Magnetism, Volume 3, Issue 4 (December 2023) – 5 articles

The popularity of permanent magnet synchronous motors (PMSMs) has increased in recent years due to their high efficiency, compact size, and low maintenance needs. Calculating iron loss in PMSMs is crucial for designing and optimizing PMSMs to achieve high efficiency and a long lifespan, as this can significantly affect motor performance. However, multiple factors influence the accuracy of iron loss calculations in PMSMs, including the intricate magnetic behavior of the motor under different operating conditions, as well as the influence of the motor’s dynamic behavior during the operation process. This paper proposes a method based on particle swarm optimization (PSO) and a recurrent neural network (RNN) to estimate the iron loss in PMSMs, independent of the empirical iron loss formula. This method establishes an iron loss calculation model considering high-order harmonics, rotating magnetization, and temperature factors. Accounting for the multifactor influence, the model studies the law of loss change under different magnetic flux densities, frequencies, and temperature conditions. To avoid the deviation problem caused by conventional polynomial fitting, a multilayer RNN and PSO are used to train and optimize the neural network. Iron loss in complex cases beyond the measurement range can be accurately estimated. The proposed method helps achieve a PMSM iron loss calculation model with broad applicability and high accuracy. Full article

The slot opening function, also called relative air gap permeance, is a function which, multiplied by the flux density distribution of a slotless geometry, gives the flux density distribution of a slotted configuration. Here, the magnetic field inside the air gap of a multi-slot surface facing a smooth one was studied, by solving the Laplace equation inside the air gap, in terms of a Fourier series. To obtain the Fourier coefficients, at first, the conformal mapping analytical solution of a single-slot configuration along the smooth surface, was considered. Then, the principle of superposition of the single-slot lost flux density distributions was applied to obtain the multi-slot distribution. The approach is valid in general, and in the case of interference among the flux density distributions of adjacent slots, where their mutual effect cannot be neglected. The field distributions obtained by using the proposed slot opening functions were compared with FEM simulations, showing satisfactory agreement. The numerical accuracy limits were also analysed and discussed. Full article

Magnetic hopfions are three-dimensional topological solitons embedded into a homogeneously magnetized background. The internal structure of hopfions is distinguished by the linked preimages—closed loops with a single orientation of the magnetization on the target space $S^2$—and is thus characterized by the integer Hopf index $Q_H$. Alternatively, hopfions can be visualized as a result of the swirling of two-dimensional bimerons around the direction of an applied magnetic field. Since the bimeron consists of a circular core and an anti-skyrmion crescent, two hopfion varieties can be achieved with either bimeron constituent facing the hopfion interior. In bulk cubic helimagnets, however, the applied magnetic field leads to a spontaneous collapse of hopfions, i.e., the eigen-energy of hopfions has the minimum for zero hopfion radius R. Anti-hopfions with $Q_H=-1$, in this case, pass through the intermediate toron state with two-point defects. Here, we demonstrate that the competing cubic and exchange anisotropies inherent in cubic non-centrosymmetric magnets (e.g., in the Mott insulator Cu${}_2$OSeO${}_3$) as a third level of the hierarchy of energy scales following the exchange and Dzyaloshinskii–Moriya interactions, may shift the energy minimum into the region of finite hopfion radii. Full article

This paper presents an analytical study of the air-gap magnetic field of a surface permanent magnet (SPM) linear, slot-less machine with a Halbach PM configuration, under the no-load condition. While other analytical formulations of the magnetic field generated by PMs are available, they exhibit some drawbacks, such as only providing a Fourier series, or being suitable to determine magnetic field average values, but not local magnetic field distributions. On the contrary, the proposed approach allows the determination of a unique, closed-form formulation for the slot-less machine air-gap field. This is obtained starting from the complex expression of the magnetic field of a conductor, inside the air gap, between two parallel smooth iron surfaces, obtained by means of the method of images. The magnetic field due to an infinitesimal conductor belonging to a current sheet is then integrated along a segment, providing the expression of the magnetic field due to the corresponding linear current density distribution, for current sheets perpendicular or parallel to the iron surfaces. Any Halbach PM segment disposition can, hence, be obtained via a suitable combination of field distributions generated by couples of current sheets with perpendicular and parallel orientation. Lastly, the no-load magnetic field expression with a Halbach array of PMs is retrieved. The proposed analytical model provides an accurate representation of the magnetic field distribution produced by any Halbach array, with an arbitrary number of segments and orientations. Additionally, the results obtained from the proposed analytical expressions are compared with FEM simulations realized by commercial software, and show an excellent agreement. Full article

A novel micro-solenoid resonator has been designed, simulated, and measured. The solenoid core consisted of a Duroid^TM circuit board with a relative permittivity of 2.2. The resonator design incorporated four embedded copper vias with a radius of 125 µm and three surface conductors to form a rectangular coil. A pitch size of 250 µm was used for a 3.02 mm thick substrate. To enhance the resonator’s performance at higher frequencies, a capacitance was introduced in series through the via. This additional capacitor effectively couples the inductance, resistance, and stray capacitance. The optimization of the quality factor was investigated through pole transfer analysis, resulting in an increased resonance frequency of 12.25 GHz and an elevated Q-factor of 306. Moreover, besides its very high Q-factor, this resonator offers a simplified design and easy integration. An analytical lumped circuit model was employed to investigate the design, and the measured S-parameters closely matched the analytical model and electromagnetic simulation results. The tuned resonator exhibited a superior quality factor compared to other micro-resonators. Full article