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Internet of Things devices prompt a rising demand for autonomous and compact power supply generators to sustain low-power wireless sensor nodes. Due to the ubiquity of waste heat in buildings and urban environments, low-grade heat sources are very attractive for applications. Thermomagnetic generators (TMG) can be small and autonomous. Ahmim’s TMG [1] produces 4.2 μW (0.24 mW/cm&lt;sup&gt;3&lt;/sup&gt; over a 35°C temperature difference. While this device exploits direct thermal contact with both reservoirs, a key element of a thermal device [2], the output power is penalized by a sub-Hertz working frequency. Khol’s TMG [3] produces 118 mW/cm&lt;sup&gt;3&lt;/sup&gt; at 84 Hz but over a larger temperature difference of 138°C. Their use of 5 μm thick Heusler Alloy films, compared to a 250 μm thick plate of LaFeSi by Ahmim, is an important factor to explain the different in the working frequency.&lt;br/&gt;&lt;br/&gt;We aim to explore the possibility to use thin films in Ahmim’s TMG while keeping its low temperature difference capability. Ahmim’s TMG has specific characteristics. Firstly, it needs to have a freestanding magnetocaloric film of several micrometers. Our recent work on Gd film deposition has shown a 17 μm film with significant magnetocaloric effect [4]. Secondly, it needs to have a magnetic field source that gives a maximum field variation but also confines the magnetic field in order to reduce the film displacement. By combining Gd films and high performance NdFeB micro-magnets [5], [6] with our design experience on macro devices (Fig.1), we will discuss the key steps of the design, e.g., the spring characteristics to achieve self-oscillating micro-devices. Several parameters need to be optimized, such as the micro-magnet pattern, the air gap and Gd film thickness. 3D numerical simulations of the magnetic force as a function of the material position and temperature (Fig. 2), which are being used to optimize the system design, will be discussed in detail. With our proposed design, if we assume a 50 Hz working frequency, there is 5mW of mechanical energy available.

![](https://assets.underline.io/uploads/markdown_image/1/image/6c8def3c8eadc39bbbf231f211465813.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/d44ec31fe73d8d8565d56c704b72f012.jpg)

Key steps in designing a micro thermomagnetic generator

2022 Joint MMM-INTERMAG

Key steps in designing a micro thermomagnetic generator

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Internet of Things devices prompt a rising demand for autonomous and compact power supply generators to sustain low-power wireless sensor nodes. Due to the ubiquity of waste heat in buildings and urban environments, low-grade heat sources are very attractive for applications. Thermomagnetic generators (TMG) can be small and autonomous. Ahmim’s TMG [1] produces 4.2 μW (0.24 mW/cm3 over a 35°C temperature difference. While this device exploits direct thermal contact with both reservoirs, a key element of a thermal device [2], the output power is penalized by a sub-Hertz working frequency. Khol’s TMG [3] produces 118 mW/cm3 at 84 Hz but over a larger temperature difference of 138°C. Their use of 5 μm thick Heusler Alloy films, compared to a 250 μm thick plate of LaFeSi by Ahmim, is an important factor to explain the different in the working frequency. We aim to explore the possibility to use thin films in Ahmim’s TMG while keeping its low temperature difference capability. Ahmim’s TMG has specific characteristics. Firstly, it needs to have a freestanding magnetocaloric film of several micrometers. Our recent work on Gd film deposition has shown a 17 μm film with significant magnetocaloric effect [4]. Secondly, it needs to have a magnetic field source that gives a maximum field variation but also confines the magnetic field in order to reduce the film displacement. By combining Gd films and high performance NdFeB micro-magnets [5], [6] with our design experience on macro devices (Fig.1), we will discuss the key steps of the design, e.g., the spring characteristics to achieve self-oscillating micro-devices. Several parameters need to be optimized, such as the micro-magnet pattern, the air gap and Gd film thickness. 3D numerical simulations of the magnetic force as a function of the material position and temperature (Fig. 2), which are being used to optimize the system design, will be discussed in detail. With our proposed design, if we assume a 50 Hz working frequency, there is 5mW of mechanical energy available.

![](https://assets.underline.io/uploads/markdown_image/1/image/6c8def3c8eadc39bbbf231f211465813.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/d44ec31fe73d8d8565d56c704b72f012.jpg)

Key steps in designing a micro thermomagnetic generator

technical paper

Early in 2021, we presented the quintuple AISI 1010 steel core coil (QCC) [1], a novel device for transcranial magnetic stimulation (TMS) able to produce focal stimulation in areas as small as 1 mm2. With it, we introduced the oriented control of the electric field (E-field) based on the path of the highest current density. This technique induces groups of peripheral and central charges of the same sign, whose electric repulsion restricts the central charges to propagate vertically below the central coil. As a result, an oriented central path of the highest current density is obtained, which focally passes through the target at a certain cortical depth, increasing the E-field on it. Now, modifying the elliptical cross-section of the QCC, we created a new figure-of-flower coil (FFC), in which the central coil (gynoecium) and peripheral coils (petals) are formed by round-cross-section multilayer solenoids with independent AISI 1010 cores. This configuration allowed us to induce controlled gradients in the current densities based on the independent modulation of every coil. This dynamically changes the orientation of the directional vector of the central path of the highest current density and -therefore- of the E-field. The technique, named Space-varying E-field Vector Modulation (SEVM), simultaneously varies amplitude, frequency, and/or phase of the coil currents, in combinations that produce a final direction, translatable to stimulation coordinates. Using ANSYS Maxwell software, we performed finite element simulations of the FFC, varying the number of petals between 4 and 10 (Fig.1). Each coil is made of 50 turns, wire diameter = 1 mm, and AISI 1010 steel cores of similar diameter and saturation at 2 T. Coil currents of 5kA at 2.5kHz were used in simulations over a 4-layer homogeneous spherical rat head model of D = 30 mm, with similar electromagnetic properties to those used to investigate TMS in rats [1-2]. The results show dynamic variations in size and position of the stimulated area (Fig.2) (including rotating patterns) with a fixed FFC, eliminating the need for multiple coils for multiple TMS targets. SEVM, QCC, and FCC are efforts towards the next generation of TMS devices with improved controllability.

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![](https://assets.underline.io/uploads/markdown_image/1/image/c5a155a592f213dcea28784ac110d774.jpg)

Oriented Control of the Stimulation Target During Transcranial Magnetic Stimulation Using Space-varying E-field Vector Modulation with Multi-Core Figure-of-Flower Coil

Oriented Control of the Stimulation Target During Transcranial Magnetic Stimulation Using Space-varying E-field Vector Modulation with Multi-Core Figure-of-Flower Coil

Introduction: Transcranial magnetic stimulation (TMS) can be affected by anatomical features. Therefore, neuroanatomy could influence corticomotor excitability after intermittent theta burst stimulation (iTBS). The relationship between iTBS aftereffects and neuroanatomy was investigated via motor evoked potentials (MEPs) and finite element analysis modeling (FEM) of TMS of MRI-derived head models. Targets were the biceps brachii and first dorsal interosseus (FDI) due to their relevance in activities of daily living. Experimental Details: Ten nonimpaired individuals participated, completing sham-controlled iTBS sessions (one each targeting the biceps and FDI cortical hotspots). MEPs were acquired at an intensity of 120% of resting motor threshold (RMT) while iTBS was delivered at 80% of active motor threshold, both via 70 mm figure-of-eight coils targeting the primary motor cortex. MEPs were recorded with surface electromyography. Each participant underwent an MRI of the head, and models were generated from T1 & T2 weighted images. Fiber tract geometry was extracted from diffusion tensor images for the biceps and FDI corticospinal tracts. Neuroanatomical parameters established were fiber tract surface area (FTSA), tract fiber count (TFC), and brain scalp distance (BSD) at the point of stimulation. Cortical electric field strength (EFS) was obtained by FEM of TMS of the head models. A linear mixed effects model was used to assess effects of these parameters and RMT on MEPs recorded after iTBS. RMT was included as a metric of the muscle's measured responsiveness to TMS. Results: iTBS targeting the biceps was faciliatory (p = 0.013), and dependent on FTSA (p &lt; 0.001) and TFC (p &lt; 0.001). There was no effect of iTBS on the FDI (p = 0.223) but individual changes in corticomotor excitability due to stimulation type scaled with RMT (p &lt; 0.001), EFS (p = 0.001), BSD (p = 0.004), and FTSA (p = 0.011). Conclusion: There were unique relationships between neuroanatomical parameters and empirical iTBS response. MRI-based measures of target-specific neuroanatomy impact how the motor system responds to iTBS, making MRI-based modeling potentially useful in selection of motor targets when designing iTBS protocols.

Effect of Neuroanatomy on Motor Evoked Potentials after Intermittent Theta Burst Stimulation

Magnetorheological fluid (MRF) is a magnetic particle reinforced fluidic material, which is mechanical properties, such as stiffness and damping, can be controlled with the application of a magnetic field.1 Smart sensor and actuator can be fabricated for adaptive vibration control systems where mechanical properties can be controlled by the application of a magnetic field. Manufacturability of MR fluid systems using the additive manufacturing (AM) process has gained great attention to enable the geometrical design of the MR fluid in an elastic component.2 In this research, MR fluid was prepared by carbonyl irons which are 6 – 10 μm in diameter with silicon oil (40% volume fraction). Thermoplastic polyurethane (TPU) with shore hardness 60A was used as an elastomeric system. A 3D printer is used to produce cylindrical TPU elastomer with grid structure using 50 % infill (Figure 1a). The MR fluid was added into the TPU elastomer, followed by adding a sealing layer with 3D printing. An external magnetic field (0 and 7 kG) was applied along the sample longitudinal axis at the time of uniaxial dynamic testing with 10% pre-strain. The TPU-MRF samples were characterized via force-displacement tests conducted at 1 Hz under strain amplitudes of 2%. The MR effect on the dynamic stiffness is defined as the ratio of the dynamic stiffness under the maximum magnetic field to the dynamic stiffness in the absence of a magnetic field. Mechanical testing results with the magnetic fields show that the MR effect on the dynamic stiffness is 1.65. (Figure 2a). The area of the force-displacement curve at 7 kG is about 6.5 times larger than the result with 0 kG, indicating a significantly large change in damping property. Frequency was varied from 1 to 10 Hz and the force-displacement curve didn’t show significant changes, indicating that the performance of the TPU-MRF system doesn’t diminish with increased frequency. (Figure 2b)

![](https://assets.underline.io/uploads/markdown_image/1/image/19adad7fc103540f67a0f0d92653914f.jpg)

Figure 1 (a) Schematic diagram of a TPU-MRF sample fabrication (b) Image of TPU grid structure, TPU sample with and without MR fluid.

![](https://assets.underline.io/uploads/markdown_image/1/image/38dc14fab1586b1c5bfaea4cfc340707.jpg)

Figure 2 (a) Force-displacement curve of TPU-MRF with 0 and 7 kG. (2% strain) (b) Force-displacement curves of TPU-MRF with a different frequency of vibration at 7 kG. (3% strain)

Encapsulations of Magnetorheological Fluids using 3D Printed Elastomeric Rectangular Cellular Structures

The key to a healthy and extended life is the early detection of diseases; abnormal cells, viruses, and bacteria could be detected in the early stages by analyzing various body fluids. To ease the detection and expedite the process, portable test kits that do not require hospitals and/or specialists have been developed. In that matter, biosensors are being developed with the capability of trapping bio-entities inside the microfluidic channels via magnetic field gradients. This work presents an innovative, easy-to-apply, and cost-efficient technique for developing at-home disposable rapid test kits with well-organized patterned arrays of Nd-Fe-B flakes in the PDMS matrix (Fig.1). Nd-Fe-B flakes (HC = 1.5 kOe) (Fig.2) were synthesized by surfactant-assisted ball milling technique (at 700 rpm for 12 hours) with an average lateral dimension of 10 μm and an average thickness of 100 nm. The ball to powder weight ratio was chosen as 10:1. Dispersant and surfactant were heptane and oleic acid, respectively. Up to 0.1 %, solid content concentration was aligned and decorated to a gingham pattern. The microfluidic channel was prepared by photolithographic method with 3 layers (50 μm each) of UV-sensitive blue dry film which was developed in Na2CO3 bath (10% (w/v)). Two individual PDMS pieces (microfluidic channel and Nd-Fe-B/PDMS region) were bonded by a two-part epoxy to finalize the Nd-Fe-B/PDMS patch. In order to test the trapping system, Fe nanoparticles were synthesized. Fe nanoparticles were synthesized by the Y-junction method in the presence of NaBH4 and FeCl2 under Ar/H2 gas flow. Synthesized particles have an average size of 92 nm. Subsequently, Fe NPs suspended in DMSO or DI water were flown inside the microfluidic channel. A high trapping efficiency (&gt;90%) of Fe nanoparticles was observed. The developed device can be a game-changer for biosensors.

![](https://assets.underline.io/uploads/markdown_image/1/image/ffed951d44910ae56aa7145ea13fbf28.jpg)

Figure 1. Patterned Nd-Fe-B/PDMS patch.

![](https://assets.underline.io/uploads/markdown_image/1/image/8935f7f33f5fcf0d7450fad1dce203b3.jpg)

Figure 2. Hysteresis loop of Nd-Fe-B/PDMS patch with 0.1 solid content ratio.

Nd-Fe-B Based Magnetophoretic Microfluidic Device with High Trapping Efficiency

The treatment of bacterial infections is becoming a serious global problem due to the increasing bacterial resistance against classical antibiotics (1). To overcome this problem, new antibacterial agents are needed (2). Silver has been known as an antibacterial agent since ancient times and nano-formulated silver has been proved to be a very effective new treatment. However, silver nanoparticles (AgNPs) have limitations related to their low yield for penetrating bacterial biofilms and their concentration-dependent toxicity to human cells. Magnetic nanoparticles based on iron oxides (IONPs) present some special features that can be exploited combining them with AgNPs to enhance the depth of biofilm penetration and to allow removal from the medium by an external magnet (3). Furthermore, the combination of silver bactericidal activity and magnetic hyperthermia is an unexplored and interesting approach. In this work, bifunctional γ-Fe2O3-Ag nanocomposites with different silver content and particle sizes, have been synthesized. They have good microbicidal capabilities against the bacterial pathogens E. coli (Gram-negative) and S. aureus (Gram-positive), which are related to their silver content, the size of the nanoparticles and the release of silver ions. This bactericidal activity can be enhanced by the application of an alternating magnetic field (Fig. 1), which increases the release of silver ions (4).

![](https://assets.underline.io/uploads/markdown_image/1/image/eca767d2925ede34b4885f41c505a2fe.jpg)

Antibacterial activity of g-Fe2O3/Ag nanocomposites under alternating magnetic fields

In this contribution the power capability of shifted inductances axes permanent magnet machines (SIAPMM) is studied. Both low speed (maximum torque) and high speed (flux weakening) operations are analyzed. The goal is to start from a common ground already defined in some contributions dedicated to power capability of synchronous machines [1-3], and extend it to SIAPMM. The concept of SIAPMM have been introduced recently [4-8]. These machines can be regarded as the combination of non-salient PM rotor and a variable reluctance (VR) rotor under the same stator [Fig. 1(a)]. Two Park’s referential frames can be then defined [Fig. 1(b)], one for the PM rotor part, and a second for the VR rotor part, shifted by an angle β [Fig. 1(b)]. The maximum torque can be increased by adequately choosing angle β. Instead of computing the "armature current / EMF" phase shift ψ maximizing the torque, as classically done, for SIAPMM the starting point consists of imposing the optimal angle value ψ = 0, and determining the optimal β angle [Figs. 1(c) and 1(d)]. It can be shown that β = π/4, if ρ &lt; 1, and β = -π/4, if ρ &gt; 1, where ρ is the saliency ratio (= Lq/Ld). Fig. 2(a) shows the percentage of "maximum torque" increase in the (Ldn, ρ) plane, of the SIAPM machines as compared to classical PM machines having the same ρ, and PM excitation flux linkage ΦPM. Ldn is the normalized value of d axis inductance, defined as (Ld×Imax/ΦPM), where Imax is the maximum armature current. The percentage increase is computed as (TSIAPM-TPM)×100/TPM. Fig. 2(b) compares power capabilities of a SIAPMM, and a classical PM machine, with (Ldn = 2.5, ρ = 1.5). The SIAPMM have a better power capability as compared to classical PM machine. In the full version, the power capability of SIAPMM is studied in the entire (Ldn, ρ) plane. The optimal flux weakening strategies to be adopted considering the values of Ldn and ρ will be defined.

![](https://assets.underline.io/uploads/markdown_image/1/image/4a5fd7b19e2e9a52505d43526cfaedf7.jpg)

Fig. 1. SIAPM machines principal. (a) Structure of a SIAPM machine. (b) Park’s referential frame definition. (c) Classical PM machine (β = 0). (d) SIAPM machine (β = π/4).

![](https://assets.underline.io/uploads/markdown_image/1/image/a04db9d7e5b4c28ffd4f848dce128a9a.jpg)

Fig. 2. Power capabilities of SIAPM machines. (a) Torque increase (low speed operation). (b) Operation over a large speed range (Ldn = 2.5, ρ = 1.5).

Power capability of shifted inductances axes permanent magnet machines

Urban air mobility is expected to play a large part in future transportation, where conventional aircraft will be superseded by thousands of highly connected automated airborne vehicles [1]. One of the key barriers to success is the development of reliable lightweight propulsion motors. The conventional method of light-weighting motors uses mechanical gearing to increase motor speed and reduce torque output, however, in this sector the relatively low reliability of the gearbox and potential for catastrophic failure by jamming preclude this method. This paper describes the advances behind a special dual rotor, magnetically geared motor [2] designed for urban air mobility applications. The mechanical gearbox is replaced by a magnetic gearbox that is mechanically and magnetically integrated into the motor itself. The main motor operates at high speed and benefits from the low torque and low motor mass, the integrated magnetic gear reduces output rotor speed and provides a corresponding increase in output torque created by virtue of the extremely high airgap magnetic shear stress available. The magnetic design of this integrated motor is discussed and an exemplar 370Nm, 212mm OD machine is presented. The corresponding thermal design is discussed and loss models linking this with the electromagnetic design are detailed. The design is complimented with advances in mixed material structural design where composites are used within the non-magnetic structural parts. By combining the light-weighting gear effect without the adverse effect on reliability an air-cooled motor with a specific continuous torque density &gt;30Nm/kg is created which is ~30% improvement on the leading competing technology.

Ultra-Lightweight Motors for Urban Air Mobility Propulsion

Autonomous Guided Vehicles (AGVs) have been implemented in modern warehouse aiming for a full automation environment[1]. As any other electric vehicle, AGV requires fast charging of batteries to maintain the workflow on busy warehouses[2], especially when online sales have increased during the pandemic. Wireless charging systems (WCS) can be applied to recharge AGV with low maintenance cost while guarantying the safety of the workforce[3, 4]. However, wireless power transfer (WPT) loss efficiency on large air gaps due to leakage magnetic flux and to the increase of impedance on primary side[5], which require to apply a compensation circuit to optimize the power transfer[6]. This project proposes a novel model for WPT utilizing a DC motor of 2750 RPM and 300 W to spin a disc that has surface mounted permanent magnets (PMs), Figure 1. This disc is composed by 12 square and 12 circular PM, placed in pairs in the disc radius line, with the square PM near the end of the disc and the circular PM 5 mm from the square PM. The adjacent PM pairs have opposite polarity, so that when a coil is placed near this spinning PM disc, the magnetic field will oscillate inducing current on the receiver coil. An investigation on how much current can be harvest through this model is being conducted, also correlating the air gap between PM disc and receiver coils. In addition, the rotation of the PM disc and the induced current on receiver is being evaluated and an analysis of the optimum RPM speed for WPT is being conducted. Finite Element Method (FEM) simulations are being executed and analyzed, currently, a 2D model simulates the movement of the PMs over the coil, which resulted in an alternating induced current of 9A (peak). The main advantage of this model is utilizing the existing magnetic field of PM material, discarding the necessity of applying power to the transmitter, thus eliminating the parasite impedance losses. The system efficiency is expected to be improved in relation to existing WCS.

![](https://assets.underline.io/uploads/markdown_image/1/image/e666dee80dedf45884cc184098b7d1aa.jpg)

Schematic of proposed Rotating Wireless Power Transfer, utilizing a DC motor with a surface mounted magnetic disc coupled to the shaft.



Rotating Permanent Magnet Disc for Wireless Charging Autonomouns Guided Vehicles

Due to the merits of high power density and efficiency, surface-mounted high-speed permanent-magnet machine (HSPMM) is regarded as a competitive candidate for high-speed application of aviation. However, the rotor flux cannot be disengaged when a short circuit (SC) is initiated, so a large interturn SC current of more than ten times of the rated current is usually generated, which seriously threatens the reliability of motor[1]. Recently, numerous studies have been reported concerning the interturn SC fault suppression methods for concentrated winding fault-tolerance PMM[2]. The arrangement sequence of wires was optimized to make the back potential of each coil the same, so that the influence of the position of shorted turns on the value of interturn SC current was eliminated[3]. With use of a new vertical strip windings, the interturn SC current was restrained near rated current[4]. Besides, the typical control methods of injecting flux-weakening current and shorting winding terminals are also investigated to limit the interturn SC current[5]. However, the healthy windings will be sacrificed and a large phase SC current may also be introduced, if shorting all the winding terminals. And the effectiveness of injecting flux-weakening current is extremely dependent on the high-accuracy and rapid detection technology, which is also a great challenge for HSPMM[6,7]. This paper found the characteristic of strong interturn SC fault tolerance of the Gramme-ring-winding HSPMM, providing a solution for HSPMM to high-reliability application. The shorted turns wound around the stator yoke have a very large inductance, so the interturn SC current can be tremendously decreased. For this motor, the analytical models of the interturn SC current and inductance are established. And the principles for characteristic of strong interturn SC fault tolerance is revealed. Then the influences of the position and turns of interturn shorted coil are studied. The analytical models are finally verified by finite-element method. The figures show the cross section of Gramme-ring-winding HSPMSM with one turn of shorted coil and the waveform of winding current. As can been, the interturn SC current is just little higher than rated current.

![](https://assets.underline.io/uploads/markdown_image/1/image/f4f9034f42a5912822ac4f4afeff26cb.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/afe68871289d1d7811de006e539cab9b.jpg)

Research on Interturn Short-circuit Characteristic of the High-speed Permanent-magnet Machine with Gramme-ring Windings

Recently an increasing demand emerges for high-speed permanent magnet motor (HSPMM) in fuel cell compressor application. Overheating is thought as one of the biggest causes for the failure of HSPMM. This paper presents a slotless Gramme-ring-winding HSPMM, so as to reduce the rotor eddy-current loss caused by stator slotting. Besides, it is convenient to fix the slotless windings. However, exposed to the alternating magnetic field of airgap, large AC loss will be generated in the slotless windings. Litz wire, with a high number of individually insulated, small gauge strands separated into bundles and continuously transposed, is employed to control the AC losses associated with high-frequency operation in this paper. Considering the influence of magnetic field of airgap, the analytical model for losses of the litz wire was built based on an external-rotor motor [1]. The components of the losses for litz wire was analyzed in an air-core pulsed alternator, and the diameter was optimized to minimize the loss[2]. Besides, the pitch of litz wire was thought has a great influence on the loss, and the design method of pitch was provided[3]. In addition, the impacts of the litz wire strand shape, such as circular, square and rectangular, were compared on AC copper loss of the HSPMM[4]. Due to the complex structure of litz wire, the calculation method of the equivalent thermal conductivity was given, based on the Gasar porous metal materials. This paper first analyzes the loss of the litz-wire gramme-ring winding based on the FEA methods, considering the different magnetic field of airgap and the outer slots of stator. Then the analytical model for the loss of litz-wire gramme-ring winding is established, and the diameter and shape are optimized to minimize the loss. After that, the thermal analysis model of the litz-wire gramme-ring winding is investigated, and the temperature rise is calculated. Moreover, the influence of diameter and shape of litz wire is also studied. Through the above studies, the design of litz wire is finally provided for the slotless gramme-ring-winding HSPMSM. Fig.1 shows the configuration of the studied motor, and Fig.2 is the distribution of current density in litz wires on different positions.

![](https://assets.underline.io/uploads/markdown_image/1/image/c26e4d7be8939286475fc381ce3c6820.jpg)

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