method divides the d-axis flux path according to the asymmetry of the d-axis magnetomotive force (MMF). Based on the divided flux paths, an improved nonlinear MEC model that considers the saturation of stator and rotor is established to calculate d- and q-axis inductances. The results of finite element analysis (FEA) verify the validity of the proposed MEC model with different geometry parameters. Experimental results of an 84-pole/360-slot FSDW I-type IPM wind generator further confirm the validity of the proposed MEC model

Selected Problems of Optimization of a Switched Reluctance Motor for an Electric Vehicle using Analytical Calculations

A model and an example of optimization of a 6/4 type SRM, designed for an electric vehicle, is described in the paper. The modelling procedure, based on simplified analytical calculations, allows for estimation of the torque, efficiency and acoustic noise of the motor, taking into account the magnetic non-linearity. Some problems arising from the existence of mutual inductances are described as well. Calculations have been performed in MATLAB environment, and verified by means of FEM analysis.

Development of an accelerator-based neutron source to prototype Mo-99 production, part I: A liquid LBE windowless target

Molybdenum-99 (Mo-99)’s decay product, technetium-99 (Tc-99 m), is one of the most critical isotopes for medical diagnostics. To provide U.S. domestic supply of Mo-99 without using high-enriched uranium (HEU), a subcritical uranium target assembly (UTA) is irradiated by an accelerator-based neutron source to create Mo-99 through fission. This study discusses the development of the accelerator-based neutron source. The high-energy electrons from the accelerator irradiate a liquid lead-bismuth eutectic (LBE) target to produce neutrons. Part I of this work focuses on numerical and experimental analysis towards the development of a liquid LBE windowless target. Unlike the existing windowless targets in literature, the current design creates a vertical free surface for a beam to irradiate. First, a hydrodynamic analysis of the LBE windowless target is performed. Simplified analytical calculations are assisted by 2D computational fluid dynamics (CFD) simulations to design the target, with the focus on eliminating recirculation zones and avoiding cavitation. With the optimized geometry, the experimental study is performed to investigate the flow hydrodynamics using liquid LBE. The experiments (1) compare pressure drop in the system to correlation predictions; (2) visualize the free surface liquid LBE flow from the beam view; (3) validate the LBE flow profile using temperature sensitive paint from the side view; and (4) validate the liquid LBE film thickness using gamma densitometer measurements. Second, the power handling capability of the designed windowless target is investigated. The divider plate in the current design is susceptible to overheating due to the thin LBE film in front. As LBE erosion and corrosion is likely to occur at an LBE velocity of 2.0 m/s and temperature above 500 °C, a power limit of 10 kW of beam power was established to prevent this corrosion from occurring, which is calculated by a Nusselt number correlation. The divider plate surface temperature at 10 kW agrees well with the 3D CFD simulation results. Part I demonstrates the fundamental physics in liquid LBE windowless target design and associated testing. A companion paper, Part II will demonstrate how to couple this windowless target into the Mo-99 production system, including an accelerator system operating under an ultra-high vacuum and the UTA cooled by water at room temperature.

A methodology for data-driven modeling and prediction of the drag losses of wet clutches

AbstractIn wet clutches, load-independent drag losses occur in the disengaged state and under differential speed due to fluid shearing. The drag torque of a wet clutch can be determined accurately and reliably by means of costly and time-consuming measurements. As an alternative, the drag losses can already be precisely calculated in the early development phase using computing-intensive CFD models. In contrast, simple analytical calculation models allow a rough but non-time-consuming estimation. Therefore, the aim of this study was to develop a methodology that can be used to build a data-driven model for the prediction of the drag losses of wet clutches with low computational effort and, at the same time, sufficient accuracy under consideration of a high number of influencing parameters. For building the model, we use supervised machine learning algorithms. The methodology covers all relevant steps, from data generation to the validated prediction model as well as its usage. The methodology comprises six main steps. In Step 1, the data is generated on a suitable test rig. In Step 2, characteristic values of each measurement are evaluated to quantify the drag loss behavior. The characteristic values serve as target values to train the model. In Step 3, the structure and quality of the dataset are analyzed and, subsequently, the model input parameters are defined. In Step 4, the relationships between the investigated influencing parameters (model input) and the characteristic values (model output) are determined. Symbolic regression and Gaussian process regression have both been proven to be suitable for this task. Lastly, the model is used in Step 5 to predict the characteristic values. Based on the predictions, the drag torque can be predicted as a function of differential speed in Step 6, using an approximation function. The model allows a user-oriented prediction of the drag torque even for a high number of parameters with low computational effort and sufficient accuracy at the same time.

Computation of high-frequency magnetoelastic waves in layered materials

The direct calculation of magnetoelastic wave dispersion in layered media is presented using an efficient, accurate computational technique. The governing, coupled equations for elasticity and magnetism, the Navier and Landau-Lifshitz equations, respectively, are linearized to form a quadratic eigenvalue problem that determines a complex web of wavenumber-frequency dispersion branches and their corresponding mode profiles. Numerical discretization of the eigenvalue problem via a spectral collocation method (SCM) is employed to determine the complete dispersion maps for both a single, finite-thickness magnetic layer and a finite magnetic-nonmagnetic double-layer. The SCM, previously used to study elastic waves in non-magnetic media, is fast, accurate, and adaptable to a variety of sample configurations and geometries. Emphasis is placed on the extremely high frequency regimes being accessed in ultrafast magnetism experiments. The dispersion maps and modes provide insight into how energy propagates through the coupled system, including how energy can be transferred between elastic- and magnetic-dominated waves as well as between different layers. The numerical computations for a single layer are further understood by a simplified analytical calculation in the high-frequency, exchange-dominated regime where the resonance condition required for energy exchange (an anticrossing) between quasi-elastic and quasi-magnetic dispersion branches is determined. Nonresonant interactions are shown to be well approximated by the dispersion of uncoupled elastic and magnetic waves. The methods and results provide fundamental theoretical tools to model and understand current and future magnetic devices powering spintronic innovation.

Simulation and Characterization of Nanostructured Electromagnetic Scatterers for Information Encoding

Nanostructured scattering arrays for the optical spectral domain can be used as passive tags for information encoding, similarly to the manner in which RFID technology does. Setting up their specific spectral response depends on their geometry and the properties of the building materials. The primary design can be provided by using an analytical calculation procedure that is more straightforward and simpler than a numerical simulation. However, the question arises as to the validity of the results. Both approaches are examined in this article. Complementary scatterer arrays were designed using simplified analytical calculation and by means of numerical modeling. The experimental samples were fabricated by the focused ion beam milling of a gold film on a glass substrate and characterized by a spectroscopic system. The results of the analytical calculations, the numerical simulations, and the experimental measurements were compared. On the basis of the comparison, it was observed that for quick array design, both approaches can be used with satisfactory accuracy. Moreover, the simple numerical model also proved the possibility of the identification of the basic dipole mode splitting. Focused ion beam milling was shown to be suitable for the rapid production of complementary scatterer arrays.

Analytical Research on the Bearing Characteristics of Oil Film Supplied with Constant Oil Flow Hydrostatic Turntables under Fixed Eccentric Load Condition

This study was initiated in view of the phenomenon that hydrostatic turntable rails are prone to scrape damage when the liquid hydrostatic turntable is running under fixed partial load. The existing bias-load hydrostatic turntable oil film bearing characteristics are mainly calculated by using the calculus integration method and CFD fluid simulation method. The calculating formula obtained by the calculus integration method is complex and inefficient. The CFD fluid simulation calculation method requires 3D modeling and meshing of the oil film, which is a tedious and time-consuming process and may not yield convergent calculation results due to improper meshing methods or boundary condition settings. In order to solve the shortage of the above calculation methods, this paper simplifies and equates the uneven thickness of the oil film of each sealing edge of the oil pad of the bias-loaded hydrostatic rotary table to the equivalent uniform thickness of the oil film, and based on this idea, the analytical calculation formula of the oil film bearing capacity, bending moment and stiffness under constant bias-load conditions of the constant-flow liquid hydrostatic rotary table is derived. In this paper, Fluent software was used to numerically simulate the oil film under this working condition, and a hydrostatic turntable test bench was established to conduct an experimental study on the biased load hydrostatic turntable; the experimental data and simulation results were compared with the results obtained from this simplified method of calculating the oil film loading characteristics. The results show that the error of oil film bearing capacity is less than 6% and the error of overturning moment is less than 7%, which has verified the validity of the calculation method. The simplified analytical calculation method proposed in this paper is used to study the influence of tilt displacement rate, lubricant flow rate and turntable speed on the basic performance parameters of oil film, which provides a theoretical basis for the study of oil film load-bearing characteristics under constant bias-load conditions of the constant-flow liquid hydrostatic turntable.

Can luminous Lyman alpha emitters at z ≃ 5.7 and z ≃ 6.6 suppress star formation?

ABSTRACT Addressing how strong UV radiation affects galaxy formation is central to understanding their evolution. The quenching of star formation via strong UV radiation (from starbursts or active galactic nuclei) has been proposed in various scenes to solve certain astrophysical problems. Around luminous sources, some evidence of decreased star formation has been found but is limited to a handful of individual cases. No direct, conclusive evidence on the actual role of strong UV radiation in quenching star formation has been found. Here, we present statistical evidence of decreased number density of faint (AB magnitude ≥ 24.75 mag) Ly α emitters (LAEs) around bright (AB magnitude < 24.75 mag) LAEs even when the radius goes up to 10 pMpc for z ≃ 5.7 LAEs. A similar trend is found for z ≃ 6.6 LAEs but only for faint LAEs within 1 pMpc radius from the bright LAEs. We use a large sample of 1077 (962) LAEs at z ≃ 5.7 (z ≃ 6.6) selected in total areas of 14 (21) deg2 with Subaru/Hyper Suprime-Cam narrow-band data, and thus, the result is of statistical significance for the first time at these high redshift ranges. A simple analytical calculation indicates that the radiation from the central LAE is not enough to suppress LAEs with AB mag ≥ 24.75 mag around them, suggesting additional physical mechanisms we are unaware of are at work. Our results clearly show that the environment is at work for the galaxy formation at z ∼ 6 in the Universe.

Salisbury screen with lossy nonconducting materials: Way to increase spectral selectivity of absorption

We present a modified Salisbury screen design in which the thin absorbing metal layer is replaced with a layer of nonconducting lossy material. The conditions for total absorption in such a structure are explained using a simplified analytical model and rigorous numerical calculations. For the proof-of-principle experiments, germanium/silicon bilayers deposited on aluminium substrates are designed and manufactured. The structures demonstrate nearly perfect absorption in the near-IR spectral range. Compared to conventional Salisbury screens, a lossy semiconductor top layer exhibits increased spectral selectivity of absorption. The wavelength of nearly perfect absorption remains tunable by optimizing the thicknesses of the lossy and transparent layers.

The use of non-spherical powder particles in Laser Powder Bed Fusion

Laser powder bed fusion (LPBF) generally involves the use of near-spherical powders due to their smooth morphology and enhanced flowability that allow for easier powder layering and laser processing. Non-spherical powders, on the other hand, are more cost-efficient to manufacture, however, the underlying mechanisms of their movement and interparticle interaction on the powder bed are still unclear. Thus, this study reports on the use of irregular iron-based powder material in LPBF, with a specific focus on particle motion and interaction behavior on the powder bed. The powder morphology, sphericity and particle size were analysed using X-ray computed microtomography and scanning electron microscopy. Based on the acquired data and by using a simplified analytical calculation, the influence of the particle shape/size on the particle movement in LPBF was established. High-speed imaging was employed to investigate the particle flow dynamics in the process zone, as well as the powder entrainment phenomenon. Particle entrainment and entrainment distances along the scanning direction were measured for near-spherical and non-spherical powders. The obtained results were compared between the powders, revealing a dissimilar particle transfer behavior. Non-spherical powder had a shorter entrainment distance partly attributed to the weaker drag force acting on these particles.

Out-of-Plane Deformation Analysis of the Thin-Walled Closed Curved Box Girder under the Temperature Gradient

For calculating the thin-walled closed curved box girder caused by the temperature gradient of the internal force and displacement, based on the fundamental differential equation of the curve beam and the principle of minimum energy, set a reverse statically indeterminate simply supported curve beam as the basic structure, consider the warping effect of the closed curve box girder, and put forward a kind of plane curve beam temperature deformation simple analytical calculation method. Compared with the finite element calculation results, the relative error of the analytical calculation results is less than 5%. It is concluded that the analytical method has sufficient accuracy in calculating the out-of-plane deformation of the thin-walled closed curved box girder under the temperature gradient.

Modeling and analytical calculation of road damage coefficient considering tire pressure and damping of vehicles

The road damage coefficient [Formula: see text] is a significant indicator to estimate the degree of the road damage caused by vehicles. The existing calculation method of [Formula: see text] is not convenient for the engineering application. To effectively evaluate the damage degree and facilitate the engineering application, this paper studied the simple and reliable analytical calculation method of [Formula: see text]. Firstly, a dynamic model of the vehicle–road system was created. The tire pressure and the tire damping were considered in the model. Moreover, the relationship between the tire vertical stiffness and the tire pressure is approximated as a linear function. Secondly, based on the dynamic model, according to the definition of [Formula: see text], a concise analytical formula of [Formula: see text] was derived and verified by numerical simulations. The relative errors of the analytical calculation results are all less than 0.1%. Thirdly, the influences of the tire pressure [Formula: see text], the damping ratio [Formula: see text] of the suspension system, and the damping ratio [Formula: see text] of the wheel system on [Formula: see text] were analyzed. Moreover, based on the analytical formula of [Formula: see text], a mathematical model of the optimal damping matching for the suspension system was established and a case study was also given. The research results show that the larger the tire pressure [Formula: see text], the larger the value of [Formula: see text] is. For each [Formula: see text], there is an optimal damping ratio [Formula: see text]. If the tire damping is ignored, it will lead to the design error for [Formula: see text]. Finally, some important conclusions were drawn. The analytical formula of [Formula: see text] and the conclusions can provide valuable references for the analysis of the road damage and the initial design of vehicle suspensions.

A Simple Approach to Evaluate Near Field Thermal Radiation From Emitters With Layered Structures and Temperature Variations in One Direction

Abstract A simple analytical calculation scheme to determine near field radiation through decomposing an emission domain into lots of thin thermal current sheets is presented. Through finding the orthogonal modes of thermal current of each thin layer, the thin current sheets can be treated as radiation sources of electromagnetic waves with determined analytical solutions. The outgoing electromagnetic waves from each thin current sheets can be either in transverse electric (TE) or transverse magnetic (TM) modes depending on the orientations of the current in the thin current sheets with respect to the directions of amplitude modulations of the orthogonal modes. Electromagnetic waves arriving to a collection domain are related to the electromagnetic waves leaving from each thin current thermal sheet with transfer coefficients. Transfer coefficient for TE and TM waves can be determined analytically with transfer matrix method or scattering matrix methods. Compared with existing dyadic Green's function method, the new calculation scheme allows material and temperature variations along one direction of the emission domain based on determined analytical expressions of TE and TM waves leaving from each thin current sheets. The simple calculation scheme is especially useful in near field radiation of layered structures with different material such as hyperbolic material with negative refractive indices. With this new approach, we recovered analytical solutions of near field radiation between two semi-infinite domains with uniform temperature and derived closed form solution of near field radiation between two semi-infinite domains with temperature profiles with/without laminated structures.

Structural silicone joint behaviour study for cold bent glass

Cold-bent or warped glass units in facades has gained in popularity as architecture in commercial buildings is showing a trend to innovative, non-rectangular “organic” shapes. Structural silicone glazing has been used successfully as the sole method of retention of the bending membrane. Recent research by the authors investigated experimentally the durability of different cold bent glass designs by coupling the loading level to the rate of deformation over time and recommend for single corner warped glass tolerable peak strains to reach a good durability. The goal of the current paper is to propose adapted evaluation methods from the early design stage to the final concept. The first part of the paper is a thorough investigation of the difficulties observed when applying FEA to the evaluation of structurally glazed cold bent glass. Building further on the recently done investigation, the effect of the mesh size, the choice of constraints, the type of bending (single corner or other) and the design of the frame or interlayer are discussed. Additionally, an additional failure criteria was evaluated to the maximum principal strain to verify whether they can predict failure as observed experimentally. The second part of the paper derives an alternative simplified analytical calculation method to assess the potential of different concepts in the early design stages for twisted glass. The effect of the interlayer is addressed as well as the effect of the IGU compound. The accuracy of the analytical results are compared to FEA models.

Experimental capabilities and limitations of a position-based control algorithm for swarm robotics

Achieving efficient and reliable self-organization in groups of autonomous robots is a fundamental challenge in swarm robotics. Even simple states of collective motion, such as group translation or rotation, require nontrivial algorithms, sensors, and actuators to be achieved in real-world scenarios. We study here the capabilities and limitations in controlling experimental robot swarms of a decentralized control algorithm that only requires information on the positions of neighboring agents, and not on their headings. Using swarms of e-Puck robots, we implement this algorithm in experiments and show its ability to converge to self-organized collective translation or rotation, starting from a state with random orientations. Through a simple analytical calculation, we also unveil an essential limitation of the algorithm that produces small persistent oscillations of the aligned state, related to its marginal stability. By comparing predictions and measurements, we compute the experimental noise distributions of the linear and angular robot speeds, showing that they are well described by Gaussian functions. We then implement simulations that model this noise by adding Gaussian random variables with the experimentally measured standard deviations. These simulations are performed for multiple parameter combinations and compared to experiments, showing that they provide good predictions for the expected speed and robustness of the self-organizing dynamics.

Оценка гарантированного срока службы для модели системы с резервированием разнотипными элементами

The paper focuses on the problem of confidence estimation of reliability indicators for a system model with loaded redundancy of elements of various sub-systems. The lower confidence limits are constructed for the system reliability function, as well as for the indicator associated with it, the indicator having a given guaranteed level of the system uptime, i.e., its gamma-percentile life. Within the research, we obtained approximate asymptotic --- for the case of high reliability --- expressions for confidence estimates of these basic indicators of system reliability. Rather simple approximate analytical calculation formulas based on these asymptotic expressions are given for the lower confidence boundary of the system reliability function and a similar confidence boundary for the guaranteed system life.

Stability of Wall Panels with One-Sided Board Sheathing for Timber Structures

The subject of this paper is a new knowledge in experimental and numerical analysis of the stability of the wall panels with one-side board sheathing. The reinforcement of the panel is provided by means of glued timber composite I-shaped element consisting of a web made of a wood-based desk – OSB board embedded into flanges of solid timber. At present, the design of wall panels with I-shaped cross-section stiffeners and double-sided sheathing is based on test results and simplified analytical calculation. For the design of wall panels with I-shaped cross-section stiffener rib and one-sided board sheathing, a reliable procedure for determining the buckling load bearing capacity has not been described so far. It is assumed that the base of this work can be used for more effective material use of subtle light timber frames. By optimization of the supporting structure, increased heat-technical properties will be effectively achieved. New outputs of experimental analysis on wall panels in real dimensions, as well as material tests of individual components such as solid wood, OSB board and staples will be presented in this paper. Moreover, this paper presents the results of detailed numerical analysis, which are validated on the basis of the experiments performed.

A Simplified Analytical Calculation Model of Average Power Loss for Modular Multilevel Converter

Modular multilevel converters (MMCs) have been widely used in voltage source converter HVdc, and the capacity of MMCs has reached 1000 MW. The accurate calculation and theoretical analysis of the loss has attracted more and more attention, especially in high-power applications. This paper presents a simplified analytical calculation model of average power loss for MMC based on the root mean square (RMS) and absolute values of the arm current. In this model, the analytical expressions of the conduction loss and the switching loss are derived in terms of the whole arm of MMC rather than a single submodule. It avoids the effect of the complexity of its switching pattern on the calculation accuracy of the model. The explicit expressions of the presented model show the relationship between the loss, the voltage balancing methods, and the main variables of MMC directly in comparison with the conventional loss evaluation methods. PSCAD/EMTDC simulation and experimental results of the ±350 kV/1000 MW MMC in the Luxi Back-to-Back DC Asynchronous Networking Project verify the correctness and the accuracy of the proposed simplified calculation model.

Turing–Hopf patterns on growing domains: The torus and the sphere

This paper deals with the study of spatial and spatio-temporal patterns in the reaction-diffusion FitzHugh–Nagumo model on growing curved domains. This is carried out on two exemplar cases: a torus and a sphere. We compute bifurcation boundaries for the homogeneous steady state when the homogeneous system is monostable. We exhibit Turing and Turing–Hopf bifurcations, as well as additional patterning outside of these bifurcation regimes due to the multistability of patterned states. We consider static and growing domains, where the growth is slow, isotropic, and exponential in time, allowing for a simple analytical calculation of these bifurcations in terms of model parameters. Numerical simulations allow us to discuss the role played by the growth and the curvature of the domains on the pattern selection on the torus and the sphere. We demonstrate parameter regimes where the linear theory can successfully predict the kind of pattern (homogeneous and heterogeneous oscillations and stationary spatial patterns) but not their detailed nonlinear structure. We also find parameter regimes where the linear theory fails, such as Hopf regimes which give rise to spatial patterning (depending on geometric details), where we suspect that multistability plays a key role in the departure from homogeneity. Finally we also demonstrate effects due to the evolution of nonuniform patterns under growth, suggesting important roles for growth in reaction-diffusion systems beyond modifying instability regimes.