Residual Magnetic Flux Research Articles

Dynamic modeling and analysis of viscoelastic hard-magnetic soft actuators with thermal effects

Hard-magnetic soft materials (HMSMs) are a class of magnetoactive smart polymers capable of sustaining a high residual magnetic flux density and can undergo large actuation strains under an external magnetic excitation. Due to these exceptional characteristics, soft actuators based on HMSMs hold enormous potential for remote-controlled applications. The temperature and viscoelasticity considerably influence the performance of these materials during the operation. This work aims to develop an analytical framework for modeling the dynamic behavior of a planar hard-magnetic soft actuators (HMSA) considering temperature and viscoelastic effects. The constitutive behavior of the viscoelastic HMSA is described by employing an incompressible neo-Hookean model in conjunction with a Zener rheological model and the Rayleigh dissipation function. The dynamic governing differential equations of motion are derived by utilizing the non-conservative form of the Euler–Lagrange equation. This study delves into the collective influence of temperature and viscoelastic properties on the stability, periodicity, and resonance characteristics of nonlinear vibrations exhibited by HMSM-based planar actuator subjected to dynamic magnetic loading, presenting the findings through time-history responses, Poincaré maps, and phase-plane plots. The presented results can help in the efficient and robust design of HMSM-based actuators and can also serve as an initial step toward the development of advanced actuators exposed to dynamic loading under variable temperatures for diverse applications in the fields of engineering and medicine.

Comparative Analysis and Design Optimization of Ferrite-Based Surface PM Vernier Machines

This paper presents the results of a comprehensive investigation into the comparative analysis and design optimization of ferrite-based surface permanent magnet vernier machines (SPMVMs). While SPMVMs boast a simple mechanical structure and enhanced torque density attributed to the flux modulation effect, they suffer from a persistent challenge of low power factor. Several factors hinder the adoption of low-cost ferrite magnets in SPMVMs. First, ferrite magnets are prone to irreversible demagnetization, constraining the allowable range of magnet thickness. Second, the reduced residual magnetic flux density of ferrite magnets exacerbates the decrease in power factor and machine efficiency. Thus, achieving optimal performance in ferrite-based SPMVMs necessitates the careful selection of various design parameters. To address these issues, this study employs a surrogate-based metaheuristic optimization algorithm with adaptive sampling to identify the optimal solution. Additionally, the integration of a Halbach array is explored to further enhance the performance of the three-slot/two-pole SPMVM topology. Subsequently, two ferrite-based SPMVM baseline models—one with a conventional SPM structure and another with a Halbach magnet array—are thoroughly designed, optimized, and subjected to detailed performance analysis using the 2D finite element method.

Field-induced interfacial instabilities in a two-phase ferrofluid flow

Forming a stable ferrofluid and non-magnetic interface in a microchannel is essential for biomedical applications with two miscible aqueous solutions. Here, we report the interface profile and its instability of aqueous ferrofluid and water co-flow in a microchannel under the influence of a magnetic field. The scaling law related to diffusion width and dimensionless Pe number is introduced by solving the momentum and diffusion equation and combining the experimental results. It is found that the dimensionless number of diffusion width δ/h ∝ X/Peα, when core flow concentration cf, residual magnetic flux density Br, sheath flow and core flow ratio Qw/Qf, and core flow velocity Qf are changed, α is 0.633–1.071, α ∝ Qβ, β = −0.059,0.147, 0.019 and −0.101, respectively. Altering the core flow velocity and magnetic field intensity can quickly impact the interface's stability by improving the transport efficiency by 32.9 % and counteracting the impacts of material diffusion by 51.8 %, respectively. Elevating the proportion of sheath flow to core flow and magnetic field will impede the diffusion of core flow. This will result in a drop of 11.9 % in the magnetic convection effect and a 20.8 % counteraction of material diffusion effects.

Spatial Distribution Analyses of Axially Long Plasmas under a Multi-Cusp Magnetic Field Using a Kinetic Particle Simulation Code KEIO-MARC

To realize the development of a long plasma source with a uniform electron density distribution in the axial direction, the spatial distribution of plasma under a multi-cusp magnetic field was analyzed using a KEIO-MARC code. Considering a cylindrical plasma source with an axial length of 3000 mm and a cross-sectional diameter of 100 mm, in which the filament electrode was the electron source, the electron density distribution was calculated using the residual magnetic flux density, Bres, and the number of permanent magnets installed at different locations surrounding the device, Nmag, as design parameters. The results show that both Bres and Nmag improved the uniformity of the electron density distribution in the axial direction. The maximum axial electron density decreased with increasing Nmag and increased with increasing Bres. These trends can be explained by considering the nature of the multi-cusp field, where particles are mainly confined to the field-free region (FFR) near the center of the plasma column, and the loss of particles due to radial particle transport. The use of multiple filaments at intervals shorter than the plasma decay length dramatically improved axial uniformity. To further improve axial uniformity, the filament length and FFR must be properly set so that electrons are emitted inside the FFR.

Improving Efficiency of a Pole-Changing Vernier Machine Considering Residual Magnetic Flux Density

This paper presents the efficiency improvement of a pole-changing vernier machine (PCVM) by considering the residual magnetic flux density (Br) of low coercivity force (LCF) permanent magnets (PMs). The PCVM operates in two modes: vernier machine (VM) mode and permanent magnet synchronous machine (PMSM) mode, achieved through pole-changing. Pole-changing involves reversing the magnetic flux direction of LCF PM to alter the number of rotor pole pairs. By changing the number of rotor pole pairs, the PCVM operates as a VM mode at low speeds, providing high torque, and as a PMSM mode at high speeds, offering high efficiency. To achieve this, a combination of high coercivity force (HCF) PM and LCF PM is utilized in a single structure. The magnetic flux direction in the LCF PM is determined by Br, and the highest efficiency is achieved when Br reaches its maximum value |Brm|. This paper focuses on improving efficiency by obtaining Brm in VM mode and −Brm in PMSM mode through the design process. Additionally, finite element analysis (FEA) is employed to compare the performance of the improved model, which considers Br, with that of the conventional model, designed without considering Br. The improved model achieves higher Br values in each mode compared to the conventional model, resulting in increased torque density. Consequently, this leads to improved efficiency.

Tunable anti-plane wave bandgaps in 2D periodic hard-magnetic soft composites

In this paper, we present a theoretical model for the analysis of large magneto-deformation and the anti-plane shear wave bandgaps in 2D periodic two-phase hard magnetic soft composite structures subjected to magnetic stimuli. The constitutive behavior of the phases in the hard-magnetic soft composite is described using the incompressible Gent model. To solve the incremental anti-plane wave equations, the finite element method and the Floquet–Bloch theorem for periodic media are utilized. Using the developed framework, we numerically study the dependency of the bandgap width and their location on the direction and magnitude of the applied magnetic flux density vector, material parameter contrasts, and geometry and volume fraction of the inclusion phase. The numerical results reveal that significant tunability of the bandgap is achieved when the applied magnetic flux density direction is along the residual magnetic flux density direction. Also, it is seen that the geometry of the inclusion has significant effect on the bandgap width. The crucial inferences from the present investigation can find their potential use in the design and manufacturing of futuristic smart soft wave devices with tunable band structures.

Viscoelastic Effects on the Nonlinear Oscillations of Hard-Magnetic Soft Actuators

AbstractThe hard-magnetic soft materials (HMSMs) belong to the magnetoactive category of smart polymers that undergo large actuation strain under an externally applied magnetic field and can sustain a high residual magnetic flux density. Because of these remarkable characteristics, HMSMs are promising candidates for the remotely controlled actuators. The magnetic actuation behavior of the hard-magnetic soft actuators (HMSAs) is considerably affected by the viscoelastic material behavior of HMSMs. In this article, we aim at developing an analytical dynamic model of a typical planar model of HMSAs concerning the viscoelasticity of HMSMs. A Zener rheological model in conjunction with an incompressible neo-Hookean model of hyperelasticity and Rayleigh dissipation function is employed for defining the constitutive behavior of the viscoelastic HMSA. The governing equations of dynamic motion are deduced by implementing the nonconservative form of the Euler–Lagrange equation. The established dynamic model is utilized for providing preliminary insights pertaining to the effect of the viscoelasticity on the nonlinear oscillations of the actuator. The phase–plane portraits, Poincaré maps, and the time–history response are plotted to investigate the stability, resonant behavior, and periodicity of the actuator. The results and inferences reported here should provide the initial step toward the design and the development of modern actuators for diverse futuristic applications in the medical and engineering fields.

Investigation on intense axial magnetic field shielding with a large melt cast processed Bi-2212 tube

The feasibility of shielding axial magnetic fields up to 1.4 T, using a Bi-2212 hollow cylinder, is investigated at a temperature of 4.2 K. The residual magnetic flux density along the axis of the tube is measured at external fields of 1 T and 1.4 T. The shielding factor, defined as the ratio between the applied and the residual magnetic flux densities at the center of the tube, is measured to be 32×104 at 1 T and 12×103 at 1.4 T. The induced current density is evaluated from the measurements taking the thickness of the tube into account. The stability of the measurements over time is also addressed. Numerical simulations for the external and the residual magnetic flux densities are performed and compared to the experimental results. The study shows a high shielding performance of the Bi-2212 superconductor tube at 4.2 K up to 1.4 T.

Anisotropic Contraction in a Magnetically Hard but Mechanically Ultra‐Soft Foam for Precise Drug Delivery

AbstractHard magnetic soft materials (HMSMS) have been recently intensively explored in soft robots, owing to its native advantages such as untethered, rapid and reversible actuation, as well as large shape changes. However, in the existing studies, HMSMS is majorly applied by a magnetic field to produce bending, folding, and even twisting, that is, shape morphing, to realize multimodal locomotion. Meanwhile, such as contraction deformation, which may be employed in precise drug delivery, has been neglected in a long term. Here, an anisotropic contraction in a porous structure, hard magnetic foam (HMF), which is mechanically ultra‐soft (with a shear modulus of 4.5 kPa) but magnetically hard (with a residual magnetic flux density of 12 mT), is reported. The investigation of HMF structures indicates that anisotropic contraction is dominated by the magnetodeformational effect and the magnetic body‐force against support constraint. By adjusting the magnetic fields directions, the relationship between these two factors can be regulated to achieve a maximum contraction of 43% (synergy) or negligible deformation (antagonism). Finally, HMF is utilized to realize precision drug delivery since it has the advantages of no leakage during moving, precisely adjustable drug release rate (from 0.008 to 0.62 mL min−1), and no residues after leaving.

Analysis and Modeling of Axial Leakage for Spoke-Type Hybrid Permanent Magnet Machines

In this study, we propose a novel analysis method for a spoke-type permanent magnet (PM) synchronous motor (PMSM) using two types of PMs that consider axial leakage flux using a magnetic equivalent circuit (MEC). Spoke-type ferrite PMSM have the advantage of concentrating magnetic flux; however owing to the shape in which the PMs are arranged along the radial direction, some magnetic flux leaks in the axial direction, which causes inconsistency between the 2D and 3D finite element analysis (FEA) results. Because 3D FEA requires considerable analysis time, using it in the initial design stage of the motor is inefficient. Therefore, we present a new analytical method combined with MEC to overcome the existing inefficient approach. To obtain analysis results equivalent to 3D FEA, the new residual magnetic flux density considering axial flux leakage was applied to 2D FEA PMs using MEC and 2D FEA. The validity of the proposed method was verified through 3D FEA and experiments conducted on the test models using two magnet types.

Development of Multi-Cation-Doped M-Type Hexaferrite Permanent Magnets

We report enhanced permanent magnet performance for multi-cation–substituted M-type Sr-hexaferrites (SrM) prepared using conventional ceramic processes. The final cation composition, Sr0.4Ca0.3La0.3Fe10.2Co0.1Mn0.1Si0.05Mg0.05O19, could be derived through stepwise and systematic cation composition designs, processing, and characterization. The hexaferrites sample sintered in the temperature range of 1200–1220 °C showed an enhanced coercivity (HC) of approximately 4.0 kOe and a residual magnetic flux density (Br) of 2.5–2.6 kG. When samples of the same composition were fabricated into anisotropic magnets through a magnetic-field molding process, performance parameters of Br = 4.42 kG, HC = 3.57 kOe, and BHmax = 4.70 M·G·Oe were achieved, a significant improvement over Br = 4.21 kG, HC = 3.18 kOe, and BHmax = 4.24 M·G·Oe for the non-substituted SrFe12O19 magnet processed under optimized conditions.

Анализ возникновения бросков магнитного потока и намагничивающего тока при включении трансформатора на холостом ходу

This article discusses the transients that occur in power transformers when they are turned on at idle. The main negative consequences arising from magnetizing current surges and their impact on the quality of electrical equipment, in particular, false alarms of relay protection devices and deformation of transformer structural elements by electrodynamic forces, are given. The mathematical derivation of physical quantities determining the process of occurrence of magnetic flux and magnetizing current surges is presented on the example of switching on a power single-phase transformer in idle mode. As a result of mathematical analysis, the main factors affecting the flow of the transient process when the power transformer is switched on in idle mode were identified. A mathematical expression was obtained that allows determining the phase of the mains voltage for a favorable moment of switching on a single-phase transformer, depending on the magnitude of the residual magnetic flux in the steel core of the transformer. Based on the analysis of transients that occur when transformers are switched on at idle, methods or algorithms for switching on power transformers can be developed that allow for a smooth start of the transformer and avoid or minimize negative consequences.

Nonlinear geometrically exact dynamics of fluid-conveying cantilevered hard magnetic soft pipe with uniform and nonuniform magnetizations

It is generally acknowledged that a hanging cantilevered pipe conveying fluid becomes unstable by flutter-type instability at a critical flow velocity; moreover, the pipe undergoes periodic self-excited oscillations in the post-flutter region. Additionally, the critical flow velocity increases when the magnetized pipe is exposed to an actuating parallel magnetic field. The question arises as to whether the actuating magnetic field leads to lessening the oscillation amplitude of the system in the post-flutter region. The nonlinear responses of a fluid-conveying cantilevered hard magnetic soft pipe with uniform and nonuniform magnetizations under an actuating parallel magnetic field are examined to answer the question. In the case of nonuniform magnetization, the pipe’s mass density and elastic modulus in addition to its residual magnetic flux density, vary along its length. The mathematical formulation is constructed via a nonlinear geometrically exact model and is solved by employing the Galerkin technique in conjunction with the Runge-Kutta finite difference scheme. The numerical results are then analyzed to reveal the role of magnetization in the system's magneto-hydro-elastic responses in the magnetic field's absence and presence.

Characteristics of Self‐Excited Rail Brake Using Capacitors

Rail brakes are a type of brakes for railway vehicles that can generate braking force by electromagnetic force. The authors of this article proposed a rail brake that applies the capacitor self‐excitation technique of induction machines to an excitation method. It does not require supplying power from the vehicle and can suppress heating rails during braking operation. This article proposes a practical excitation circuit that solves the problem of self‐excitation of rail brakes where residual magnetic flux cannot be used for the initial excitation. The results of bench tests using a full‐scale armature indicated that the rail brake can be driven by the proposed method. In addition, the results show the characteristics of rail brakes with capacitor self‐excitation. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Residual Magnetic Moment Influences the Features of Fe3s XPS Spectrum: A Case Study

Background: Fe 3sXPS spectrum exhibits doublet peak instead of predicted singlet peak based on spin-orbit coupling theory. This anomalous behavior is considered to be of magnetic origin. However, the effect of residual magnetic moment on the features of Fe3s doublet peak is not understood fully. Objective: This study aims to verify the effect of residual magnetic moment on the spectral features of Fe3s XPS spectrum of magnetic material. Method: As a case study, we have carried out a high-temperature XPS study of the Fe 3s spectrum of magnetic domain aligned (MDA) sample with composition composed of SrFe10.8Al1.2O19. In addition, the XPS data have been compared with the data acquired at different temperatures of magnetic domain non-aligned (MDNA) sample. Results: The results show that the majority peak intensity and minority peak width of Fe 3s spectrum of MDA are smaller than those of the MDNA sample, and they increase systematically with increasing temperature. However, it is noted that the features of Fe3s spectrum of both MDA and MDNA samples completely overlap near and above the Curie temperature, Tc ~ 670K. Discussion: The residual magnetic flux in the MDA sample alters the interaction between 3s electrons and valence 3d spin. In addition, the presence of residual magnetic moment leads to deviation of the escaped electrons from their path, therefore the majority peak intensity of MDA sample becomes smaller than the MDNA sample at below the Curie temperature. Consequently, the spectral features of MDA samples are different than the MDNA samples at below the Curie temperature. Conclusion: The analysis of XPS data suggests that the residual magnetic moment influences the spectral features of the Fe3s spectrum. These results provide evidence that it is important to consider the contribution of the residual magnetic moment while deriving information from the Fe 3s XPS spectrum of the MDA sample.

Magnetic Characterization of the Nugget Microstructure at Resistance Spot Welding

Conventional resistance spot welds are not visible from the outside. Therefore, it is not straightforward to evaluate the joint quality non-destructively. The pulse-echo method of manual ultrasonic is widely used for non-destructive testing. Another option is the passive magnetic flux density testing, which is being developed at Technische Universität Dresden, Germany. The spot weld is magnetized in the normal direction and the residual magnetic flux density is measured on top of the surface of the joint. This method is suitable for spot welds on typical car body steels. Previous investigations show that the magnetic properties of the materials influence the test result. In order to develop this new non-destructive testing method further, it is necessary to know the magnetic properties of the different microstructure regions of a spot weld. This article focuses on methods to measure and evaluate the magnetic properties of these regions, especially of the base material and the weld. Different measuring methods and approaches are presented and compared with each other. Based on the results, recommendations for future measurements for magnetic characterizations are given.

Estimation of Depth Direction of Crack by measuring the Residual Magnetic Vector Flux Density around Grains

We suggests an algorithm to estimate the depth direction of fatigue cracks. This algorithm uses the distribution of residual magnetic vector flux density (RMVFD) on the specimen. Magnetic domains are the region with a magnetic moment in the same direction. A grain has several magnetic domains. Domain wall is the boundary of the magnetic domain. Magnetic energy stabilized when no external magnetic field applied. That is, the sum of the total magnetic moments is close to zero. It is because that the magnetic flux densities are canceling each other at both ends of the domain wall. The domain wall moves when an external magnetic field applied. As a result, the magnetic domain, which has the same direction with the external magnetic field, enlarged. This phenomenon is magnetization. The domain wall stops moving when it meets with factors that limit the domain wall movement (FLWM). Here FLWM are dislocations, defects, and crystal boundaries. The magnetic energy is unstable at the end of FLWM in the magnetic hysteresis phenomenon. Other end of FLWM has to have the opposite direction of RMVFD to stabilize the magnetic energy. Thus, there are opposite direction of RMVFD each other around crack or grain boundaries. Three dimensional RMVFD (3-RMVFD) can indicates crack existence and depth direction of crack. To verify this theorem, we prepared fatigue crack specimens with different depth direction. The three dimensional shapes of grains reconstructs at the crack. The RMVFD measured by scanning a 3-axis magnetic sensor. And the 3-RMVFD indicated in each grains around crack. The depth directions of crack and grains could estimated by using the 3-RMVFD.

A model of hard-magnetic soft curved beams at large deformation

<p indent="0mm">Magnetic-activated soft materials have shown their considerable advantages such as quick response, remote and reversible control, and programmable shape-shifting, making them promising in functional designs of bionic robots, bionic sensors, grippers, valves and metamaterials. Magnetoactive elastomers (MAEs) (also referred to as magnetic polymer composites (MPCs) or magnetorheological elastomers) are a kind of soft active composites that can respond to magnetic field excitation, which are generally composed of micrometer-scale magnetizable particles (e.g., NdFeB particles) embedded in a soft matrix (e.g., silica gel, hydrogel and shape memory polymer). The matrix acts as a continuum medium transmitting the internal force, while the magnetic particles have the interaction among themselves and with the external magnetic field. Compared with soft magnetic materials which are difficult to achieve robust programming, hard-magnetic materials hold residual magnetic flux density vector that does not change with the external magnetic field. After saturation of magnetization, the interaction with the external magnetic field produces micro torque, and programming the micro torque distribution generated by hard-magnetic particles can further form complex shapes. Owing to the intricate interplay between inherent electromagnetic coupling and geometric nonlinearity, it is still a challenge to model and predict the mechanical behaviors of hard-magnetic soft materials. Most of existing models of hard-magnetic elastomers are based on the assumption that the remanence direction is along the axis, which limits the diversification degree of deformation to some extent. In addition, most hard-magnetic beam models are based on Euler-Bernoulli hypothesis (normal remains normal) by neglecting shear deformations. When the beam becomes thick, the effect of shear deformation may turn out to be significant and cannot be ignored. Here, we develop a nonlinear curved beam model to predict large deformations of hard-magnetic soft elastica. The model follows Timoshenko’s first-order shear deformation theory, by accounting for axis elongation and the constitutive law of hard-magnetic elastomers. A set of ordinary differential governing equations containing seven basic unknowns are deduced theoretically. The model can thus describe shear deformation, axis elongation and curvature change of hard-magnetic soft beams upon large deformation. Combined with boundary conditions, the model can be efficiently solved by using shooting methods. In order to verify the accuracy of our hard-magnetic soft beam model, we compare it with the experiments, finite element simulations, and the Euler-Bernoulli hypothesis-based beam model in the literature, for different directions of applied magnetic field. The results verify and highlight the accuracy and universality of our hard-magnetic soft curved beam model which has higher accuracy and wider application range (applicable to thick beams, thin beams and curved beams) compared to the hard-magnetic thin beam model based on Euler-Bernoulli hypothesis (only considering bending deformations). Besides, we explore the bending and buckling deformations of hard-magnetic soft beams with different length-thickness ratios, under different applied magnetic fields. We reveal that the decrease of length-thickness ratio and of applied magnetic fields can enhance shear effects on deformations of hard-magnetic soft beams. Our model could be used not only to analyze geometrically nonlinear behaviors of hard-magnetic elastomers, but also to guide rational designs of ferromagnetic slender structures and soft continuum robots.

Evoking the snap-through instability in hard-magnetic soft materials: Rapid actuation and giant deformation

In this paper, we break into an appropriate strategy for achieving a rapid actuation and giant deformation in hard magnetoactive elastomers (MAEs). We devise a flat arch with a properly distributed residual magnetic flux field and realize the large deformation by harnessing the snap-through instability. With an ingenious design of the residual magnetic flux field within the arch that has a large slenderness ratio, the applied magnetic field for inducing the onset of instability can be relatively small. Even if the size of the flat arch is up to millimeter level, the applied magnetic field is as small as hundreds of oersted. We also develop a theoretical model for revealing the mechanism of the magnetic-driven instability in hard magnetoactive elastomers. The stress, induced by the coupling between the external magnetic field and the residual magnetic flux field, is transformed into a surface load. We formulate the total energy of the magneto-mechanical system and carry out the first and second variations to study the equilibrium states and their stability. To verify our theoretical predictions, we fabricate the corresponding MAE specimen and observe the tantalizing magneto-mechanical behaviors in the lab. Our theoretical predictions agree with the experimental observations in the case of flat arches of MAEs. This paper is desirable to open new ways of designing multifunctional MAE devices with rapid actuation and giant deformation.

A Comparative Study on Methods of Distinction Between Near- and Far-Side Defects as Techniques Used Alongside with the Magnetic Flux Leakage Testing

Results of the finite element analysis show that a far-side defect in a steel plate, with the depth greater by 10% of the plate thickness than a near-side defect, can produce a very similar magnetic flux leakage (MFL) signal. Due to the fact that a measurement of MFL itself can lead to misclassification of a far-side defect as a near-side one, and thus to underestimation of its depth, a comparative study of three complementary magnetic techniques was performed. The following techniques were studied: surface topology air-gap reluctance system (STARS), residual magnetic flux leakage (RMFL) and stray magnetic flux leakage (SMFL). Numerical results showed that in the case of the STARS and SMFL, defect signatures in signals were observed for investigated near-side defects, but not for far-side defects. The signature of the far-side defect in the RMFL was observed, however its peak-to-peak value was only about 8% of the value corresponding to the near-side defect.