France



Additive manufacturing technology carries its potential to develop high-performance electrical machines enabling direct printing of complex shapes and incorporating the complex sequence of feedstock materials in a single build to optimize the demanding physical parameters such as low weight, cost, energy loss, and high mechanical strength and corrosion resistance. We printed Fe-3%Si stator core using selective laser melting and machined it down to thin laminates to assemble a prototype brushless permanent magnet electric motor. The magnetic and electrical properties of the thin heat-treated laminates and back emf of the electrical motors are studied. The thin laminates exhibit maximum relative permeability of 7494 with an approximate 0.8 T applied field and core-loss of 0.473 watts/lb at 60 Hz. We will report in detail about the magnetic and mechanical properties of Fe3Si soft magnets and their influence on the electrical motor. The designed machine is analyzed using finite element analysis and compared with measured electrical parameters.

**References:**



**Images:**





INTERMAG 2021

 Additively manufactured Fe-3Si stator for high-performance electrical motor

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technical paper

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.

 Reduction of Rotational Vibration Using Coriolis Force Generated by Electromagnetic Oscillatory Actuator Moving in Radial Direction

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.

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

I. INTRODUCTION Environment recognition is a crucial task for autonomous mobile systems such as robots and drones, and vison information obtained by a camera is important. These systems require a high spatial awareness while undergoing various disturbances in an unknown environment. However, there are some problems: degradation of recognition accuracy caused by vibration and increase in size of the structure using a multi-degree-of-freedom (DOF) driving mechanism. Therefore, we focused on a multi-DOF actuator. Various types of multi-DOF actuators have been proposed, which use principles based on synchronous motors [1], stepping motors [2]. Nevertheless, the conventional actuators have a large structure and control device, for high torque density and continuous rotation. For applying to a driving source of a camera attitude control system, an actuator that can be configured with a few components and driven by a simple control device is required. Therefore, a multi-DOF voice coil actuator (DOF-VCA) is discussed in this paper, which has high responsiveness because it has only a few components. Kim et al. proposed a two-DOF-VCA with four-coils and permanent magnets [3,4]. This actuator can generate two-DOF motion driven by two H-bridge circuits. Moreover, our group proposed a three-DOF-VCA with eight-coils driven by three H-bridge circuits [5]. However, further simplification of a structure and control device is required for robotic eyes in humanoid robots. In this paper, we propose novel multiple-DOF-VCAs: two-DOF actuator driven by a three-phase half-bridge circuit and three-DOF actuator driven by a four-phase half-bridge circuit. The proposed actuators can be driven by a smaller number of switching elements and coils compared to the conventional actuators. The proposed magnetic structure and driving principle are described. The torque characteristics are clarified by a magnetic field analysis using a three-dimensional finite element method (3D-FEM), and it is shown that the proposed actuator can be driven by the proposed principle. II. PROPOSAL OF NOVEL STRUCTURE AND PRINCIPLE Figs. 1(a) and (b) show the proposed two-DOF-VCA driven by three-phase and three-DOF-VCA driven by four-phase, respectively. The mover consists of three-coils arranged at intervals of 120 degrees. The stator consists of an outer stator yoke and an inner stator with a yoke and permanent magnets. This actuator can be driven two-DOF by combined torques generated in each coil. The coils are connected at a neutral point, and the coils are excited in a balanced state. Thus, the actuator can be driven by only a three-phase half-bridge circuit. The proposed three-DOF-VCA has a structure that coils and permanent magnets are arranged at intervals of 90 degrees, and the mover consists of four-coils. This actuator can be driven by combined torques in each coil connected at a neutral point and can be operated by a four-phase half-bridge circuit. III. TORQUE CHARACTERISTICS The evaluated models are designed for verifying the proposed principle. The static torques are calculated by the 3-D FEM when the mover is forcibly rotated. The torque characteristics of the proposed VCAs are shown in Fig. 2. Fig. 2(a) shows the calculated torque of the proposed two-DOF-VCA when the current is applied to generate torque in the x-axis direction. The torque in the y- and z-axis directions are not generated, and the torque in the x-axis can be only obtained. The torque is maximum at the origin position and decreases by increasing the rotational angle. This is because the centers of poles in permanent magnets and coils are close together, and the magnetically attracted torque decreases. Fig. 2(b) shows the torque characteristics of the proposed three-DOF-VCA. From the analyzed results, it is found that the torque can be generated by the proposed principle. The decrease of the torque by rotation is also occurred due to the same reason in that of the two-DOF-VCA. The maximum torque in the z-axis is times compared with that of the x- and y-axis. This is because the permanent magnets are arranged with tilts of 45 degrees. From this result, it is suggested that the maximum torque in each axis direction can be adjusted by changing the tilt angle of the permanent magnets. IV. CONCLUSION The novel multi-DOF-VCAs were proposed in this paper, which can be driven by a small number of switching elements and components. The structure and principle were shown, and it was clarified that the actuators can generate torque, through 3-D FEM analysis.

**References:**

[1] K. Kahlen, I. Voss, C. Priebe, and R. De Doncker, "Torque Control of a Spherical Machine With Variable Pole Pitch", IEEE Transactions on Power Electronics, Vol. 19, No. 6, pp. 1628-1634, 2004. [2] G. S. Chirikjian and D. Stein, "Kinematic Design and Commutation of a Spherical Stepper Motor", IEEE/ASME Transactions on Mechatronics, Vol. 4, No. 4, pp. 342-353, 1999. [3] H. Kim, H. Kim, D.Ahn, and D. Gweon, "Design of a new type of spherical voice coil actuator", Sensors and Actuators A: Physical, Vol. 203, pp. 181-188, 2013. [4] H. Y. Kim, H, Kim, D.-G. Gweon, and J. Jeong, "Development of a Novel Spherical Actuator With Two Degrees of Freedom", IEEE Transactions on Mechatronics, Vol. 20, No. 2, pp.532-540, 2015. [5] A. Heya, K. Hirata, and N. Niguchi, "Dynamic Modeling and Control of Three-Degree-of-Freedom Electromagnetic Actuator for Image Stabilization", IEEE Transactions on Magnetics, Vol. 54, No. 11, 8207905, 2018.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a311d6e64e9682e948dfa950b8094323.jpg)
Fig. 1. Proposed multi-DOF-VCAs

![](https://assets.underline.io/uploads/markdown_image/1/image/c9809c9091f2c198de95fa3470c5986a.jpg)
Fig. 2. Analysis results

 Proposal of Novel Multiple-Degree-of-Freedom Voice Coil Actuator

I.INTRODUCTION Tubular flux-switching permanent magnet machine (TFSPMM) inherits the advantages of tubular machine and flux-switching machine with simple structure, strong robustness and no radial force[1]. However, it is not practical to make a TFSPMM entirely from axially stacked silicon steel sheet in machine manufacturing, because the flux will pass vertically through the silicon steel at the yoke of stator and mover and cause eddy current loss. Soft Magnetic Composite (SMC) material can solve the problem of three-dimensional permeability due to its magnetic isotropy[2]. However, TFSPMM with a magnetic core made only by SMC have low thrust due to low permeability and saturation magnetic density of the material. Moreover, core loss of the SMC is very high at low frequency. In order to change the above situation, hybrid magnetic core combined silicon steel sheet and SMC is proposed in this paper, which combines the high permeability of silicon steel and the magnetic isotropy of SMC. In hybrid magnetic core, the silicon steel sheet and SMC have a parallel and series relationship in the magnetic field, so the distribution of the two materials will affect the performance of the machine, including the core loss. Therefore, core loss reduction is important in hybrid magnetic core. II. MAIN CONTENT Fig. 1 shows the configuration of the TFSPMM with hybrid magnetic core and stacking direction of the silicon steel sheet. The silicon steel sheets in hybrid magnetic core are stacked along several tangential directions, and each part of the silicon steel is of the same stack width. The remaining space on the circumference, which cannot be stacked by silicon steel sheet, will be filled by SMC. Fig. 2 (a) shows the position of the point on the yoke when the silicon steel sheet stack width is 21mm. Point 1 is on the end of the silicon steel sheet and point 5 is on the middle silicon steel sheet. Wss is the stack width of the silicon steel sheet. As the position of the point is farther from the end, the amplitude of By decreases. By is the component of magnetic density in the stacking direction of silicon steel sheet. According to Faraday's law of electromagnetic induction, eddy current loss will be generated on the silicon steel sheet affected By. The larger the amplitude of By, the larger the eddy current loss will be. Therefore, it is considered to reduce the stack width and increase the number of blocks with appropriate stack width. Fig. 2 (b) shows the By of point 1 with different stack widths and different silicon steel sheet blocks. 4 parts 12mm means number of silicon steel blocks is 4 and the stack width is 12mm and 8 parts 12mm means number of silicon steel blocks is 8 and stack width is 12mm shown in Fig. 1 (a). As can be seen, with the reduction of stack width, the amplitude of Bydecreases. When the stack width is 12mm, the amplitude of By of 8 silicon steel sheets is smaller than that of 4 silicon steel sheets. Compared with the silicon steel sheet located in the radial direction, the larger the stack width is, the larger By is on the silicon steel sheet at the end. Fig. 2 (c) shows the core loss of TFSPMMs with different hybrid magnetic cores. The results show that the loss difference is not significant, because the material is not assigned electrical conductivity, and the software does not calculate the eddy current loss at the end. If the silicon steel is set as a solid in the calculation, the solid loss calculated by the finite element method is shown in Fig. 2 (d). In practice, large eddy currents are not generated in the axial section because there is an insulating layer between the silicon steel sheets. But in the software, lamination setting cannot simulate the insulation layer. Therefore, solid manual partitioning is needed to approximate the actual situation. III. CONCLUSION In this paper, core loss of TFSPMMs with hybrid magnetic core are compared and analyzed. The stacking direction and width of silicon steel sheet as well as the match with SMC are described. Although the silicon steel sheet and the flux path are parallel to each other, the magnetic flux is not strictly limited to the plane of the silicon steel sheet. The component of magnetic density in the stacking direction of silicon steel sheet varies with the stack width. As the stack width of the silicon steel sheet decrease, By of point 1 will decrease. Since By is the magnetic density component perpendicular to the silicon steel sheet, the smaller By is, the smaller the eddy current loss generated on the silicon steel sheet will be. When the number of silicon steel blocks is 4, the eddy current loss at the end decreases with the reduction of stack width, but the reduction of the proportion of silicon steel in the hybrid magnetic core will reduce the flux linkage and reduce the thrust. Therefore, when the stack width is 12mm, the number of silicon steel blocks is increased to 8, so as to increase the proportion of silicon steel in the hybrid magnetic core, ensuring small eddy current loss at the end and increased thrust.

**References:**

[1] R. Cao et al., “Quantitative comparison of linear flux-switching permanent magnet motor with linear induction motor for electromagnetic launch system,” IEEE Trans. Ind. Electron., vol. 65, no. 9, pp. 7569_7578, Sep. 2018. [2] C. Liu et al., “Performance evaluation of an axial flux claw pole machine with soft magnetic composite cores,” IEEE Trans. Appl. Supercond., vol. 28, no. 3, Apr. 2018, Art. no. 5202105.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9d355e97588dc96892a4bbf22b162f14.jpg)
Fig. 1 (a) Configuration of TFSPMM with hybrid magnetic core; (b) point 1 on stator yoke and stacking direction of silicon steel sheet.

![](https://assets.underline.io/uploads/markdown_image/1/image/e16de32d628da9877cbdc10f448ee469.jpg)
Fig. 2 (a) point on stator yoke; (b) By at point 1 under different stack widths; (c) core loss of TFSPMMs with different hybrid magnetic cores; (d) solid loss of TFSPMMs with different hybrid magnetic cores.

 Core Loss Reduction of Tubular Flux-Switching Permanent Magnet Machine with Hybrid Magnetic Core

Tubular linear permanent magnet machines (TLPM) have gained increasing popularity over the past years due to their versatile nature. Whether used as actuators for linear motion applications or as generators for energy production applications, these machines can provide accurate and precise motion with relatively compact structures and simpler control systems [1]-[3]. Like any other mechanical application, TLPMs might suffer from different structural deformations during either operation or assembly. The moving part of the machine called the translator is the most vulnerable to such mechanical deformations. One commonly occurring deformation happens at the level of the translator shaft and is usually called a translator eccentricity where the translator shaft is no longer aligned perfectly with the central axis of the machines's cylindrical structure. Eccentricity can take different forms and has been studied previously by some authors [4]-[7]. In [4] [5], eccentricity analysis was done using analytical and 3D FEM modeling and the calculated results were compared and validated by experimental results. In [6], eccentricity effects were studied for a surface mounted TLPM structure using the 3D finite element method (3D FEM). The study was continued in [7] by analyzing the eccentricity effects on another TLPM structure, also using 3D FEM, and comparing the eccentricity effects on the two structures. The authors of [6] [7] noted the extensive amount of time and effort required to compute some of the 3D FEM models and generate the results. Hence, an alternative modeling technique for eccentricity analysis that can provide relatively good results with less computation time is needed. The aim of this paper is to present a quasi-3D modeling technique that can represent the 3D problem using the superposition of multiple 2D models. It will be shown that the proposed model takes much less computation time and effort and produce relatively accurate results in comparison to the 3D model. Translator eccentricity unbalances the radial electromagnetic forces acting on the translator by forming a non-uniform air gap between it and the primary. Static eccentricity, which is a common eccentricity form, is the state of having the translator axis displaced by a constant distance ε from the primary axis while both axes remain parallel to each other. This work only focuses on the static eccentricity form leaving other forms for future works. The proposed quasi-3D model is achieved by dividing the 3D structure in the tangential direction (θ direction) into a certain number of sections (see Fig. 1). Since the air gap is non-uniform around the translator in the tangential direction, there is a different air gap value e (Fig. 1) for each θ along the tangential direction where θ∈[0, 2π]. Hence, each section in the tangential direction is modeled as a standalone 2D linear machine having an air gap equal to the air gap value at the central angle of the corresponding section. Then, for each 2D linear machine model, the magnetic induction in the air gap is calculated where it will have two components x and y corresponding to the axial (z-direction) and normal (r-direction) cylindrical components of the 3D model respectively. The tangential component can be associated with a z component which is impossible to determine in a 2D model that has only x and y directions, and hence it will be neglected. After gathering the results from all the 2D modeled sections, using the Maxwell stress tensor the electromagnetic forces acting on the translator in the axial and radial directions are calculated. Both the 2D and 3D models used are finite element method based models, and for this work, they were constructed using the FLUX commercial software. The quasi-3D model will be used to study two TLPM structures having static eccentricity. The first one is a surface-mounted PM structure, the second one is an inserted PM flux focusing structure, and the two have similar dimensions. Both open circuit and on load operations will be studied, and the two cases of linear and non-linear ferromagnetic materials will be considered as well. Studying the different cases will provide an insight into the accuracy and efficiency of the proposed quasi-3D model. Fig. 2 shows a comparison between the quantities (cogging force and attraction force) calculated using the quasi-3D and the 3D FEM models for the surface mounted TLPM having an eccentricity value ε equal to 0.75mm (75% of the air gap value). For this comparison, the ferromagnetic materials were defined in their linear case with a constant μr = 10000. Also, the relative permeability of the PM was defined as μr = 1 and its magnetic remanence as Br = 1T. Noting that the attraction force computed is acting along the axis aligned with the angles having the minimum and maximum air gap values. The results shown in Fig. 2 are relatively accurate and acceptable especially that the solution of 65 time steps of the quasi-3D model with 32 tangential divisions took only around 15 minutes with much less construction effort, while it took around 3 days to solve 33 time steps of the 3D FEM model with much more construction and computation efforts. Computation time differences will be even more noticeable and remarkable when solving non-linear models that will be presented and compared in the full paper release.

**References:**

[1] N. Bianchi, S. Bolognani, D. D. Corte and F. Tonel, "Tubular linear permanent magnet motors: an overall comparison," in IEEE Transactions on Industry Applications, vol. 39, no. 2, pp. 466-475 (2003) [2] J. Wang, W. Wang and K. Atallah, "A Linear Permanent-Magnet Motor for Active Vehicle Suspension," in IEEE Transactions on Vehicular Technology, vol. 60, no. 1, pp. 55-63 (2011) [3] L. Szabo, C. Oprea, I. Viorel and K. A. Biro, "Novel Permanent Magnet Tubular Linear Generator for Wave Energy Converters," IEEE International Electric Machines & Drives Conference, pp. 983-987 (2007) [4] F. Marignetti, P. Cancelliere, and M. Scarano, “Analytical formulation of the no-load magnetic field in IPM tubular machines with translator eccentricity,” in IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics, pp. 829–835 (2006) [5] L. Cappelli, Y. Coia, F. Marignetti and Z. Q. Zhu, "Analysis of Eccentricity in Permanent-Magnet Tubular Machines," in IEEE Transactions on Industrial Electronics, vol. 61, no. 5, pp. 2208-2216 (2014) [6] D. Sarr Lo, H. Lawali Ali, Y. Amara, G. Barakat, and F. Chabour, “3D Finite Element Analysis of Eccentricity in a Tubular Linear Permanent Magnet Machine,” in 2018 XIII International Conference on Electrical Machines (ICEM), Alexandroupoli, p. 1996–2001 (2018) [7] H. Diab, Y. Amara and G. Barakat, "Comparison of Two Tubular Linear Permanent Magnet Machines with Translator Eccentricity," 2020 International Conference on Electrical Machines (ICEM), Gothenburg, pp. 612-618 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2fedcffd641e7ac4c796e19d941f5391.jpg)
Fig.1 A 3D TLPM structure divided in the tangential direction with a 2D axial cross-section view with dimensions

![](https://assets.underline.io/uploads/markdown_image/1/image/094e73a6fefce9ab02b34bf22374e05b.jpg)
Fig.2 Comparison of the cogging and attraction forces generated by the quasi-3D and 3D FEM models

 Translator Eccentricity Analysis in Tubular Linear Machines using Quasi-3D Finite Element Method Modeling

I. INTRODUCTION Ferromagnetic materials have complex nonlinear hysteresis characteristics, which play a decisive role in simulating electrical equipment's magnetic properties, such as the power loss and the magnetic remanence of the core in transformers and motors[1]. Therefore, the accurate and efficient hysteresis model is fundamental to improving the power equipment's operational efficiency. As a fast and precise hysteresis model, the Preisach model is widely used in analyzing the magnetic properties of the electromagnetic device coupled with the FEM method. However, some problems remain to exist in the current Preisach model parameter identification methods, such as the convergence speed and the accuracy need to be further improved[2,3]. To develop a more efficient parameter identification method of the Preisach model, a hybrid algorithm combining conjugate gradient method (CGM) and velocity-controlled particle swarm optimization (VCPSO) algorithm is proposed in this paper: Firstly, a one-dimensional magnetic property test system is built to measure the hysteresis loop data of B30P150 steel sheet under quasi-static conditions. Secondly, the parameters of the Preisach model with closed-form Everett function are identified based on the proposed hybrid optimizing algorithm. Finally, in the full paper, the proposed method's accuracy is discussed by comparing the convergence speed and calculation accuracy of the proposed hybrid algorithm with other single intelligent algorithms. II. THE IMPLEMENT AND IDENTIFICATION OF PREISACH MODEL A. The Preisach model based on the closed-form Everett function The traditional Preisach model is implemented by the double integral of the distribution function in the Preisach plane, which is time-consuming and inefficient. To overcome the complex parameters identification process of the traditional Preisach model, the distribution function is simplified to the product of two single-valued functions, and a numerical Preisach model based on the closed-form Everett function is established. The improved model only needs a series of basic operations and a few parameters to be identified, which implement efficiency is much improved. B. Parameters identification of the Preisach model by combing the CGM and VCPSO algorithm A hybrid intelligent algorithm based on the conjugate gradient method (CGM) and a velocity-controlled particle swarm optimization (VCPSO) algorithm is proposed to overcome the low convergence speed and easily fall into a locally optimal solution. The identification process of a hybrid algorithm is shown in Fig 1. Firstly, according to the fast optimization of the VCPSO algorithm, finding the optimal solution range of parameters. Secondly, the searching range of VCPSO is taken as the initial parameter of the conjugate gradient method. Then the optimal solution is determined by local search. Finally, the optimal parameters are obtained by CGM. The measured and simulated hysteresis loop are compared after the identification process. The efficiency of the hybrid algorithm with other single optimal identification algorithms will be discussed in the full paper. III. RESULT AND DISCUSSION The simulated and measured hysteresis loops of the B30P150 silicon steel sheet are shown in Fig 2. It can be found that the model parameters identification results can well simulate the hysteresis loop of the B30P150 silicon steel sheet. The error is due to the approximate substitution of the Everett function, and increasing the number of relevant terms of the Everett function can improve the Model accuracy. What’s more, considering the reversible and irreversible magnetization, the simulation accuracy at the model's turning point can also be improved. IV. CONCLUSION In this paper, a hybrid optimization algorithm combining a velocity-controlled particle swarm optimization algorithm and the conjugate gradient method is proposed to identify the parameters of the Preisach model. The hybrid algorithm is an effective means for parameter identification of the Preisach model and contributes to the design and upgrading of electrical equipment.

**References:**

[1]Szabo Z, Fuezi J,Journal of magnetism and magnetic materials, 406(may):251-258(2016). [2] N. Duan et al., IEEE Trans. Magn. 51, 7300904 (2015) [3]Stoleriu L, Andrei P, Journal of Applied Physics, 103(7p.3):132-134(2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fb4bc67340641cc2bfad0149fde867f8.jpg)
Fig. 1 Identification process based on the hybrid algorithm of CGM and VCPSO

![](https://assets.underline.io/uploads/markdown_image/1/image/21705d8230b4c6fc54b147f747d1730c.jpg)
Fig. 2 Comparison between the measured and the simulated hysteresis loops

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