France



I.Introduction&lt;br/&gt;Because the hybrid magnetic bearing (HMB) has the advantages of long life, high precision and low loss, the high-speed rotor supported by HMBs instead of traditional bearings can obtain higher speed and higher power. It is widely used in life science, flywheel energy storage, aerospace and other occasions [1]-[2]. According to the bias magnetic circuit, radial HMBs can be divided into homopolar HMBs and heteropolar HMBs. However, the axial length of homopolar HMB is long, which limits the critical speed of rotor. Comparing with DC 4-pole HMB and AC 3-pole HMB, the AC 6-pole HMB not only has the advantages of symmetrical structure, but also can be driven by the three-phase inverter to decrease the volume and cost. Therefore, a novel AC 6-pole HMB are proposed in this paper. Firstly, the structure and suspension mechanism of the proposed HMB are introduced. Secondly, the equivalent magnetic circuit is established. Then the main parameters of the HMB are designed. Finally, the electromagnetic simulation is carried out by software MagNet to verify the theoretical analysis.&lt;br/&gt;II.Configuration And Suspension Principle&lt;br/&gt;The proposed novel AC 6-pole HMB includes stator, permanent magnets, control coils and rotor, as shown in Fig. 1. Six permanent magnets arrange with &lt;i&gt;NS-SN-NS-SN-NS-SN, &lt;/i&gt;embedded in the stator slots of each pole, which forms heteropolar magnetic flux distributions. There are three outer air gaps under pole &lt;i&gt;A&lt;/i&gt;, &lt;i&gt;B&lt;/i&gt; and &lt;i&gt;C&lt;/i&gt;, and the air gap reluctance are noted as &lt;i&gt;R&lt;sub&gt;A&lt;/sub&gt;&lt;/i&gt;~&lt;i&gt;R&lt;sub&gt;C&lt;/sub&gt;&lt;/i&gt;. The air gap reluctance of the inner air gaps are noted as &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;~&lt;i&gt;R&lt;/i&gt;&lt;sub&gt;6&lt;/sub&gt;. The control windings, marked as &lt;i&gt;A&lt;/i&gt;, &lt;i&gt;a&lt;/i&gt;, &lt;i&gt;B&lt;/i&gt;, &lt;i&gt;b&lt;/i&gt;, &lt;i&gt;C&lt;/i&gt;, and &lt;i&gt;c&lt;/i&gt;, are wound on the poles. The solid lines denote the control flux, and the dotted lines describe the bias flux. The bias flux generated by permanent magnet starts from &lt;i&gt;N&lt;/i&gt; pole and return to &lt;i&gt;S&lt;/i&gt; pole, one passing through internal stator core, inner air gap, the other passing through internal stator core, outer air gap, stator suspension pole and external stator core. The coils of &lt;i&gt;A&lt;/i&gt; and &lt;i&gt;b&lt;/i&gt;, &lt;i&gt;B&lt;/i&gt; and &lt;i&gt;c&lt;/i&gt;, &lt;i&gt;C&lt;/i&gt; and &lt;i&gt;a&lt;/i&gt;, are respectively connected in series. Then the coils of &lt;i&gt;A&lt;/i&gt;, &lt;i&gt;B&lt;/i&gt; and &lt;i&gt;C&lt;/i&gt;, the coils of &lt;i&gt;a&lt;/i&gt;, &lt;i&gt;b&lt;/i&gt; and &lt;i&gt;c&lt;/i&gt;, are respectively connected in parallel as three phase control winding. Then, the three-phase winding is electrified by one three-phase inverter. Assume that the rotor has the displacement to the pole &lt;i&gt;b&lt;/i&gt;, the three phase symmetrical currents flow into &lt;i&gt;A&lt;/i&gt;~&lt;i&gt;c&lt;/i&gt; coils. As a result, the air gap flux density increases under the poles &lt;i&gt;A&lt;/i&gt;, &lt;i&gt;a&lt;/i&gt; and &lt;i&gt;c&lt;/i&gt;, while decreases under the poles &lt;i&gt;b&lt;/i&gt;, &lt;i&gt;B&lt;/i&gt; and &lt;i&gt;C&lt;/i&gt;. Thus, the suspension force pointing to pole &lt;i&gt;A&lt;/i&gt; will pull the rotor back to the balance position.&lt;br/&gt;III.Main Parameter Design&lt;br/&gt;The average inner air-gap length, noted as &lt;i&gt;g&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;, is 0.5mm and the outer air-gap length noted as &lt;i&gt;g&lt;sub&gt;w &lt;/sub&gt;&lt;/i&gt;is 2mm. The diameter of the rotor is 50.5mm. The outer diameter of the stator is 106 mm. The turn number of coil &lt;i&gt;A&lt;/i&gt;, &lt;i&gt;B&lt;/i&gt; and &lt;i&gt;C&lt;/i&gt; is 200T, and the turn number of coil &lt;i&gt;a&lt;/i&gt;, &lt;i&gt;b&lt;/i&gt; and &lt;i&gt;c&lt;/i&gt; is 40T. The axial length of the stator is 45mm. The equivalent magnetic circuits are analyzed.&lt;br/&gt;According to the equivalent magnetic circuit, the resultant suspension forces of the rotor in the x and y directions, are deduced as&lt;br/&gt;&lt;i&gt;F&lt;sub&gt;xmax&lt;/sub&gt;&lt;/i&gt;=(&lt;i&gt;B&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;B&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;+&lt;i&gt;B&lt;sub&gt;0&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;B&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;)&lt;i&gt;S&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;÷(2&lt;i&gt;μ&lt;sub&gt;0&lt;/sub&gt;&lt;/i&gt;)&lt;br/&gt;&lt;i&gt;F&lt;/i&gt;&lt;sub&gt;&lt;i&gt;ymax&lt;/i&gt;&lt;/sub&gt;=√3×&lt;i&gt;B&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;B&lt;sub&gt;s&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;S&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;÷(2&lt;i&gt;μ&lt;sub&gt;0&lt;/sub&gt;&lt;/i&gt;)&lt;br/&gt;where &lt;i&gt;µ&lt;sub&gt;0&lt;/sub&gt;&lt;/i&gt; is the permeability of vacuum, &lt;i&gt;B&lt;sub&gt;S &lt;/sub&gt;&lt;/i&gt;is the saturated flux density, &lt;i&gt;B&lt;sub&gt;0&lt;/sub&gt;&lt;/i&gt; is bias flux density, &lt;i&gt;S&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; is the internal pole area.&lt;br/&gt;A.Inner and Outer Air-Gap&lt;br/&gt;In order to avoid magnetic saturation, the saturation magnetic induction (&lt;i&gt;B&lt;sub&gt;S&lt;/sub&gt;&lt;/i&gt;) is 1.2&lt;i&gt;T&lt;/i&gt;, inner air gap bias flux (&lt;i&gt;B&lt;sub&gt;0&lt;/sub&gt;&lt;/i&gt;) is designed as 0.6&lt;i&gt;T&lt;/i&gt;. &lt;i&gt;R&lt;sub&gt;i&lt;/sub&gt;=R&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt; (&lt;i&gt;i&lt;/i&gt;=1,2,3,4,5,6), &lt;i&gt;R&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;=&lt;i&gt;R&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt; (&lt;i&gt;j&lt;/i&gt;=&lt;i&gt;A&lt;/i&gt;,&lt;i&gt;B&lt;/i&gt;,&lt;i&gt;C&lt;/i&gt;). According to the equivalent control magnetic circuit, the relationship of the inner and outer air-gap can be obtained&lt;br/&gt;（&lt;i&gt;g&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;÷&lt;i&gt;S&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;）×（&lt;i&gt;S&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt;÷&lt;i&gt;g&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt;）=1/4&lt;br/&gt;B.Number of Coil Turns&lt;br/&gt;According to equivalent control magnetic circuit, the relationship of the turn number of coil &lt;i&gt;A&lt;/i&gt;,&lt;i&gt;B&lt;/i&gt;,&lt;i&gt;C&lt;/i&gt;, noted as &lt;i&gt;N&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt;, and the turn number of coil &lt;i&gt;a&lt;/i&gt;,&lt;i&gt;b&lt;/i&gt;,&lt;i&gt;c&lt;/i&gt;, noted as &lt;i&gt;N&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;, as described by&lt;br/&gt;&lt;i&gt;N&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt;:&lt;i&gt;N&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;=5:1&lt;br/&gt;IV.Finite Element Analysis&lt;br/&gt;The analysis model is established by MagNet 3D. Fig. 2(a) presents the permanent magnetic static bias flux density distribution in the bearing. Fig. 2(b) shows the control flux in produced by coil &lt;i&gt;A&lt;/i&gt;, &lt;i&gt;B&lt;/i&gt; and &lt;i&gt;C&lt;/i&gt;. Fig. 2(c) shows the control flux in produced by coil &lt;i&gt;a&lt;/i&gt;, &lt;i&gt;b&lt;/i&gt; and &lt;i&gt;c&lt;/i&gt;. And the corresponding resultant flux is shown in Fig. 2(d). Fig. 2(e) shows the maximum suspension force can be obtained in +&lt;i&gt;x&lt;/i&gt; direction, while the force in y direction is close to zero, which shows a good linearity. And the theoretical value is consistent with the calculated value.&lt;br/&gt;V.Conclusions&lt;br/&gt;In this paper, the novel AC 6-pole HMB is proposed and designed. The structure and suspension mechanism are analyzed. The magnetic circuits are presented. According to the main design parameters, the analysis model is established by MagNet 3D. Then, the electromagnetic performances of the novel AC 6-pole HMB are researched. The simulation results have shown that correctness of the structure, magnetic circuit and mathematical models.

**References:**

[1]T. Schuhmann, W. Hofmann, and R. Werner, “Improving operational performance of active magnetic bearings using Kalman filter and state feedback control,” IEEE Transactions on Industrial Electronics, vol. 59, no. 2, pp. 821–829, 2012&lt;br/&gt;[2]H. Q. Zhu, Y. X. Shen, and Q. H. Wu, “Modeling and control system for AC hybrid magnetic bearing,” Proceedings of the CSEE, vol 29, no. 18, pp. 100-105, 2009.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/097c5a7e789b66006b6a10abe26e9bdb.jpg)
Fig. 1. Structure of novel AC 6-pole RHMB: 1-external stator core, 2-control windings, 3-permanent magnet, 4-internal stator core, 5-inner air gap, 6-shaft, 7-rotor core, 8-outer air gap, 9-stator suspension teeth, 10-bias flux, 11-control flux.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc12d4bb225c2275b30260c6a68ec5e2.jpg)
Flux distributions and the force-current relationships

INTERMAG 2021

 Electromagnetic Analysis of a Novel AC Six-Pole Hybrid Magnetic Bearing

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I.Introduction Because the hybrid magnetic bearing (HMB) has the advantages of long life, high precision and low loss, the high-speed rotor supported by HMBs instead of traditional bearings can obtain higher speed and higher power. It is widely used in life science, flywheel energy storage, aerospace and other occasions [1]-[2]. According to the bias magnetic circuit, radial HMBs can be divided into homopolar HMBs and heteropolar HMBs. However, the axial length of homopolar HMB is long, which limits the critical speed of rotor. Comparing with DC 4-pole HMB and AC 3-pole HMB, the AC 6-pole HMB not only has the advantages of symmetrical structure, but also can be driven by the three-phase inverter to decrease the volume and cost. Therefore, a novel AC 6-pole HMB are proposed in this paper. Firstly, the structure and suspension mechanism of the proposed HMB are introduced. Secondly, the equivalent magnetic circuit is established. Then the main parameters of the HMB are designed. Finally, the electromagnetic simulation is carried out by software MagNet to verify the theoretical analysis. II.Configuration And Suspension Principle The proposed novel AC 6-pole HMB includes stator, permanent magnets, control coils and rotor, as shown in Fig. 1. Six permanent magnets arrange with NS-SN-NS-SN-NS-SN, embedded in the stator slots of each pole, which forms heteropolar magnetic flux distributions. There are three outer air gaps under pole A, B and C, and the air gap reluctance are noted as RA~RC. The air gap reluctance of the inner air gaps are noted as R1~R6. The control windings, marked as A, a, B, b, C, and c, are wound on the poles. The solid lines denote the control flux, and the dotted lines describe the bias flux. The bias flux generated by permanent magnet starts from N pole and return to S pole, one passing through internal stator core, inner air gap, the other passing through internal stator core, outer air gap, stator suspension pole and external stator core. The coils of A and b, B and c, C and a, are respectively connected in series. Then the coils of A, B and C, the coils of a, b and c, are respectively connected in parallel as three phase control winding. Then, the three-phase winding is electrified by one three-phase inverter. Assume that the rotor has the displacement to the pole b, the three phase symmetrical currents flow into A~c coils. As a result, the air gap flux density increases under the poles A, a and c, while decreases under the poles b, B and C. Thus, the suspension force pointing to pole A will pull the rotor back to the balance position. III.Main Parameter Design The average inner air-gap length, noted as gn, is 0.5mm and the outer air-gap length noted as gw is 2mm. The diameter of the rotor is 50.5mm. The outer diameter of the stator is 106 mm. The turn number of coil A, B and C is 200T, and the turn number of coil a, b and c is 40T. The axial length of the stator is 45mm. The equivalent magnetic circuits are analyzed. According to the equivalent magnetic circuit, the resultant suspension forces of the rotor in the x and y directions, are deduced as Fxmax=(Bs×Bs+B0×Bs)Sn÷(2μ0) Fymax=√3×Bs×Bs×Sn÷(2μ0) where µ0 is the permeability of vacuum, BS is the saturated flux density, B0 is bias flux density, Sn is the internal pole area. A.Inner and Outer Air-Gap In order to avoid magnetic saturation, the saturation magnetic induction (BS) is 1.2T, inner air gap bias flux (B0) is designed as 0.6T. Ri=Rn (i=1,2,3,4,5,6), Rj=Rw (j=A,B,C). According to the equivalent control magnetic circuit, the relationship of the inner and outer air-gap can be obtained （gn÷Sn）×（Sw÷gw）=1/4 B.Number of Coil Turns According to equivalent control magnetic circuit, the relationship of the turn number of coil A,B,C, noted as Nw, and the turn number of coil a,b,c, noted as Nn, as described by Nw:Nn=5:1 IV.Finite Element Analysis The analysis model is established by MagNet 3D. Fig. 2(a) presents the permanent magnetic static bias flux density distribution in the bearing. Fig. 2(b) shows the control flux in produced by coil A, B and C. Fig. 2(c) shows the control flux in produced by coil a, b and c. And the corresponding resultant flux is shown in Fig. 2(d). Fig. 2(e) shows the maximum suspension force can be obtained in +x direction, while the force in y direction is close to zero, which shows a good linearity. And the theoretical value is consistent with the calculated value. V.Conclusions In this paper, the novel AC 6-pole HMB is proposed and designed. The structure and suspension mechanism are analyzed. The magnetic circuits are presented. According to the main design parameters, the analysis model is established by MagNet 3D. Then, the electromagnetic performances of the novel AC 6-pole HMB are researched. The simulation results have shown that correctness of the structure, magnetic circuit and mathematical models.

**References:**

[1]T. Schuhmann, W. Hofmann, and R. Werner, “Improving operational performance of active magnetic bearings using Kalman filter and state feedback control,” IEEE Transactions on Industrial Electronics, vol. 59, no. 2, pp. 821–829, 2012 [2]H. Q. Zhu, Y. X. Shen, and Q. H. Wu, “Modeling and control system for AC hybrid magnetic bearing,” Proceedings of the CSEE, vol 29, no. 18, pp. 100-105, 2009.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/097c5a7e789b66006b6a10abe26e9bdb.jpg)
Fig. 1. Structure of novel AC 6-pole RHMB: 1-external stator core, 2-control windings, 3-permanent magnet, 4-internal stator core, 5-inner air gap, 6-shaft, 7-rotor core, 8-outer air gap, 9-stator suspension teeth, 10-bias flux, 11-control flux.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc12d4bb225c2275b30260c6a68ec5e2.jpg)
Flux distributions and the force-current relationships

poster

In order to study the electromagnetic and vibration performance of transformer under different tensile and compressive stresses.This paper firstly studies the magnetic properties of core silicon steel sheets for transformers under different tensile and compressive stresses,the B-H curves, B-P curves, and permeability curves of silicon steel sheets under different tensile and compressive stresses are given.Secondly, based on the test results of magnetic characteristics of the silicon steel sheet, the electromagnetic performance and vibration of a 3kVA transformer are simulated and analyzed. In the simulation process, the influence of different tensile and compressive stresses on the performance of the silicon steel sheet core of the transformer is considered. It provides a new idea for the electromagnetic-vibration analysis of transformers. 1 Introduction The magnetostrictive property of silicon steel sheet is the main reason for the vibration and noise of electrical equipment such as transformers and reactors, and its characteristics are particularly sensitive to the mechanical stress[1].Based on the analysis of the mechanism of core vibration noise and experimental verification, the influence of magnetic properties and magnetostrictive effect of electrical steel sheet on the performance of power transformer under different stress is studied. This paper, by using a magnetostriction stress effect of the magnetic properties of measuring equipment and measuring instrument system, on oriented silicon steel (brand: 27 sqgd090) along the rolling direction under different tension and compression stress and magnetic properties of magnetostrictive properties were tested and the research of silicon steel sheet under different tension and compression stress are given B-H curve, B-P curve and permeability curve and curve of single value, as shown in figure 1 flow chart of research.Secondly, based on the above-mentioned measurement results, the model material library was established. Based on the finite element analysis software COMSOL, the finite element analysis was carried out on a 3KVA transformer under different tensile and compression stress conditions.Finally, an experimental study is carried out to verify the correctness of the proposed scheme, which provides a reference for the study of power transformer vibration noise under different tension and compression stresses. 2 Simulation study of power transformer under different stresses The results obtained by substituting the magnetic characteristic curves in Fig. 1 into the transformer FEM model considering the boundary conditions are shown in Fig. 2. The compressive stress increases the magnetostriction, while the tensile stress reduces the magnetostriction, magnetostriction is particularly sensitive to the compressive stress. The stress reduces the magnetic conductivity of electrical steel sheet.When there is no external force,the maximum magnetic density reaches 1.7T. 3 conclusion In this paper, the magnetic characteristics and magnetostrictive characteristics of silicon steel sheet are measured firstly, and then the electromagnetic and vibration characteristics of power transformer under different stresses are studied by using finite element analysis software.The results show that the compressive stress increases the magnetostriction, and the tensile stress decreases the magnetostriction, and the compressive stress is especially obvious.Detailed test results and simulation analysis will be shown in the full text.

**References:**

Anderson P I, Moses A J, Stanbury H J. An automated system for the measurement of magnetostriction in electrical steel sheet under applied stress [J]. Journal of Magnetism and Magnetic Materials, 2000, 215: 714-716.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8573aa5ce5a099e60e45effcfc62de79.jpg)
Fig.1 Reserch process flowchart

![](https://assets.underline.io/uploads/markdown_image/1/image/eda33ec72433e01bb513537c5910d8c6.jpg)
Fig.2 Simulation result

 Study of Electromagnetic Characteristics of Silicon Steel Sheet and Transformer Vibration Under Different Tension/Compression Stress

To improve the thermal stability, reduce vibration/noise and system cost of mediate frequency transformers for DC-DC converters in low-voltage DC distribution networks. This paper presents a design study of a 20kW three-winding medium frequency transformer using 0.15mm oriented silicon steel sheet. First, the magnetic properties of silicon steel wafers at different frequencies were measured based on a single silicon steel wafer magnetic property measurement system, and the B-H curve, B-P curve and excitation curve at different frequencies were given. Next, a three-winding mediate frequency transformer with 537V input and 375V and 48V output is designed using particle swarm algorithm with loss minimization as the optimization objective, and finite element simulation and magnetic performance experiments are conducted. The flux density, loss and temperature field distribution curves of mediate frequency transformers under different operating conditions, and B-H curves, hysteresis lines and B-P curves at different frequencies are given. Finally, the experimental platform of DC-DC converter is built and its characteristics under different load conditions (no-load, rated load and overload) are experimentally studied to verify the correctness of the proposed scheme. 1. Introduction Compared with AC distribution networks, DC distribution networks have significant advantages in terms of distributed energy access, improving system efficiency, reducing line losses and operating costs, and increasing system capacity. As one of the main links of the DC distribution network, the bi-directional full-bridge converter (power electronic transformer), through the introduction of power electronic converters on the primary and secondary sides of the primary and secondary side of the voltage amplitude and phase of real-time digital control, compared to the traditional power transformer, power electronic transformer can be more accurate, flexible, stable and reliable regulation of the output side voltage[1]. As shown in Fig. 1(a), the mediate frequency transformer, as an important component of the bi-directional DC-DC converter, has an important impact on the size, weight, loss, and price of the power electronics transformer[2]. This paper takes low-voltage DC distribution network as the application background, converts PV power generation into DC 375V and DC 48V through DC-DC converter, and directly enters the home to supply power for TV sets, refrigerators, washing machines, lighting, etc. in the home, eliminating the loss generated by the AC-DC link and saving energy significantly. Fig. 1(b) shows the technical roadmap of this paper. Firstly, the topology of power electronic transformer is analyzed and bi-directional CLLLC resonant converter topology is adopted. Secondly, the magnetic characteristics of 0.15mm electrical steel sheet are tested to lay the foundation for the subsequent design, performance analysis and prototype development of mediate frequency transformer. Then, the design study of mediate frequency transformer is carried out, and one three-port mediate frequency transformer is designed based on particle swarm optimization algorithm with loss minimization as the goal, and finite element analysis is carried out. Finally, a power electronic transformer is fabricated and experiments under no-load, load and overload are completed to verify the correctness of the proposed scheme. 2. Simulation and Experiment on the Medium Frequency Transformers Fig. 1 (c) shows the design process of the three-port mediate frequency transformer proposed in this article; Fig. 1 (d) shows the optimization flow chart of the mediate frequency transformer; Fig. 1(e) shows the 0.15mm electrical steel sheet test platform and test results; Fig. 1(f) shows the magnetic flux density, loss and temperature field distribution of the mediate frequency transformer. It can be seen from Fig. 1 that the medium frequency transformer has a flux density of 0.5T, core loss of 137W, copper consumption of 123W, and an average temperature of 84.4°C at rated load. The design scheme meets the system requirements. 3. Conclusion This paper has carried out systematic research work on power electronic transformers in low-voltage DC distribution networks. Based on the monolithic silicon steel wafer measurement system, the test work of magnetic characteristics of silicon steel wafers at different frequencies was completed. A 537V/375V/48V three-port mediate frequency transformer was designed with the goal of loss minimization. A three-dimensional finite element model with electromagnetic-temperature field coupling was established to analyze the magnetic properties and temperature characteristics of the mediate frequency transformer under different operating conditions, which provides guidance for the design of the mediate frequency transformer. Detailed experimental results and comparisons are shown in the full paper.

**References:**

[1] T. F. Wu, C. H. Chang, L. C. Lin. DC-Bus Voltage Control With a Three-Phase Bidirectional Inverter for DC Distribution Systems[J]. IEEE Transactions on Power Electronics, 2013, 28(4):1890-1899. [2] Posada Contreras J, Ramirez J M. Multi-Fed Power Electronic Transformer for Use in Modern Distribution Systems[J]. IEEE Transactions on Smart Grid, 2014, 5(3):1532-1541.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f50c2eae56786038dee6f506d77234cd.jpg)

 Study of Magnetic Properties of Ultra-thin Silicon Steel Sheet and Medium Frequency Transformer

This paper investigates and optimizes processes on the influencing of the magnetic shunts design to reduce the generated losses and temperature in power transformers are done. An 3D FEM model is established based on the OSFPSZ-200000/230 power transformer, considering the influence of magnetic flux leakage distribution with different shielding structure. Calculation and experiment of loss and temperature of power transformer are supplied to obtain the optimal shield structure, which are required for safe operation. Finally, the simulation results of the loss and temperature of the three-phase power transformer verified by the experimental results under the different shielding structure. 1Introduction Magnetic shielding is generally laid on the transformer tank and clamps to reduce the eddy current loss, which can prevent overheating. However, the leakage flux will be concentrated, if the design of the magnetic leakage shielding structure is unreasonable.Thus, it is necessary to analyze the the best geometrical size and electrical, magnetic, thermal, and mechanical considering different shielding structures effect. [1] is proposed that the the tank magnetic shields can reduce stray losses of structural parts, and horizontal shunts are as effective as vertical shunts in reducing stray load losses. However, he did not consider the effect of yoke shielding on the magnetic flux leakage distribution. Whereas, In [2], it is presented an application of yoke shunts to control the leakage flux on a case study transformer. However, the structure of yoke shielding is not reasonable, which results in the waste of materials. The effect of yoke shielding on the magnetic flux distribution at the end of the winding is not considered. In [3] a transient FEM analysis was used to optimize the magnetic shunts for minimum eddy current loss and temperature rise, considering different taps of the windings, without relevant experimental data to verify the theoretical analysis. This paper investigates the effects of different shielding structures on power transformer losses and temperature by theory analysis and experiment verification. As in the research flowchart of Fig.1, the shielding structure is optimized by analyzing the distribution of magnetic flux leakage and the distribution of magnetic flux leakage at the winding ends.Then based on the requirements of the IEC standard, the FEM model considering shielding structure is completed to judge whether the loss and temperature rise of the structural parts meet the requirements. If not, modify the shielding structure and perform FEM analysis again until the loss and temperature rise meet the requirements of the IEC standard. and modified for better performance.Simulation results of distribution of power transformer loss and hot spot are shown in Table 1, where the experimental results of the three-phase power transformer also lists to verify the simulation results. 2Simulation and experiment on power transformers with different shielded structures Established 3D model and shielding structure are shown in Figure 1-I. Divided four types shielding structure are shown in Figure 1. Calculated the leakage flux distribution of the transformer and winding with different shielding structures. The results are shown in Figure 1-II and Table 1. It shows that the improved structure of the shielding can effectively reduce the leakage flux into the structural parts(tank, lamp, pull plate), which can minish the loss of the structural parts, thus mitigating the extent of local overheating. Adding the lung magnetic shields can particularly effective influence the loss of structural parts. When the tank adopts magnetic shielding, it can significantly reduce the leakage flux into the tank. 3Conclusion This paper investigates the losse and temperature of power transformers considering the different shielding structures. The coupled 3D-FEM model in electromagnetic-temperature field is established based on OSFPSZ-200000/230 power transformer. The leakage flux distribution of the transformer and winding analyzed, which provides guidance for the usual transformers magnetic shielding design. It shows that the temperature simulation is in a reasonable agreement with the experimental (error=4.8%), verifying the validity of the proposed method. Detailed experimental results and comparison will be shown in the full paper.

**References:**

[1] M. Moghaddami, A. I. Sarwat, and F. de Leon. Reduction of Stray Loss in Power Transformers Using Horizontal Magnetic Wall Shunts, DOI 10.1109/TMAG.2016.2611479, IEEE Trans. Magn., 2016. [2] Leonardo Štrac, Three-Phase Shunts for Stray Magnetic Field, Procedia Engineering 202, pp. 183–188, 2017. [3] H. Yang and Y. Zhang, Analysis on the magnetic shunt structure of large power transformer, IET Generation, Transmission & Distribution, vol. 12, no. 11, pp. 2755-2761, 2018. (doi: 10.1049/iet-gtd.2017.1490)

**Images:**
![](https://assets.underline.io/uploads/markdown_image/1/image/a7e7b14642c7dfbc4734dbd6f169ea6f.jpg)

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 Study of Loss and Temperature Considering Different Shielding Structure in Power Transformer

How to effective control losses of large power transformer, such as tank and structural parts, shielding and others, which is significant to reduce the manufacturing cost of power transformer and the safety of network operation. Based above, this paper investigated on the structural parts (pull plates, clamps and others) loss of power transformer with analytical and experimental method under different harmonic conditions. First, measured the B-H, B-P and permeability curves of different materials (silicon steel sheet, non-magnetic steel and steel) under different frequencies. Second, established the loss calculation model of power transformer based on analytical method; at the same time, calculated the losses of the structural parts under different shields with the finite element method. Finally, an experimental study is carried out to verify the correctness of the proposed simulation results. 1 Introduction Due to the increasing of the capacity of power transformer, the leakage magnetic field and the effect of the stray loss caused in the tank and structural parts have increased significantly. It is contrary to the national policy of "energy saving priority" for sustainable development. Therefore, it has great potential for energy saving by reducing structural parts loss. So, it is significance for analysising the leakage magnetic field, eddy current loss and temperature field of the tank and the internal structural parts of transformer deeply and accurately. At present, domestic and foreign scholars have carried out extensive research work on electrical steel sheets for electromagnetic devices. In reference [1], the magnetic properties of oriented silicon steel sheets under different temperature and harmonic conditions were tested. The magnetic properties of electrical steel sheet for transformer are studied in reference [2,3]. In [4], the horizontal mounted tank magnetic shunts were proposed to reduce stray losses in power transformers. But there is no comparative analysis of different shielding structures. In [5] a transient FEM analysis was used to optimize the magnetic shunts for minimum eddy current loss and temperature rise, considering different taps of the windings, without relevant experimental data to verify the theoretical analysis. This paper investigates the loss of structural parts with different structures and materials under different shielding structures, through theoretical analysis and experimental verification. As shown in Figure 1, first, measured the B-H, B-P and permeability curves of different materials under different frequencies. Second, designed structural parts and shielding structure, then optimize the shielding structure by analyzing the distribution of magnetic flux leakage, adopt 3-D FEM analysis and analytical method to calculate the loss and temperature of the power transformer, then judge the loss and temperature rise of the structure based on the requirements of the IEC standard. If not, the shielding structure is modified, and do it again until the loss and temperature rise meet the requirements. Finally, an experimental study is carried out to verify the correctness of the proposed simulation results. The simulation results of power transformer loss distribution and hot spot distribution are shown in Table 1, which also lists the experimental results of the three-phase power transformer. 2 Simulation and experiment on the loss of power transformer Substitute the data of B-H and B-P curves from Fig.1 (a) into the FEM model of transformer in Fig.1 (c) considering different shielding condition, then the results can be obtained as in Table 1 and Fig.1 (c). It can be seen from Fig.1 (a) results that when the harmonic content is a constant, with the increase of the harmonic power, the magnetic permeability of the silicon steel sheet will gradually decrease, and the loss will gradually increase obviously. It can be seen from Fig.1 (c) the calculation results: 1) In the case of each shielding structure, the total loss with clamps and pull plates is higher than without them, but the structural loss of tank is the opposite. So, it is difficult to directly measure the stray loss, and it is also difficult to accurately separate the loss on the component from the total loss. 2) With the addition of body shielding, the total loss of structural parts will be reduced by 17.1%-21%, so a reasonable arrangement of the shielding structure will effectively reduce structural parts loss and hot spot temperature rise. 3) Whether to use magnetic shielding, it is still necessary to consider the increase in magnetic shielding loss and the decrease in tank loss, as well as the shielding material and size. Specific comparison data will be given in the full text. 4) The magnetic shielding effect of tank is better than the copper shielding. 3 Conclusion This paper investigates the losses of transformer structural parts (pull plates, clamps and others) considering the different structural parts, materials and shielding structures from two methods (FEM and analytical). The coupled 3D-FEM model in electromagnetic- temperature field is established based on SZ-50000/110 model. The structural losses calculation results of FEM method, analytical method and experimental results are compared and analyzed, which provides guidance for the usual transformers design. It shows that the loss simulation is in a reasonable agreement with the experimental one (error=5.9% ,error &lt;7K), verifying the validity of the proposed method. Detailed experimental results and comparison will be shown in the full paper.

**References:**

[1]Chen D., Fang L., Kwon B I., et al: Measurement research on magnetic properties of electrical sheet steel under different temperature, harmonic and dc bias. AIP Advances, 7.5 (2017), 056682. [2]Oda, Yoshihiko, M. Kohno, and A. Honda: Recent development of non-oriented electrical steel sheet for automobile electrical devices. Journal of Magnetism & Magnetic Materials, 320.20 (2008), 2430-2435. [3]Freitag, C, C. Joost, and T. Leibfried: Modified Epstein frame for measuring electrical steel under transformer like conditions. International Conference on High Voltage Engineering & Application, (2014), 1-4. [4]M. Moghaddami, A. I. Sarwat, and F. de Leon, "Reduction of Stray Loss in Power Transformers Using Horizontal Magnetic Wall Shunts", DOI 10.1109/TMAG.2016.2611479, IEEE Trans. Magn. 2016 [5]H. Yang and Y. Zhang, "Analysis on the magnetic shunt structure of large power transformer", IET Generation, Transmission & Distribution, vol. 12, no. 11, pp. 2755-2761, 2018.

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 Research on Structure Loss Separation of Power Transformer

I. INTRODUCTION The Maglev train have aroused worldwide research efforts due to numerous advantages over the conventional wheel-on-rail system, such as less maintenance costs, lower noise and vibration, higher grades and curves and so on [1-3]. There are two types of levitation technologies:1) electromagnetic suspension; 2) electrodynamic suspension; The EDS system is based on a repulsive force of magnets. Therefore, EDS, which is highly suitable for high-speed operation and freight, is so stable magnetically that it is unnecessary to control the air gap. Because of its significant advantages of high speed, large levitation gap and no need for any active control, the EDS train has attracted a wide research [4-5]. However, this system needs sufficient speed to acquire enough induced currents for levitation and so, a wheel like a rubber tire is used below a certain speed (around 100 km/h). This paper proposes a new EDS MAGLEV scheme which needs no auxiliary wheels. II. MACHINE TOPOLOGIES The configuration of the EDS maglev system is shown in Fig. 1(a). The main structure of this maglev system includes one mover (primary) and one stator (secondary). In order to increase the thrust density as possible, a novel Traveling Magnetic Electromagnetic Halbach Array (TMEHA) was proposed to the EDS maglev as the primary windings, of which is composed of three-phase windings. Three phase coils are displaced symmetrically at every 120 electrical angle and the current waveform in the phases is a 120 wave. Each phase winding consists of two coils and the coils are divided into two general arrangements, i.e., vertical-piece and horizontal-piece arrangements. The vertical-piece arrangement is spatially displaced by 90 electrical angle from horizontal-piece arrangements. The TMEHA, of which has inherent self-shielding property shown as in Fig. 1(b), have ability for creating magnetic flux enhanced on one side (strong side) of the array while the flux cancelled on the other side (weak side). By placing the windings as Traveling Magnetic Electromagnetic Halbach Array, the higher flux density and more sinusoidal magnetic Field in the air-gap (strong side) can get as possible than rectangular coil forms, so that the thrust density is increased and ripple decreased. Therefore, the proposed TMEHA is suitable for the future ultra-high-speed transportations because of high thrust density and low ripple. The secondary made of Aluminum or copper facing the primary windings embedded in ground. Different geometric of the winding will generate different air gap magnetic and influence the performance of the EDS maglev system. The vertical-piece and horizontal-piece arrangements in TMEHA can be utilized in a few different manners. The arrangements options focusing on the offset, shown as in Fig. 1(c), between the vertical-piece and horizontal-piece are investigated in full paper in detail. III. RESULTS AND VALIDATION By using an improved analytical method and the 2-dimensional finite element analysis (2D-FEA), the dimensional parameter optimization design of the proposed EDS maglev system is conducted, and the performance comparison with a conventional primary with core is also carried out to prove the TMEHA superiority of the proposed design (not shown here due to space limits). Finally, a prototype is fabricated for experimental testing, shown as in Fig.2(a), and the measured results are in good agreement with the FEA and analytical method, shown as in Fig.2(b), which verifies the validity of the proposed EDS maglev system topology and its theoretical flux-regulation principle analysis. More results will be present in the full paper.

**References:**

[1]K. Dong-Hun, L. Ji-Kwang, H. Song-Yop , IEEE Trans. Magn., vol. 32, no. 5, pp. 5151-5153, 1996. [2] J. Z. Bird, 2019 12th International Symposium on Linear Drives for Industry Applications (LDIA), ,pp. 1-6,1-3 July 2019 2019. [3]T. Gong, G. Ma, Y. Cai , IEEE Transactions on Applied Superconductivity, vol. 29, no. 5, pp. 1-6, 2019. [4] T. Fujimoto, M. Aiba, T. Umeki, H. Suzuki, and S. Nakamura, J-STAGE Quarterly Report ofRTRI, vol. 41, no. 2, pp. 63–67, 2000. [5] K. Kuwano et al., IEEE Trans. Appl. Supercond., vol. 17, no. 2, pp. 2125–2128, 2007.

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![](https://assets.underline.io/uploads/markdown_image/1/image/85255256870b85c1c017ac8ac93f9124.jpg)
Fig.1 Proposed EDS maglev system configuration

![](https://assets.underline.io/uploads/markdown_image/1/image/60d531dde4ec4b17fc79918875ea50e5.jpg)
Fig.2 Proposed EDS maglev system prototype and part of results.

 New Levitation Scheme with Traveling Magnetic Electromagnetic Halbach for EDS MAGLEV System

I. Introduction Magnetic levitation technologies are widely used in many fields, such as the electromagnetic bearings in high-speed compressor, the maglev in transportation, and the magnetic levitation planar motor in ultra-precision positioning systems. In addition, there are also potential application for magnetic levitation technology in some special fields [1-6]. For instance, the passive magnetic force between permanent magnets could be used to compensate the gravity of the large optical loads to achieve the ground test. Compared with the air bearings or air springs, the magnetic levitation gravity compensator (MLGC) can realize multiple degrees of freedom and vacuum compatibility. Furthermore, the complex air supply system can be removed. According to Earnshaw's theorem, the stable levitation state cannot be realized only with permanent magnets. Therefore, the non-contact actuators are required to achieve the active control. Generally, a constant passive levitation force within effective stroke is expected in order to reduce the active force level and the volume of the actuators. In this paper, a large-load magnetic levitation gravity compensator with two-dimensional permanent magnet array is analyzed in aspects of levitation force and lateral force. II. Topology and Model The large-load MLGC composed of three two-dimensional permanent magnet arrays. The middle PM array is the mover. The top PM array and bottom PM array are the stator. The mover is attracted by the top stator and repelled by the bottom stator, so a levitation force can be generated to compensate the load mass [7]. Each PM array are composed of 36 pieces of cuboid PM distributed in a checkerboard pattern. Basically, the passive force between two cuboid PM can be calculated using the magnetic charge model [8-9] or the equivalent current model. However, the relative permeability in both two classical models is assumed to 1.0, which causes a negligible error for MLGC. In [10], the actual working point of PM in magnetic spring is considered, using which the accurate model of the large-load MLGC can be built. III. Levitation Force and Lateral Force Analysis In this section, the influence of the parameters on the levitation force level and levitation force variation are analyzed based on the model and FEM. The levitation force level of the large-load MLGC is determined by some structural parameters. Compared with the PM thickness and pole arc coefficient, the pole pitch and air gap length are two critical parameters to decide the levitation force level. When the structural parameters are selected, the levitation force with different vertical and lateral displacement are analyzed. The maximum and minimum levitation force within 2mm vertical displacement is 17282N and 17155N. The maximum and minimum levitation force within 2mm lateral displacement is 17155N and 17108N. The change rate of levitation force is less than 1%. Additionally, the value of the lateral force is also very low. However, it should be noted that the lateral force increases with the increase of the vertical displacement. The maximum lateral force is 102N within 2mm lateral displacement when the vertical displacement is 1mm. IV. Experiment To verify the accuracy of the model and the correctness of the related analysis, a prototype of the large-load MLGC is manufactured. In order to maintain the relative position of the PM in each layer, all of the PM are inserted into the slots of aluminum plates. As shown in Fig. 1, the testing platform consists of base plate, adjusting bolts, multimeter, load sensor, sensor transmitter and power supply, in which the adjusting bolts are used to change the vertical displacement of the large-load MLGC. The measurement range of the load sensor is 25000N. To improve test accuracy, the components on the test platform should be made of non-magnetic materials as many as possible. As shown in Fig. 2, the levitation force increases with the vertical displacement, and the test value of the levitation force in the center position is 16860N. the error between the experiment and FEM is less than 2%. The levitation force variation within 2mm vertical displacement is 1.2%. V. Conclusion In this paper, a large-load magnetic levitation gravity compensator is analyzed and tested. To achieve a high levitation force, the 2-D permanent magnet array are used. To reduce the levitation force variation, the double-sided stator is applied. The ultimate load capacity of the prototype is 16860N (i.e., 1720kg). The testing results match well with the 3D FEM.

**References:**

[1] W. Robertson, B. Cazzolato, and A. Zander, IEEE Trans. Magn., vol. 41, no. 10, pp. 3826–3828, Oct. 2005. [2] S. A. J. Hol, E. Lomonova, and A. J. A. Vandenput, Precision Eng., vol. 30, no. 3, pp. 265–273, Jul. 2006. [3] H. Zhang, B. Kou, Y. Jin, IEEE Trans. Magn., vol. 50, no. 11, pp. 8001304, Nov. 2014. [4] H. Zhang, B. Kou, Y. Jin, IEEE Trans. Ind. Electron., vol. 62, no. 6, pp. 3629–3639, Jun. 2015. [5] J. L. G. Janssen, J. J. H. Paulides, J. C. Compter, IEEE Trans. Magn., vol. 46, no. 6, pp. 1748–1751, Jun. 2010. [6] J. L. G. Janssen, J.J.H. Paulides, E.A. Lomonova, Mechatronics, vol. 23, no. 2, pp. 197–203, Mar. 2013. [7] H. Zhang, B. Kou, Y. Zhou, ICEMS Conference, Harbin, 2019. [8] M. F. J. Kremers, J. J. H. Paulides, E. Ilhan, IEEE Trans. Magn., vol. 49, no. 5, pp. 2299–2302, May. 2013. [9] J. M. M. Rovers, J. W. Jansen, and E. A. Lomonova, IEEE Trans. Magn., vol. 49, no. 6, pp. 2913–2919, Jun. 2013. [10] H. Zhang, B. Kou, L. Zhou, IEEE Trans. Magn., Early Access, Nov. 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/209811bf033f963c8dd3b7346836ea51.jpg)
Fig. 1. Prototype and testing device of the large-load MLGC.

![](https://assets.underline.io/uploads/markdown_image/1/image/c5dbf3d448797cf80632581b8102876d.jpg)
Fig. 2. Comparison of the levitation force characteristic curves.

 Levitation Force and Lateral Force Analysis of a Large-Load Magnetic Levitation Gravity Compensator with Two-Dimensional Permanent Magnet Array.

I.Introduction Magnetic bearing (MB) is a new support bearing, which can suspend a rotor in the space by magnetic forces without machinery contact between the rotor and the stator. It has the advantages of no-friction, no-abrasion, high precision of rotor position, support high speed rotor, no-lubricant. The MBs have a wide application prospect in the fields of energy, transportation, machinery, life science. At present, the permanent magnet in hybrid magnetic bearings (HMBs) is adopted to produce the bias magnetic field, which saves the energy, reduces the size and improves the bearing capacity.However, the structure of the traditional HMBs is single-rotor or single-stator, and the radial suspension force is only produced on the inner or outer of the rotor. It leads to the low suspension force density, which makes it difficult to satisfy the performance requirements of some special applications. Therefore, the aim of this work is the investigation of a novel double-stator hybrid magnetic bearing to solve this drawback. This DSHMB consists of an inner stator and an outer stator, which are designed to share the same rotor. It has the compact structure and can decrease the power consumption. In addition, the control windings are wound on the outer stator and the inner stator so that it can reduce the axial length and increase the radial bearing capacity. The model of proposed DSHMB is constructed and analyzed by the method of equivalent magnetic circuit. Then, the air-gap magnetic fields and radial suspension forces are analyzed through 3-D finite element analysis (FDA). The research results prove the correctness of the structure and suspension principle of this novel DSHMB. II.Configuration and Suspension Principle Fig.1 shows the configuration of the proposed DSHMB which consists of double stator cores, two axial magnetized permanent magnets (PMs) and a rotor core. Each stator core has four stator poles. The inner stator and the outer stator place the relative position. The rotor core is separated into two blocks by the nonmagnetic material between double stator cores. Two PMs are located between two outer and inner stator cores. Two PMs have opposite magnetization directions. Radial control windings are wound on the inner and outer stator poles. The magnetic circuit of the static bias flux and radial suspension control flux is shown in Fig.1. The static bias flux is generated by the magnetized permanent magnet ring, and the radial suspension control flux is generated by radial control coils. The static bias flux and the control flux are superimposed or subtracted in each air gap. When the rotor suspends stably, the rotor locates in the center under the action of the static magnetic suction produced by permanent magnet. Based on the equivalent magnetic circuit analysis, the mathematical models of suspension force are deduced. The radial suspension force can be written as Fj=kj×j+kij×ij(1) where the subscript “j” denotes x and y. kj is the radial force-displacement stiffness. kij is the radial force-current stiffness. kj and kij can be given as kj=Fm×Fm×μ0×Si×So÷[2g(Si+So)×(Si+So)] kij=Fm×μ0(NiSi+NoSo)÷[g2(Si+So)] where Fm is the magnetic potential of permanent magnets. μ0 is vacuum permeability. S0 is the outer pole face area. Si is the inner pole face area. g is the average length of inner and outer air-gap. radial air gap length. Ni is number of inner radial control coils. No is number of outer radial control coils. III.Models, Design and Analysis According to the 3D model, the distribution of the flux in different cases is obtained by finite element analysis. Fig.2 (a) shows the bias flux distribution. The magnetic flux is symmetrical in the radial direction, and the permanent magnetic induction of each air gap is equal. Fig.2 (b) shows the magnetic density diagram generated only by the control current in the X direction. The excitation current of 3 A is applied to the radial control winding according to the design result. As can be seen from Fig.2 (c), the resultant magnetic density diagram is generated by the control current in the X direction and the permanent magnet ring. The control flux and the bias flux overlap increases in positive X direction, while overlap decreases in negative X direction. The inner and outer air gap bias flux density has the same magnitude. Therefore, the correctness of magnetic circuit and suspension mechanism is proved. The force-current relationships are measured on a four-pole DSHMB in Fig. 2 (d). Inject control current into radial control windings in the X direction from 0 to 3 A. It can be seen that the finite element simulation results are in good agreement with the theoretical values. The trends of suspension force-current curves are the same. IV.Conclusion The flux distribution and suspension force in proposed DSHMB are calculated and analyzed in this paper. The inner and outer stators are designed to produce the larger suspension force at the same time. It can be seen that the final scheme can meet the design indexes proposed in the beginning with the mathematical models of suspension force and the verification by finite element calculation.

**References:**

[1]D. Ning, H. Kai, and J. Long, "Review on High Speed Permanent Magnet Machines Including Design and Analysis Technologies," in Proceedings of the CSEE, vol. 34, no. 27, pp. 4640-4653, Sep, 2014. [2]J. Ju, H. Zhu and C. Zhao, "Radial Force-Current Characteristic Analysis of Three-Pole Radial-Axial HMB," 2016 IEEE Vehicle Power and Propulsion Conference (VPPC), Hangzhou, 2016, pp. 1-6. [3]R. Zhu, W. Xu, C. Ye, J. Zhu, G. Lei and X. Li, "Design Optimization of a Novel Heteropolar Radial Hybrid Magnetic Bearing Using Magnetic Circuit Model," in IEEE Transactions on Magnetics, vol. 54, no. 3, pp. 1-5, March 2018, Art no. 8201105.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fb19ba5a5a20cdadf6c7567533f7d856.jpg)
Fig. 1. Structure and magnetic circuit of the proposed DSHMB.

![](https://assets.underline.io/uploads/markdown_image/1/image/f164a9f18511ca6c950f639d68569305.jpg)
Fig. 2. Flux distribution and the force-current relationships.

 Modeling and Finite Element Analysis on the Novel Double-stator Hybrid Magnetic Bearing

I.Introduction Hybrid Magnetic bearing (HMB) is a kind of high-performance bearing which can realize magnetic suspension of the rotor without mechanical contact. Therefore, it has many advantages, such as no contact, no friction, no lubrication, low noise and so on. It has been widely employed in some industrial applications, such as flywheel energy storage system, compressor and turbine. HMBs have easier controllability and higher stiffness than the passive magnetic bearings. However, the area of magnetic pole is small, which make a small magnetic force. In addition, the traditional HMBs has the shortcoming of low mechanical strength. To solve these drawbacks, an improved axial-radial four-pole DC HMB with integrated stator poles is put forward in this paper. Moreover, compared with the existing radial four-pole three degrees of freedom HMBs, it can effectively increase the radial magnetic pole area, thus increasing the suspension force. The structure and working principle of the designed HMB is introduced, and its mathematical model is also derived. The prototype is established by finite element analysis. The electromagnetic simulation is carried out by software MagNet 3D to verify the theoretical analysis. II.Configuration and Suspension Principle As shown in Fig. 1 (a), the proposed HMB is composed of axial stator, radial stator, four radially magnetized permanent magnets (PMs) and a rotor. The radial stator and PM are divided into four parts by four non-magnetic materials. The outer of each stator core is provided with four axial cores. Radial control coils are wound on eight axial cores. In the proposed HMB, the static bias flux is generated by the radial magnetized PMs. Radial and axial control flux is generated by radial and axial control coils. The magnetic circuit is shown in Fig.1 (b). If an external force actors on the rotor and the rotor move to one direction, control current is applied to generate the control flux. The control flux adds to the static bias flux in the opposite direction, and then an active restoring force will bring the rotor back to the equilibrium position. According to the equivalent magnetic circuit method, the axial suspension force in the Z direction and the radial forces in the X and the Y directions are deduced as follows: Fz=kz×z+kiz×iz Fj=kj×j+kij×ij Kz=-Fm×Fm×μ0÷{[gz÷Sz+2gr÷(3Sr)]2gz×Sz} Kiz=Fm×Nz×μ0÷{[gz÷(2Sz)+gr÷(3Sr)]×gr} where the subscript “j” denotes x, and y. kj is the radial force-displacement stiffness. kij is the radial force-current stiffness. kz is the axial force-displacement stiffness. kiz is the axial force-current stiffness. Fm is the magnetic potential of permanent magnets. μ0 is vacuum permeability. Sm is radial magnetic pole area. gr is radial air gap length. gz is axial air gap length. Nr is number of radial control coils. Nz is number of axial control coils. III.Models, Design and Analysis The electromagnetic performances of the proposed HMB are analyzed by MagNet 3D, which verifies the correctness of the structure and suspension mechanism. The distribution of the flux in different cases is shown in Fig.2. Fig. 2(a) shows the bias flux distribution produced by the PMs. The values under four suspension poles are approximately equal. When current is only applied to the radial control coils to generate the force in the X direction, the distribution of control flux is illustrated in Fig.2 (b). Fig. 2 (c) shows the radial resultant flux distribution. The bias flux is superimposed by the control flux in the radial air gap for producing the radial suspension force in the positive X direction. Fig. 2(d) shows the axial resultant flux distribution, in which the axial suspension force is produced in the negative Z direction. Therefore, the correctness of magnetic circuit and suspension mechanism is proved. Fig. 2(e) demonstrates the calculated radial and axial force-current relationship curves respectively. The simulation value is close to the theoretical value. The suspension forces of the proposed HMB are changing linearly with the control current. IV.Conclusion This paper presents a novel axial-radial four-pole DC HMB with integrative stator poles. The area of the radial suspension poles is to the maximum, thereby effectively improving the radial suspension force. The research results verify the correctness of magnetic circuit, suspension mechanism and mathematical model.

**References:**

[1]H. Q. Zhu, Y. X. Shen, and Q. H. Wu, “Modeling and control system for AC hybrid magnetic bearing,” Proceedings of the CSEE, vol 29, no. 18, pp. 100-105, 2009. [2]J. Ju, H. Zhu and C. Zhao, "Radial Force-Current Characteristic Analysis of Three-Pole Radial-Axial HMB," 2016 IEEE Vehicle Power and Propulsion Conference (VPPC), Hangzhou, 2016, pp. 1-6.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a924b9e0f0c5de7e7a904cdcc64dc1f1.jpg)
Fig. 1. Structure and magnetic circuit of the HMB. (a) Structure. 1-axial stator, 2-radial control coil, 3-axial core, 4-radial stator, 5-non-magnetic material, 6-permanent magnet ring, 7-axial control coil, 8-non-magnetic part, 9-rotor core, 10-static bias flux, 11-axial control flux, 12-radial control flux. (b) Magnetic circuit.

![](https://assets.underline.io/uploads/markdown_image/1/image/5ac6e2f82b06f0634657144c5f72b8dc.jpg)
Fig. 2. Flux distribution and the force-current relationships.

 Electromagnetic Analysis of a Novel Axial-Radial Four-Pole DC Hybrid Magnetic Bearing

For the past two decades, conventional centrifugal pumps continued to face the challenge. Lubrication oil and fluid leakage cause pump failures. The conventional centrifugal pump separates the pump and the motor, and it needs a seal placed between the shaft and the pump housing. As the seals age and harden, it results in leakages. According to the studies [1], in the chemical industry, 80% of centrifugal pump failures are caused by the mechanical seals, and 20% are caused by bearing, couplings and others. It is possible to remove the seal by using 2-in-1 pump and canned motor design or a magnetic coupler, but sleeve bearings are needed. Chemical slurries such as CMP slurry aid cooling and lubricating the sleeve bearings. They generate abrasive particles stuck in the gap between the bearing and the shaft. The condition accelerates bearing wear. To eliminate the problem of bearing wear, bearingless maglev motors (BLMMs) [2]-[4] have recently emerged as a potential alternative solution in the chemical pump market. Although, there are other alternative solutions [5], BLMM meets the size and the energy saving demand of the market. Centrifugal pumps with BLMM can be totally bearing free. BLMM centrifugal pumps are contactless, oil-free, particle-free, compact, cost-effective, and produce much lower vibrations. Our institute is devoted to developing BLMM for use in centrifugal pumps. The target of the first phase is to develop the BLMM with a maximum shaft output power and speed of the motor which are 120W and 5,000 rpm. However, high-speed, high-power density BLMM has levitation stability, thermal, and centrifugal stress issues which may result in unstable levitation, permanent-magnet (PM) demagnetization[6], and blade deformation. In addition, the coupling effect between magnetic circuits of magnetic bearing and motor has to be considered. Therefore, the main goal of this paper is to propose a total solution to overcome the aforementioned issues. We present the design, analysis, fabrication and test results of our BLMM pump prototype. Due to the non-linear nature of the rotor position sensors, we designed a tunable eddy-current sensor with a sensing circuit which incorporates control algorithms from a digital signal processor (DSP). A measurement method for validating the linearity and sensitivity of a single-pair position sensor (Fig. 1) is demonstrated in this paper. After the position of the rotor is correctly detected, the rotor is levitated with precision bearingless levitation control which includes start up, steady state, dynamic, and shut down processes. Furthermore, key magnetic indices such as current density, torque ripple to output torque ratio, back-EMF are calculated to evaluate motor performance. CFD and mechanical analysis and simulations are completed to predict static and dynamic stabilities at high-speed revolution to demonstrate the thermal distribution, shear strength, unbalance, and deformation of the PM blade. The heat sources of whole system are also monitored to avoid PM demagnetization and system failure. A new BLMM centrifugal pump (Fig. 2) with a delta pressure of 0.36 bar and a flow rate of 5 LPM is designed based on our analysis, and a rotor orbit &lt; 20% radial air gap can be maintained at 120W/5,000 rpm.

**References:**

 [1]R. Schob, World Pumps, Vol. 2002, p. 34 (2002). [2]S. Silber, W. Amrein, and P. Boesch, IEEE Trans. on Mechatronics, Vol. 10, p. 611 (2005). [3]X. Sun, L. Chen, and Z. Yang, IEEE Trans. Ind. Electron., Vol. 60, p. 5528 (2013). [4]J. Asama, D. Kanehara, and T. Oiwa, IEEE Trans. Ind. Appl., Vol. 50, p. 288 (2014). [5]D. Guangren and D. Howe, IEEE Trans. on Control Systems Technology, Vol. 11, p. 204 (2003). [6]R. N. Johnson, G. B. Kliman, and Y. F. Liao, U.S. Patent 5 801 470 (1998).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/06b866232a7fcc21b52087044af9fdec.jpg)
Fig. 1. Position sensor test rig.

![](https://assets.underline.io/uploads/markdown_image/1/image/411000e82e0e0c2af11e847ea0b29db8.jpg)
Fig. 2. BLMM components.

 Development of a 120W Bearingless Maglev Motor for Centrifugal Pumps

The magnetic levitation using the pinning force of the high temperature superconductor (HTS) has an advantage to achieve stable levitation without control. Applications for the contact less magnetic bearing system have been developed [1][2]. For example, there is application to a flywheel electric power storage device. In this study, the magnetic bearing using the HTS has been developed. The rotor is supported by the pinning effect of the HTS. The rotor is rotated using the principle of induction motor. An iron core with a slot, and a winding with distributed winding are installed on the fixed side. The rotor is rotated by a rotating magnetic field from the stator. A rotating field is generated by applying a three-phase voltage to the stator. The rotating field generates an eddy current in the aluminum part on the outer periphery of the rotor, and torque is generated. On the other hand, the flux inside the rotor is disturbed by the influence of the rotating field. Therefore, it is necessary to examine the effects of rotational torque and rotating field on the rotor when using an induction motor. This paper proposes the design of HTS magnetic bearing rotor incorporated the secondary of the induction motor. In this study, the yoke equipped ring type rotor is proposed. Fig. 1 shows the system of the yoke equipped ring type rotor. In this rotor, the ring type permanent magnet is covered the yoke to increase the linkage flux to the HTS. The flux is distributed widely because of the ring type permanent magnet. The flux of this rotor is concentrated to the outer peripheral part of the HTS[3]-[5]. In this rotor, the aluminum is installed to generate torque from the rotating field. The flux of the permanent magnet is disturbed by the effect of the rotating field generated from the stator. To solve this problem, the iron is installed as a shield and it is defined as the magnetic shield. The air gap and the magnetic shield are attached between the yoke and the aluminum. The magnetic shield and the air gap are used to guide the rotating field to the outside without getting inside the rotor. The air gap increases the reluctance and suppresses the flux from the inside of the magnetic shield toward the yoke. As a result, the influence of the rotating field on the inside the rotor decreases. The diameter of this magnetic circuit is 86[mm]. If the rotor becomes large than the HTS, the stability decreases. Total diameter of this rotor is 100[mm] in consideration of the HTS whose diameter is 80[mm]. The thickness of the aluminum WAl, the magnetic shield WShield and the air gap WAir are defined. These W are changed, and the effect of the torque generated by the rotating field, and of the rotating field on the magnetic circuit are considered. However, total width W makes 7[mm], and the levitation gap between the upper surface of the HTS and the lower surface of the rotor is 10[mm]. In addition, the analysis is performed using the 3D FEM software JMAG Designer. The analysis conditions are coil current 4[A], frequency 60[Hz] and the number of turns 300[turn]. And the rotation conditions are sliding s = 0.01 that provides sufficient torque, and the number of rotations 1782[rpm]. The thickness of the aluminum WAl is changed. At that time, the generate rotational torque is analyzed. The torque of the three-phase induction motor using in this experiment is 0.25 [Nm]. It is converted torque value into dimension of the rotor. When WAl is 1[mm], generated rotational torque is 0.13 [Nm]. When WAl is 2[mm], generated rotational torque is 0.27[Nm]. From the result, WAl is defined as 2[mm] that generates enough torque to rotate the rotor. The effect of the rotating field on the magnetic circuit of the rotor is considered. Because of the WAl=2[mm], the sum of WShield and WAir is 5 [mm]. When the thicknesses are (WShield, WAir) = (1,4), (3,2), the flux density distribution is analyzed on the outer side of the aluminum and the yoke. Fig. 2 shows the analysis result. From the result, as WShield increases, the flux density on the outer peripheral side of aluminum increases. This is because the flux is moved to the magnetic shield inside the aluminum. On the other hand, the flux density on the outer peripheral side surface of the yoke decreases. This is because the magnetic shield prevents the flux generated by the rotating field from entering the inside of the rotor. However, at WShield = 4 [mm], the flux density increases. This is because the magnetic resistance is small at WAir = 1 [mm], and the flux leaked from the magnetic shield reaches the yoke. Consequently, when (WShield, WAir) =(3,2) , the influence of the rotating field is most suppressed. In conclusion, by installing a magnetic shield inside the aluminum and setting an air gap between the shield and the yoke, the influence of the rotating field on the magnetic circuit is suppressed. The HTS magnetic bearing rotor incorporated the secondary of the induction motor is designed.

**References:**

[1] F. C. MOON, “SUPERCONDUCTING LEVITATION”, JOHN WILEY & SONS, NEW YORK, (1994) [2] J. HULL, M. MURAKAMI, “APPLICATIONS OF BULK HIGH TENOERTURE SUPERCONDUCTORS”, PROC. OF IEEE, VOL.92, 2004, PP1705-1718 [3] T. Minami, S. Sakai, S. Ohashi, “Improvent of Stability against Vibration at the Mechanical Resonance in Attractive type HTS Permanent Hybrid Magnet Bearing.”, (TENCON2016), 16657805, pp3294-3297, (2016) [4] S. Sakai, K. Oguni, S. Ohashi, “Effect of the Magnetic Configuration on the Rotational Motion in the Attractive type HTS-Permanent Magnet Hybris Bearing”, IEEE Trans. On Applied Superconductivity, Vol. 26, No.4, 3601204, (2016) [5] S. Takimura, T. Arai., T. Minami, S. Ohashi, “Basic Characteristics of the Yoke Equipped Rotors in the Magnetic Bearing using HTS Pinning effect”, IEEE Xplore Digital Library IEEE, 12th International Symposium on Linear Dives for Industry Applications (LDIA2019), 8770991, (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/33f20cdca02a9c4b9d593f692449e7ab.jpg)
Fig.1 System of the yoke equipped ring type rotor

![](https://assets.underline.io/uploads/markdown_image/1/image/f0a92d9a001c069e9effea2897c3fcd5.jpg)
Fig.2 Flux density distribution

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