France



I Introduction&lt;br/&gt;A soliton is a wave that maintains its shape while it propagates at a constant velocity. The soliton exists in various nonlinear systems such as fiber optics, biology, magnetics, and electric circuit. In particular, Hirota proposed an LC ladder circuit, in which inductors and capacitors are connected like a ladder [1], [2]. Hirota experimentally proved the magnetic soliton was excited on the LC ladder circuit by using the capacitor whose capacitance is an exponential function of voltage. The observed magnetic soliton propagates along the LC ladder circuit at a constant velocity while maintaining the shape [3]. In other words, the magnetic soliton corresponds to a kind of rotating magnetic field.&lt;br/&gt;The rotating magnetic field is produced by a three-phase alternating current (AC) and is essential for AC motors. The current technology requires to use Pulse Width Modulation (PWM) inverters for generating the rotating magnetic field. On the other hand, the magnetic soliton can be generated by applying a pulsed voltage only at one point on the LC ladder circuit, which is expected to simplify the PWM inverter and its control algorithm [4].&lt;br/&gt;This paper proposes an LC ladder circuit consisting of linear capacitors and nonlinear inductors. we also show the magnetic soliton can be excited if the inductance of the inductor becomes an exponential function of the current. However, the coil inductance wound on soft magnetic materials becomes symmetric with respect to the positive and negative currents, not exponential. To solve this problem, we propose a permanent magnet flux biased inductor (PMFB inductor) in which a permanent magnet is mounted into the magnetic circuit and the operating point of the iron core is biased. Finite element analysis (FEA) reveals that the inductance varies exponentially with the current. Finally, we solve numerically the differential equation of the LC ladder circuit consisting of the PMFB inductors and capacitors, and show the magnetic soliton propagates at a constant speed in the LC ladder circuit.&lt;br/&gt;&lt;br/&gt;II Permanent Magnet Flux Biased Inductor&lt;br/&gt;Fig. 1(a) shows the basic structure of the PMFB inductor. It consists of a stator core, a mover core, a coil, and a permanent magnet (PM). Its magnetic circuit is axisymmetric. An axially magnetized permanent magnet is embedded in the stator core. Here, we explain the reason why the inductance of the PMFB inductor changes exponentially as follows. The flux by PM mainly flows through the stator core as shown by the solid blue line. This leads to biasing the B-H curve of the stator core. When a positive current is applied, the flux by current strengthens the flux by PM. This results in magnetic saturation of the stator core and the inductance decreases with the current. When a negative current is applied, the flux by current weakens the flux by PM. This results in eliminating the magnetic saturation of the stator core and the inductance increases with the current. Therefore, exponential inductance characteristics is obtained when we design the shape of the PM, stator and mover cores property.&lt;br/&gt;Fig. 1(b) shows the analyzed relation between the flux and current obtained through FEA. The slope of this curve corresponds to the inductance. The solid line shows the bias flux provides asymmetric characteristics for positive and negative current. The dashed line is an approximation using the exponential function shown below,&lt;br/&gt;&lt;i&gt;I&lt;/i&gt; = &lt;i&gt;a&lt;/i&gt;(1-e&lt;sup&gt;-&lt;i&gt;b&lt;/i&gt;(&lt;i&gt;Φ&lt;/i&gt;-&lt;i&gt;ΦPM&lt;/i&gt;)&lt;/sup&gt;) (1)&lt;br/&gt;Here, &lt;i&gt;a&lt;/i&gt; and &lt;i&gt;b&lt;/i&gt; are the parameters and &lt;i&gt;Φ&lt;/i&gt;&lt;sub&gt;PM&lt;/sub&gt; is the bias flux by PM. The exponential function is a good approximation of the &lt;i&gt;I&lt;/i&gt;-&lt;i&gt;Φ&lt;/i&gt; property. This result implies the magnetic soliton can be excited on the LC ladder circuit consisting of the PMFB inductors and linear capacitors.&lt;br/&gt;&lt;br/&gt;III Numerical Results and Discussion&lt;br/&gt;In this chapter, we numerically solve the differential equation of the nonlinear LC ladder circuit mentioned in the previous chapter, and presents the successful excitation and propagation of the magnetic soliton. Kirchhoff’s voltage law gives the following differential equation,&lt;br/&gt;d&lt;sup&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/sup&gt;&lt;i&gt;Φ&lt;sub&gt;n&lt;/sub&gt; &lt;/i&gt;/ d&lt;i&gt;t&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;=a/C(2e&lt;sup&gt;(-b&lt;i&gt;Φ&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;)&lt;/sup&gt;-e&lt;sup&gt;(-b&lt;i&gt;Φ&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;-1&lt;/sub&gt;)&lt;/sup&gt;-e&lt;sup&gt;(-b&lt;i&gt;Φ&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;&lt;sub&gt;+1&lt;/sub&gt;)&lt;/sup&gt;) (2)&lt;br/&gt;Here, &lt;i&gt;Φ&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; is the flux through the &lt;i&gt;n&lt;/i&gt;th inductor and &lt;i&gt;C&lt;/i&gt; is the capacitance of the capacitor. The internal resistance of the PMFB inductor and capacitor is neglected. Note that this differential equation has a similar form to the one presented in [1] and [2].&lt;br/&gt;Fig. 2 shows the numerical result of the differential equation in Equation (2). The number of LC units is 26 and the capacitance is 100µF. The start and end of the LC ladder circuit are connected and periodic. One magnetic soliton excited at 0s propagates at a constant speed in the positive and negative directions while maintaining its shape. Since the LC ladder circuit is periodic, the two magnetic solitons collide at a certain time. The waveform before and after the collision clearly shows the solitons are not affected by the collision. This is one of the most important properties of solitons. These results concludes magnetic solitons has a potential to be applied as a kind of the rotating magnetic field.&lt;br/&gt;In the final paper, we will describe the detailed design procedure for the PMFB inductor because this digest paper only presents the straight type PMFB inductor, not an annular one. Moreover, we will visualize and evaluate the rotating magnetic field produced by the magnetic soliton through FEA.

**References:**

[1] R. Hirota and K. Suzuki, Journal of the Physical Society of Japan., Vol. 28, pp. 1366–1367 (1970)&lt;br/&gt;[2] K. Muroya and S. Watanabe, Journal of the Physical Society of Japan., Vol. 50, pp. 2762–2769 (1981)&lt;br/&gt;[3] D.L. Sekulic, M.V. Sataric, M.B. Zivanov, and J.S. Bajic, Electronics and Electrical Engineering., Vol. 121, pp. 53–58 (2012)&lt;br/&gt;[4] M. Kato, S. Lee, and K. Hirata, IEEE Transactions on Magnetics., to be published, DOI:10.1109/TMAG.2020.3018118 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a078e0e6a099c620cb22dd40ed96d8d2.jpg)
(a) Basic structure of PMFB inductor. (b) Analyzed relation between flux linkage and current.

![](https://assets.underline.io/uploads/markdown_image/1/image/1980322477f343c6154555d623e5e3d0.jpg)
Numerical result of magnetic soliton excited on the nonlinear LC ladder circuit.

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 Numerical Analysis of Magnetic Soliton Excited on Nonlinear LC Ladder Circuit Array Using Permanent Magnet Flux Biased Inductor

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I Introduction A soliton is a wave that maintains its shape while it propagates at a constant velocity. The soliton exists in various nonlinear systems such as fiber optics, biology, magnetics, and electric circuit. In particular, Hirota proposed an LC ladder circuit, in which inductors and capacitors are connected like a ladder [1], [2]. Hirota experimentally proved the magnetic soliton was excited on the LC ladder circuit by using the capacitor whose capacitance is an exponential function of voltage. The observed magnetic soliton propagates along the LC ladder circuit at a constant velocity while maintaining the shape [3]. In other words, the magnetic soliton corresponds to a kind of rotating magnetic field. The rotating magnetic field is produced by a three-phase alternating current (AC) and is essential for AC motors. The current technology requires to use Pulse Width Modulation (PWM) inverters for generating the rotating magnetic field. On the other hand, the magnetic soliton can be generated by applying a pulsed voltage only at one point on the LC ladder circuit, which is expected to simplify the PWM inverter and its control algorithm [4]. This paper proposes an LC ladder circuit consisting of linear capacitors and nonlinear inductors. we also show the magnetic soliton can be excited if the inductance of the inductor becomes an exponential function of the current. However, the coil inductance wound on soft magnetic materials becomes symmetric with respect to the positive and negative currents, not exponential. To solve this problem, we propose a permanent magnet flux biased inductor (PMFB inductor) in which a permanent magnet is mounted into the magnetic circuit and the operating point of the iron core is biased. Finite element analysis (FEA) reveals that the inductance varies exponentially with the current. Finally, we solve numerically the differential equation of the LC ladder circuit consisting of the PMFB inductors and capacitors, and show the magnetic soliton propagates at a constant speed in the LC ladder circuit. II Permanent Magnet Flux Biased Inductor Fig. 1(a) shows the basic structure of the PMFB inductor. It consists of a stator core, a mover core, a coil, and a permanent magnet (PM). Its magnetic circuit is axisymmetric. An axially magnetized permanent magnet is embedded in the stator core. Here, we explain the reason why the inductance of the PMFB inductor changes exponentially as follows. The flux by PM mainly flows through the stator core as shown by the solid blue line. This leads to biasing the B-H curve of the stator core. When a positive current is applied, the flux by current strengthens the flux by PM. This results in magnetic saturation of the stator core and the inductance decreases with the current. When a negative current is applied, the flux by current weakens the flux by PM. This results in eliminating the magnetic saturation of the stator core and the inductance increases with the current. Therefore, exponential inductance characteristics is obtained when we design the shape of the PM, stator and mover cores property. Fig. 1(b) shows the analyzed relation between the flux and current obtained through FEA. The slope of this curve corresponds to the inductance. The solid line shows the bias flux provides asymmetric characteristics for positive and negative current. The dashed line is an approximation using the exponential function shown below, I = a(1-e-b(Φ-ΦPM)) (1) Here, a and b are the parameters and ΦPM is the bias flux by PM. The exponential function is a good approximation of the I-Φ property. This result implies the magnetic soliton can be excited on the LC ladder circuit consisting of the PMFB inductors and linear capacitors. III Numerical Results and Discussion In this chapter, we numerically solve the differential equation of the nonlinear LC ladder circuit mentioned in the previous chapter, and presents the successful excitation and propagation of the magnetic soliton. Kirchhoff’s voltage law gives the following differential equation, d2Φn / dt2=a/C(2e(-bΦn)-e(-bΦn-1)-e(-bΦn+1)) (2) Here, Φn is the flux through the nth inductor and C is the capacitance of the capacitor. The internal resistance of the PMFB inductor and capacitor is neglected. Note that this differential equation has a similar form to the one presented in [1] and [2]. Fig. 2 shows the numerical result of the differential equation in Equation (2). The number of LC units is 26 and the capacitance is 100µF. The start and end of the LC ladder circuit are connected and periodic. One magnetic soliton excited at 0s propagates at a constant speed in the positive and negative directions while maintaining its shape. Since the LC ladder circuit is periodic, the two magnetic solitons collide at a certain time. The waveform before and after the collision clearly shows the solitons are not affected by the collision. This is one of the most important properties of solitons. These results concludes magnetic solitons has a potential to be applied as a kind of the rotating magnetic field. In the final paper, we will describe the detailed design procedure for the PMFB inductor because this digest paper only presents the straight type PMFB inductor, not an annular one. Moreover, we will visualize and evaluate the rotating magnetic field produced by the magnetic soliton through FEA.

**References:**

[1] R. Hirota and K. Suzuki, Journal of the Physical Society of Japan., Vol. 28, pp. 1366–1367 (1970) [2] K. Muroya and S. Watanabe, Journal of the Physical Society of Japan., Vol. 50, pp. 2762–2769 (1981) [3] D.L. Sekulic, M.V. Sataric, M.B. Zivanov, and J.S. Bajic, Electronics and Electrical Engineering., Vol. 121, pp. 53–58 (2012) [4] M. Kato, S. Lee, and K. Hirata, IEEE Transactions on Magnetics., to be published, DOI:10.1109/TMAG.2020.3018118 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a078e0e6a099c620cb22dd40ed96d8d2.jpg)
(a) Basic structure of PMFB inductor. (b) Analyzed relation between flux linkage and current.

![](https://assets.underline.io/uploads/markdown_image/1/image/1980322477f343c6154555d623e5e3d0.jpg)
Numerical result of magnetic soliton excited on the nonlinear LC ladder circuit.

technical paper

I. Introduction. With the merits of broad speed range and high efficiency at high-speed region, variable flux machine (VFM) is gaining more and more attentions in the wide-speed applications, such as electric vehicle, railway traction and numerical control machine tool. With the high coercive-force (HCF) and low coercive-force (LCF) permanent magnets (PMs) both utilized, VFMs with hybrid PMs are widely investigated. According to the combination way of hybrid PMs, VFM can be divided into series scheme and parallel scheme. Parallel VFMs are proven with relatively small demagnetization current and wide speed-adjusting range. But the HCF PM of parallel VFM has demagnetization effect on LCF PM, which will reduce the stability of LCF PM. While the LCF PM of series VFM is relatively stable, but the demagnetization current of series scheme is always large. This digest proposes a novel series-parallel VFM, which improves the stability of LCF PM by applying segmented PMs. The structure of the machine is introduced firstly, and then the magnetization-regulation principle is analyzed. The influences of V-shape pole parameters on electromagnetic torque and speed adjusting range of the machine are investigated. II. Machine Structure and Magnetization-Regulation Principle The structure of the proposed series-parallel VFM with segmented PMs is shown in Fig.1, which is evolved from traditional V-shape PM synchronous machine (PMSM). The magnetic pole of the machine is composed of NdFeB and AlNiCo, and each side of the V-shape PM is divided into three parallel segments along the long-side direction of PM slot. The inner and outer PM segments are composed of series NdFeB and AlNiCo, and the middle PM segment is pure AlNiCo. Compared with the traditional parallel VFM, the proposed VFM has higher stability at load state, because of the NdFeB PM placed at the outer part of V-shape pole, where is more likely to be demagnetized by q-axis armature reaction. In addition, the series segments composed of NdFeB and AlNiCo has weaker demagnetization effect on middle AlNiCo than pure NdFeB, which can also improve the stability of the magnetic pole. The no-load flux distributions of the proposed VFM at forward and reverse magnetization state are shown in Fig. 1. It is illustrated that the flux provided by inner and outer PM segments are shorted by middle AlNiCo at reverse magnetization state, and the fundamental amplitude of no-load back electromotive force (EMF) is decreased from 73.00V to 5.94V, which proves the wide speed-adjusting range of the proposed VFM. III. Research on Electromagnetic Torque and Speed-Adjusting Range Electromagnetic torque and speed-adjusting range are important characteristics of VFM, and thus influence laws of V-shape pole parameters on them are investigated. Since the change of PM dimensions will influence the magnetization result of middle AlNiCo when the same forward magnetization current is applied, the magnetization states of middle AlNiCo in VFMs with different PM dimensions at fully forward magnetization state are different. Therefore, the influences of V-shape pole parameters are different from traditional interior PMSM. According to the relationship between NdFeB thickness and the average flux density of series segments at no-load state, it can come to the conclusion that the equivalent remanence of the series segment can be adjusted by changing NdFeB thickness with the series-segment thickness unchanged. Afterwards, the influence of middle-AlNiCo positon on electromagnetic torque and back EMF is investigated. It is found that moving the middle AlNiCo closer to the air gap can decrease the total harmonic distortion (THD) of back EMF at reverse magnetization state, and almost has no impact on electromagnetic torque and back EMF at forward magnetization state. The influence of PM ratio is analyzed, and it is indicated that VFM with larger PM ratio has wider speed-adjusting range, but the average torque is relatively low. With PM ratio kept unchanged, the average torque increases firstly, and then decreases with the increase of PM-pole width. Moreover, the difference between d- and q-axis inductances is found having the same variation law with the average torque. The reason is that changing PM-pole width will change the distance between poles, which will change the d- and q-axis magnetic circuits distribution of the machine. When the thickness of the PM pole is increased, the average torque is increased firstly, and then decreased, while the torque ripple is increased continuously. The efficiency maps of the proposed VFM at forward and reverse magnetization states are shown in Fig. 2. It is illustrated that when VFM is reversely magnetized, the maximum speed of the machine is increased, and the efficiency at high-speed region is increased. The maximum torque of the machine at high speed region is also increased. IV. Conclusions A novel series-parallel VFM with segmented hybrid PMs is proposed, and the selection principles for PM parameters of the machine is proposed. The speed-adjusting ability of the machine is elaborated by analyzing the magnetization-regulation progress, and the speed-adjusting performance is revealed by efficiency maps at different magnetization states.

**References:**

[1] H. Yang, H. Zheng, and H. Lin, in Proc. IEMDC, CA, USA, pp. 2259-2264 (2019) [2] M. Wang, C. Tong, and P. Zheng, IEEE Trans. Magn., vol. 55, no. 7, pp. 1-7 (2019) [3] G. Qiao, M. Wang, and F. Liu, IEEE Trans. Magn., doi: 10.1109/TMAG.2020.3013624 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/65d9adf6d6d4c391b17a14c0637170b0.jpg)
Fig. 1. Structure of the proposed VFM and no-load flux distributions at forward and reverse magnetization states.

![](https://assets.underline.io/uploads/markdown_image/1/image/ac4bb1f3709e11f0f381ec109389cfa3.jpg)
Fig. 2. Efficiency maps of the proposed VFM at forward and reverse magnetization states.

 Design and Analysis of a Novel Series-Parallel Variable Flux Machine with Segmented Hybrid Permanent Magnets

A synchronous machine can have both mutual torque due to the permanent magnet (PM) excitation and reluctance torque due to the rotor saliency. According to the ratio of these two torque components, the machine can be classified as (i) the salient permanent magnet synchronous machine (PMSM) in which the mutual torque is dominant or (ii) the permanent magnet-assisted synchronous reluctance machine (PMA-SynRM) in which the reluctance torque is dominant. Both categories can be called permanent magnet synchronous reluctance machines (PMSynRM). Of course, the PMSM with no rotor saliency and the SynRM with no PM assistance can be regarded as special PMSynRM which have no reluctance torque or mutual torque, respectively. In the salient PMSM, there are many interior permanent magnet (IPM) rotor structures, such as the V-shaped and the Delta-shaped structures. The magnets not only produce magnetic excitation but also act as flux barriers to make the rotor magnetically salient. Basically, the Delta-shaped structure brings better rotor saliency than the V-shaped structure, as it has more layers of flux barriers. On the other hand, in the PMA-SynRM, there are even more layers (usually 3~5 layers) of flux barriers to further enhance the rotor saliency, but the magnets inserted in these flux barriers have inefficient utility due to the severe leakage in the circumferential bridges of the rotor and the series structure of all the magnets in each pole. In the conventional PMSynRM, the rotor is identical in the axial direction, but in the radial direction, from the rotor center to the airgap, there are iron core, flux barriers and magnets which are all merged, therefore, this kind of rotor can be called radially merged rotor structure (RMRS). A characteristic of the RMRS is that the PM excitation is along the d-axis of the rotor, whilst the rotor saliency is symmetric about the d-axis as well as the q-axis. In the RMRS machines, referring to Fig. 1(a), the current vector should be located along the q-axis to maximize the mutual torque per ampere, and ideally located in the middle between the q-axis and d-axis to maximize the reluctance torque per ampere. In other words, it is not achievable to maximize both torque components simultaneously, and thus the current vector has to be located at a compromised phase angle (see Fig. 1(a)). In this paper, the d-axis is re-defined as that about which the rotor saliency is symmetric, and the q-axis is away from the d-axis by 90 electric degrees. If the PM excitation vector is shifted from the conventional position (i.e., the d-axis) towards the q-axis by 45 electric degrees, as shown in Fig. 1(b), the back EMF vector will then be located in the middle between the q-axis and d-axis. In this case, the current vector can be simply placed at the same phase angle as the EMF vector, so that both the mutual torque and the reluctance torque can be maximized simultaneously. Fig. 1. Vectors in permanent magnet synchronous reluctance machines. (a) for conventional RMRS machines, (b) for proposed ACRS machines. An asymmetric rotor structure with extra flux barriers is proposed in [1], where the flux barriers force the PM flux to shift from the original d-axis towards the q-axis. However, it is very difficult to make the shifting angle as large as 45 electric degrees. Therefore, the current vector still has to be located at a compromised phase angle. In order to better shift the PM flux vector, it is proposed to use two types of rotor segments [2], one is the conventional surface-mounted permanent magnet (SPM) rotor, and the other is the conventional SynRM rotor without permanent magnet assistance. As shown in Fig. 2, these two types of rotor segments are axially combined on the shaft. Hence, this is called axially combined rotor structure (ACRS). Clearly, any shifting angle of the PM flux vector from the d-axis can be achieved. Fig. 2. Schematic of axially combined rotor structure (ACRS). In the full presentation, pros and cons of the ACRS machines will be detailed. For example, when using the same stator, the SPM rotor and the SynRM rotor can be optimized individually. Moreover, the SPM rotor has less leakage than the IPM rotor, hence the permanent magnets can be utilized more efficiently. And, the SynRM rotor contains no permanent magnet, so that the circumferential bridges suffer from less stress due to the centrifugal force, thus the bridges can be thinner and the rotor saliency can be better. Furthermore, in the full presentation, different criteria will be described to determine the shifting angle and the axial length ratio of the two rotor segments, so as to maximize the two torque components simultaneously as well as the machine torque density, or to enhance the power factor for increasing the voltage utilization, or to make the torque ripple on the two rotor segments cancel each other and consequently reduce the overall torque ripple. Moreover, each of the SPM and SynRM rotors can be divided into several segments, so that the axial combination will be more flexible though the 3D effect will be severer.

**References:**

[1] W. Zhao, et al, IEEE Trans. Mag., Vol. 50, p.8104504 (2014). [2] J.X.Shen, et al, Chinese Patent No.202020519211.7.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/5bd4d96288e9d536a0fbdbabf0e993b7.jpg)
Fig. 1. Vectors in permanent magnet synchronous reluctance machines. (a) for conventional RMRS machines, (b) for proposed ACRS machines.

![](https://assets.underline.io/uploads/markdown_image/1/image/ea2d35a1aff9207903d24a604a746a36.jpg)
Fig. 2. Schematic of axially combined rotor structure (ACRS).

 Permanent Magnet Synchronous Reluctance Machines with Axially Combined Rotor Structure INVITED

INTRODUCTION: Recently an increasing demand for high-speed permanent-magnet synchronous motor (HSPMSM) emerges in the high-power density, high-efficient and limited-installation space applications, such as electric vehicles and aircraft [1,2]. However, high-power density inevitably results in high-loss density and limited heat dissipation surface, which will pose great difficulty in motor cooling. Besides, a high-strength sleeve is usually necessary to guarantee the mechanical strength of the surface-mounted HSPMSM rotor. But additional loss will be generated in the conductive sleeve, further increasing the difficulties on cooling. The overheating of magnets, which will cause the irreversible demagnetization, is regarded as one of the biggest problems in the HSPMSMs [3]. The slotless HSPMSM was thought has less rotor eddy-current loss, since without high-frequency space harmonics of the magnetic field in the airgap caused by stator slotting [4]. Nevertheless, it's well known that the flux density of the airgap is usually lower. But the power density is closely related with it. So as to counteract the shortage, higher electrical load of the winding can be regarded as a feasible approach, but which in turn increases the copper loss. Both the efficiency and heating of HSPMSM are determined by the losses. And the losses mainly consists of copper loss, iron loss, rotor eddy-current loss and friction loss, all of which are closely correlates with dimensions [5, 6]. Therefore, it is essential to find the optimal design to achieve the competitive power density and minimum losses in the limited space for the slotless HSPMSM. This paper introduces a slotless toroidal-winding HSPMSM with non-magnetic fillers in stator for fuel cell air compressor application. A multi-objective optimization process was discussed and carried out to find the best compromise between power density and efficiency for a 15 kW, 120 000 rpm HSPMSM. Based on optimization results, the optimal design scheme was selected and compared with a slotted scheme. BASIC TOPOLOGY AND PRELIMINARY DESIGN CHOICES: The configuration of the proposed HSPMSM was shown in Fig. 1. Slotless configuration was chosen in order to reduce the electric losses in the sleeve and magnet. The toroidal winding was adopted. Some slots are machined on the outside edge of stator core and the part of toroidal windings outside of the stator core are embedded in these slots. So the leakage flux will increase in the outside slots and the inductance of windings are accordingly increased. Moreover, the toroidal windings is tightly surround the stator core, so the fixation of slotless windings is very convenient. Litz wires was employed to alleviate the eddy-current losses of windings, due to skin effect and proximity effect. So as to achieve the good insulation between different phases of windings, some non-magnetic insulating fillers are desired to be mounted between them. The inside edge of stator core are machined with some notches, and the fillers are inserted to them with epoxy resin glue. After impregnation processing, the stator becomes a strong overall structure. The fillers are also benefical to withstand the tangential electromagnetic force of the winding, consequently protecting the insulation of magnet wires. In addition, the fillers can help transfer the heat of windings to iron lamination. Boron nitride ceramics was selected as the candidate of non-magnetic fillers material, because of the good electrical insulation and thermal conductivity. MULTI-OBJECTIVE OPTIMISATION: Power density and efficiency were selected as the objective functions to be maximized. The key design variables and constraint variables were described and discussed in detail, as well as the multi-objective modeling method based on genetic algorithm and finite-element analysis of electromagnetic field. OPTIMISATION RESULTS AND DISCUSSION: In order to achieve the optimum design for the studied HSPMSM, 2246 evaluations has been performed and about 15 offspring populations was generated until the optimization converged. The optimization results were provided in Fig. 2, where all the feasible designs explored are represented by colored points. Besides, the solid black line is the Pareto front. The best designs are those that located on the Pareto front or closest to it. It can be clearly seen that the two optimization objectives are conflicting, which means that an increase in power density is generally associated with a reduction in efficiency, and vice versa. A large number of design schemes were generated in the optimization process. Weighing a tradeoff between power density and efficiency, the final scheme was selected and the candidate point was also indicated in Fig. 2. As a comparison, a common slotted-configuration HSPMSM was also designed. The performance of the final scheme was analyzed and compared with the slotted scheme. The axil length of windings for the slotless HSPMSM is 24.8% lower than the slotted one, which is benefical to improve the critical speeds of the rotor. The self-inductance calculated was higher than the slotted scheme. Besides, the slotless scheme has higher copper loss. But thanks to the removement of stator teeth, the iron loss was significantly decreased. So the total stator loss are basically the same for the two scheme. Finally, the slotless schemes exhibits higher efficiency and power density than the slotted scheme.

**References:**

[1] D. Hong, B. Woo, and J. Lee, and D. Koo, IEEE Trans on Magn., vol. 48, no. 2, pp. 871-874 (2012). [2] N. Uzhegov, A. Smirnov, and C. H. Park, IEEE Trans. Ind. Electron., vol. 64, no. 11, pp. 8427-8436 (2017). [3]D. Gerada, A. Mebarki, and N. L. Brown, IEEE Trans. Ind. Electron., vol. 61, no. 6, pp. 2946-2959 (2014). [4] F. Luise, A. Tessarolo, and F. Agnolet, 2014 International Symposium on Power Electronics, 18-20 June 2014, pp.1237-1244. [5] G. H. Jang, J. H. Ahn, and B. O. Kim, IEEE Trans on Magn., vol. 54, no. 11, pp. 1-6, (2018). [6] W. D. Zhao, X. J. Wang, and C. Gerada, IEEE Trans on Magn., vol. 54, pp. 1-5(2016).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7247dcf6fb939140744ef7646c10419b.jpg)
Configuration of the proposed HSPMM

![](https://assets.underline.io/uploads/markdown_image/1/image/85da787ea993b78ea704d13d3d8363da.jpg)
Fig.2 Optimization results

 Design and Optimization of a Slotless High-speed Permanent-Magnet Synchronous Motor with Non-magnetic Fillers in Stator

High-speed permanent magnet synchronous machines (PMSM) are widely used. However, there are challenges in the machine design [1-3]. To protect the magnets against the centrifugal force, a retaining ring is often employed on the rotor with interference fit, applying a strong compressive stress on the magnets. When the machine runs at high speed, the centrifugal force further enlarges the compressive stress on the magnets. On the other hand, high-speed machines have a disadvantage of high loss density which results in high temperature rise [1] [4]. Since different materials on the rotor have different thermal expansion, the high temperature rise produces more stress on the magnets. Therefore, the magnets in the high-speed PMSM suffer from high stress which may be up to 90 MPa, as well as high temperature such as 130 °C or higher. It has been well studied that the property of the permanent magnets varies (usually deteriorates) at high temperature, and such variation of property is usually considered in the machine design. However, it is hardly reported in existing literatures how the magnet property changes under high compressive stress. Therefore, an experimental study on this issue is carried out, by measuring the magnet property under various stress and temperature. A test rig is designed and built, and 7 types of NdFeB and 2 types of SmCo magnets are tested. Fig. 1 shows the test results of the NdFeB 42SH magnet at 24°C. When the compressive stress is applied on the magnet, its remanence increases slightly and then stays almost constant, as the curve of test-1 shows. However, when the pressure is released, it is found that the magnet remanence decreases. Then, compressive stress is applied again, and the remanence increases more remarkably, as shown as the curve of test-2. If the pressure is released again, the remanence returns with no extra decrease. Pressure is applied and released repeatedly, and the magnet property variation also repeats (see the curves of test-3, 4, and 5). Moreover, the same property variation trend is observed for the other NdFeB magnets and the SmCo magnets, i.e., the magnet property under the second application of compressive stress is lower than that under the first application of stress, but, the property will not become worse when the stress is applied more times. Therefore, it can be said that the magnet property is stabilized by the compressive stress. Fig. 2 shows the stabilized property variation versus the compressive stress for the other NdFeB magnets at room temperature. Each grade of NdFeB magnet has its own significance of property variation, and so is the case of the SmCo magnets. Similarly, the property variation versus the compressive stress at other temperature is also measured, demonstrating the negative thermal coefficient of the magnet remanence. In high-speed PMSM, the magnets suffer from significant compressive stress and temperature rise, therefore, their property of remanence is different from the data given by the manufacturer, as the manufacturer’s data does not take into account the stress influence. Clearly, the stress influence is negligible in regular-speed machines, but should be considered in the high-speed machine designs. Acknowledgement This work was supported by the Natural Science Foundation of China under the grants

**References:**

[1] J. Shen, et al, CES Transactions on Electrical Machines and Systems, Vol.2, p.23 (2018). [2] D. Gerada, et al, IEEE Trans. Industrial Electronics, Vol.61, p.2946 (2014). [3] F. Zhang, et al, IEEE Transportation Electrification Conference and Expo, Busan, Korea, p.843 (2016). [4] W. Li, et al, IEEE Trans. Industrial Electronics, Vol.61, p.3056 (2014).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4d497c5f4dde87ca9f08c6197100f287.jpg)
Fig.1 Remanence variation of NdFeB 42SH magnet versus compressive stress at room temperature.

![](https://assets.underline.io/uploads/markdown_image/1/image/e5371582c44082cee9d7f1184e82052c.jpg)
Fig.2 Stabilized remanence variation of different NdFeB magnets versus compressive stress at room temperature.

 Experimental Study on Remanence Variation of Permanent Magnets for High-Speed Machines

—The eddy current loss in the permanent magnet (PM) and the sleeve of high-speed surface-mounted permanent magnet synchronous motors (HS-SPMSMs) increases the temperature rise of the rotor, which increases the risk of irreversible demagnetization of the PM. In order to reduce the rotor eddy current loss (RECL) of HS-SPMSM, this paper analyzes the suppression effect of four different segmented rotor structures (axially segmented sleeve, circumferentially segmented PM, axially segmented PM, PM and sleeve are simultaneously segmented) on the RECL of HS-SPMSM. On this basis, the applicability of the rotor segmented structure to the RECL with different sleeve materials is further analyzed. Finally, the C-core experiment was used to verify the influence of different segmented rotor structures on the RECL. I. Introduction High-speed permanent magnet synchronous motors (HS-PMSMs) have the characteristics of high-power density, but they also have the characteristics of high loss density and high temperature rise [1]. The high temperature of the rotor not only affects the performance of the motor, but also increases the risk of irreversible demagnetization of the PMs [2]. In order to suppress the RECL of the PMSM, the PM is usually divided into pieces [3-4]. This method is usually applied to conventional speed motors without sleeves. For HS-SPMSM, which is widely used in HS-PMSM, the RECL is mainly concentrated in the PM and sleeve [5], and the segmentation of the PM will affect the eddy current loss in the sleeve. However, there is little research on the effect of permanent magnet segmentation on the RECL of HS-SPMSM with sleeve structure. In this paper, four segmented rotor structures are established, including axial segmented sleeve, circumferential segmented PM, axial segmented PM, PM and sleeve segmented simultaneously. This paper uses different segmented rotor structures with three commonly used sleeve materials (carbon fiber, titanium alloy, stainless steel), and analyzes the influence of different segmented rotor structures on the RECL of HS-SPMSM. Finally, the C-core experiment is used to verify the influence of different rotor structures on RECL. II. Segmented Rotor Structure and Analysis A 15 kW, 30000 rpm HS-PMSM is taken as an example to analyze the RECL under different sleeve structures. When the motor is running at the rated speed, the four segmented rotor structures are analyzed for their suppression effect on RECL. The four segmented rotor structures are shown in Fig. 1. This paper analyzes the RECL of HS-PMSM with several commonly used sleeve materials (carbon fiber, titanium alloy, stainless steel), and studies the influence of segmented rotor structure on the RECL of HS-PMSM by using the four structures shown in Fig. 1. According to the calculation results, for the high conductivity sleeve material, when the number of axial segments reaches a certain degree, it is helpful to reduce the RECL, while for the carbon fiber sleeve, the axial segmentations have little effect on the RECL. When the PM is segmented axially or circumferentially, the RECL can be significantly reduced for the carbon fiber sleeve, and the effect of axial segmentation is better than that of circumferential segmentation. However, for the sleeve made of high conductivity material, the shielding effect on the eddy current magnetic field is weakened due to the segmentation of the permanent magnet, which makes the sleeve produce more eddy current loss and increases the total RECL. If the rotor structure shown in Fig. 1 (d) is used, the RECL can be reduced for all three sleeve materials, but the number of segments of PMs and sleeves needs to be reasonably configured. III.Experimental Verification In order to verify the influence of various sleeve materials on rotor eddy current loss and the suppression effect of sleeve axial segment structure on rotor eddy current loss. This paper verifies the influence of different sleeve structures on the eddy current loss of the rotor through the C-core experiment. The C-core experimental platform and different sleeve materials are shown in Fig. 2. IV.CONCLUSIONS This paper compares and analyzes the RECL of HS-SPMSM with different rotor structures. The RECL generated by the high-conductivity material sleeve is relatively high, but it can shield the eddy current loss of the permanent magnet. For high-conductivity sleeves, the axial segmentation can reduce the eddy current loss of the sleeve by increasing the equivalent resistance of the sleeve and further suppress the RECL, when using PM segments, the sleeve will generate more eddy current loss, resulting in increased RECL. However, for carbon fiber sleeves, circumferentially or axially segmented PMs can help reduce the RECL, but the axial segmentation of the sleeve has almost no effect on the RECL. For the three sleeve materials, segmenting the sleeve and the PM at the same time will reduce the RECL, but the number of segmentations of the sleeve and the PM should be reasonably configured.

**References:**

 [1] C. Chen, Y. Wang and J. Wei, "Research on method for reducing eddy current loss of magnet in high-speed permanent magnet synchronous motor," 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 2019, pp. 1-4. [2] J. Dong, Y. Huang, and L. Jin, "Thermal Optimization of a High-Speed Permanent Magnet Motor," IEEE Transactions on Magnetics, vol. 50, no. 2, pp. 749-752, Feb. 2014. [3] J. Shen, H. Hao, and M. Jin, "Reduction of Rotor Eddy Current Loss in High-Speed PM Brushless Machines by Grooving Retaining Sleeve," IEEE Transactions on Magnetics, vol. 49, no. 7, pp. 3973-3976, July 2013. [4] K. Yamazaki, M. Shina, and Y. Kanou, "Effect of Eddy Current Loss Reduction by Segmentation of Magnets in Synchronous Motors: Difference Between Interior and Surface Types," IEEE Transactions on Magnetics, vol. 45, no. 10, pp. 4756-4759, Oct. 2009. [5] H. Jun, J. Lee, and H. Lee, "Study on the Optimal Rotor Retaining Sleeve Structure for the Reduction of Eddy-Current Loss in High-Speed SPMSM," IEEE Transactions on Magnetics, vol. 51, no. 3, pp. 1-4, March 2015.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3f1f9570ee1a8851a342459ca9f76158.jpg)
Fig. 1. Various rotor structures. (a) Axial segmented sleeve. (b) Circumferential segmented PM. (c) Axial segmented PM. (d) PM and sleeve are segmented simultaneously.

![](https://assets.underline.io/uploads/markdown_image/1/image/a804f5a1b6871890c6cf1460dfa099d5.jpg)
Fig. 2. Experimental verification. (a) C-core loss test experiment platform. (b) Sleeve materials.

 Analysis and Experimental Verification of Segmented Rotor Structure on Rotor Eddy Current Loss of High-Speed Surface-Mounted Permanent Magnet Machine

I.Introduction Direct drive wave energy conversion (DD-WEC) is a typical low-speed long-stroke application, harvesting wave energy presents enormous challenges, because wave energy naturally exists in the form of extremely low speed, high force, or torque motion [1]. In DD-WEC, linear generators with multi-pole design all suffer from drawbacks such as low power density [2]. However, the frequency of flux linkage in field-modulated machine can be increased by the magnetic gear effect, and the output voltage and power density can also be effectively enhanced. Therefore, field-modulated machines have attracted more attentions in DD-WEC. A magnetic field-modulated linear permanent magnet (PM) generator for DD-WEC is proposed. The generator with a high power density converts wave energy effectively and enhances power density in DD-WEC [2]. A mover separated linear magnetic-field modulated motor for long stroke applications is proposed, the motor exhibits high thrust force by effectively employing the magnetic-field modulation effect [3]. A large-scale inner stator radial flux magnetically geared generator for wave energy conversion is proposed, the magnetic gear will not be damaged when exposed to overload torques [1]. Most recent work on field-modulated machines in DD-WEC focuses on the radial flux and axial flux machine, there is few literature about field-modulated transverse flux machine. In this paper, based on the field modulated principle, a field-modulated hybrid excitation transverse flux linear generator (FM-HE-TFLG) is proposed. Different combinations of PM pole pair, armature winding pole pair and translator pole pair are selected and their performances are compared and analyzed. II.Machine Configuration and Operation Principle Fig.1 In the proposed structure, as shown in Fig. 1, the armature winding is placed in outer stator slots. Excitation methods include electric excitation and PM excitation. Direct current (DC) field winding and PM are both located in inner stator. The translator consists of spiral silicon steel sheets and nonmagnetic sheets. In the proposed FM-HE-TFLG, armature winding pole pair paw, translator pole number Nt, and PM pole pair match pPM: Nt,=pPM+paw (1) The relationship between the translator position in electric and mechanical degrees is as follows: θe=Ntθm (2) where θe and θm are translator positions in electric and mechanical degrees respectively. III.Results Fig.2 The 18/12/17 topology has higher electric frequency, and the amplitude of flux linkage is lower than 12/12/11 counterpart. As the armature current increases, the saturation of 12/12/11 topology is earlier than that of 18/12/17, so the structure with higher modulation ratio is more suitable for high current applications. IV.Conclusion The simulation results support several interesting conclusions. As the modulation ratio increases, the electric frequency is enhanced. The structure with higher modulation ratio is more suitable for high current applications. The proposed 18/12/17 FM-HE-TFLG is a good candidate for DD-WEC.

**References:**

[1] M. Johnson, M. C. Gardner, H. A. Toliyat, S. Englebretson, W. Ouyang and C. Tschida, "Design, Construction, and Analysis of a Large-Scale Inner Stator Radial Flux Magnetically Geared Generator for Wave Energy Conversion," in IEEE Transactions on Industry Applications, vol. 54, no. 4, pp. 3305-3314, July-Aug. 2018. [2] N. Feng, H. Yu, M. Zhao, P. Zhang and D. Hou, "Magnetic field-modulated linear permanent-magnet generator for direct-drive wave energy conversion," in IET Electric Power Applications, vol. 14, no. 5, pp. 742-750, 5 2020. [3] W. Zhao, S. Wang, J. Ji, L. Xu and Z. Ling, "A New Mover Separated Linear Magnetic-Field Modulated Motor for Long Stroke Applications," in IEEE Transactions on Magnetics, vol. 53, no. 11, pp. 1-5, Nov. 2017, Art no. 4002205.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/18a90a429fe6f3e23b7a5005670edb71.jpg)
Fig.1 Sectional view and trimetric view of FM-HE-TFLG

![](https://assets.underline.io/uploads/markdown_image/1/image/b646b6fc5585d660f766fd9417590852.jpg)
Fig. 2. Waveforms of flux linkage and back EMF in 12/12/11 and 18/12/17 FM-HE-TFLG

 Analysis of Magnetic Gearing Effect in Field-modulated Hybrid Excitation Transverse Flux Linear Generator for Direct Drive Wave Energy Conversion

&lt; I. INTRODUCTION &gt; Recently, oscillatory actuators have been applied in various fields, including consumer electronics, entertainment, and industrial equipment. Especially, haptic devices that induce a virtual force are attracting attention. Haptic display systems using oscillatory actuators utilize the non-linearity of human perception, and it is possible to illusion a continuous unidirectional force by an asymmetric vibration [1]. Such oscillatory actuators are expected to become smaller and can be three-dimensionally (3-D) driven to display 3-D traction, for improving portability and functionality. Kato et al. developed a three-degree-of-freedom linear oscillatory actuator (3-DOFLOA) [2]. This actuator consists of four sets of coils has mutual interference of force for driving to each axis. Moreover, Heya et al. proposed a 3-DOFLOA that consists of three sets of coils and can be driven in three axes without interference [3]. However, the conventional 3-DOFLOAs need complex and large support mechanisms outside the magnetic circuit, which increase the size and weight of the device. Then, we propose a novel magnetic structure of a 3-DOFLOA in this paper. The magnetic pole and permanent magnet shapes are designed to integrate with the elastic support mechanism using mechanical springs. The proposed structure contributes to reduce the size and weight of the actuator. The force characteristics are clarified using a magnetic field analysis modeled with a 3-D finite element method (3-D FEM). The calculated results show that the proposed actuator can be independently driven for each axis. &lt; II. PROPOSAL OF MAGNETIC STRUCTURE AND OPERATING PRINCIPLE &gt; &lt;&lt; A. DESIGN &gt;&gt; Conceptual scheme of the magnetic structure is shown in Fig. 1(a). In the case of the conventional support mechanisms, mechanical springs are attached to the outside of the magnetic circuit sections. On the other hand, by adopting magnetic pole and permanent magnet shapes that allow the mover and stator to be connected by mechanical springs, it is possible to reduce the size without losing the function as a support mechanism. Fig. 1(b) shows the overview of the proposed a 3-DOFLOA. The inner mover has cylindrical permanent magnets for installing mechanical springs inside the stator. The stator consists of six sets of coils and the stator yoke. The coil is wound around the iron core with a hole of the same size as the permanent magnet. The mechanical springs made of non-magnetic material are used to support the mover. A total of six springs are arranged, two for each shaft, through the holes of the permanent magnet and the iron core. From this design, the proposed actuator can be integrated the support mechanism. The movable range is ± 0.5 mm to each axis. Fig. 1(c) illustrates the magnetic circuit. The magnetization direction of the permanent magnets arranged in the x-axis and y-axis directions is outward, and the magnetization direction of the permanent magnets arranged in the z-axis direction is inward. Therefore, the magnetic flux generated from the permanent magnets passes through the stator yoke and forms a closed magnetic circuit. &lt;&lt; B. OPERATING PRINCIPLE &gt;&gt; Fig. 1(d) shows the operating principle of the proposed actuator. When the Coil-X1 and Coil-X2 are excited, a magnetic pole is induced and the mover moves in the x-axis direction due to magnetic attraction and repulsion forces. Similarly, the mover can move in the y-axis and z-axis directions by the excitation of the Coil-Y1/2 and Coil-Z1/2. &lt; III. STATIC FORCE ANALYSIS &gt; The static force is calculated employing a magnetic field analysis using 3-D FEM. The inner yoke and stator yoke are made of SUY. The residual magnetic flux density of the permanent magnets is 1.3 T. The number of turns of each Coil-X1/2 and Coil-Y1/2 is 85 turns, and the number of turns of each Coil-Z1/2 is 68 turns. The input current is 0.3 A. The detent and excitation forces when the mover is moved in the x-axis, y-axis, and z-axis directions are shown in Fig. 2(a), (b), and (c), respectively. From Fig. 2(a), the magnetic spring constant in the x-axis direction due to the detent force is 2.10 N/mm, and the average excitation force in the x-axis is 0.23 N. From Fig. 2(b), the magnetic spring constant in the y-axis direction is 2.10 N/mm, and the average excitation force in the y-axis is 0.23 N. From Fig. 2(c), the magnetic spring constant in the z-axis direction is 2.25 N/mm, and the average excitation force in the z-axis is 0.22 N. The detent and excitation forces are generated only in the direction of the driving direction. In addition, the linear detent force characteristics are obtained. Therefore, it has to become a stable system at the origin by incorporating mechanical springs to cancel the detent force. From these analyzed results, it is confirmed that the proposed actuator can be independently driven in three axes, and the interference of forces between each axis is not observed. &lt; IV. CONCLUSION &gt; The novel small 3-DOFLOA was proposed in this paper. It can be driven three axes, and has not interference between each axis. The proposed actuator can contribute to the miniaturization of 3-D haptic devices.

**References:**

[1] T. Amemiya, and T. Maeda, Asymmetric oscillation distorts the perceived heaviness of handheld objects, IEEE Trans. Haptics, vol. 1, no. 1, pp. 9–18, (2008) [2] M. Kato, and K. Hirata, Control of Three-Degree-of-Freedom Resonant Actuator Driven by Novel Vector Control, TRANSPORTATION SYATEMS AND TECHNOLOGY, Vol. 4, No. 3, pp. 90-101, (2018) [3] A. Heya, K. Hirata, T. Matsushita, and Y. Kono, Design and Analysis of a Three-Degree-of-Freedom Linear Oscillatory Actuator, IEEE Transactions on Magnetics, Vol. 56, No. 2, 6701404, (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/314c6e54fbcb7aa8d3feead54c1895b4.jpg)
Fig. 1. Proposed 3-DOFLOA (a) Conceptual scheme of the structure., (b) The overview of the proposed actuator., (c) Magnetic circuit., and (d) Operating principle.

![](https://assets.underline.io/uploads/markdown_image/1/image/db0a1cd9c36d06adb010609127b31c33.jpg)
Fig. 2. Analysis results of the static force (a) When the mover moves in the x-axis., (b) When the mover moves in the y-axis., and (c) When the mover moves in the z-axis.

 Design and Analysis of a Three-Degree-of-Freedom Linear Oscillatory Actuator Integrated with Support Mechanism

This paper presents an efficient multi-objective optimization method for linear induction motors (LIMs). With this modified method, the eddy current analysis and optimization design can be realized with speediness and accuracy. To ensure the consideration of skin effect, transverse end effect and longitudinal end effect, the raw data are obtained from 3D finite element model (FEM). Latin hypercube sampling (LHS) is adopted to facilitate the extraction of data, including every structural parameter of secondary. With these samples, eXtreme Gradient Boosting (XGBoost) is utilized to establish a multiple analysis model. Assuredly, the analysis model of thrust force, vertical force, eddy current and magnetic flux density owns concurrency and precision. Considering the limitation and rationality of designing structure and velocity, an objective function is specified to determine the ultimate optimization scheme. I. INTRODUCTION As a vital component of an LIM, secondary induces eddy current and generates thrust force. Therefore, the rectification method and optimization design of eddy current plays a crucial role in performance improvement. Due to the complexity of approximate analytical method, finite element analysis (FEA) is a conventional analysis method for eddy current distribution and magnetic flux density instead. Evidently, 2D FEM is inadequate for eddy current analysis [1]. 3D FEM can ensure the reliability of the calculation, and yet has the fatal flaw of being laborious and time-consuming. Therefore, this paper proposed a modified analysis and optimization method based on XGBoost and LHS. The mathematical modeling method can explore the output characteristic and electromagnetic performance under different secondary topologies with efficiency and accuracy. II. TOPOLOGY AND EDDY CURRENT DENSITY DISTUIBUTION To weaken the impact of skin effect and end effect, modifying eddy current path can apparently improve the performance, but the optimization capability is bound up with the selection of secondary topology. Figs. 1(a)-(c) show the topologies and eddy current density distributions of LIMs with different types of secondary. Obviously, the existence of back-iron strengthens the eddy current. Compared with the distribution in single-slit structure, the transverse component of current density at the edge is higher, while the longitudinal component at the active zone and overhang area shows an opposite trend. III. ALGORITHM AND PRINCIPLE Considering correctness, efficiency and generalization are the core of optimization, the mainstay of proposed strategy is streamlined as follows. As shown in Fig. 2, the optimization process can be divided into five main steps. Objective to determine the general value range of structural parameters, equivalent circuit is effective for preliminary assessment. Then, Latin hypercube sampling (LHS), as a method can ensure the maximum of feature information and minimum of sample points, is adopted to obtain data with good rationality and coverage. Respecting that the analysis model erected by XGBoost has the combination of accurateness and speediness, the relationship between structural parameters and analysis objectives will be observed intuitively [2]. Thereinto, the structural parameters contain overall dimension and ladder structural dimension of secondary; thrust force, vertical force, current density and magnetic flux density are taken into consideration as analysis objectives. The objective function can conveniently judge the comprehensive performance of analysis targets, so as to select the most appropriate optimization scheme. IV. CHARACTERISTIC ANALYSIS Figs. 1(b)-(e) show the distributions of eddy current density and the force characteristics of LIMs under different secondary topologies. Through the analysis and optimization method proposed in this paper, both electromagnetic properties and force characteristics achieved modification. Crucially, the ultimate optimization scheme is in good agreement with the FEA result, but the achievement only takes a little time after the analysis model is erected. V. CONCLUSION In this paper, the proposed analysis method, which adopts LHS and XGBoost, realizes the speedy and accurate optimization of electromagnetic properties and force characteristics by selecting the most suitable secondary scheme. The superiorities are listed as follows. (1) The proposed method can analyze the relationship between secondary structural parameters and performance indexes with efficiency. Both electromagnetic properties and force characteristics are taken into consideration. (2) With LHS, random samples in the whole range possess a balance of distribution and representativeness. (3) Excluding the speediness of modeling and prediction, XGBoost has a great imputation capability of missing data. Additionally, the autonomy of objective function and evaluation function is a high guarantee for the adjustability of multi-objective optimization. Therefore, this proposed multi-objective analysis method can achieve an efficient, accurate and reliable optimization for LIMs. The detailed analysis will be listed in the full paper.

**References:**

[1] Q. F. Lu, L. X. Li, J. W. Zhang, X. Y. Huang, J. J. Cai , “Design Optimization and Performance Investigation of Novel Linear Induction Motors With Two Kinds of Secondaries,” IEEE Trans. Ind. Appl., vol.55, no.6, Nov.-Dec. 2019. [2] B. S. Bhati, G. Chugh, F. Almilurjman, N. S. Bhati, “An improved ensemble based intrusion detection technique using XGBoost,”. Trans. Emerg. Telecommun. Technol., 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d0eaa82636f53ebafb2312f0d3f1e5dd.jpg)
Fig. 1. 3D finite element models and results of LIMs.

![](https://assets.underline.io/uploads/markdown_image/1/image/9d89d631bc0340b3157751677c59ffd5.jpg)
Fig. 2. Flow chart of proposed multi-objective method.

 Eddy Current Analysis and Optimization Design of Linear Induction Motors with Different Secondary Topologies Based on XGBoost

Conventional conveyance systems using wheels and belt conveyors occur friction and wear at the contact portions. In order to solve these problems, a noncontact conveyance system has been developed[1][2]. In this research, a permanent magnet repulsion levitation system and superconducting magnetic levitation system are adopted. The permanent magnet repulsion levitation system cause a large levitating force at the loading part. Superconducting magnetic levitation system cause a stable levitation at the carrier body. There is no influence of large load weight on the levitation of the carrier because the loading part and the carrier body are connected by the linear way. The carrier moves above the magnetic rail. The coils are installed on magnetic rail, and the magnetic field gradient is generated by the exciting coils. The carrier is propelled by the magnetic field gradient. By increasing the flux of the coil behind the HTS in the propulsion direction and reducing the flux of the HTS in the propulsion direction, magnetic field gradient is generated and the carrier propels. The coil pitch is optimized and propulsion force is examined by adding the exciting coils [3] [4] Fig.1 shows the experimental device[4]. The change of the magnetic field gradient is analyzed when changing the coil pitch by 5mm in the range of 25~50mm with the FEM analysis software JMAG-Designer[5]. The propulsion force is confirmed by the experimental results. The experimental condition is as follows; current of the coil I=2.0A and levitation gap g=23mm. The propulsion force is measured by the load cell installed in front of the carrier. From the analytical result, when the coil pitch is changed, the position of peak value of the flux density due to the magnetization and demagnetization on the magnetic rail changes, but the crest value of the magnetic field gradient is not changed. In the range of coil pitch 40~50mm, the excitation coils are separated. The flat section is formed between the positive peak value and the negative one in the magnetic gradient field. Thus, in the z-axis direction, the surface flux density of the HTS is the strongest at the center. Fig.2 (a) shows the average value and the maximum value of the propulsion force at each the coil pitch. At the coil pitch 50mm, both the average propulsion force and the maximum propulsion force are largest. As a result, the optimum value of the coil pitch under the HTS is 50mm. Center of the HTS keeps the largest flux from the permanent magnet. The coils are arranged on the magnetic rail at the coil pitch 50mm, as the diameter of the coil used in this research is 22mm, only the odd number coil in Fig.1 (b) will be installed. Thus, the excitation switching interval becomes large. Thus, as shown in Fig.1 (b), coils are installed at intervals of 25mm. At first, No.1 coil and No.3 coil in Fig.1 (b) are excited. Next, No.2 coil and No.4 coil are excited. In this way, the coils to be excited are switched, and coil pitch 50mm is realized. The case of exciting the coil between the two excited coils is considered.No.1 coil shown in Fig.1 (b) is magnetized, No.2 and No.3 coils are demagnetized. The flux density in the y-axis direction at that time is analyzed with the magnetic analysis software JMAG-Designer. In the range of x=-20~20, the flux density in the y-axis direction in three excitation coil case is smaller than that in two excitation coil case. As the magnetic rail is composed of Halbach array, the y-axis direction flux density is strong on the magnetic rail. Therefore, the change of the flux due to the excitation of the coil tends to occur in the y-axis direction. The propulsion force is compared when exciting two coils at intervals of 50mm with the propulsion force when three coils are excited at intervals of 25mm. No.1 coil in Fig.1 (b) is magnetized, No.2 and No.3 coils are demagnetized. The load weight up to 58.8N is placed on the carrier. Fig.2 (b) shows the maximum propulsion force for each load weight. Larger propulsion force is given when No.1, No.2 and No.3 coil in Fig.1 (b) are excited t at all load weight. This is because the range of the magnetic field gradient is increased by adding a coil to be excited. In the case of three coils excitation, as the change of flux density in the y-axis direction is large, it is necessary to consider the magnetic gradient field in the y-axis direction. In the case of two coils excitation, it is suitable to install the coils at intervals of 50mm so as to catch the center of the HTS. In addition, in the case of three coils excitation the propulsion force increases by generating a gradient in the flux density in the y-axis direction.

**References:**

[1]F. C. Moon, Superconducting levitation, John Wiley & Sons, New York, 1994. [2]J. Hull, M. Murakami, “Applications of bulk high-temperature Superconductors”, Proc. of IEEE, vol.92, 2004, pp1705-1718. [3]S. Ohashi, D. Dodo, “Influence of the Propulsion System on the Levitation Characteristics of the HTSC-Permanent Magnet Hybrid Magnetically Levitated System”, IEEE Transactions on Applied. Superconductivity. vol.17, no.2, 2007, pp2083-2086. [4]Y. Takaki, T. Sumida, S. Ohashi, “Improvement of Velocity Control in the Permanent Magnet-HTS Hybrid Magnetically Levitated Conveyance System”, IEEE Region 10 Conference (TENCON), 2016, pp3105-3108 [5] T. Sumida, Y. Kamitani, N. Yamada, S. Ohashi, “Propulsion Characteristics using Pinned flux of the HTS in the Permanent Magnet-HTS Hybrid Magnetically Levitated Conveyance System”, IEEE Transaction on Applied Superconductivity, 2016, Vol.26, No.4, 3600905.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b238f5b473b4485f39cd59d4d26df252.jpg)
Experimental device of the conveyance system

![](https://assets.underline.io/uploads/markdown_image/1/image/ca7ed8c3000c56c4b2c7fc0a1c756c36.jpg)
Propulsion force between HTS and the permanent magnet

 Optimization of the Excitation Method of the Propulsion Coils in the Permanent Magnet-HTS Hybrid Magnetically Levitated Conveyance System

1 Introduction Reciprocating engines generate torque only during the explosion process and this causes a large ripple in output torque. When the torque ripple is transmitted through the engine drive system, torsional vibration is induced in a drive shaft, resulting in uncomfortable vibration and noise. This rotational vibration is a problem not only in automobiles, but also in ships, cableways, and other transportation equipment. Various vibration suppression methods have been proposed to solve this problem. Matsuhisa et al. proposed a dynamic vibration absorber (DVA) with an additional mass that oscillates in the radial direction of the cableway to suppress rotational vibration caused by wind [1]. When the natural frequency of the added mass is set to about twice the natural frequency of the gondola, the Coriolis force generated by the radial vibration of the added mass has been shown to be effective in damping the rotational vibration. However, since the additional mass is passively vibrated by the centrifugal force of the gondola, itis not possible to control the magnitude of the Coriolis damping force. This paper proposes a new hybrid DVA to reduce rotational vibration of a rotor. The additional mass operates as the mover of the electromagnetic linear oscillatory actuator (LOA). The LOA actively oscillates the mover by current control and obtains the variable damping force caused by the Coriolis effect. LOAs have been applied to various industrial equipment due to their simple structure, direct drive, and high efficiency [2].They have also been applied to an active control device for automobiles [3]. In this paper, we describe the structure and mathematical model of the proposed hybrid DVA. Moreover, we evaluate numerically the vibration suppression effect under the active operation of the LOA. 2 Hybrid DVA Using Electromagnetic Oscillatory Actuator 2.1 Basic Structure and Operational Principle Fig. 1 shows the basic configuration and operational principle of the proposed hybrid DVA. 1-DOF LOA is embedded on the surface of a rotor and oscillates in the radial direction (r-direction). Excitation of the coil generates an electromagnetic force in the r-direction, which works to increase the mover stroke of the LOA. Consequently, the Coriolis force is produced in the circumferential direction (θ-direciton),which suppresses the rotational vibration in the θ-direction. Since the coil of the LOA rotates synchronously with the rotor, we need to discuss power supply. We assume a direct power supply from a battery mounted on the rotor surface. Therefore, we include the equivalent moments of inertia of the stator and the battery in the moment of inertia for the rotor. Our hybrid DVA can be also understood as a opposite phenomenon of a parametric excitation (parametric damper). Fig. 1(b) shows an example of the mover trajectories under parametric excitation and parametric damper. This figure clearly suggests that the vibration in the θ-direction increases after one oscillation period because of the positive energy provided by the parametric excitation. When the trajectory becomes reversed, the vibration decreases because of the negative energy provided by the parametric damper. The important point is that both cases require to satisfy the following relationship, ωr:ωθ = 2:1. (1) Here, ωr and ωθ are the natural frequency in the r- and θ-directions, respectively. 2.2 Equations of Motion for Hybrid DVA The Euler-Lagrange equation gives the following equations of motion in the r- and θ-directions, Jd2θ/dt2=m(l+r)d2θ/dt2+cθdθ/dt+2m(l+r)dθ/dt*dr/dt+kθθ=Tincosωt, (2) md2r/dt2+crdr/dt+krr=m(l+r)(dθ/dt)2+KtI+Kdr. (3) Here, the fourth term on the left-hand side of equation (2) is the Coriolis force, which works to decrease the vibration in the θ-direction. The first term on the right-hand side of equation (3) is the centrifugal force, which works to increase the vibration in the r-direction. The kinetic parameters of the hybrid DVA are determined as follows so that equation (1) holds, 2√(kθ/(J+ml2))=√((kr-Kd)/m). (4) 3 Reduction of Rotational Vibration under Active Control In this section, we solve the above equations of motion and verify the effectiveness of the proposed hybrid DVA through numerical simulation. Fig. 2 shows the rotational vibration of the rotor and the displacement of the mover with and without the LOA. In this simulation, The mover is oscillating passively until 4s. After that, Electromagnetic force generated by the LOA starts to oscillate the mover actively. Focusing on the envelopes of the waveform (blue solid line: without LOA, orange dashed line: with LOA), the active operation with LOA reduced the rotational vibration of the rotor by about 30%. In response to the decrease in the rotational vibration, the amplitude of the mover displacement is approximately doubled. We are able to conclude that the electromagnetic force generated by the LOA increases the displacement of the mover and the resulting damping effect by the Coriolis force also increases. In the final paper, we will describe the detailed design of the hybrid DVA and evaluate performances of the LOA through finite element analysis. Because this technique may also be applied to reduce torque ripple in AC motors, the rotational vibration by torque ripple will also be discussed.

**References:**

[1] L.D. Viet, N.D. Anh, H. Matsuhisa, Journal of Sound and Vibration, Vol. 330, no. 9, pp. 1904–1916 (2011) [2] M. Kato, Y. Kono, K. Hirata, and T. Yoshimoto, IEEE Transactions on Magnetics, Vol. 50, no. 11, 8206404 (2014) [3] F. Kitayama, K. Hirata, N. Niguchi, and M. Kobayashi, Sensors, Vol. 16, No. 377 (2016)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/560279a19b259c411514e6dd264efe2c.jpg)
(a) Basic structure of the proposed hybrid DVA. (b) The trajectories of the mover under parametric excitation and damper.

![](https://assets.underline.io/uploads/markdown_image/1/image/f9bd317da50aeaf568c06373bc992f63.jpg)
Rotational vibration of the rotor and the displacement of the mover with and without the LOA.

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