France



&lt;br/&gt;I.Background&lt;br/&gt;&lt;br/&gt;Transmission line (TL) is a fundamental structure that can easily be identified in an electric system by various forms, for instance, the external incoming/outgoing line and internal windings of an electrical machine, etc. [1]–[4]. These TLs represent dominant propagation paths for radiated noises coupling into an apparatus, resulting in potential susceptibility effects like over-voltage breakdown, insulation failure. As a result, with the objective to ensuring safety operation of system in complex electromagnetic environment and assessing its radiated immunity, it is of great interest to predict the voltage/current responses of TL under the illumination of external electromagnetic interferences.&lt;br/&gt;&lt;br/&gt;In this connection, the TL model based on solving telegrapher&#39;s equation receives undoubtedly the most attention. To incorporate the impinging field contribution into TL model, pioneer works by Taylor et al. [5], Agrawal et al. [6] and Rachidi et al. [7] argued three different but equivalent approaches to cast the field contributions as a set of equivalent circuit sources. Besides, researches started to look outside of classic FC models for alternatives approaches, the motivation includes interpreting Taylor&#39;s, Agrawal&#39;s and Rachidi&#39;s approach in a unified theory [8], predicting transient field responses [9], analyzing the worst-case load responses [10]–[12], etc. Lorentz reciprocity theorem, which was exploited in [8]–[12], demonstrated great potentials in modeling the FC problem. However, a simple concise FC model in parallel to Agrawal&#39;s model was still missing in the literature.&lt;br/&gt;&lt;br/&gt;In this study, we re-consider the FC problem by taking advantage of the reciprocity theorem, specifically, through solving the TL in transmitting mode, analytical solution of far-field radiation pattern and input impedance are obtained, which leads to closed-form expressions of equivalent voltage sources accounting for the field contributions. The sources are then incorporated into a passive TL model, resulting in a solvable two-port network with active feeding sources and terminal impedances connecting to the terminals.&lt;br/&gt;&lt;br/&gt;II.The Proposed FC Approach&lt;br/&gt;&lt;br/&gt;As shown in Fig.1, a lossless single conductor transmission line of length &lt;i&gt;l&lt;/i&gt; and radius &lt;i&gt;r&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt; is placed parallel above the ground plane at height &lt;i&gt;h&lt;/i&gt;. The system can be regarded as a two-port system under the assumption &lt;i&gt;h&lt;/i&gt;&amp;lt;&amp;lt;&lt;i&gt;c&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;/&lt;i&gt;f&lt;/i&gt;, where &lt;i&gt;c&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt; is speed of light in free space, &lt;i&gt;f&lt;/i&gt; is frequency. The TL is illuminated by a linearly polarized uniform plane wave of electrical field &lt;i&gt;E&lt;/i&gt;, magnetic field &lt;i&gt;H&lt;/i&gt;, and propagates vector &lt;i&gt;k&lt;/i&gt;. Incidence angles (&lt;i&gt;θ&lt;/i&gt;, &lt;i&gt;Φ&lt;/i&gt;) and polarization angle (&lt;i&gt;η&lt;/i&gt;), are defined in the spherical coordinates.&lt;br/&gt;&lt;br/&gt;In this regard, the TL under study can be treated as a two-port network with two voltage sources connected to two ports, representing the contribution of external field, resorting to the generic multi-port reciprocity theorem discuss in [13], the sources can be cast as function of radiation pattern and input impedance, which needs to be solved by considering TL in transmitting mode, namely, a dummy voltage source is connected to the port whereas the opposite terminal is left open. According to passive TL model and solution in [14], [15], the far-field radiation field can be solved analytically, which finally leads to the proposed closed-form TL model.&lt;br/&gt;&lt;br/&gt;The proposed method is verified by comparing to the classic FC model [16]. Without the loss of generality, we consider a TL of &lt;i&gt;l&lt;/i&gt;=1 m, &lt;i&gt;h&lt;/i&gt;=1 cm, &lt;i&gt;r&lt;sub&gt;w&lt;/sub&gt;&lt;/i&gt;=1 mm and impedances &lt;i&gt;Z&lt;/i&gt;&lt;sub&gt;L&lt;/sub&gt;=10 Ω, &lt;i&gt;Z&lt;/i&gt;&lt;sub&gt;R&lt;/sub&gt;=50 Ω. Let |&lt;i&gt;E&lt;/i&gt;|=1 V/m. Different impinging waves are considered, namely, wave #1 (&lt;i&gt;θ&lt;/i&gt;=138.6&lt;sup&gt;o&lt;/sup&gt;, &lt;i&gt;Φ&lt;/i&gt;=40.9&lt;sup&gt;o&lt;/sup&gt;, &lt;i&gt;η=&lt;/i&gt;184.1&lt;sup&gt;o&lt;/sup&gt;), wave #2 (&lt;i&gt;θ&lt;/i&gt;=90&lt;sup&gt;o&lt;/sup&gt;, &lt;i&gt;Φ&lt;/i&gt;=73&lt;sup&gt;o&lt;/sup&gt;, &lt;i&gt;η=&lt;/i&gt;180), wave #3 (&lt;i&gt;θ&lt;/i&gt;=90&lt;sup&gt;o&lt;/sup&gt;, &lt;i&gt;Φ&lt;/i&gt;=73&lt;sup&gt;o&lt;/sup&gt;, &lt;i&gt;η=&lt;/i&gt;270&lt;sup&gt;o&lt;/sup&gt;).&lt;br/&gt;&lt;br/&gt;The magnitude of the induced voltage across the left load |&lt;i&gt;V&lt;/i&gt;&lt;sub&gt;L&lt;/sub&gt;| predicted by both proposed reciprocity model and classic TL model from 1 MHz to 1 GHz, the results are summarized in Fig. 2. The predicted load voltages by two methods agree perfectly with each other for all three cases. Therefore, it can be concluded that the proposed model could offer trustworthy predictions to the FC problems.&lt;br/&gt;&lt;br/&gt;III.Conclusions&lt;br/&gt;&lt;br/&gt;An algorithm for computing the field-to-wire coupling problem is proposed based on the reciprocity theorem. The contributions due to the external field are modeled as equivalent voltage sources, whose expressions are obtained in closed-form. Owing to the non-conventional definitions of incidence and polarization angles, the proposed method offers a more concise and physical interpretation for the field-to-wire coupling phenomena, the effects of incidence and polarization angles are conveniently decoupled in the closed-form solution. In this connection, the proposed method is more advantageous in addressing the wave angles associating to maximal/minimal coupling efficiency.

**References:**

[1] Y. Ryu, B. Park, and K. J. Han, “Estimation of High-Frequency Parameters of AC Machine From Transmission Line Model,” &lt;i&gt;IEEE Transactions on Magnetics&lt;/i&gt;, vol. 51, no. 3, pp. 1–4, Mar. 2015, doi: 10.1109/TMAG.2014.2355718.&lt;br/&gt;[2] Y. Huangfu, L. D. Rienzo, and S. Wang, “FDTD Formulation Based on High-Order Surface Impedance Boundary Conditions for Frequency-Dependent Lossy Multi-Conductor Transmission Lines,” &lt;i&gt;IEEE Transactions on Magnetics&lt;/i&gt;, vol. 56, no. 1, pp. 1–4, Jan. 2020, doi: 10.1109/TMAG.2019.2950603.&lt;br/&gt;[3] Q. Zhang &lt;i&gt;et al.&lt;/i&gt;, “Application of an Improved Multi-Conductor Transmission Line Model in Power Transformer,” &lt;i&gt;IEEE Transactions on Magnetics&lt;/i&gt;, vol. 49, no. 5, pp. 2029–2032, May 2013, doi: 10.1109/TMAG.2013.2245874.&lt;br/&gt;[4] H. D. Gersem and A. Muetze, “Finite-Element Supported Transmission-Line Models for Calculating High-Frequency Effects in Machine Windings,” &lt;i&gt;IEEE Transactions on Magnetics&lt;/i&gt;, vol. 48, no. 2, pp. 787–790, Feb. 2012, doi: 10.1109/TMAG.2011.2172197.&lt;br/&gt;[5] C. D. Taylor, R. S. Satterwhite, and C. W. Harrison, “The response of a terminated two-wire transmission line excited by a nonuniform electromagnetic field,” &lt;i&gt;IEEE Transactions on Antennas and Propagation&lt;/i&gt;, vol. 13, no. 6, pp. 987–989, 1965, doi: 10.1109/TAP.1965.1138574.&lt;br/&gt;[6] A. K. Agrawal, H. J. Price, and S. H. Gurbaxani, “Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field,” &lt;i&gt;IEEE Transactions on Electromagnetic Compatibility&lt;/i&gt;, vol. EMC-22, no. 2, pp. 119–129, 1980, doi: 10.1109/TEMC.1980.303824.&lt;br/&gt;[7] F. Rachidi, “Formulation of the field-to-transmission line coupling equations in terms of magnetic excitation field,” &lt;i&gt;IEEE Transactions on Electromagnetic Compatibility&lt;/i&gt;, vol. 35, no. 3, pp. 404–407, 1993, doi: 10.1109/15.277316.&lt;br/&gt;[8] M. Stumpf and G. Antonini, “Electromagnetic Field Coupling to a Transmission Line—A Reciprocity-Based Approach,” &lt;i&gt;IEEE Transactions on Electromagnetic Compatibility&lt;/i&gt;, pp. 1–9, 2018, doi: 10.1109/TEMC.2018.2884038.&lt;br/&gt;[9] R. G. Olsen and A. G. Tarditi, “EMP Coupling to a Straight Conductor Above Ground: Transmission Line Formulation Based on Electromagnetic Reciprocity,” &lt;i&gt;IEEE Transactions on Electromagnetic Compatibility&lt;/i&gt;, pp. 1–9, 2018, doi: 10.1109/TEMC.2018.2838080.&lt;br/&gt;[10] F. Vanhee, D. Pissoort, J. Catrysse, G. A. E. Vandenbosch, and G. G. E. Gielen, “Efficient Reciprocity-Based Algorithm to Predict Worst Case Induced Disturbances on Multiconductor Transmission Lines due to Incoming Plane Waves,” &lt;i&gt;IEEE Transactions on Electromagnetic Compatibility&lt;/i&gt;, vol. 55, no. 1, pp. 208–216, Feb. 2013, doi: 10.1109/TEMC.2012.2208754.&lt;br/&gt;[11] T. Liang and Y.-Z. Xie, “Determining Incidence and Polarization of Electromagnetic Field for Maximal/Minimal Coupling to Transmission Line System,” &lt;i&gt;IEEE Microwave and Wireless Components Letters&lt;/i&gt;, vol. 30, no. 11, pp. 1021–1024, Nov. 2020, doi: 10.1109/LMWC.2020.3021695.&lt;br/&gt;[12] T. Liang, G. Spadacini, F. Grassi, and S. A. Pignari, “Coupling of wideband radiated IEMI to cables above ground,” &lt;i&gt;IEEE Transactions on Electromagnetic Compatibility&lt;/i&gt;, vol. 61, no. 6, pp. 1–9, 2018, doi: 10.1109/TEMC.2018.2877508.&lt;br/&gt;[13] T. Liang, G. Spadacini, F. Grassi, and S. A. Pignari, “Worst-Case Scenarios of Radiated-Susceptibility Effects in a Multiport System Subject to Intentional Electromagnetic Interference,” &lt;i&gt;IEEE Access&lt;/i&gt;, vol. 7, pp. 76500–76512, 2019, doi: 10.1109/ACCESS.2019.2921117.&lt;br/&gt;[14] R. Ianconescu and V. Vulfin, “Radiation from transmission lines PART I: free space transmission lines,” &lt;i&gt;arXiv preprint arXiv:1701.04878&lt;/i&gt;, vol. 2, no. 1, pp. 1–9, 2017, [Online]. Available: http://arxiv.org/abs/1701.04878.&lt;br/&gt;[15] R. Ianconescu and V. Vulfin, “Radiation from free space TEM transmission lines,” &lt;i&gt;IET Microwaves, Antennas &amp; Propagation&lt;/i&gt;, Jun. 2019, doi: 10.1049/iet-map.2018.6061.&lt;br/&gt;[16] C. R. Paul, &lt;i&gt;Analysis of multiconductor transmission lines&lt;/i&gt;. New York: IEEE, 2007.

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INTERMAG 2021

 Closed-Form Electromagnetic Field Coupling to Transmission Line Model Exploiting the Reciprocity Theorem

The aim of ESSCIRC and ESSDERC is to provide an annual European forum for the presentation and discussion of recent advances in solid-state devices and circuits.
The level of integration for system-on-chip design is rapidly increasing.

This is made available by advances in semiconductor technology. Therefore, more than ever before, a deeper interaction among technologists, device experts, IC designers, and system designers is necessary. ESSCIRC and ESSDERC are governed by a common Steering Committee and share Plenary Keynote Presentations and Joint Sessions bridging both device and circuit communities.

Highlights:
* 3 joint keynote presentations
* 3 keynote presentations ESSCIRC
* 3 keynote presentations ESSDERC
* Invited papers with overall coverage of all aspects of advanced devices and circuits
* Presentation of IEEE and ESSCIRC/ESSDERC Awards
* Educational Events

JOINT PLENARY talks live broadcast: September 13, 2021 
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ESSCIRC ESSDERC 2021

The aim of ESSCIRC and ESSDERC is to provide an annual European forum for the presentation and discussion of recent advances in solid-state devices and circuits.
The level of integration for system-on-chip design is rapidly increasing.

This is made available by advances in semiconductor technology. Therefore, more than ever before, a deeper interaction among technologists, device experts, IC designers, and system designers is necessary. ESSCIRC and ESSDERC are governed by a common Steering Committee and share Plenary Keynote Presentations and Joint Sessions bridging both device and circuit communities.





I.Background Transmission line (TL) is a fundamental structure that can easily be identified in an electric system by various forms, for instance, the external incoming/outgoing line and internal windings of an electrical machine, etc. [1]–[4]. These TLs represent dominant propagation paths for radiated noises coupling into an apparatus, resulting in potential susceptibility effects like over-voltage breakdown, insulation failure. As a result, with the objective to ensuring safety operation of system in complex electromagnetic environment and assessing its radiated immunity, it is of great interest to predict the voltage/current responses of TL under the illumination of external electromagnetic interferences. In this connection, the TL model based on solving telegrapher's equation receives undoubtedly the most attention. To incorporate the impinging field contribution into TL model, pioneer works by Taylor et al. [5], Agrawal et al. [6] and Rachidi et al. [7] argued three different but equivalent approaches to cast the field contributions as a set of equivalent circuit sources. Besides, researches started to look outside of classic FC models for alternatives approaches, the motivation includes interpreting Taylor's, Agrawal's and Rachidi's approach in a unified theory [8], predicting transient field responses [9], analyzing the worst-case load responses [10]–[12], etc. Lorentz reciprocity theorem, which was exploited in [8]–[12], demonstrated great potentials in modeling the FC problem. However, a simple concise FC model in parallel to Agrawal's model was still missing in the literature. In this study, we re-consider the FC problem by taking advantage of the reciprocity theorem, specifically, through solving the TL in transmitting mode, analytical solution of far-field radiation pattern and input impedance are obtained, which leads to closed-form expressions of equivalent voltage sources accounting for the field contributions. The sources are then incorporated into a passive TL model, resulting in a solvable two-port network with active feeding sources and terminal impedances connecting to the terminals. II.The Proposed FC Approach As shown in Fig.1, a lossless single conductor transmission line of length l and radius rw is placed parallel above the ground plane at height h. The system can be regarded as a two-port system under the assumption h&lt;&lt;c0/f, where c0 is speed of light in free space, f is frequency. The TL is illuminated by a linearly polarized uniform plane wave of electrical field E, magnetic field H, and propagates vector k. Incidence angles (θ, Φ) and polarization angle (η), are defined in the spherical coordinates. In this regard, the TL under study can be treated as a two-port network with two voltage sources connected to two ports, representing the contribution of external field, resorting to the generic multi-port reciprocity theorem discuss in [13], the sources can be cast as function of radiation pattern and input impedance, which needs to be solved by considering TL in transmitting mode, namely, a dummy voltage source is connected to the port whereas the opposite terminal is left open. According to passive TL model and solution in [14], [15], the far-field radiation field can be solved analytically, which finally leads to the proposed closed-form TL model. The proposed method is verified by comparing to the classic FC model [16]. Without the loss of generality, we consider a TL of l=1 m, h=1 cm, rw=1 mm and impedances ZL=10 Ω, ZR=50 Ω. Let |E|=1 V/m. Different impinging waves are considered, namely, wave #1 (θ=138.6o, Φ=40.9o, η=184.1o), wave #2 (θ=90o, Φ=73o, η=180), wave #3 (θ=90o, Φ=73o, η=270o). The magnitude of the induced voltage across the left load |VL| predicted by both proposed reciprocity model and classic TL model from 1 MHz to 1 GHz, the results are summarized in Fig. 2. The predicted load voltages by two methods agree perfectly with each other for all three cases. Therefore, it can be concluded that the proposed model could offer trustworthy predictions to the FC problems. III.Conclusions An algorithm for computing the field-to-wire coupling problem is proposed based on the reciprocity theorem. The contributions due to the external field are modeled as equivalent voltage sources, whose expressions are obtained in closed-form. Owing to the non-conventional definitions of incidence and polarization angles, the proposed method offers a more concise and physical interpretation for the field-to-wire coupling phenomena, the effects of incidence and polarization angles are conveniently decoupled in the closed-form solution. In this connection, the proposed method is more advantageous in addressing the wave angles associating to maximal/minimal coupling efficiency.

**References:**

[1] Y. Ryu, B. Park, and K. J. Han, “Estimation of High-Frequency Parameters of AC Machine From Transmission Line Model,” IEEE Transactions on Magnetics, vol. 51, no. 3, pp. 1–4, Mar. 2015, doi: 10.1109/TMAG.2014.2355718. [2] Y. Huangfu, L. D. Rienzo, and S. Wang, “FDTD Formulation Based on High-Order Surface Impedance Boundary Conditions for Frequency-Dependent Lossy Multi-Conductor Transmission Lines,” IEEE Transactions on Magnetics, vol. 56, no. 1, pp. 1–4, Jan. 2020, doi: 10.1109/TMAG.2019.2950603. [3] Q. Zhang et al., “Application of an Improved Multi-Conductor Transmission Line Model in Power Transformer,” IEEE Transactions on Magnetics, vol. 49, no. 5, pp. 2029–2032, May 2013, doi: 10.1109/TMAG.2013.2245874. [4] H. D. Gersem and A. Muetze, “Finite-Element Supported Transmission-Line Models for Calculating High-Frequency Effects in Machine Windings,” IEEE Transactions on Magnetics, vol. 48, no. 2, pp. 787–790, Feb. 2012, doi: 10.1109/TMAG.2011.2172197. [5] C. D. Taylor, R. S. Satterwhite, and C. W. Harrison, “The response of a terminated two-wire transmission line excited by a nonuniform electromagnetic field,” IEEE Transactions on Antennas and Propagation, vol. 13, no. 6, pp. 987–989, 1965, doi: 10.1109/TAP.1965.1138574. [6] A. K. Agrawal, H. J. Price, and S. H. Gurbaxani, “Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field,” IEEE Transactions on Electromagnetic Compatibility, vol. EMC-22, no. 2, pp. 119–129, 1980, doi: 10.1109/TEMC.1980.303824. [7] F. Rachidi, “Formulation of the field-to-transmission line coupling equations in terms of magnetic excitation field,” IEEE Transactions on Electromagnetic Compatibility, vol. 35, no. 3, pp. 404–407, 1993, doi: 10.1109/15.277316. [8] M. Stumpf and G. Antonini, “Electromagnetic Field Coupling to a Transmission Line—A Reciprocity-Based Approach,” IEEE Transactions on Electromagnetic Compatibility, pp. 1–9, 2018, doi: 10.1109/TEMC.2018.2884038. [9] R. G. Olsen and A. G. Tarditi, “EMP Coupling to a Straight Conductor Above Ground: Transmission Line Formulation Based on Electromagnetic Reciprocity,” IEEE Transactions on Electromagnetic Compatibility, pp. 1–9, 2018, doi: 10.1109/TEMC.2018.2838080. [10] F. Vanhee, D. Pissoort, J. Catrysse, G. A. E. Vandenbosch, and G. G. E. Gielen, “Efficient Reciprocity-Based Algorithm to Predict Worst Case Induced Disturbances on Multiconductor Transmission Lines due to Incoming Plane Waves,” IEEE Transactions on Electromagnetic Compatibility, vol. 55, no. 1, pp. 208–216, Feb. 2013, doi: 10.1109/TEMC.2012.2208754. [11] T. Liang and Y.-Z. Xie, “Determining Incidence and Polarization of Electromagnetic Field for Maximal/Minimal Coupling to Transmission Line System,” IEEE Microwave and Wireless Components Letters, vol. 30, no. 11, pp. 1021–1024, Nov. 2020, doi: 10.1109/LMWC.2020.3021695. [12] T. Liang, G. Spadacini, F. Grassi, and S. A. Pignari, “Coupling of wideband radiated IEMI to cables above ground,” IEEE Transactions on Electromagnetic Compatibility, vol. 61, no. 6, pp. 1–9, 2018, doi: 10.1109/TEMC.2018.2877508. [13] T. Liang, G. Spadacini, F. Grassi, and S. A. Pignari, “Worst-Case Scenarios of Radiated-Susceptibility Effects in a Multiport System Subject to Intentional Electromagnetic Interference,” IEEE Access, vol. 7, pp. 76500–76512, 2019, doi: 10.1109/ACCESS.2019.2921117. [14] R. Ianconescu and V. Vulfin, “Radiation from transmission lines PART I: free space transmission lines,” arXiv preprint arXiv:1701.04878, vol. 2, no. 1, pp. 1–9, 2017, [Online]. Available: http://arxiv.org/abs/1701.04878. [15] R. Ianconescu and V. Vulfin, “Radiation from free space TEM transmission lines,” IET Microwaves, Antennas & Propagation, Jun. 2019, doi: 10.1049/iet-map.2018.6061. [16] C. R. Paul, Analysis of multiconductor transmission lines. New York: IEEE, 2007.

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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.

 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

 Design of the HTS Magnetic Bearing Rotor Incorporated the Secondary of the Induction Motor

This paper has proposed two bearingless axial motors (BLAM) with different combination of the number of the rotor poles and the stator slots. The proposed BLAMs are analyzed by 3D finite element analysis (FEA) when the suspension currents are imposed. The winding in the BLAM with the high number of the rotor poles is designed carefully to limited the coupling of different degree of freedoms (DOF) and the ripple of the active suspension force as well as the active restoring torque. The suspension performances are compared between the proposed BLAMs and it shows that ripple of the active suspension force and ripple of the active restoring torque of the BLAM with high number of the rotor poles has at least 33.6 times less than that of the BLAM with low number of the rotor poles. At the same time, the average of the radial suspension force of the BLAM with high number of the rotor poles is 2.65 times larger than that of the BLAM with low number of the rotor poles. I.Introduction The bearingless motor (BLM) is attractive in high speed applications, special environment applications and so on, since it has no lubricant, no pollution, less friction, long device lifetime and maintenance-free [1]-[3]. In the traditional bearingless radial motor (BLRM), the output torque is limited by the volume of the rotor which is limited by the active suspension force. The output torque of the BLAM is not limited due to the active suspension force varies directly as the square of the rotor radius. The BLAM can performed as an all DOF active suspension motor, which is difficult to achieve in the traditional BLRM [4]-[6]. To further enhance the suspension performance of the BLAM, the BLAMs with different combine of the number of the rotor poles and the number of the stator slots are proposed and compared in this paper, and the result shows a well-designed BLAM can reduce the ripple of the active suspension force and restoring torque obviously, and can limited the coupling of different DOF. II.Topologies of BLAM The topology of proposed BLAMs are shown in Fig. 1, which can be divided into two stators and a rotor. The concentrated winding is applied to simplify the manufacture and reduce the length of the end winding. The BLAM-HP has 14 rotor poles combined with 18 stator slots and the BLAM-LP has 4 rotor poles combined with 6 stator slots. Each coil is controlled independently so two kind of armature fields can be controlled. For the BLAM-HP, 12/14 armature fields are imposed and the former is used to control the radial active suspension force as well as the radial active restoring torque, the latter is used to control the output torque as well as the axial active suspension force. For the BLAM-LP, 2/4 armature fields will be imposed and used to control all DOF. The outer radius, the inner radius the gap thickness, the line current density and the axial length of the proposed BLAMs are uniform. III.Performance Comparison of BLAM Topologies The suspension performance comparison between the two BLAMs when only produces the x-axis active suspension force is shown in fig.2. As shows in fig.2, the x-axis active suspension force created by the BLAM-LP is 16.2N in average with 148.6% ripple, which is 43N and 4.4% for the BLAM-HP. It shows the BLAM-HP can enhance the radial active suspension force and reduce the ripple remarkable. From a different perspective, the max unexpected suspension force in the BLAM-LP is 12N, 74.1% of the average active suspension force. For the BLAM-HP, the max unexpected suspension force is 1.02N, 2.4% of the average active suspension force. It confirms that the BLAM-HP can restrain the coupling of different DOF effectively. IV.Conclusions Two BLAMs with different combine of number of rotor poles and stator slots are proposed in this paper. The suspension performances are analyzed by the FEA. According to the comparison of the results, it shows an impressively enhance of the active suspension force and reduce of the ripple and the coupling of the other DOF when the high number of the rotor poles and stator slots are chosen. Compare to the BLAM-LP, the average active suspension force is 2.65 times larger, the ripple is 33.6 times less and the coupling of different DOF is 31.2 times less when the BLAM-HP is applied.

**References:**

[1] X. Sun, L. Chen, Z. Yang. “Overview of Bearingless Permanent-Magnet Synchronous Motors，” TIE, vol. 60, no. 2, pp. 5528-5538, Dec. 2013. [2] T. Nussbaumer, P. Karutz, F. Zurcher, J. W. Kolar. “Magnetically Levitated Slice Motor – An Overview，” TIA, vol. 47, no. 2, pp. 754-766, Mar. 2011. [3] B. Warberger, R. Kaelin, T. Nussbaumer, J. W. Kolar, “50-Nm/2500-W Bearingless Motor for High-Purity Pharmaceutical Mixing” TIE, vol. 59, no. 5, pp. 2236-2247, May. 2012. [4] M. Takemoto, S. Iwasaki, H. Miyazaki, A. Chiba, and T. Fukao, "Experimental evaluation of magnetic suspension characteristics in a 5-axis active control type bearingless motor without a thrust disk for wide-gap condition," in 2009 IEEE Energy Conversion Congress and Exposition, pp. 2362-2367, 2009. [5] S. Ueno, K. Nakazawa and C. Jiang, "Improvement of Stability of an Tilt-Controlling Axial Gap Self-bearing Motor with Single Stator," in 2019 12th Asian Control Conference (ASCC), pp. 1216-1221, 2019. [6] M. Osa, T. Masuzawa, R. Orihara, and E. Tatsumi, "Compact maglev motor with full DOF active control for miniaturized rotary blood pumps," in 2017 11th International Symposium on Linear Drives for Industry Applications (LDIA), pp. 1-6, 2017.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ae2f84d3e4552a49ced6b79519e9540c.jpg)
Fig.1 The topology of the proposed BLAM. a) shows the BLAM with high number of rotor poles and b) shows the BLAMwith low number of rotor poles.

![](https://assets.underline.io/uploads/markdown_image/1/image/13d1bc476ea33d1a0792cf554c3db4b4.jpg)
Fig.2 The suspension performance comparison when only the x-axis active suspension force is produced.

 A suspension performance comparison of the bearingless axial motor with different number of the rotor poles and stator slots

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

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

Magnetoelectric (ME) inductors are one of the promising elements of tunable energy efficient electronics. The main attention is paid to the possibility of controlling the inductance of such devices by electric field [1]. In this paper, we consider magnetic and electric tuning for two ME ring inductors of different geometries. The devices were manufactured as follows. Ferromagnetic (FM) layers of an amorphous magnetic alloy Metglas 2605SA1, 23 μm thick and 5 mm wide, were glued using cyanoacrylate adhesive to the outer (sample 1) or inner (sample 2) side of the piezoelectric PbZrTiO3 (PZT) ring (see Fig.1). The rings with Ag-electrodes had an inner diameter of 16 mm, thickness of 1 mm, and height of 1 mm. The rings were poled in the radial direction. The samples were placed inside a plastic frames and then 100 turns of wire with a diameter of 0.2 mm were wound around them. A constant electric voltage of up to 1 kV was applied to the PE rings parallel to the direction of polarization, which generated inside PE an electric field up to E=1 kV/cm. A constant magnetic field H=0-200 Oe, created by Helmholtz coils, was applied along or perpendicular to the axis of the devices. The frequency dependences of the inductance L(f) were measured in the frequency range 100 Hz – 5 MHz, and the inductance tuning coefficient γ = (L0-L)/L, at a frequency f = 300 Hz was calculated. Here L is the inductance in a given electric or magnetic field, L0 is the inductance in the absence of fields. The possibility of tuning the inductance with the simultaneous application of electric and magnetic fields is also shown for both samples. Fig. 1 shows measured dependences of the devices’ inductance on the electric field. With an increase in E, a decrease in the inductance of the structures was observed from 74 μH to 41.4 μH for sample 1. The inductance tuning coefficient in a field E = 1 kV/cm was γ ≈ 78% for sample 1, and γ ≈ 34% for the sample 2. Fig. 2 shows similar dependences when a constant magnetic field was applied to the structure. With an increase in H, the tuning coefficient nonlinearly increased and then saturated following the saturation of the FM layer. The tuning coefficient for sample 1 reached 1000% for in-plane magnetization at H = 20 Oe and 700% for magnetization along the axis at H = 200 Oe. Tuning coefficients for the sample 2 reached 1300% for both directions of magnetization.When the structures were magnetized with a field created by additional coil, the tuning coefficient reached ~850% at H ≈ 9 Oe. The observed dependences can be explained as follows. When an electric field E is applied to the PZT ring, it deforms as a result of the inverse piezoelectric effect. This deformation is transferred to the FM layer and generates an effective uniaxial magnetic anisotropy field as a result of the Villari effect. Thus, magnetic permeability µ and L becomes proportional to ~ 1/E. Since the magnitude of tensile strains on the outer side of the PE ring exceeds the magnitude of compression strains on the inner side, the tuning coefficient for the sample 1 is almost 2 times higher [2]. During magnetization of the FM layer with external magnetic field H, the change in inductance L is associated with a change in the magnetic permeability µ. The magnetic field inside the FM layer is Hin ≈ H/(1+χ×N), where χ is magnetic susceptibility, N is the demagnetizing factor [3]. Thus, upon in-plane magnetization of the samples, a decrease in the tuning coefficient was observed in an order of magnitude smaller magnetic fields. We have shown a possibility of creation ME inductors which inductance can be tuned by both electric and magnetic fields. The control of inductance by an electric field is more effective for the structure with a FM layer on the outer side of the PZT ring. At the same time, a larger magnetic field tuning coefficient was observed for a structure with an FM layer on the inner side of the PZT ring. The work was supported by the Russian Science Foundation, grant 19-79-10128.

**References:**

1. G. Srinivasan, N.X. Sun, SPIN, v. 2, p. 1240004 (2012). 2. Y. Yan, L.D. Geng, L. Zhang et al, Scientific reports, v.7, p. 16008 (2017). 3. J.A. Osborn, Phys. Rev., v. 67, p. 1351-1357 (1945).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8b623528f938c46bcee8bbeb40942191.jpg)
Fig. 1. Dependences of the inductance tuning coefficient γ on the electric field E for both samples.

![](https://assets.underline.io/uploads/markdown_image/1/image/43db9d722ecb02c0d6ccff76eda7b146.jpg)
Fig. 2. Dependences of the inductance tuning coefficient γ on the magnetic field H for in-plane magnetization and for magnetic field created by additional coil for sample 1.

 Magnetoelectric inductor tuned by electric and magnetic fields

Permanent magnet eddy current coupling (PMECCs) are electromagnetic devices which can transmit power from a motor to a load with no electrical or mechanical connections. Therefore, resulting in vibration isolation, low maintenance, and overload protection. However, PMECCs which have been considered so far, exhibit relatively lower efficiencies due to their torque slip- speed characteristics. Consequently, their industrial applications as power transmission devices has been limited, and they have mostly been employed in braking and damping applications. PMECCs topologies described in the literature have mainly employed plain copper sheets as a conducting material [1][2]. Although, these were simpler and more cost-effective solutions, they suffered from relatively lower efficiencies. The effiency, η, of a PMECC is given by: η=1-ΔΩ/Ω (1) Where, Ω is the input speed and ΔΩ is the slip-speed corresponding to the transmitted torque. From (1), it can be seen that the efficiency of PMECCs increase with larger speeds and reduced slip-speeds. In [3], it was theoretically shown that employing short-circuited conductors in slots (SCCSs), has the potential to improve efficiency, and it was proposed that high efficiency PMECCs can be employed as limited-slip differentials in electric vehicles. Nevertheless, in more recent investgations, SCCSs have been used in configurations which didn't fully exploit their potential in improving efficiency, thereby, resulting in PMECCs, with efficiencies similar to those using conductor sheets [4][5]. Therefore, in this paper an investigation into the design and analysis of PMECCs for power transmission applications, where efficiency is a primary requirement, is undertaken. The performances of radial and axial field topologies, using conductor sheets and SCCSs, in terms of torque slip-speed characteristics and efficiency are compared. It is shown, that when appropriately employed, SCCSs result in significant improvement in efficiency, even when less conductive materials, such as Aluminium, are employed. Fig. 1 shows schematics of radial and axial field PMECCs employing SCCSs, and Fig. 2 shows the variation of transmitted torque with slip-speed for a prototype radial field PMECC employing SCCSs. It can be seen that a good agreement between measured and predicted results exists. It can also be seen that the slip-speed corresponding to the maximum transmitted torque is only 100rpm. This represents a signficant improvement when compared to previously published PMECCs [1][2][4][5], where the slip-speed corresponding to the maximum transmitted torque can typically vary between hundreds of rpm to more than a 1000rpm.

**References:**

[1] A. Canova and B. Vusini, IEEE Transactions on Industrial Appllications, Vol. 39 (2003). [2] A. S. Erasmus, M. J. Kamper, IEEE Energy Conversion Congress and Exposition, (2015) [3] K. Atallah, J. Wang, IEEE Transactions on Magnetics, Vol. 47, (2011) [4] X. Dai,Q. Liang, J. Cao, Y. Long Y, J. Mo J and S. Wang, IEEE Transactions Magnetics, Vol. 52, (2016) [5] Z. Li , L. Yan, B. Qu and K. Fu, International Journal Appllied Electromagnetics and Mechanics, Vol. 62, (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8854de6ae3b3234a0fd274b02b0e6bc1.jpg)
Fig. 1 Radial and axial field PMECCs with SCCSs.

![](https://assets.underline.io/uploads/markdown_image/1/image/14a3776cff9b258ba9ed5d20060399a8.jpg)
Fig. 2 Variation of transmitted torque with slip-speed.

 High efficiency eddy current couplings

I.INTRODUCTION As one of the epoch-making technologies, the wireless power transfer (WPT) has significantly changed the power-accessing pattern owing to the distinctive merits of high convenience, reliability and security [1]. Possessing the capability to cordlessly transmit the energy via a long air gap, the emerging WPT has been widely investigated by many researchers [2]-[3]. Recently, the study objectives of WPT concentrate on efficiency enhancement, topology development, coil optimization and fresh applications such as the wireless lighting, wireless heating and wireless-powered implant [4]-[6]. In particular, the concept of wireless motor was newly conceived which can eliminate the metallic connection to facilitate the motor operation in an isolated environment [7]. By integrating the selective WPT with the motor drive, the wireless switched reluctance motor was proposed to remove the converter in the receiver side and centralize all controls in the transmitter side [8]. With the adoption of self-driving circuits and a full-bridge inverter in the receiver, the wireless shaded-pole induction motor was developed as tagged as the first wireless AC motor [9]. And the frequency-modulated wireless direct-drive motor was established for the underground in-pipe pumping application [10]. It should be noted the aforementioned wireless motor systems are universally evolved from the multifrequency selective WPT system which is designed to energize receivers by operating at different resonant frequencies. Nevertheless, it unavoidably adopts complicated switched capacitors, bulky transmitter coil and multiple independent receiver coils which in turn will result in a clumsy system and the unbalanced phase current of motor. To address concerns of previous wireless motor drives, a new wireless motor drive using decoupled bipolar coils is proposed and implemented for the coordinated operation of robotic arms. Specifically, two bipolar coils are orthogonally integrated to form a compact magnetic coupler while two magnetic couplers serve as the transmitter and receiver coils, respectively. The same-side coils are magnetically decoupled which indicates the transmitter-side bipolar coils can be independently controlled to facilitate the coordinated operation of two permanent magnet (PM) DC motors in the receiver side. Meanwhile, the series-inductor-capacitor-capacitor (S-LCC) compensation is adopted to ensure high transmission efficiency over a wide load range. Therefore, the proposed system is highly suitable for cordless robotic arms operating in an isolated or watery environment with electrocution free and high reliability. II.METHODOLOGY As depicted in Fig. 1 (a), the proposed system involves two half-bridge inverters, magnetic couplers, S-LCC compensations, diode rectifiers and PMDC motors. By independently controlling bipolar coils in coupler #1 in the transmitter, the motors can be separately excited by bipolar coils in coupler #2 in the receiver due to the magnetic decoupling characteristics of the same-side coils. Instead of adopting multiple resonant frequencies and multiple power-transfer channels, the proposed system can readily activate two motors with a single resonant frequency through the single power-transfer channel which in turn will significantly shrink the system volume and reduce the system complexity. In order to intuitively illustrate the magnetic coupling characteristics of the proposed coil, the finite element method (FEM) based simulations are conducted for better visualization as shown in Fig. 1 (b). It can be observed that two horizontal bipolar (Hb) coils and two vertical bipolar (Vb) coils are strongly coupled, respectively. However, the net amount of magnetic flux flows from the Hb coil to Vb coil is zero due to the symmetrical distribution of the magnetic flux. Consequently, the Hb and Vb coils are naturally decoupled which indicates the independent and wireless excitation of two PMDC motors can be realized by separately control the Hb and Vb coils from the transmitter side. III.EXPERIMENTAL VERIFICATION The experimental prototype and testing setup are built as shown in Fig. 2 (a) in which two gallium nitride (GaN) half-bridge inverters serve as the high-frequency AC source and two 150 W PMDC motors act as the load, respectively. All coils are made by Litz wires and all rectifiers are made by Schottky diodes to reduce the undesired power loss. Fig. 2 (b) shows the measured waveforms of three basic modes, namely, Mode I: motor A is active while motor B is idle; Mode II: motor A is idle while motor B is active; Mode III: both motor A and B are active. Meanwhile, it can be observed that no unexpected currents appear in the idle motor which well illustrates the good decoupled characteristics between Hb and Vb coils. Moreover, the ZVS can be readily achieved at the resonant frequency of 85 kHz in all modes. Finally, the measured results well confirm the feasibility and flexibility of the proposed wireless motor drive for the coordinated operation of robotic arms. This work was supported by Hong Kong Research Grants Council, Hong Kong, China under project 17207420.

**References:**

[1] G. A. Covic, and J. T. Boys, “Inductive power transfer,” Proceedings of the IEEE, vol. 101, no. 6, pp. 1276-1289, Jun. 2013. [2] Z. Zhang, H. Pang, A. Georgiadis and C. Cecati, “Wireless power transfer – an overview,” IEEE Trans. Ind. Electron., vol. 66, no. 2, pp.1044-1058, Feb. 2019. [3] S. Li and C. C. Mi, “Wireless power transfer for electric vehicle applications,” IEEE J. Emerg. Sel. Topics Power Electron., vol. 3, no. 1, pp. 4-17, March 2015. [4] W. Han, K. T. Chau, C. Jiang, W. Liu and W. H. Lam, “High-order compensated wireless power transfer for dimmable metal halide lamps,” IEEE Trans. Power Electron., vol. 35, no. 6, pp. 6269-6279, Jun. 2020. [5] W. Han, K. T. Chau, and Z. Zhang, “Flexible induction heating using magnetic resonant coupling,” IEEE Trans. Ind. Electron., vol. 64, no. 3, pp. 1982-1992, Mar. 2017. [6] C. Liu, C. Jiang, J. Song and K. T. Chau, “An effective sandwiched wireless power transfer system for charging implantable cardiac pacemaker,” IEEE Trans. Ind. Electron., vol. 66, no. 5, pp. 4108-4117, May 2019. [7] L. Wang, J. Li, H. Nie, J. Liu and S. Ke, “Coaxial nested couplers-based offset-tolerance rotary wireless power transfer systems for electric excitation motors,” IEEE Access, vol. 8, pp. 44913-44923, 2020. [8] C. Jiang, K. T. Chau, C. Liu, and W. Han, “Design and analysis of wireless switched reluctance motor drives,” IEEE Trans. Ind. Electron., vol. 66, no. 1, pp. 245-254, Jan. 2019. [9] H. Wang, K. T. Chau, C. H. T. Lee, L. Cao and W. H. Lam, “Design, analysis and implementation of wireless shaded-pole induction motors,” IEEE Trans. Ind. Electron., doi: 10.1109/TIE.2020.3007116. [10] W. Liu, K. T. Chau, C. H. T. Lee, L. Cao and C. Jiang, “Frequency-modulated wireless direct-drive motor control,” IEEE Trans. Magn., doi: 10.1109/TMAG.2020.3021708.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1049ee4681cae363c70b8ba26c367283.jpg)
Fig.1 Proposed wireless motor drive. (a) Configuration. (b) Magnetic field distributions of bipolar coils.

![](https://assets.underline.io/uploads/markdown_image/1/image/46c8226acabb0fe004625c1e59a36396.jpg)
Fig.2 Experimental verification. (a) Prototype. (b) Measured waveforms.

 Compact Wireless Motor Drive Using Decoupled Bipolar Coils for Coordinated Operation of Robotic Arms

Battery Electric Vehicles can significantly shorten battery life if not maintained at the proper temperature. PTC heater is used as a temperature control system for commercial vehicles. But PTC is heavy so the mileage of the vehicle is reduced. In addition, the insulation structure of PTC is complicated. Research on induction heaters is underway to compensate for the shortcomings of PTC in the ventilation industry. The structure of the induction heater consists of a workpiece and a coil. An alternating magnetic flux is generated by the coil to which the AC current is applied. Core loss occurs as heat in the workpiece by the alternating magnetic flux. This heating method does not require an insulating structure between the workpiece and the electrode, so it can increase mileage by reducing the volume and weight of the vehicle. The induction heater operates in a high frequency region, and the skin effect occurs due to the operation of the high frequency. Thus, the current is concentrated on the coil surface. Since a magnetic skin effect occurs in the workpiece, the magnetic flux generated by the current is concentrated on the inner and external workpiece surfaces adjacent to the coil. Due to the concentrated magnetic flux on the surface of the workpiece, the magnetic flux density from the surface of the workpiece rapidly with rising. So the relative permeability of the workpiece is high before the saturation point. Additionally, the coil is wound several times inside the induction heater. Therefore, a proximity effect occurs between coils by magnetic force generated when current flows. The current that is affected of the magnetic force is tilted inside the coil according to the direction and magnitude of the magnetic force, and the tilted direction and magnitude change continuously for a very short time by high frequency. The workpiece is directly affected by these phenomena. The skin effect and proximity effect occur due to the magnetic force between the coils and the high-frequency current, so these effects should be reduced for efficiency of induction heating. In this paper, the design of an optimal model was studied to increase the efficiency of the induction heater by considering skin effect and proximity effect. The induction heater is composed of a series resonance circuit among LC series resonance circuit and LC parallel resonance circuit. When the LC series resonance circuit operates at the resonance frequency, the reactance becomes 0 and the power factor approaches to 1. Since the reactance is zero at the resonant frequency, the impedance is minimized. Therefore, maximum current and magnetic flux can be generated with the same voltage. In other words, it is possible to maximize the output of the induction heater through the operation of the resonant frequency. For the operation of the resonance frequency of the induction heater, the required capacity of the capacitor is determined according to the inductance of the workpiece. And the capacity of the capacitor is proportional to the size and price. Small capacitors require high inductance to operate at resonant frequencies. For high inductance, proper workpiece design of induction heater is required. For example, if the workpiece is thicker more material is required. However, the magnetic flux is concentrated only on the workpiece surface due to the skin effect. Thus, the surface of the workpiece adjacent to the coil is saturated. Other regions except the surface have low flux linkage. As a result, the overall inductance of the workpiece is lowered. Conversely, if the workpiece is too thin, it becomes saturated due to overheating. So the inductance decreases and the required output is not obtained. Relative permeability is a parameter that directly affects inductance. In order to measure the exact relative permeability of the workpiece according to the skin effect, the magnetic flux density was derived by electromagnetic field analysis. After considering the saturation of magnetic flux density, the relative permeability of the workpiece was derived according to the distance from the coil. The average of the derived relative permeability was calculated to obtain the depth of penetration. The relative permeability of the workpiece was highest at the point depth of penetration, which is the result of calculation. Also, the magnetic force influencing the proximity effect was analyzed. The magnetic force was calculated by deriving the current density inside the coil by electromagnetic field analysis. And then a design flow chart was established and a basic model was selected. The 6kW induction heating model was chosen as the base model, a total of 101 coils consisted of two layers, and the workpiece was made of SUS430 material. For the basic model analysis, capacitance that satisfies the operation of capacity, voltage, and resonance frequency was derived using electromagnetic field analysis. In addition, a sensitivity analysis of the design parameters was performed and a high sensitivity parameter was derived. High sensitivity parameters included the height and thickness of the workpiece, the distance between the workpiece and the coil, the diameter of the workpiece, and the diameter of the coil. The optimal model was derived by comparing and analyzing the basic model with the model in which the height, thickness of the workpiece, and diameter of the coil were changed.

**References:**

[1] Hiroyuki Kagimoto, Daisuke Miyagi and Norio Takahashi, IEEE Trans. Magn., vol.46, no.8, pp.3018-3021 (2010) [2] Alexander Boadi, Yuji Tsuchida and Takashi Todaka, IEEE Trans. Magn., vol.41, no.10, pp.4048-4050 (2005) [3] M. Messadi, L. Hadjout and Y. Ouazir, IEEE Trans. Magn., vol.52, no.3 (2016) [4] Jesus Acero, Claudio Carretero and Rafael Alonso, IEEE Trans. Magn., vol.49, no.4, pp.1382-1389 (2013) [5] Nikolaos Tsopelas and Nicolaos J. Siakavellas, IEEE Trans. Magn., vol.44, no.12, pp.4711-4720 (2008)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c0288fa84de6d7a75c8e55271ba0e6f5.jpg)
Figure 1. 3D Base Model of the Induction Heater

![](https://assets.underline.io/uploads/markdown_image/1/image/ffc1a233b6f4dd1391c5d41ff3b429c0.jpg)
Figure 2. Magnetic Flux Density Distribution and Current Density Distribution

Closed-Form Electromagnetic Field Coupling to Transmission Line Model Exploiting the Reciprocity Theorem

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