I.Introduction Hybrid magnetic bearings (HMBs) have several merits, such as no friction and abrasions, no lubrication and no sealing, high speed, high precision and long life. In HMBs, the permanent magnet is adopted to generate bias flux for the low power consumption and small volume. However, in existing HMBs, several suspension poles are designed in the same stator core. The suspension force is generated by the interaction of the bias flux and control flux. The HMB of this structure realizes the radial two-degree-of-freedom (2-DOF) suspension in one stator core, especially when the rotor is deviated from unbalance position, the suspension force coupling in the X-Y direction is severe and the control is complicated. To compensate for this deficiency, a novel DC HMB with crossed poles is studied. The suspension poles in the X and Y direction are designed different stator cores. Therefore, it can solve the radial 2-DOF coupling of traditional four-pole HMBs and simplify the control. A simple mathematical models are presented, which can make the maximum magnetic levitation force in the X and Y directions. The nonlinearity of suspension forces and the coupling of electromagnetic among this four-pole magnetic bearing are analyzed by MagNet 3D. The finite element simulation is carried out to verify the theoretical analysis. II.Configuration and Suspension Principle The configuration and magnetic circuit of a novel DC HMB with crossed poles are presented in Fig. 1. As shown in Fig. 1(a), the main parts of this HMB are two slice stators, namely X-stator and Y-stator, axial magnetized permanent magnets and two slice rotor irons. Two symmetrical suspension poles in the X direction are evenly distributed along the circumference of X-stator, and the suspension poles in the Y direction are crossed in the Y-stator. Radial control windings are wound on each stator. The magnetic circuit of radial suspension control flux and static bias flux is represented in Fig. 2(b). The solid lines denote the static bias flux generated by the permanent magnets. The dotted lines describe the radial suspension control flux generated by radial control current. If the rotor irons are displaced from the balance position in the radial position by the radial disturbances, the fluxes between the magnetic flux and the bias flux are overlapped, which results in force to bring the rotor to the radial balance position. According to the equivalent magnetic circuit method, the radial suspension forces in the X and the Y directions are deduced as follows: Fj=Fpm+kij×ij(1) where the subscript “j” denotes x and y. Fpm is the magnetic attraction force produced by the bias flux at the equilibrium position. kij is the radial force-current stiffness. Fpm and kij can be given as: Fpm=-S×μ0×Fm×Fm÷g3 Kij=2S×μ0×Fm×N÷g2(2) where Fm is the magnetomotive force. μ0 is vacuum permeability. S is radial magnetic pole area. g is radial air gap length. N is number of radial control coils. III.Models, Design and Analysis Based on above-mentioned analysis, electromagnetic performance of the presented HMB is manufactured by the MagNet software. The prototype is simulated to analyze the electromagnetic performance by the three-dimensional finite element method, and the different simulation cases are given in Fig. 2. Fig. 2(a) shows the distribution of the bias flux. The radial air-gap magnetic flux density of each pole is 0.6T symmetrically. In Fig. 2(b), the radial control winding in the X direction is electrified with 3A current, and the control flux density distribution in the X direction is generated. It can be seen from Fig. 2(c) that there is an increase of air-gap flux in the positive X direction and a decrease in the negative X direction by the superposition of the control flux in the X direction and bias flux. Therefore, only the suspension force in the X direction is produced. To verify the correctness of the mathematical models, the control current is applied to generate radial suspension force only in the positive X direction. The relationships between the suspension force and control current are shown in Fig. 2(d). The currents change from 0 to 3 A. The maximum suspension force reaches 260 N. It can be seen that the finite element simulation results are in good agreement with the theoretical values, and there is a linear force-current relationships. IV. Conclusion This paper aims to construct a novel DC HMB with crossed poles to simplify the structure, obtain the maximum bearing capacity and solve the radial two-degree-of-freedom coupling. The simulation results have shown that the suspension forces produced by the crossed poles have better linearity around the balance position and no movement. There is no coupling of two directions for the independent magnetic circuit. The research results verify the correctness of magnetic circuit, suspension mechanism and mathematical model.

**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.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b086123141f2db12e85d7de06a7be696.jpg)
Fig. 1. The configuration and magnetic flux path of the proposed HMB.

![](https://assets.underline.io/uploads/markdown_image/1/image/2114063a67fc96a8d89fdd14022a9115.jpg)
Fig. 2. Flux distribution and the force-current relationships. (a) Bias flux. (b) Control flux. (c) Resultant flux. (d) Force-current relationship.

 Modeling and Electromagnetic Performance Analysis of the Novel DC Hybrid Magnetic Bearing with Crossed Poles

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

I.Introduction Switched reluctance motors (SRMs) inherently have the advantages of simple structure, no mechanical friction, flexible control and long service life so that they have a good application prospect in hybrid electric vehicle, military and rail transit. Bearingless switched reluctance motors (BSRMs) combine the merits of SRMs and magnetic bearings. However, in the traditional BSRMs, double windings are wound on the stator poles to produce suspension force and torque at the same time. It leads to a problem of nonlinear strong coupling between the torque flux and suspension flux. Therefore, a novel three-pole BSRM is presented, which produces torque and radial controllable suspension force. Each torque pole is designed to be two poles in the axial direction, and suspension poles can be designed larger. The torque poles take up less radial space of the stator in order to increase the radial suspension force density. Firstly, the configuration and suspension principle of the novel BSRM are introduced. Then, the mathematical model of radial suspension force calculation is presented by means of equivalent magnetic circuit. Finally, according to the main parameters of the BSRM, the air-gap magnetic fields and radial suspension forces are analyzed by MagNet 3D. The research results verify the performance of the proposed BSRM. II.Configuration and Suspension Principle According to Fig.1, the proposed BSRM consists of two pieces of stator cores with six stator poles, two rotor cores with six rotor poles and two radial magnetized permanent magnets. The stator poles can be divided into torque poles and suspension poles. Different from conventional BSRM, the torque poles are designed to place axially, the width of rotor pole and torque pole is designed to be equal, the width of suspension pole is designed to be larger than that of the rotor pole. Therefore, there is always a rotor pole under the suspension pole when the rotor is rotating. Radial suspension control flux is generated by radial control current, and the bias flux is generated by two permanent magnets, which form a close path through two stator cores and two rotor cores. Torque flux passes through the torque poles, air gaps and rotor poles, which is separated from the control flux. The paths of suspension flux and torque flux are separated. The torque and suspension force are decoupling naturally. Based on the equivalent magnetic circuit analysis, the mathematical models of suspension force are deduced. The radial suspension force can be written as Fj=Fpm+kij×ij where the subscript “j” denotes A, B and C. Fpm is the magnetic attraction force produced by the bias flux at the equilibrium position. kij is the radial force-current stiffness. Fm and kij can be given as Fpm=S×μ0×Fm×Fm÷(4g2) Kij=S×μ0×Fm×N÷(2g2) where μ0 is vacuum permeability. S is radial magnetic pole area. g is radial air gap length. N is number of radial control coils. III.Models, Design and Analysis To analyze the electromagnetic performance of the proposed three-pole BSRM, including magnetic flux distribution and the force-current relationships, the software MagNet is used to build the finite element model. The simulation results are shown in Fig. 2. Fig. 2(a) shows the bias flux distribution of the proposed BSRM. When the rotor is located in the balance position, the air gap bias flux density under three suspension poles is equal. Fig. 2(b) shows the control flux distribution when the maximum suspension force in the X direction is generated .The reluctant flux distribution is shown in Fig. 2(c) and Fig. 2(d). In Fig. 2(c), it can be seen that the air gap flux density increases under pole A and decreases under pole B and pole C, resulting in a suspension force pointing to the positive X direction. Fig. 2(d) shows another case of the reluctant flux distribution. The air gap density increases under pole B and decreases under pole C. It leads to the suspension force pointed to the positive Y direction. Therefore, the correctness of magnetic circuit and suspension mechanism is proved. The relationship between the control current and radial suspension force Fx and Fy can be calculated. Comparison between the simulation value and theoretical value is shown in Fig. 2(e) and Fig. 2(f). In Fig. 2(e), the suspension force in the X direction is produced, when the current changes from 0 to 3 A. When the control current changes from 0 to 3 A, the force-current relationship is shown in Fig. 2(f). Based on the above analysis, the correctness of the mathematical model is proved. Fig. 2(g) shows the fluctuation suspension force Fx and Fy. It can be seen that the force is stable in the rotating condition. IV.Conclusion This paper presents a novel three-pole BSRM with independent torque and suspension force magnetic circuit. The theory analysis and simulation results are verified the electromagnetic performance of the proposed BSRM.

**References:**

[1]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. [2]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/2ebd4d829e367720548b33bc78b6d169.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/d10611797b80ff80963b76415555085a.jpg)

 Suspension Characteristics for a Novel Three-pole Bearingless Switched Reluctance Motor

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Modeling and Electromagnetic Performance Analysis of the Novel DC Hybrid Magnetic Bearing with Crossed Poles

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

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

Suspension Characteristics for a Novel Three-pole Bearingless Switched Reluctance Motor

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