France



I.Introduction&lt;br/&gt;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.&lt;br/&gt;II.Configuration and Suspension Principle&lt;br/&gt;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.&lt;br/&gt;Based on the equivalent magnetic circuit analysis, the mathematical models of suspension force are deduced. The radial suspension force can be written as&lt;br/&gt;&lt;i&gt;F&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;=&lt;i&gt;k&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;j&lt;/i&gt;+&lt;i&gt;k&lt;sub&gt;ij&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;ij&lt;/i&gt;(1)&lt;br/&gt;where the subscript “&lt;i&gt;j&lt;/i&gt;” denotes x and y. &lt;i&gt;k&lt;/i&gt;&lt;i&gt;&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt; is the radial force-displacement stiffness. &lt;i&gt;k&lt;/i&gt;&lt;i&gt;&lt;sub&gt;ij&lt;/sub&gt;&lt;/i&gt; is the radial force-current stiffness.&lt;i&gt; k&lt;/i&gt;&lt;i&gt;&lt;sub&gt;j&lt;/sub&gt;&lt;/i&gt; and &lt;i&gt;k&lt;/i&gt;&lt;i&gt;&lt;sub&gt;ij &lt;/sub&gt;&lt;/i&gt;can be given as&lt;br/&gt;&lt;i&gt;k&lt;sub&gt;j&lt;/sub&gt;=F&lt;sub&gt;m&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;F&lt;sub&gt;m&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;μ&lt;sub&gt;0&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;S&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;S&lt;sub&gt;o&lt;/sub&gt;&lt;/i&gt;÷&lt;i&gt;[2g&lt;/i&gt;(&lt;i&gt;S&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;+&lt;i&gt;S&lt;sub&gt;o&lt;/sub&gt;&lt;/i&gt;)×(&lt;i&gt;S&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;+&lt;i&gt;S&lt;sub&gt;o&lt;/sub&gt;&lt;/i&gt;)]&lt;br/&gt;&lt;i&gt;k&lt;sub&gt;ij&lt;/sub&gt;&lt;/i&gt;=&lt;i&gt;F&lt;sub&gt;m&lt;/sub&gt;&lt;/i&gt;×&lt;i&gt;μ&lt;sub&gt;0&lt;/sub&gt;&lt;/i&gt;(&lt;i&gt;N&lt;sub&gt;i&lt;/sub&gt;S&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;+&lt;i&gt;N&lt;sub&gt;o&lt;/sub&gt;S&lt;sub&gt;o&lt;/sub&gt;&lt;/i&gt;)÷[&lt;i&gt;g&lt;sup&gt;2&lt;/sup&gt;&lt;/i&gt;(&lt;i&gt;S&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;+&lt;i&gt;S&lt;sub&gt;o&lt;/sub&gt;&lt;/i&gt;)]&lt;br/&gt;where &lt;i&gt;F&lt;/i&gt;&lt;i&gt;&lt;sub&gt;m&lt;/sub&gt;&lt;/i&gt; is the magnetic potential of permanent magnets.&lt;i&gt; μ&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt; is vacuum permeability. &lt;i&gt;S&lt;/i&gt;&lt;i&gt;&lt;sub&gt;0&lt;/sub&gt;&lt;/i&gt; is the outer pole face area. &lt;i&gt;S&lt;/i&gt;&lt;i&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt; is the inner pole face area. &lt;i&gt;g&lt;/i&gt; is the average length of inner and outer air-gap. radial air gap length. &lt;i&gt;N&lt;/i&gt;&lt;i&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt; is number of inner radial control coils. &lt;i&gt;N&lt;/i&gt;&lt;i&gt;&lt;sub&gt;o&lt;/sub&gt;&lt;/i&gt; is number of outer radial control coils.&lt;br/&gt;III.Models, Design and Analysis&lt;br/&gt;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.&lt;br/&gt;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.&lt;br/&gt;IV.Conclusion&lt;br/&gt;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, &quot;Review on High Speed Permanent Magnet Machines Including Design and Analysis Technologies,&quot; in &lt;i&gt;Proceedings of the CSEE&lt;/i&gt;, vol. 34, no. 27, pp. 4640-4653, Sep,  2014.&lt;br/&gt;[2]J. Ju, H. Zhu and C. Zhao, &quot;Radial Force-Current Characteristic Analysis of Three-Pole Radial-Axial HMB,&quot; &lt;i&gt;2016 IEEE Vehicle Power and Propulsion Conference (VPPC)&lt;/i&gt;, Hangzhou, 2016, pp. 1-6.&lt;br/&gt;[3]R. Zhu, W. Xu, C. Ye, J. Zhu, G. Lei and X. Li, &quot;Design Optimization of a Novel Heteropolar Radial Hybrid Magnetic Bearing Using Magnetic Circuit Model,&quot; in &lt;i&gt;IEEE Transactions on Magnetics&lt;/i&gt;, 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.

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

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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.

poster

The research for the temperature distribution of the transformer is significant for design [1]. Methods applied pervasively in academic field are thermal-network method [2], finite element method [3] and Computational Fluid Dynamics (CFD) [4]. Although CFD method can improve the accuracy of the transformer temperature field calculation, it is time-consuming and difficult to mesh finely for some sophisticated structures such as the insulating paper between foil windings. In this paper, an equivalent thermal-network model for a SCB2500kVA dry-type transformer with foil winding as low-voltage (LV winding) and subsection and layer winding as high-voltage (HV winding) is established under natural convection. Considering the nonuniformity of the power loss density in LV winding [5], the heat sources at different positions need to be corrected by using correction factor. The cooling conditions are different with the varying locations in transformer such as the airways with asymmetric one-adiabatic-side heat flux density between HV winding and insulating barrier and the groove surrounded by LV coils with approximately symmetrical heat flux density [6]. To settle this, corresponding experimental formulas are applied to solve the convective heat dissipation coefficients and the thermal parameters like thermal resistances, heat capacities and heat sources of each part [7]. After all of this, temperature rise curves are obtained. Simulation by computational fluid dynamics (CFD) is conducted to verify the validity of thermal network model. The results are consistent with the data from analytical method and experiments. Ι. The Establishment of Thermal Network Model Separated by DMD insulation prepreg papers, each layer of LV winding is one turn. Consisted of enameled rectangular copper wires, the HV segmented layers windings are divided into four sections, which are insulated by glass fiber mesh cloth. Upon core part, 9 nodes are selected as shown in Fig1(a), among which 5 points are from the core limb, 2 from half of core yokes and 2 from the lapping joints of core limb and yoke. The LV winding is divided into 6 sections along the axial direction as shown in Fig1(b), so 6 nodes are achieved. The HV winding is segmented into 9 sections as shown in Fig1(c) according to the location of the heat source distribution. The single-phase thermal network model of the transformer is set up. ΙΙ. Calculation of Thermal Parameters Thermal parameters in the thermal network model are heat source, heat resistance and heat capacity. The heat sources mainly come from core loss and winding loss. Due to the existence of the transverse leakage magnetic field, eddy currents are induced in the ends of foil coils, which lead to inhomogeneous distributions of currents and power losses among the LV winding. The current density can surge up to be 3 times at the ends than in the middle. Based on electromagnetic FEM computing software, parameter Ce is introduced to characterize this effect and correct the input power loss at end. The thermal resistances contain the conduction thermal resistance, the convection heat resistance and the radiant thermal resistance, which happen to be the three heat transfer pathways. The equivalent thermal conductivity can be obtained by Fourier's law. According to the diverse thicknesses, spatial directions, heat transfer areas and material compositions in different positions, thermal resistances between nodes can be calculated respectively. The radiant thermal resistance is related to the surface temperature and emissivity, which can be calculated by the Stephen Boltzmann equation. In view of the fact that when the dry-type transformer reaches heat dissipation equilibrium, the temperature in most areas can up to more than 100 degrees, the heat emitted to the environment by radiation is too considerable to neglect. Since the convective heat transfer coefficients are affected by the internal structural complexity of the transformer, the asymmetry heat sources and the buoyancy lift of natural convection, it is obviously inaccurate to apply an average value for the whole plane. By analyzing the heat dissipation conditions at different planes as shown in Fig1(d), the Nusselt number of vertical surface and horizontal are calculated. ΙΙΙ. Numerical Simulation The methods for solving convective heat dissipation coefficient include analytical method, experimental method and numerical analysis method. The numerical analysis is a wide used method for solving the problems of various shapes and boundary conditions at present. By finite volume method, the results of temperature rise and velocity distribution can be obtained not only, but also the convective heat dissipation coefficient on different surfaces. ΙV. Experiment In order to verify the validity of the model, the temperature rise experiment of load is carried out. The experimental results show that the hottest spot is located in the highest disc of outer HV winding with the temperature of 425.15K, which is in good agreement with the results of thermal network model and CFD simulation. V. Conclusion: According to the thermoelectric analogy effect, the thermal network method simulates the temperature field through the method of circuit. By considering the heat source, thermal resistance and heat capacity of different structures respectively, the average temperature rise curve of every node is obtained. The precision of the hottest spot by thermal network method is reliable.

**References:**

[1] M. Xiao and B. X. Du, IEEE Transactions on Dielectrics and Electrical Insulation., Vol. 23, p.2413–2420 (2016) [2] Cremasco, Andrea, and Wei, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering., Vol. 37, p.1039-1053 (2018) [3] Ahn. H. M, Oh. Y. H, and Kim J K, IEEE Transactions on Magnetics., Vol.48, p.819-822 (2012) [4] L. Caibo, IEEE Transactions on Magnetics., Vol.50, p.1-4 (2014) [5] L. Yongjian, IEEE Transactions on Magnetics., Vol.55, p.1-5 (2019) [6] L. moonhee, Electric Power Systems Research., Vol.80, p.121-129 (2010) [7] F. P. Incropera, D. P. Dewitt, and T. L. Bergman, Chemical Industry Press (2007)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7c40975f0961189391165df42ab36eb2.png)
Fig.1 The establishment of thermal network model

![](https://assets.underline.io/uploads/markdown_image/1/image/67d030081f6b28940cccc9706807bf09.png)
Fig.2 Results of simulation and experiment

 Thermal Network Model of A SCB2500kVA Dry-type Transformer Coupled with Electromagnetic Loss

This paper aiming to solve the vibration and noise problem of transformer core under DC bias, the magnetostrictive characteristics of 30ZH120 oriented silicon steel sheet in rolling direction and vertical rolling direction were studied firstly based on the measurement system of silicon steel sheet, and the influence rules of different DC bias on the magnetostrictive butterfly characteristics in different directions were studied. Secondly, the vibration and noise of transformer under the condition of DC bias are simulated, and the calculation results under different DC bias conditions are given. Thirdly, by means of modal numerical calculation and modal experimental study, the elastic modulus assignment methods and intervals suitable for modal calculation of transformers of different sizes are obtained and determined. Finally, the vibration and noise of the transformer are studied experimentally, and the correctness of the simulation content is verified. Key words: DC bias, vibration noise, magnetostriction, modal analysis 1 Introduction DC transmission grid, geomagnetic changes and other reasons can cause the ground potential of the transformer neutral point to rise, the presence of DC magnetic flux in the core, resulting in increased transformer no-load losses, vibration noise, and bring safety hazards to the power system transmission and distribution networks. Therefore, the study of transformer vibration noise is important. [1] simulated the 2-D magnetic properties of a silicon steel sheet and proposed a vector J-A hysteresis model considering the non-hysteresis magnetization intensity, and simulated its rotational magnetic properties. In [2], the magnetic properties of silicon steel sheets were studied at different temperatures and DC bias conditions, and the magnetization curves, permeability curves and loss curves were given. In [3], the magnetostriction characteristics of the silicon steel sheet were measured and the results were taken into the MagNet finite element software to study the vibration and noise of the power transformer, but the effect of DC bias on the vibration and noise of the transformer was not considered. This paper investigates the vibration noise of the transformer under DC bias through simulation and experimental verification. As in the research flowchart of Fig.1, the measured magnetic characteristic curves of the silicon steel sheet under DC bias magnetism can be brought into the transformer FEM model to obtain more accurate results. Finally, modal numerical calculations and modal experimental studies of transformers are also carried out to obtain and determine the elastic modulus assignment methods and intervals applicable to modal calculations of transformers of different sizes. 2 Simulation and experiment of vibration and noise under DC bias of transformer The results obtained by substituting the magnetic characteristic curves in Fig. 1 into the transformer FEM model considering the boundary conditions are shown in Table 1. The results show that the vibration and noise of the transformer increase with the increase of the DC bias. When the DC bias is greater than 2.3A, the vibration displacement reaches 0.4442 μm and the noise reaches 72.96 dB. In addition, the noise distribution curve of the transformer under DC bias shows that the noise increases with the increase of DC bias, but the noise remains stable when the DC bias is greater than 2.3A, indicating that the transformer core is saturated. 3 conclusion This paper first measures the magnetic properties of silicon steel wafers, and then uses finite element analysis to investigate the vibration noise performance of transformers under DC bias magnetism, and conducts experimental verification. The results show that the vibration and noise simulation results are in good agreement with the experimental results. Detailed experimental results and comparisons as well as modal analysis results will be shown in the full paper.

**References:**

[1] X. Wang, Y. Zhang and W. Jiang, Transactions of China Electrotechnical Society., Vol. 12(33), p.257-262 (2016) [2] D. Chen, L. Fang and B. Kwon, AIP Advances., Vol. 7(5), 056682 (2017) [3] D. Chen, W. Zhao and B. Bai, International Journal of Applied Electromagnetics and Mechanics., Vol. 52(3-4), p.1477-1484 (2016)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9829e76ee06d93aac00152e448b05973.jpg)
Fig.1 Reserch process flowchart

![](https://assets.underline.io/uploads/markdown_image/1/image/47c70f202c70de0908ef9f5d55732d23.jpg)
Table.1 Simulation and modal experiment results

 Study of Vibration and Noise Considering DC Bias in Power Transformer

The high-frequency transformer (HFT) will produce sharp noise when working and the long-term excessive vibration will not only accelerate the aging of the equipment but also influence the surrounding environment, so it is great significance to study the vibration and noise characteristics of the HFT. In this paper, the core-type nanocrystalline high frequency transformer with capacity of 5400kVA and frequency of 5000Hz is simulated and analyzed by two factors of magnetostrictive and Maxwell. At last, a high frequency transformer is designed and a test platform is set up. The vibration and noise is tested and analyzed, and compared with the simulation results. Index Terms—Nanocrystalline, high frequency transformer, vibration, noise Introduction The high-frequency transformer (HFT) of large capacity in DC/DC converter will be able to achieve voltage and power transmission in the electric power system, high and low voltage side electrical isolation between inverter and rectifier circuit through the magnetic coupling, which can more easily achieve the electrical control of DC/DC converter on both sides. The vibration and acoustic noise emission of electromagnetic devices is not a new research area. However, the focus in the past has been on electrical machines and line frequency transformers, which have been thoroughly investigated in [1-3]. A clear understanding of the vibration and noise characteristics of HFT is necessary for detecting electrical and mechanical faults in a transformer using vibration-based monitoring strategies. Vibration mechanism of iron core There are two main factors in the vibration of HFT, the first factor is the magnetostriction effect of the iron core and the second factor is Maxwell force at the air gap. From the perspective of conservation of mechanical and internal energy, the magnetostrictive intrinsic model which is suitable for grain oriented silicon steel sheets is established. The test platform is built to test the vibration and noise of the core-type HFT, the test platform is shown in Fig. 1(a). The measuring points are shown in Fig.1 (b), and the noise is measured at the front and side of HFT. The simulation results show that the displacement of point 3 at 1000Hz is 5.5×10-7m when the flux density in the core is 0.6T, and the displacement of point 4 is 7.9×10-7m. The displacement increased by 43.63% compared with point 3, which indicates that the air gap is greatly influenced by Maxwell force due to the large leakage magnetic field. The time domain vibration of three points working at 1000Hz and 0.6T is shown in Fig. 2(a), it can be seen that the vibration of the upper part of the iron core is more serious. The vibration and noise trend of HFT at different frequencies is shown in Fig. 2(b). It can be seen that the vibration and noise of HFT gradually become larger with the increase of the frequency of excitation. At the same time, the vibration and noise are much larger than the conventional transformers, and the noise values are completely beyond the tolerable range. Therefore, it is necessary to study the vibration and noise characteristics of the high frequency transformer. Acknowledge This work was supported in part by National Natural Science Foundation of China under Grant 52007192. and in part by the Fundamental Research Funds for the Central Universities (2020XJJD02).

**References:**

[1] B. Weiser, H. Pfutzner, and J. Anger, “Relevance of magnetostriction and forces for the generation of audible noise of transformer cores,” IEEE Transactions on Magnetics, vol. 36, no. 5, pp. 3759–3777, 2000. [2] R. S. Masti, W. Desmet, and W. Heylen, “On the influence of core laminations upon power transformer noise,” in Proceedings of ISMA, 2004, pp. 3851–3862. [3] A. Moses, P. Anderson, T. Phophongviwat, and S. Tabrizi, “Contribution of magnetostriction to transformer noise,” in 45th International Universities Power Engineering Conference (UPEC), 2010, pp. 1–5.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/acda7613f831c6d092bf97fe19ccfc34.jpg)
Fig. 1 The experiment set-up and the structure and the vibration measuring points

![](https://assets.underline.io/uploads/markdown_image/1/image/2b0f337098d90de7df3ebf6144a4dbff.jpg)
Fig. 2 The vibration time domain waveform and the change of vibration and noise with magnetic flux density

 Study on Vibration and Noise Characteristics of Nanocrystalline High-frequency Transformer

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.

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Fig.1 Reserch process flowchart

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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.

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 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)

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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.

**Images:**
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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.

**Images:**

![](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 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.

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