3D Magnetic Circuit Research Articles

A novel 3D magnetic circuit method for calculating shielding factors of rectangular magnetically shielded rooms

Rectangular magnetically shielded rooms (MSRs) are favored for their construction simplicity and efficient space usage. However, current rectangular MSRs lack an effective shielding factor (SF) theoretical system due to their inherent asymmetric geometry and process defects such as door gap. Therefore, an effective three-dimensional (3D) magnetic circuit method for calculating the SF of rectangular MSRs is proposed in this paper. Firstly, the theoretical model for the 3D magnetic circuit of rectangular MSRs is established, and the SF in three directions is derived. Secondly, the theoretical model is modified by introducing demagnetization factors to further improve the calculation accuracy of the SF based on the magnetization theory. Finally, formula systems for the SF considering door gap are derived, and their effect is also analyzed. To validate the proposed method, two rectangular MSRs with distinct structures are tested using a constructed experimental platform. The results show that the discrepancy between the calculated SF and the tested SF is less than 7%, affirming the efficacy of the proposed methodology. This method can be applied to rectangular MSRs of different sizes, and provide a valuable theoretical guidance for the construction of MSRs.

Topology optimization for magnetic circuits with continuous adjoint method in 3D

PurposeThe purpose of this paper is to present a new approach to optimizing the design of 3D magnetic circuits. This approach is based on topology optimization, where derivative calculations are performed using the continuous adjoint method. Thus, the continuous adjoint method for magnetostatics has to be developed in 3D and has to be combined with penalization, filtering and homotopy approaches to provide an efficient optimization code.Design/methodology/approachTo provide this new topology optimization code, this study starts from 2D magnetostatic results to perform the sensitivity analysis, and this approach is extended to 3D. From this sensitivity analysis, the continuous adjoint method is derived to compute the gradient of an objective function of a 3D topological optimization design problem. From this result, this design problem is discretized and can then be solved by finite element software. Thus, by adding the solid isotropic material with penalization (SIMP) penalization approach and developing a homotopy-based optimization algorithm, an interesting means for designing 3D magnetic circuits is provided.FindingsIn this paper, the 3D continuous adjoint method for magnetostatic problems involving an objective least-squares function is presented. Based on 2D results, new theoretical results for developing sensitivity analysis in 3D taking into account different parameters including the ferromagnetic material, the current density and the magnetization are provided. Then, by discretizing, filtering and penalizing using SIMP approaches, a topology optimization code has been derived to address only the ferromagnetic material parameters. Based on this efficient gradient computation method, a homotopy-based optimization algorithm for solving large-scale 3D design problems is developed.Originality/valueIn this paper, an approach based on topology optimization to solve 3D magnetostatic design problems when an objective least-squares function is involved is proposed. This approach is based on the continuous adjoint method derived for 3D magnetostatic design problems. The effectiveness of this topology optimization code is demonstrated by solving the design of a 3D magnetic circuit with up to 100,000 design variables.

Topological optimization in 3D-magnetostatics: development of adjoint methods using the equations of magnetic moments

PurposeThe purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.Design/methodology/approachFirst, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.FindingsIn this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.Research limitations/implicationsThis research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.Originality/valueThe problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

Analytical modeling of linear oscillating motor with a mixed method considering saturation effect

Linear oscillating motor receives much attention recently due to direct and efficient linear motion output. In order to achieve high thrust and eliminate eddy current effect, circumferential silicon steel stack is usually utilized in stator as a universal topology design. However, circumferential arrangement of silicon steel introduces 3D magnetic circuit, which complicates the design process and cannot be solved using conventional modeling method. In addition, it leads to severe magnetic saturation effect and must be taken into accounts in the analytical model for accurate results. In this paper, a novel mixed analytical modeling method for linear oscillating motor with silicon steel stator is proposed. Magnetic potential vector (MPV) and 3D equivalent magnetic circuit (3D-EMC) methods are combined together in this mixed model. Magnetic potential vector method sets up the coarse flux density distribution, while 3D equivalent magnetic circuit method is used for refinement considering saturation. Moreover, the performance between radial and parallel magnetized structure is compared based on this model. For validation, FEM and experimental results are compared with the proposed model and proves its effectiveness and accuracy, which can be used in further motor structure optimization. It may also act as a universal guidance to other PM motor design.

Magnetic Circuit Analyses and Turning Chatter Suppression Based on a Squeeze-Mode Magnetorheological Damping Turning Tool

As a smart material, magnetorheological fluid (MRF) has been utilized in fields including civil engineering and automotive engineering, and so on. In this study, the MR damping turning tool based on the squeeze-mode was developed to improve the vibration resistance of the tool system on the lathe. The 3D magnetic circuit simulations of the damper were performed. The influences of damper structural parameters, such as coil positions, plate thicknesses, and others, on the magnetic induction strength were investigated. Orthogonal experiments were carried out and the optimal combination of damper parameters was determined. The chatter suppressive experiments were carried out to evaluate the performance of the MR damping turning tool.

Design and Manufacture of a Near 3 T High Field Permanent Magnet Assembly

This paper introduces a design methodology for a multi-tesla permanent magnet. Normally the permanent magnet is designed to provide the magnetic fields below 2 T. By employing high performance materials and the 3D magnetic circuit design method, a prototype magnet has been built and generates maximum 2.987 T field strength in 0.008 m air gap with less than 20 kg total weight. It is expected a practical, compact and light-weight high field source for NMR, MRI or other instruments.

A Design of 1.5 T Permanent Magnet for MR Molecular Imaging

This paper introduces a design methodology for a 1.5 T MR Molecular Imaging permanent magnet. In order to develop a compact, lightweight and high field magnet, here we introduce a 3D magnetic circuit design method. As a result, the magnet generates 1.5 T field strength in 0.06 m air gap with less than 800 kg total weight. Compared to the traditional C-shape magnet, it only consumes about 1/3 permanent-magnet material and 1/8 magnetically soft material. Our measurement results show that it is a good method to obtain a higher field with permanent magnet.

非線形性を考慮した直交磁心の鉄損特性の一算定法

This paper Presents a method for calculating the nonlinear iron loss in an Orthogonal-core. The authors have analyzed the iron loss by using the 3D magnetic circuit of the orthogonal-core on the reluctance network analysis. The magnetic hysteresis is expressed by the inductances connected in series with reluctances in the circuit in accordance with the Chua-type magnetization model. The computed results approximately agree with experimental ones. It was found that the proposed method is very suitable for calculating the iron loss in an orthogonal-core.