Sinusoidal Density Research Articles

Analytical expressions of the dynamic magnetic power loss under alternating or rotating magnetic field

Analytical methods are recommended for rapid predictions of the magnetic core loss as they require less computational resources and offer straightforward sensitivity analysis. This paper proposes analytical expressions of the dynamic magnetic power loss under an alternating or rotating magnetic field. The formulations rely on fractional derivative analytical expressions of trigonometric functions. The simulation method is validated on extensive experimental data obtained from state-of-the-art setups and gathered in the scientific literature. Five materials are tested for up to at least 1 kHz in both alternating and rotating conditions. The relative Euclidean distance between the simulated and experimentally measured power loss is lower than 5 % for most tested materials and always lower than 10 %. In standard characterization conditions, i.e., sinusoidal flux density, the dynamic power loss contribution under a rotating magnetic field is shown to be precisely two times higher than an alternating one. The knowledge of electrical conductivity reduces the dynamic magnetic power loss contribution to a single parameter (the fractional order). This parameter has the same value for a given material's rotational and alternating contribution. This study confirms the viscoelastic behavior of the magnetization process in ferromagnetic materials and, consequently, the relevance of the fractional derivative operators for their simulation.

The Formation of Filaments and Dense Cores in the Cocoon Nebula (IC 5146)

We present 850 μm linear polarization and C18O (3 − 2) and 13CO (3 − 2) molecular line observations toward the filaments (F13 and F13S) in the Cocoon Nebula (IC 5146) using the JCMT POL-2 and Heterodyne Array Receiver Program instruments. F13 and F13S are found to be thermally supercritical with identified dense cores along their crests. Our findings include that the polarization fraction decreases in denser regions, indicating reduced dust grain alignment efficiency. The magnetic field vectors at core scales tend to be parallel to the filaments, but disturbed at the high density regions. Magnetic field strengths measured using the Davis–Chandrasekhar–Fermi method are 58 ± 31 and 40 ± 9 μG for F13 and F13S, respectively, and it reveals subcritical and sub-Alfvénic filaments, emphasizing the importance of magnetic fields in the Cocoon region. Sinusoidal C18O (3 − 2) velocity and density distributions are observed along the filaments’ skeletons, and their variations are mostly displaced by ∼1/4 × the wavelength of the sinusoid, indicating core formation occurred through the fragmentation of a gravitationally unstable filament, but with shorter core spacings than predicted. Large-scale velocity fields of F13 and F13S, studied using 13CO (3 − 2) data, present a V-shape transverse velocity structure. We propose a scenario for the formation and evolution of F13 and F13S, along with the dense cores within them. A radiation shock front generated by a B-type star collided with a sheet-like cloud about 1.4 Myr ago. The filaments became thermally critical due to mass infall through self-gravity ∼1 Myr ago, and subsequently, dense cores formed through gravitational fragmentation, accompanied by the disturbance of the magnetic field.

Complex analytical transducer model of a permanent magnet synchronous motor for vibroacoustic applications

This paper presents the complex analytical transducer model of a Permanent Magnet Synchronous Motor (PMSM) for vibroacoustic applications, meaning when the motor actually does not rotate but only the rotor oscillates with low amplitude around an equilibrium position relative to the stator. Using only two assumptions – sinusoidal air-gap flux density and evenly distributed winding – the single phase transducer model is introduced, which is then extended to cover motors with any number of phases. The article proposes adequate transducer symbols and transmission equations as well. In order to enhance the practical relevance of the proposed approach, it is shown that using complex amplitudes and appropriate phase shift vectors in the transducer equations, a complex parameter transducer model can be obtained for sinusoidal signals.

Design and Performance Analysis of 25 kW Class HTS Induction/Synchronous Motor With Self-Organizing Method for Transportation Applications

We proposed a non-empirical self-organizing design method to obtain a unique stator structure for a high-temperature superconducting induction/synchronous machine. The method starts from a line current model with an approximately ideal sinusoidal distribution of the air-gap magnetic field. It keeps increasing the cross-sectional area of the windings under appropriate constraints to achieve a model with realistic current density. In this work, we applied this method to design a 25 kW-class high-temperature superconducting induction/synchronous motor. In the model, each slot has three-phase windings with different areas representing different numbers of turns. The width and height of the two slots are different for each pole and phase. The results demonstrated that the self-organizing design method significantly suppressed the torque ripple of the motor and reduced the high-order harmonics. The self-organizing windings are equivalent to a short-pitching configuration, which produce a more sinusoidal air-gap flux density than windings in general design. Reducing torque ripple to the lowest possible level facilitates the practical use of superconducting machines for transportation applications.

Effects of dutasteride and tamsulosin on penile morphology in a rodent model.

To evaluate the penile morphology after the isolated and combined administration of dutasteride and tamsulosin in a rodent model. Forty male rats were assigned into the following groups: Control group (C, receiving distilled water, n=10); Dutasteride group (D, receiving 0.5 mg/Kg/day of dutasteride, n=10); Tamsulosin group (T, receiving 0.4 mg/Kg/day of tamsulosin, n=10); and Dutasteride associated with Tamsulosin group (DT, receiving both drugs n = 10). All drugs were administered via oral gavage. After 40 days, the animals were submitted to euthanasia and their penises were collected for histomorphometric analyses. Data were compared using one-way ANOVA followed by Bonferroni's post-test, considering p<0.05 as significant. The sinusoidal space and smooth muscle fiber surface densities (Sv), and the cross-sectional penile areas of rats in groups D, T and DT were reduced in comparison to controls with the most notable reductions in the combined therapy group. The connective tissue and elastic system fibers Sv were augmented in groups D, T and DT in comparison with the control group, again with the most pronounced changes observed in animals receiving the combined therapy. Both treatments with dutasteride or tamsulosin promoted penile morphometric modifications in a rodent model. The combination therapy resulted in more notable modifications. The results of this study may help to explain the erectile dysfunction observed in some men using these drugs.

Design and analysis of in-wheel motor with sinusoidal permanent magnet shape for electrical vehicles

This paper deals with the design and analysis of a surface-mounted outer rotor in-wheel motor (IWM) with the aim of reducing cogging torque and torque ripple for electric vehicles. The proposed IWM is equipped with axial sinusoidal surface-mounted permanent magnets (PMs), with the purpose of producing sinusoidal air gap flux density distribution, thus to realize sinusoidal back electromotive force (EMF) and smooth electromagnetic torque. To highlight the advantage of the proposed IWM, the conventional IWM with tile-shaped PMs and the IWM with stepwise-shaped PMs are also studied for comparison. The finite element method in the commercial software package is utilized to analyze the performance of the three motors, including the radial flux density of air gap, back EMF, cogging torque, and electromagnetic torque. Through the quantitative comparison, it is found that the proposed IWM greatly reduces the cogging torque, highly improves the sinusoidality of back EMF, and nearly eliminates the torque ripple.

Research on Torque Ripple Optimization of Permanent Magnet Synchronous Motor for Electric Vehicle Based on Modular Poles

AbstractAbstract in order to study the torque ripple of permanent magnet synchronous motor for electric vehicle, the method of modular poles instead of single pole is adopted to reduce the torque ripple. The modular poles consist of three kinds of permanent magnets with different remanence and are arranged in a sinusoidal distribution. The pole arc length and position of each magnetic pole are calculated according to the cutting area of sinusoidal air gap flux density wave. By changing the cutting area of sinusoidal air gap flux density wave, the optimal pole arc coefficient of each permanent magnet was determined, and the magnet pole combination with the smallest torque ripple value is obtained. The results show that the sine degree of back electromotive force is improved obviously, the cogging torque is decreased greatly, and the motor with modular poles has obvious effect on torque ripple suppression. The torque of the motor with different kinds of magnetic pole combination is more stable than that of the motor with the same kind of magnetic pole combination. In this paper, the method of using modular poles instead of single pole to reduce torque ripple is of positive significance, which provides a reference for the subsequent performance optimization of electric vehicle motor. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

2-D Analytical Model for Computing Eddy-Current Loss in Nonlinear Thick Steel Laminations

In this article, we propose an analytical method to compute the eddy-current loss in nonlinear thick steel laminations (3–12 mm) by considering the return path of the eddy currents. Initially, a 2-D finite-element (FE) model is applied to segregate losses measured from toroidal material samples into hysteresis and eddy-current loss components to use them as reference. Afterward, a 2-D analytical time-domain model is proposed for the eddy currents based on the solution of the 2-D field problem. The time-domain model is then used to derive a simple frequency-domain eddy-current loss formulation for the sinusoidal flux density case with the inclusion of a skin-effect correction factor, which accounts for the nonlinearity of the material. Highly accurate results are obtained from the proposed model compared to FE reference results with a mean relative error of 5.1% in the nonlinear region.

A New Spoke PM Motor with ECC ASPs to Reduce Flux Density Harmonics

This paper proposes new eccentric (ECC) auxiliary salient poles (ASPs) applied in spoke permanent-magnet (PM) motors. These ECC ASPs optimize flux density harmonics and further reduce torque pulsation. Then, the optimization procedure is proposed to reveal the relationship between the ECC method and ASP, and optimization steps are reduced. Firstly, the design of the ECC ASPs is based on the stairs, which are equivalent to sinusoidal flux density. Second, the expressions of offset length for maximum air gap, pole arc angle, and thickness ratio are revealed. Through theoretical analysis and the finite element method (FEM), the proposed ECC ASPs can generate low torque pulsation and improve sound and vibration features.

Revealing the Drag Instability in One-fluid Nonideal Magnetohydrodynamic Simulations of a 1D Isothermal C-shock

C-type shocks are believed to be ubiquitous in turbulent molecular clouds thanks to ambipolar diffusion. We investigate whether the drag instability in 1D isothermal C-shocks, inferred from the local linear theory of Gu & Chen, can appear in nonideal magnetohydrodynamic simulations. Two C-shock models (with narrow and broad steady-state shock widths) are considered to represent the typical environment of star-forming clouds. The ionization-recombination equilibrium is adopted for the one-fluid approach. In the 1D simulation, the inflow gas is continuously perturbed by a sinusoidal density fluctuation with a constant frequency. The perturbations clearly grow after entering the C-shock region until they start being damped at the transition to the post-shock region. We show that the profiles of a predominant Fourier mode extracted locally from the simulated growing perturbation match those of the growing mode derived from the linear analysis. Moreover, the local growth rate and wave frequency derived from the predominant mode generally agree with those from the linear theory. Therefore, we confirm the presence of the drag instability in simulated 1D isothermal C-shocks. We also explore the nonlinear behavior of the instability by imposing larger-amplitude perturbations to the simulation. We find that the drag instability is subject to wave steepening, leading to saturated perturbation growth. Issues concerning local analysis, nonlinear effects, one-fluid approach, and astrophysical applications are discussed.

X-Wave Propagation Characteristics in a Collisional, Inhomogeneous Plasma Slab

Abstract: Normally incident electromagnetic wave on a collisional, inhomogeneous magnetoplasma slab has been treated as a multilayered system of homogeneous sub-cells within the transfer matrix method. For incident wave frequencies much above the ion cyclotron frequency, the extraordinary elliptically polarized wave mode is relevant for wave propagation normal to a dc-magnetic field. For a sinusoidal plasma density profile, the transmittance, reflectance and absorbance are plotted versus wave frequency normalized to electron cyclotron frequency for different ratios of electron cyclotron to electron plasma frequencies. For fixed and by varying the wave frequency, the curves of the transmittance and reflectance show two pass and two stop bands. When the ratio of cyclotron frequency to plasma frequency is increased, all bands shift to the region of low wave frequency, the pass bands become broader and the stop bands become narrower. The absorbance show three absorption bands; namely, two collisional absorption bands of evanescent waves at the X-wave cut-off frequencies and a resonance absorption band at the upper hybrid frequency. It has also been found that a homogeneous plasma slab overestimates the collisional absorption at cut-offs and has a broader absorption band of the upper hybrid resonance. Keywords: Waves in inhomogeneous magnetoplasma, Upper hybrid resonance, Reflectance, Absorbance, Transmittance.

Symmetric Resonance Mechanism for Elimination of Parasitic Torque of a Permanent Magnet Generator under Stable Load

Vibration and torque ripple of the permanent magnet generator axis cause excessive wearing up of the generator, noise, efficiency reduction. The article theoretically considers the possibility of eliminating the oscillation of the rotation torque of the permanent magnets generator at constant load due to mutual compensation of the interaction of coils with the field of permanent magnets in the case of certain symmetry of this field. This effect is called pi resonance. For a given class of model functions of the magnetic field density of permanent magnets, it is shown that full compensation occurs with a certain number of coils (Ns) and magnets (Nr), while for other combinations of {Ns, Nr} the interaction is in the nature of oscillations. Pi resonance tables are given for a number of model field density functions represented by Fourier series up to the fifth power. Pi resonance is primarily realized in the case of a small difference in the values of Nr and Ns, which corresponds to the location near the main diagonal of the pi resonance table, as well as at the values of Nr, Ns corresponding to prime numbers. The number of configurations {Nr, Ns} providing pi resonance (compensation of parasitic torques) is the largest for the sinusoidal magnetic flux density and decreases if the magnetic flux density function is approximated by a high-degree Fourier series. It is shown that in the absence of coil cores, pi resonance is possible at Nr = Ns. An additional possibility of pi resonance is shown when placing coils on opposite sides of the rotor. A simplified method of investigating the system (without integrating the equation for the induction current) is substantiated. The results can be used in the design of permanent magnets generators and motors.

Structures of glasses created by multiple kinetic arrests.

X-ray scattering has been used to characterize glassy itraconazole (ITZ) prepared by cooling at different rates. Faster cooling produces ITZ glasses with lower (or zero) smectic order with more sinusoidal density modulation, larger molecular spacing, and shorter lateral correlation between the rod-like molecules. We find that each glass is characterized by not one, but two fictive temperatures Tf (the temperature at which a chosen order parameter is frozen in the equilibrium liquid). The higher Tf is associated with the regularity of smectic layers and lateral packing, while the lower Tf with the molecular spacings between and within smectic layers. This indicates that different structural features are frozen on different timescales. The two timescales for ITZ correspond to its two relaxation modes observed by dielectric spectroscopy: the slower δ mode (end-over-end rotation) is associated with the freezing of the regularity of molecular packing and the faster α mode (rotation about the long axis) with the freezing of the spacing between molecules. Our finding suggests a way to selectively control the structural features of glasses.

Mesoscale visualization of three-dimensional microvascular architecture and immunocyte distribution in intact mouse liver lobes.

Rational: The complex vascular architecture and diverse immune cells of the liver are critical for maintaining liver homeostasis. However, quantification of the network of liver vasculature and immunocytes at different scales from a single hepatic lobule to an intact liver lobe remains challenging.Methods: Here, we developed a fast and fluorescence-preserving transparency method, denoted liver-CUBIC, for systematic and integrated analysis of the microcirculation and the three-dimensional distribution of dendritic cells (DCs)/macrophages in intact liver lobes.Results: Whole-mount imaging at mesoscale revealed that the hepatic classical lobule preferred the oblate ellipsoid morphology in the mouse liver and exhibited hepatic sinusoids with heterogeneous arrangement and intricate loop structure. Liver fibrosis not only induces sinusoidal density increase but also promotes sinusoidal arrangement with increased sinusoidal branch and loop structure. Meanwhile, we found that CD11c+ DCs followed a lognormal distribution in the hepatic lobules, skewing toward lobular boundary in steady state. CCl4-induced chronic liver injury promoted CD11c+ DC rearrangement at the lobular border before the formation of liver fibrosis. Furthermore, through whole-mount imaging of tumor-immune cell-vascular crosstalk in intact lobes based on liver-CUBIC, we characterized an accumulation of CX3CR1+CCR2+F4/80+ macrophages at metastatic foci in early colorectal liver metastases. Importantly, colorectal cells secrete CCL2 to mobilize CX3CR1+CCR2+F4/80+ macrophages to accumulate at liver micrometastases, and the interruption of CCL2-induced macrophage accumulation inhibits early colonization of metastasis in the liver.Conclusions: Our investigation of the sinusoidal network and DC/macrophage arrangements through the liver-CUBIC approach and whole-mount imaging provide a powerful platform for understanding hepatic circulatory properties and immune surveillance in the liver.

Surface effects in a capacitive argon discharge in the intermediate pressure regime

One-dimensional particle-in-cell/Monte Carlo collisional simulations are performed on a capacitive 2.54 cm gap, 1.6 Torr argon discharge driven by a sinusoidal rf current density amplitude of 50 A m−2 at 13.56 MHz. The excited argon states (metastable levels, resonance levels, and the 4p manifold) are modeled self-consistently with the particle dynamics as space- and time-varying fluids. Four cases are examined, including and neglecting excited states, and using either a fixed or energy-dependent secondary electron emission yield due to ion and/or neutral impact on the electrodes. The results for all cases show that most of the ionization occurs near the plasma-sheath interfaces, with little ionization within the plasma bulk region. Without excited states, secondary electrons emitted from the electrodes are found to play a strong role in the ionization process. When the excited states, and secondary electron emission due to neutral and ion impact on the electrodes are included in the discharge model, the discharge operation transitions from α-mode to γ-mode, in which nearly all the ionization is due to secondary electrons. Secondary electron production due to the bombardment of excited argon atoms was approximately14.7 times greater than that due to ion bombardment. Electron impact of ground state argon atoms by secondary electrons contributes about 76% of the total ionization; primary electrons, about 11%; metastable Penning ionization, about 13%; and multi-step ionization, about 0.3%.

Permanent magnet shape optimization method for PMSM air gap flux density harmonics reduction

This paper proposed a permanent magnet optimization method to suppress the air gap flux density harmonic of permanent magnet synchronous motor (PMSM). The method corrected the effective air gap length of the motor, calculated the magnetization length of the permanent in the case of parallel magnetization, and took the influence of the permanent magnet relative permeability into consideration. Based on these works, for a given sinusoidal air gap flux density waveform, the corresponding structural parameters can be calculated, so as to achieve the optimization of the permanent magnet. By using this method to optimize the shape of the magnet, the fundamental wave of the air gap flux density can be retained to the greatest extent, so as to eliminate harmonics and maintain the output capacity at the same time. The feasibility and accuracy of the method have been verified by finite element analysis (FEA) and prototype machine experiment. This method is simple and time-saving, and has a satisfactory accuracy, which provides a reference method for permanent magnet optimization of PMSM.

Adaptation and parametrization of an iron loss model for rotating magnetization loci in NO electrical steel

PurposeThe magnetic characterization of electrical steel is typically examined by measurements under the condition of unidirectional sinusoidal flux density at different magnetization frequencies. A variety of iron loss models were developed and parametrized for these standardized unidirectional iron loss measurements. In the magnetic cross section of rotating electrical machines, the spatial magnetic flux density loci and with them the resulting iron losses vary significantly from these unidirectional cases. For a better recreation of the measured behavior extended iron loss models that consider the effects of rotational magnetization have to be developed and compared to the measured material behavior. The aim of this study is the adaptation, parametrization and validation of an iron loss model considering the spatial flux density loci is presented and validated with measurements of circular and elliptical magnetizations.Design/methodology/approachThe proposed iron loss model allows the calculation and separation of the different iron loss components based on the measured iron loss for different spatial magnetization loci. The separation is performed in analogy to the conventional iron loss calculation approach designed for the recreation of the iron losses measured under unidirectional, one-dimensional measurements. The phenomenological behavior for rotating magnetization loci is considered by the formulation of the different iron loss components as a function of the maximum magnetic flux density Bm, axis ratio fAx, angle to the rolling direction (RD) θ and magnetization frequency f.FindingsThe proposed formulation for the calculation of rotating iron loss is able to recreate the complicated interdependencies between the different iron loss components and the respective spatial magnetic flux loci. The model can be easily implemented in the finite element analysis of rotating electrical machines, leading to good agreement between the theoretically expected behavior and the actual output of the iron loss calculation at different geometric locations in the magnetic cross section of rotating electrical machines.Originality/valueBased on conventional one-dimensional iron loss separation approaches and previously performed extensions for rotational magnetization, the terms for the consideration of vectorial unidirectional, elliptical and circular flux density loci are adjusted and compared to the performed rotational measurement. The presented approach for the mathematical formulation of the iron loss model also allows the parametrization of the different iron loss components by unidirectional measurements performed in different directions to the RD on conventional one-dimensional measurement topologies such as the Epstein frames and single sheet testers.

Calculation and Analysis of Eddy-Current Loss in Switched Reluctance Motor

The eddy-current loss of switched reluctance motor (SRM) is studied and analyzed in this paper. As a significant part of core loss, eddy-current loss has a great influence on motor performance. First, the average magnetic flux waveforms in every distributed region are derived from the magnetic equivalent circuit (MEC) model. Based on this, each harmonic of magnetic density is obtained by adopting the fast Fourier transform (FFT) method for further calculation. Then, each harmonic eddy-current loss is computed by sinusoidal magnetic density and the total eddy-current loss in different region of motor is derived by superposing of them. Therefore, the calculated results at different speed and conduction angles of each region are analyzed. Finally, the 3D finite element (FE) model is established in software FLUX and the experimental platform of the SRM prototype is built.

Influences of sinusoidal density modulation on stimulated Raman scattering in inhomogeneous plasmas

The influence of sinusoidal density modulation on stimulated Raman scattering (SRS) reflectivity in inhomogeneous plasmas is studied using three-wave coupling equations, fully kinetic Vlasov simulations, and particle-in-cell (PIC) simulations. Through a numerical solution of the three-wave coupling equations, we find that the sinusoidal density modulation is capable of inducing absolute SRS even though the Rosenbluth gain is smaller than π, and we describe a region of modulational wavelength and amplitude in which absolute SRS can be induced, which agrees with earlier studies. The average reflectivity obtained by the Vlasov simulations has the same trend as the growth rate of absolute SRS obtained from the three-wave equations. Instead of causing absolute instability, a modulation wavelength shorter than the basic gain length can suppress the inflation of SRS through harmonic waves. In addition, the PIC simulations qualitatively agree with our Vlasov simulations. Our results offer an alternative explanation for high reflectivity in experimental underdense plasmas, which is due to long-wavelength modulation, and a potential method to suppress SRS using short-wavelength modulation.

Modeling of PWM-Induced Iron Losses With Frequency-Domain Methods and Low-Frequency Parameters

The high-frequency iron losses caused by sinusoidal flux density variations with frequencies ranging from 2.5 to 40 kHz, amplitudes from 1 to 70 mT, and dc-biased magnetic inductions from 0 to 1.62 T are measured with the dual-transformer system. Then, in this article, a simple frequency-domain model is proposed based on the linear fitting and two-dimensional interpolation methods for engineering applications. In addition, another two frequency-domain models, respectively, considering and neglecting the excess losses are investigated and compared for the high-frequency iron-loss modeling, which only need low-frequency parameters and contain the physical interpretation to the variation of high-frequency iron-loss coefficients with the frequency, ac flux density amplitude, and dc-biased magnetic induction. The iron losses generated by the unipolar and bipolar pulsewidth modulation (PWM) voltages with different switching frequencies and modulation factors are measured to testify the three models. It is shown that the three models in this article are more accurate than the previously proposed one for calculating the PWM-induced iron loss by considering the variation of model parameters with the dc-biased magnetic induction and ac flux density amplitude, especially when silicon steel sheets reach the saturation.