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1. A High Torque Density Halbach Rotor Coaxial Magnetic Gear

   Hong, H Y; Bird, J Z; Barnett, D; Williams, W. (January 2019, IEEE International Conference on Electrical Machines and Drives)

   This paper presents the design, analysis, and experimental testing results for a 5.67:1 Halbach rotor magnetic gearbox with a ferromagnetic back support. Using 3-D finite element analysis software the Halbach magnetic gearbox was calculated to achieve a volumetric torque density of 284N·m/L with only an active region outer diameter of 120mm. The experimental prototype obtained an active region volumetric torque density of 261.4N·m/L 

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2. Shape and Topology Optimization of Circular Halbach Array using a Cardinal Basis Function (CBF) Based Parametric Level Set Method

   Gao, Lingfeng; Torrey, David; Luo, Fang; Longtin, Jon; Chen, Shikui (August 2025, American Society of Mechanical Engineers (ASME))

   A Halbach array is a specialized arrangement of permanent magnets designed to generate a strong, uniform magnetic field in the designated region. This unique configuration has been widely utilized in various applications, including magnetic levitation (maglev) systems, electric motors, particle accelerators, and magnetic seals. The advantages of Halbach arrays include high efficiency, reduced weight, and precise directional control of the magnetic field. Halbach arrays are commonly categorized into two configurations: linear and cylindrical. A linear Halbach array produces a concentrated magnetic field on one face and is frequently employed in maglev trains and conveyor systems to ensure stable and efficient operation. In contrast, a cylindrical Halbach array consists of magnets arranged in a ring, generating a uniform magnetic field within the cylinder while suppressing the external field. This configuration is particularly advantageous in applications such as brushless electric motors and magnetic resonance imaging (MRI) systems. Traditionally, the design of electromagnetic systems incorporating Halbach arrays relied on engineers’ expertise and intuition due to the complexity of the permanent magnet configuration. However, advancements in numerical methods, particularly topology optimization, have introduced a systematic approach to optimizing the shape and distribution of permanent magnets within a given design domain. In the context of Halbach array design, topology optimization aims to maximize the total magnetic flux within a designated region while simultaneously determining the optimal material distribution to achieve a specified design objective. This approach enhances the performance and efficiency of Halbach arrays, providing a more precise and automated framework for their development. In this paper, we propose a Cardinal Basis Function (CBF)-based level-set method for designing a circular Halbach array capable of generating a uniform magnetic field within a designated region. The CBF-based level-set method offers significant computational advantages by reducing the computational cost and accelerating the convergence process. This approach enhances the efficiency of the optimization process, making it a promising technique for the systematic design of Halbach arrays. 

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3. A Review of Segmented Stator and Rotor Designs in AC Electric Machines: Opportunities and Challenges

   https://doi.org/10.3390/eng6010007  

   Khoshoo, Bhuvan; Aggarwal, Anmol; Foster, Shanelle (January 2025, Eng)

   The use of segmented stator and rotor designs in AC electric machine construction offers several significant advantages, including a high-copper fill factor, increased torque density, improved field-weakening performance, simplified manufacturing processes, and enhanced mechanical strength. Additionally, segmented designs allow for the incorporation of oriented steel—either partially or fully—which exhibits excellent magnetic properties in the rolling direction, resulting in more efficient machine performance. However, lamination segmentation also introduces challenges. Parasitic air gaps between segments and an increased number of cut edges in the assembled stack can alter the magnetic properties of the machine, potentially leading to degraded performance. Furthermore, the use of oriented steel remains complex, as its highly nonlinear magnetic properties vary depending on the direction of the magnetic flux. This paper reviews the widely adopted stator and rotor segmentation techniques available in the literature, discussing their potential benefits and limitations. It also covers key aspects such as popular manufacturing approaches, the impact of segmentation on machine performance, advanced finite-element analysis (FEA) techniques for numerical modeling, and experimental methods for evaluating the performance of segmented stator and rotor constructions in AC machines. By addressing these areas, this work provides a comprehensive resource for machine designers seeking to develop AC machines with segmented stators and rotors. 

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4. Robust Topology Optimization of Synchronous Reluctance Motors Using Cardinal Basis Function Based Level Set Method

   https://doi.org/10.1115/DETC2023-115068  

   Tian, Jiawei; Torrey, David; Luo, Fang; Longtin, Jon; Chen, Shikui (August 2023, American Society of Mechanical Engineers)

   Abstract Synchronous reluctance motors (SynRMs) have gained considerable attention in the field of electric vehicles as they reduce the need for permanent magnets in the rotor, resulting in less material and manufacturing costs. However, their lower average torque and torque ripple vibrations have been identified as key issues that require resolution. In this study, we present a SynRM design framework employing the cardinal basis functions (CBF)-based parametric level set method. The SynRms design problem is recast as a variational problem constrained by Maxwell’s equations which describe the behavior of electric and magnetic fields in the SynRM. A continuum shape sensitivity analysis is carried out using the material derivative and adjoint method. A distance regularization energy function is employed to maintain the level set function as a signed distance function during the optimization. The parametric topology optimization problem is computationally solved using the Method of Moving Asymptotes (MMA). To demonstrate the effectiveness of our approach, we present a numerical example that compares the torque characteristics of the optimal design with those of a reference design. Preliminary results show that the optimized SynRM has a 30.30% increase in average torque, along with a slight increase in torque ripple, compared to the reference model. 

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5. Quantum torque on a non-reciprocal body out of thermal equilibrium and induced by a magnetic field of arbitrary strength

   https://doi.org/10.1140/epjs/s11734-023-01068-0  

   Kennedy, Gerard (January 2024, The European Physical Journal Special Topics)

   Abstract A stationary body that is out of thermal equilibrium with its environment, and for which the electric susceptibility is non-reciprocal, experiences a quantum torque. This arises from the spatially non-symmetric electrical response of the body to its interaction with the non-equilibrium thermal fluctuations of the electromagnetic field: the non-equilibrium nature of the thermal field fluctuations results in a net energy flow through the body, and the spatially non-symmetric nature of the electrical response of the body to its interaction with these field fluctuations causes that energy flow to be transformed into a rotational motion. We establish an exact, closed-form, analytical expression for this torque in the case that the environment is the vacuum and the material of the body is described by a damped oscillator model, where the non-reciprocal nature of the electric susceptibility is induced by an external magnetic field, as for magneto-optical media. We also generalise this expression to the context in which the body is slowly rotating. By exploring the high-temperature expansion of the torque, we are able to identify the separate contributions from the continuous spectral distribution of the non-reciprocal electric susceptibility, and from the resonance modes. In particular, we find that the torque persists in the limiting case of zero damping parameter, due to the contribution of the resonance modes. We also consider the low-temperature expansion of the torque. This work extends our previous consideration of this model to an external magnetic field of arbitrary strength, thereby including non-linear magnetic field effects. 

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