United States

I. Introduction&lt;br/&gt;Single-phase permanent magnet linear oscillating actuators (SP-PMLOA) have widely used in the application field of short-stroke and high frequency linear reciprocating, because of simple mechanical structure, without the rotary-to-linear conversion, low maintenance costs and fast dynamic response.&lt;br/&gt;In the design of SP-PMLOA, the detent force was seldom paid attention by scholars. Due to the unique assembly structure and the operation mode of the LOA, the detent force, which changes linearly in the stroke, can be equivalent to a magnetic resistance spring, and its effect on the electromagnetic performance can be ignored. However, the consequence of ignoring the detent force is that the power density of the SP-PMLOA becomes very low or the axial length of the SP-PMLOA is increased. Therefore, the principle of end force generation is introduced, and a new method to reduce end force and alveolar force is proposed in this paper.&lt;br/&gt;II. Analyze the Detent Force&lt;br/&gt;Generally, the detent force is the superposition of end force and cogging force, both of which are caused by the interaction between the permanent magnets in the mover and the stator core. Therefore, according to the principle of cogging force and end force generation, when the cogging force gradually increases, end force gradually decreases. The cogging force and the end force can be offset by changing the position of the permanent magnet.&lt;br/&gt;III. Results&lt;br/&gt;Fig.1 shows the structure of the novel SP-PMLOA, which adopts double-sided stators and one active mover. Three permanent magnets are arranged on the non-magnetizing back iron. The thickness of the middle permanent magnet is larger than that of the permanent magnets on both sides, which can effectively reduce the detent force.&lt;br/&gt;The detent force comparison of three models is shown in Fig.3. as can be seen, the maximum detent force of the improved model is slightly greater than that of one PM model, but smaller than that of the traditional three PMs model.&lt;br/&gt;IV. Conclusion&lt;br/&gt;In this paper, the detent force generation principle of SP-PMLOA has been analyzed. it has been validated that the proposed model can effectively reduce detent force and the amount of PMs used.

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![](https://assets.underline.io/uploads/markdown_image/1/image/f1ef6143310300ab96788ff7956bd90b.jpg)

Electromagnetic Design of Single-Phase Permanent Magnet Linear Oscillation Actuator Considering Detent Force Minimum



2022 Joint MMM-INTERMAG

Electromagnetic Design of Single-Phase Permanent Magnet Linear Oscillation Actuator Considering Detent Force Minimum

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.

I. Introduction Single-phase permanent magnet linear oscillating actuators (SP-PMLOA) have widely used in the application field of short-stroke and high frequency linear reciprocating, because of simple mechanical structure, without the rotary-to-linear conversion, low maintenance costs and fast dynamic response. In the design of SP-PMLOA, the detent force was seldom paid attention by scholars. Due to the unique assembly structure and the operation mode of the LOA, the detent force, which changes linearly in the stroke, can be equivalent to a magnetic resistance spring, and its effect on the electromagnetic performance can be ignored. However, the consequence of ignoring the detent force is that the power density of the SP-PMLOA becomes very low or the axial length of the SP-PMLOA is increased. Therefore, the principle of end force generation is introduced, and a new method to reduce end force and alveolar force is proposed in this paper. II. Analyze the Detent Force Generally, the detent force is the superposition of end force and cogging force, both of which are caused by the interaction between the permanent magnets in the mover and the stator core. Therefore, according to the principle of cogging force and end force generation, when the cogging force gradually increases, end force gradually decreases. The cogging force and the end force can be offset by changing the position of the permanent magnet. III. Results Fig.1 shows the structure of the novel SP-PMLOA, which adopts double-sided stators and one active mover. Three permanent magnets are arranged on the non-magnetizing back iron. The thickness of the middle permanent magnet is larger than that of the permanent magnets on both sides, which can effectively reduce the detent force. The detent force comparison of three models is shown in Fig.3. as can be seen, the maximum detent force of the improved model is slightly greater than that of one PM model, but smaller than that of the traditional three PMs model. IV. Conclusion In this paper, the detent force generation principle of SP-PMLOA has been analyzed. it has been validated that the proposed model can effectively reduce detent force and the amount of PMs used.

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Electromagnetic Design of Single-Phase Permanent Magnet Linear Oscillation Actuator Considering Detent Force Minimum

poster

Abatract:Multi-phase permanent magnet synchronous motor(PMSM) is widely used in high power and high precision fields. The fault-tolerant performance of the drive motor is of great significance for all-electric aircraft applications, and it will be related to the safe operation of the whole machine. In this paper, a 100kW six-phase external rotor permanent magnet synchronous motor is designed, and its electromagnetic performance is analyzed by finite element method(FEM). And meanwhile the output torque ability of the motor under different open-circuit faults is analyzed in detail. Aiming at the reduction of output torque and torque fluctuation under one-phase and two-phase open circuit, different fault compensation measures are proposed based on the principle of magnetomotive force invariance and the principle of eliminating negative sequence components.And the parametric method is used to analyze and compare them. The analysis results show that the compensation strategy based on the magnetomotive force constant can keep the output torque of the motor unchanged and the torque fluctuation is small, and the compensation strategy is simple. After the open circuit of the drive motor, if the external environment of the aircraft cannot be forced to drop urgently, this compensation strategy can be adopted. The compensation strategy based on eliminating negative sequence sequence component starting from reducing torque fluctuation is more flexible.

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The distribution of no-load magnetic density

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The torque curve under X phase compensation

Fault Tolerant Performance and Open Circuit Compensation Strategy of Six-phase Permanent Magnet Synchronous Motor for All-electric Aircraft

The submersible motor is common equipment used in the water supply and drainage systems. However, the bearing fault is a critical issue in submersible motors. It is an effective method to analyze the vibration signal of the motor end cover for bearing fault diagnosis [1]. But the submersible motor runs underwater, and the vibration signal will be easily disturbed by the flowing water. It is a feasible bearing fault diagnosis method to analyze the variation of the electromagnetic properties (such as the stator current) of the motor [2]. Nevertheless, there is a lack of an available fault model which is capable of reflecting the electromagnetic response of the motor under the bearing fault. In this paper, a single point fault model of a closed-slot rotor submersible motor is established for bearing fault diagnosis. The heathy submersible motor model is established by the Finite Element Method (FEM). In the model, two relative permeability variation regions are created in the rotor edge and air gap. Because the bearing fault will lead to the periodic eccentricity (static eccentricity) of the shaft, the influence of the bearing fault on the motor performance can be considered by periodically changing the relative permeability of these regions. The model of the bearing fault submersible motor is shown in Fig.1. The relative permeability variation regions (black regions) are determined by the non-coincidence regions of the healthy and static eccentric rotors and are marked as regions 1 and 2. When the motor is running without the fault, the relative permeability in region 1 is set as the vacuum permeability, and region 2 is set as the silicon steel sheet permeability. In case of bearing fault, the setting is the opposite. Fig.2 shows the stator current and its spectrum diagram of the bearing fault model. It can be seen in Fig.2 (a) that the stator current is slightly distorted, which is marked in the red circle. Meanwhile, the characteristic frequency of the fault is shown in Fig.2 (b).

![](https://assets.underline.io/uploads/markdown_image/1/image/67fd49145e3f797e3fa0f20806fb088e.jpg)

Fig. 1 The model of bearing fault submersible motor.

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Fig. 2 The stator current and its spectrum diagram of the bearing fault model. (a) Stator current waveform. (b) Spectrum diagram of the stator current.

Bearing Fault Numerical Model for the Closed-slot Rotor Submersible Motor

Induction motors have been widely used in various fields because of economy and reliability. Its’ secondary winding harmonic losses are always a problem that scholars devote themselves to solve. Zhao Haisen et. eliminated the slot harmonic, which is caused by slot opening, by using asymmetrical rotor slots[1]. Lin Qifang et. improved the efficiency of the motor by using split teeth on stator[2]. The auxiliary slots on the rotor side can weaken the first-order tooth harmonic of the rotor by changing the air-gap magnetic permeability. In higher power ranges of the water-filled submersible induction motors, the rotor widely employs copper bar rotor with closed slots. Opening the auxiliary slots on the rotor surface will increase the water friction loss, so this paper chooses to open auxiliary slots inside the rotor between the rotor teeth. As shown in Fig.1, to simplify the analysis and modeling process, using α1, α2, and l1 as the variable to express the width and the length of the auxiliary slot. The effects of the width and height of the auxiliary slot on harmonic reduction were studied by controlling variables. Taking into account the actual size of the motor, the value range of α2 is 0.5°- 1.5°, and the value range of l1 is 2.7- 18.7 mm. The initial distance between the top of the auxiliary groove and the outer circle of the rotor is the same as the height of the slot bridge, which affects harmonic content and motor performance will also be analyzed in this paper. As shown in Fig.2, the harmonic content of the first-order teeth harmonic of the rotor decreases with the increase of the size of the auxiliary slot while the second-order teeth harmonic keeps almost remain. The weakening effect is more obvious when the width of the auxiliary slot is increased. At the same time, the saturation of tooth magnetic density is more serious. The losses reduced by the auxiliary slot and the harmonics introduced will be analyzed in detail in this paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/01a03e3b8c56656dfa491957af660fb8.jpg)

Fig. 1 Diagram of Auxiliary Slot.

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Fig. 2 Tooth Harmonic Amplitude Change Diagram.

A Comprehensive Effect Analysis of the Rotor Auxiliary Slot Geometry for the Water-filled Submersible Induction Motors

1. Study Objective This research develops a method for the design and implementation of a magnetic sensor constructed with super capacitor electromagnetic device for fast charging of the smart vehicles, which realizes the magnetic motor functional with Internet of Things (IoT) [1,2]. To establish and design the proto type machines for the electric vehicles, it is mainly to meet the sustainable energy manufacturing and lower cost for electric vehicles. 2. Method This study, it used an axial permanent magnet generator to generate direct current (DC) power. The process of charging and discharging the super capacitor system is developed. This system is integrated the fractional-order proportional-integral-derivative (FOPID) controllers with neural network (NN) to consider parameters in interception, calculation, and evaluation of the best solution to provide the maximum value of the electric vehicle, as shown in Figure 1. 3. Experiment Result and Discussion The magnetic sensor and generator signal uses the embedded system (fog computing) platform to detect the sensing signal, included as electric vehicle of the motor and image recognition function. The intercepted image signal and the sensing signal thorough NN and FOPID controller to feedforward signal, which are transmitted signal to the cloud server and provide sustainable power for electric vehicles, , as shown in Figure 2. This study is to establish a fast electromagnetic charging device with fog computing controller, which is used to quickly process the electromagnetic energy generated by the generator, and intercept the voltage and current signals, and then perform data collection and storage operations. Among of them, a larger number of electromagnetic and electrical signals are collected, and its stability and operating characteristics of IoT are calculated and controlled to provide the electric vehicle quickly charging performance. The process of integration and experimentation for the motor and generator device can be obtained.

![](https://assets.underline.io/uploads/markdown_image/1/image/c29686d3c4a80e615e24494d7a70d8ab.jpg)

Figure 1 The structure of the charging and discharging system: (a) PMSM with super capacitor system, (b) PMSM control by with NN+PSO.

![](https://assets.underline.io/uploads/markdown_image/1/image/8c84b6ae7e97bb250fc733038024ae4f.jpg)

Figure 2 The IoTs system detects motor power, vibration and electric vehicle image recognition.

Study of Charging and Discharging of Regenerative Electric Energy of Direct Drive Generator on Electric Vehicle

1.Introduction Magnetorheological fluid (MRF) is a material whose viscous and plastic rheological property can be changed sharply under an external magnetic field [1]. The brake based on MRF characteristics has the advantages of simple structure, fast response and convenient control compared with traditional brakes [2-3]. However, the current studies on MRF brake mostly use an independent structure [4-5] connecting in series with motor to form joint module,which has the defect of large axial length. It greatly limits the space of joint modules. In this paper, an axial flux permanent magnet motor (AFPMM) with MRF brake structure is proposed to obtain the small axial size and fast braking response. 2.Machine topology Fig.1(a) shows the top view of an AFPMM with MRF brake structure (no rotating seal cap for easy viewing), which has two working modes: rotation and brake mode. Fig.1(b) shows the front cutaway view of the proposed machine. Fig.1(c) shows 2D radial flux circuit of MRF brake structure. When the MRF is magnetized and thus the viscous force of MRF is rapidly increased, the large shear stress is produced to brake the AFPMM. 3.FE analysis In this paper, the speed and the maximum current density of the AFPMM are set to 1200 r/min and 8A/mm2 respectively. Fig.2(a) shows the variation of motor torque under different axial excitation currents. Fig.2(b) shows radial component distribution of magnetic flux density in MRF along axial direction under two working modes. It can be found that the axial flux in rotation mode does not magnetize the MRF to produce brake torque. Based on Bingham model, the brake torque formula of MRF is shown in Fig.2(c). Fig.2(d) shows the variation of MRF brake torque under different radial excitation currents. It can be seen that the brake torque under the brake mode is enough to get an effective braking.

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An Axial Flux Permanent Magnet Motor with Magnetorheological Fluid Brake Structure

An Axial Flux Permanent Magnet Motor with Magnetorheological Fluid Brake Structure

The dual three-phase permanent magnet synchronous motors (DTP-PMSMs) possess two sets of three-phase winding exhibiting the high capability in fault-tolerant operations [1]. The open-phase fault is one typical fault and various research has been conducted on open-phase fault modeling and control of the DTP-PMSMs [2], [3]. Recently, a dynamic fault modeling and control for six-phase PMSMs based on multireference frame has been proposed [4]. In this paper, other than using the multireference frame, the fault modeling is based on the existing vector space decomposition (VSD) for DTP-PMSMs, and the open-phase fault is regarded as a combination of positive and negative sequence components. Therefore, the number of current regulators is reduced and dynamic performance is improved. By using VSD, currents of the dual three-phase winding are projected into three orthogonal subspaces, namely αβ plane (torque-producing plane) and xy plane (non–torque–producing plane).Fig. 1(b) shows the current waveforms under open-phase fault, which can be represented by positive sequence currents (healthy operation) and negative sequence currents. The positive sequence currents are projected to αβ plane and the negative sequence currents are projected to xy plane. As shown in Fig. 2(a), in the αβ plane, the projected faulty currents are the dc currents as the projected positive sequence currents, and while in the xy plane, the projected faulty currents are the ac currents with the same dc components as the projected negative sequence currents. Since the torque only generated in the αβ plane, the torque generated under open-phase fault is stable as that under healthy operation. Fig. 2(b) compares the torque waveforms under the proposed fault modeling in this paper and the modeling based on a multireference frame. Since the harmonic components can be suppressed using VSD, the torque ripple is about 10% lower by using the proposed method. The detailed modeling and experimental verification will be presented in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/5554576db6419082200d5eea93edf5b7.jpg)

Fig. 1 (a) Vector space decomposition. (b) Dual three-phase current waveforms under open-phase fault.

![](https://assets.underline.io/uploads/markdown_image/1/image/37b4fd338698d1a4ba6111454e56ece6.jpg)

Fig. 2. (a) Current waveforms in different planes using VSD. (b) Torque waveforms comparison.

Open-phase fault modeling for dual three-phase PMSM using vector space decomposition and negative sequence components

Due to its excellent performances like high efficiency and high power factor[1], line-start permanent magnet (LSPM) machine is widely used in long-time operated applications, i.e., textile, pump, fan [1]. LSPM machine with squirrel cage doesn’t need inverter to start, thus it has advantages of lower cost and smaller volume[2]. However, The rotor of LSPM machine just combine one interior permanent magnet (IPM) rotor and one induction rotor together into a whole rotor, thus the two rotor would compete the limited space when designing the rotor. Also, the aluminum-bar induction winding in the rotor only works in starting process, and it will occupy the limited magnet path of the rotor, which would be the extra burden to the machine because aluminum has permeability similar as air. Hence, a novel steel-bar starting cage line-start permanent magnet machine is proposed to solve this paradox. Low carbon steel 1010[3] is selected as rotor cage material to allow magnet flux pass through at steady state. Steel 1010 has high permeability but lower conductivity compared with aluminum and copper, the proposed machine shown in Fig.1 shows that steel-bar rotor could still start easily without the help of inverter, and has better performance at steady state as is shown in Fig.2. The spoke type insulation layers of the steel-bar is meant to reduce the core loss, but simulation results show that the starting process is also shorten. Besides, the torque ripple at steady state is also lower with the help of insulation layers. A LSPM machine with aluminum-bar cage is also designed to compare in Fig.2. The steel-bar is of larger cross area because steel-bar doesn't occupy magnetic path, which is a main advantage of steel bar. However, steel-bar is like closed opening slot when induced current flows through, so the steel-bar should be saturated before it produces flux to airgap, which is why steel-bar rotor has lower starting torque. But for pump load which requires low torque at low speed, proposed machine shows dominant advantages.

![](https://assets.underline.io/uploads/markdown_image/1/image/8bdd205fcac26f5f06a0a57a58ba855d.jpg)

Fig.1 Proposed Steel-Bar Starting Cage Line-start PM Machine with Spoke Type Insulation Layers

![](https://assets.underline.io/uploads/markdown_image/1/image/1945ed1b37a7be0ec62150788975e1ef.jpg)

Fig.2 Torque and Torque Ripple vs Current Angle Curve of Proposed Machine and Traditional Aluminum-Bar Machine

Novel Steel-Bar Starting Cage Line-Start Permanent Magnet Machine with Spoke Type Insulation Layers

Abstract—This paper focuses on the force ripple minimization of consequent pole permanent magnet linear synchronous motor (CP-PMLSM). By using arc teeth without tooth shoe, CP-PMLSM is investigated in detail by extensive finite element analysis (FEA). With Taguchi parameters method, the geometry of end teeth and auxiliary teeth is optimized to reduce the force ripple, and the optimal combination of parameters can be obtained. the contrasting result between the initial and the optimized PMLSM shows that the force ripple is suppressed to a quite low value in all load conditions by the aforesaid procedure. Keywords—Force ripple, finite element analysis, consequent pole, permanent magnet linear synchronous motor (PMLSM). I. Introduction Recently, Permanent Magnet Synchronous Linear Motors (PMSLMs) have been widely used in industry applications owing to their outstanding performance. However, as the magnetic circuit is disconnected at the end of the primary core, the distorted magnetic field makes the motor high force ripple. The addition of the auxiliary teeth and teeth notching are employed to reduce the detent force[1]. The geometry of end-teeth is optimized to reduce the force ripple in all load conditions [2]. High-order harmonic components can be suppressed by the optimal skewed PM design, and a discrete-time linearization observer is utilized to compensate low-order harmonic ones [3]. In this paper, arc teeth without tooth shoe is optimized to reduce the force ripple by extensive finite element analysis (FEA). The dimensions of end teeth and auxiliary teeth is optimized by Taguchi method to obtain the optimal combination of parameters. The contrasting result shows that the force ripple is suppressed to a quite low value in all load conditions by the aforesaid procedure. II.Electromagnetic Performance Evaluation The simulation results of flux density, back-EMF, and electromagnetic torque are analyzed by the finite element analysis (FEA). The load flux distribution is shown in Fig. 2. The Comparison of force wave and back-EMF in no-load and load between the initial and the optimized is shown in Fig. 3. The back-EMF and electromagnetic torque with various excitation modes are shown in Fig. 3.


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Force Ripple Minimization Design for Consequent Pole Permanent Magnet Linear Synchronous Motor

I. INTRODUCTION Transverse flux permanent magnet (TFPM) machine owns the characteristics of large torque and high efficiency[1]. Many new TFPM structures such as double C-hoop stator and double Ω-hoop stator machines have been proposed[2][3]. Accordingly, the new structure of back-to-back Ω-type stator TFPMLM is proposed to improve the stator space utilization based on the above mentioned previous machines. Owning to the better utilized stator space and the mutual decoupled electrical and magnetic loads the machine achieves better performances on higher peak force and thrust-weight ratio which is suitable for the application of urban rail transit. II. STRUCTURE OF Back-to-back Ω STATOR TFPMLM The distinguishing feature of the proposed machine is that one pair stator hoops share the same winding to achieve more compact space utilization. Fig. 1(a) shows the schematic diagram of the fabricated prototype, which has pairs of back-to-back Ω-type stator hoops and a mover composited by cores and PMs. The stator hoops fixed in the non-ferromagnetic stationary pedestal and the mover cores and flux-concentrated PMs are screwed independently onto two non-ferromagnetic mover brackets. A linear guide rail contacts the stationary pedestal and the mover bracket. The sliding rail is lapped on head-end of the pedestal while the slide block is screwed onto the bracket. The armature winding binding each stator hoop pairs to form two half magnetic circuits twining round the stator hoops and the mover cores which are laminated by facile silicon-steel. III. FEM ANALYSIS AND TEST RESULT Fig. 1 (b) shows the 3D-FEM magnetic field distributions with maximum flux density of 0.7T. Fig. 2 (a) shows the flux density with optimum value as 0.6 around to achieve the best performance. The flux linkage and the measured back-EMF waveforms with amplitudes of 70mWb and 30V respectively at rated moving speed of 1.5m/s are shown in Fig. 2 (b). The positioning force is obtained and optimized also to verify the analyses and feasibility of the structure design. A prototype with 120N peak force is fabricated and some experiments are conducted.

![](https://assets.underline.io/uploads/markdown_image/1/image/babca408bfccabab374c3af4c67d9492.jpg)

Fig. 1 The schematic diagram and the magnetic field distributions.

![](https://assets.underline.io/uploads/markdown_image/1/image/ba8731a242763654ddd39db5ccaf7418.jpg)

Fig. 2 Flux linkage and measured back-EMF waveforms.

Back-to-back Ω Stator Transverse Flux Permanent Magnet Linear Machine

With the development of drive system, the linear-rotary (LR) actuators have been applied in robotics due to its multiple freedom degree characteristic [1]. Rare-earth permanent magnet (PM) materials, such as NdFeB, have high remanence density and coercivity, which can provide high energy density. Hence, the LR PM actuator has been widely used in the drive systems due to simple structure and small volume. In this paper, a LR PM actuator which involves linear, rotary and spiral motions is proposed for the application of multiple freedom degree robotics. The proposed actuator is composed of unique single stator with two sets of independent windings and consequent-pole staggered (CPS) PM mover, as shown in Fig. 1. The novelty is that one CPS PM mover is specially designed to generate radial and axial magnetic field, and to reduce PM consumption. Combined with it, two sets of independent orthogonal non-overlapping concentrated armature windings are employed to generate enough torque, thrust force and to achieve the decoupling operation of linear and rotary motions. The CPS mover is composed of several step-staggered parts. The magnetized direction of PMs in the adjacent step-staggered parts is opposite. The staggered degree of adjacent parts is π/Pr, where Pr is PMs pole pairs along the circumferential direction. Thus, the even-order harmonics of no-load back-electromotive force are eliminated by the CPS mover, which greatly reduce the torque ripple. To reduce the axial leakage flux, there is axial flux barrier between the step-staggered parts. Furthermore, the fault-tolerance (FT) teeth and armature teeth are alternately arranged on the stator to enhance FT performance. The electromagnetic performance of the proposed machine is predicted by finite-element method. Fig. 2 shows the output characteristic of proposed actuator. The average values of torque and thrust force are 6Nm and 158N, respectively. The torque ripple and thrust force ripple are 0.97% and 33%, respectively. More details and optimization will be discussed in the full paper.

![](https://assets.underline.io/uploads/markdown_image/1/image/ef95bd46db8f194fdd1b292bbf385d23.jpg)

Fig. 1 Structure of proposed LR PM actuator.

![](https://assets.underline.io/uploads/markdown_image/1/image/75599f1217e49c75c52aa4fb5ab96341.jpg)

Fig. 2 Output characteristic of proposed LR PM actuator.

Next from 2022 Joint MMM-INTERMAG

Fault Tolerant Performance and Open Circuit Compensation Strategy of Six-phase Permanent Magnet Synchronous Motor for All-electric Aircraft

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