Design and analysis of a new bearingless switched reluctance motor

Abstract

A bearingless switched motor with permanent magnets in the stator yoke (BSRM-PMSY) with two sets of windings on each stator tooth pole is studied. The current in one set of windings mainly controls the motor torque, and rotor suspension can be realised by adjusting the current in the other set of windings. Each stator module unit of the motor is composed of a permanent magnet and two U-shaped iron cores. Finally, a BSRM-PMSY finite element simulation model is established to explore the static characteristics of the motor, including magnetic field distribution, permanent magnet flux linkage and harmonic analysis, back electromotive force (EMF) and harmonic analysis, suspension performance, and so on. The analysis of the simulated results lays a foundation for the establishment of a BSRM-PMSY mathematical model and control system.

Keywords

Bearingless motor magnetic suspension finite element analysis

1. Introduction

The stator and rotor of switched reluctance motor (SRM) are of salient pole structure, and only the stator tooth pole is equipped with a winding. This has the advantages of a simple, solid structure, providing high reliability, at low cost and with good fault-tolerance; it has thus attracted extensive attention among researchers working on high-speed motors [1–3]. Since there is neither a winding nor permanent magnet on the rotor, it is especially suitable for operation under harsh working conditions and is widely used in aerospace engineering and other scenarios. So far, through the in-depth research and continuous efforts of scholars, the performance of switched reluctance motor in all aspects has been continuously improved and the cost has been continuously reduced, and it has been widely used in various fields, such as oil extraction, aerospace, automobile drive, textile machinery and other important fields closely related to the national economy [4,5].

A large number of studies show that the construction of high specific power maglev flywheel battery is an effective way to solve the mileage anxiety of electric vehicles. As the core component of flywheel battery, magnetic suspension bearing system directly determines the running quality of flywheel battery. To improve the motor speed and improve the power density of the electric drive system in civil and aerospace application [1], the active suspension control of motor shaft by use of magnetic bearing technology can realise friction-free, lubrication-free operation of a high-speed shaft, thus addressing the problem of severe bearing wear and heating in high-speed motors [6]. The further to improve system integration and rotor critical speed, a set of windings can be added to the stator tooth pole of the motor to replace the magnetic bearing stator winding, and rotor active suspension is realised by controlling the winding current, thus forming a bearingless motor technique [7,8]. This technique is applied to the field of a switched reluctance motor, so as to obtain a bearingless switched reluctance motor (BSRM), with the further improvement of system integration, single winding BSRMs have been widely studied. Although the number of single BSRM windings is reduced by half, the degree of coupling of suspension and torque control increases and the control algorithm is rendered more complex [9]. Based on this, the 6/4-pole BSRM-PMSY with significantly reduced coupling degree of suspension and torque control is studied. Firstly, the structural characteristics of the BSRM-PMSY are described in detail in this chapter. The permanent magnet is embedded between the iron cores of the stator yoke. The permanent magnet is magnetised tangentially, and the directions of magnetisation of the two adjacent permanent magnets are opposed thereto, therefore, the BSRM-PMSY produces a magnetic gathering effect, which can improve the air gap magnetic density, while controlling the suspension winding and torque winding separately, reducing the coupling performance. Secondly, the operating mechanism of the BSRM-PMSY is described based on “suspension principle” and “minimum path principle of reluctance”. Then, the “consistency” and “complementarity” of the armature winding are revealed through the magnetic circuit analysis of four typical rotor positions of the BSRM-PMSY. Finally, the finite element simulation model of a BSRM-PMSY will be established to analyse the static characteristics of the motor, including magnetic field distribution, permanent magnet flux linkage and harmonic analysis, back electromotive force and harmonic analysis, electromagnetic torque and radial suspension force, etc. Through analysis of the simulated results, the feasibility and effectiveness of the principle analysis and method are verified, laying a foundation for the mathematical model.

2. Working principle of BSRM-PMSY suspension

2.1. Motor structure

The structure of single winding BSRM is similar to that of an ordinary SRM. Only one set of concentrated windings is wound around each stator tooth pole, but the suspension mechanism of the single-winding BSRM determines that each set of winding currents must be controlled independently to construct a relative tooth pole unbalanced air gap magnetic flux density. As shown in Fig. 1(a), the subject of the present research is a traditional, three-phase 6-slot/4-pole single-winding BSRM. A single-winding BSRM has only two sets of independent windings per phase. Asymmetric excitation can only produce a one-dimensional radial force. If only two sets of windings of phase B are excited, it can only produce a suspension force in the X-direction. Therefore, for 6/4-pole single-winding BSRMs, at least three windings must be connected in two phases to produce a radial levitation force in any direction in the two-dimensional plane, and each winding of each phase produces levitation force and torque at the same time, making the system difficult to control.

Fig. 1.

Two kinds of BSRM.

In order to solve the above problems, this paper proposes a BSRM-PMSY. The stator is composed of six “U” shaped cores of stator module units. Among them, the stator module units B2 and C2 and the stator module units B1 and C1 are each embedded with a permanent magnet between the cores of the stator yoke. The permanent magnet is charged tangentially, and the magnetization directions of the adjacent two permanent magnets are opposite. The armature winding adopts a centralised winding layout, which is wound on the armature teeth. Therefore, this BSRM-PMSY produces a magnetic gathering effect, which can improve the air gap magnetic flux density. The 6/4-pole BSRM-PMSY investigated here, is operated using two-phase common conduction arising from four sets of windings to realise radial two-degree-of-freedom suspension. Each phase has two sets of windings, namely a suspension winding and torque winding. For example, when phase A and phase B work, radial suspension is realised through windings on the four tooth poles A1, A2, B1, and B2 at the same time, so as to decompose the electromagnetic force under each conduction tooth pole into a rectangular coordinate system. See Table 1 for parameters of the prototype. The shape of the permanent magnet in this paper is different from that of the previous research. This is because during the manufacturing process, we found that the permanent magnet designed before was embedded between the iron cores of the stator yoke. During the high-speed process, the permanent magnet fell off, resulting in the loss of mechanical friction and motor driving function. Therefore, on the basis of the same size and structural parameters of the stator and rotor, the embedded permanent magnet structure is redesigned. Compared with the permanent magnet in the previous article, it can more effectively prevent the permanent magnet from being damaged and falling off, improve the mechanical strength of the rotor, better generate the magnetic focusing effect and improve the air gap magnetic density [4,10].

Table 1

Parameters of the prototype

Parameters	Values
Outer diameter of stator (mm)	100
Inner diameter of stator (mm)	79
Rotor pole arc (deg.)	13
Air-gap length (mm)	0.5
Stator tooth width (mm)	12
Polar altitude of stator (mm)	34
Outer diameter of rotor (mm)	44
Inner diameter of rotor (mm)	34

2.2. Working principle of a BSRM-PMSY

The radial levitation force generation principle of BSRM-PMSY is the same as that of ordinary bearingless permanent magnet synchronous motor. The levitation force is generated by applying the levitation force current to the levitation winding and interacting with the permanent magnetic field to form the levitation magnetic field, resulting in the distortion of the original magnetic field, making the air gap magnetic flux density in a certain area of the air gap larger and the air gap magnetic flux density in the opposite direction smaller, The radial levitation force in the direction in which the magnetic flux density of the direction pointing to the gap becomes smaller is obtained to offset the Maxwell force generated when the eccentricity occurs. If the rotor is eccentric, the radial levitation force in the opposite direction can be obtained by controlling the current of the levitation force winding to cancel and pull the rotor back to the central balance position. On the contrary, if the current opposite to the current of the given suspension force winding is applied, the radial suspension force opposite to the preset direction will be generated.

Since the BSRM-PMSY rotor has four poles, the mechanical cycle is 22.5°. When the rotor is in the initial position (shown in Fig. 2(a)), θ_r = 0° and, at that time, the rotor teeth R1 coincide with the armature teeth A1, and the permanent magnet flux generated by the permanent magnet passes through the stator teeth, enters the rotor teeth through the air gap, and turns with the armature coil A1. At that time, the amplitude of permanent magnet flux linkage in armature coil A1 is the maximum positive polarity, as shown in Fig. 2(a).

Fig. 2.

Working principle of BSRM-PMSY.

When the rotor position rotates through 22.5° counter-clockwise, such that when θ_r = 22.5°, as shown in Fig. 2(b), the permanent magnetic flux cannot form a closed loop, and the flux linkage of the turn chain in the armature winding is almost 0.

The rotor continues to rotate counter-clockwise through 45°, such that when θ_r = 45°, as shown in Fig. 2(c), the BSRM-PMSY rotor teeth R2 coincide with the armature teeth A1, and the permanent magnet flux generated by the permanent magnet passes through the air gap from the rotor teeth into the stator armature teeth and turns with the armature coil A1. At this time, the amplitude of the permanent magnet flux linkage in armature winding A1 is the maximum negative polarity. At this time, the amplitude of the permanent magnet flux linkage in armature coil A1 is the maximum positive polarity.

When the rotor position is such that θ_r = 67.5°, as shown in Fig. 2(d), the air gap between adjacent rotor modules, that is, the air gap on the rotor module, is just opposite stator armature tooth A1, and the effective flux of the turn chain in armature coil A1 is 0.

2.3. Mathematical model

On the one hand, the mathematical model is the basis of analyzing the levitation force characteristics of the stator yoke permanent magnet bearingless switched reluctance motor, on the other hand, it is also the need of establishing the digital control system of the magnetic bearing. For the convenience of derivation, the reluctance loss and hysteresis loss of stator and rotor are ignored, and the influence of temperature, magnetic saturation and cogging effect are not considered. In Fig. 1, Φ_m is the offset total flux, Φ_a1, Φ_a2, Φ_b1, Φ_b2, Φ_c1, Φ_c2, Φ_a1 is the flux of each phase; Nm and ns are the turns of torque winding and suspension winding of each phase respectively; F _m is the magnetomotive force of the permanent magnet; P _a1, P _a2, P _b1, P _b2, P _c1, P _c2 and Pa1 are respectively the sum of the permeances of a pair of stator and rotor tooth poles and the air gap between them. The radial control coil is driven by three-phase power inverter.

If the magnetic potential of the torque winding and the suspension winding is represented by the symbol “” and the air gap permeability is represented by the symbol “”, because the magnetic resistance of the core material is much smaller than that of the air gap, it can be ignored. At this time, the three-phase winding of bearingless switched reluctance motor can be represented by the equivalent magnetic circuit diagram shown in Fig. 3.

Fig. 3.

Equivalent magnetic circuit diagram.

According to the analysis of the operation principle of the stator yoke permanent magnet bearingless switched reluctance motor, based on the similarity of the motor structure and the radial suspension mechanism, this paper uses the mathematical model of the stator yoke permanent magnet bearingless switched reluctance motor with two-phase conduction, which is derived from reference [11], and then the complete expression of the radial force on the stator pole can be obtained. If we want to calculate the suspension force on the rotor, we only need to calculate the radial forces on the four stator poles in one phase in the above way, and then according to the principle of force and reaction force, we can get the following results by subtracting the radial forces on the two opposite stator poles $\begin{eqnarray}\displaystyle F_{{\alpha}}\text{} & =\text{} & \displaystyle F_{r1}-F_{r3}\end{eqnarray}$ (1) $\begin{eqnarray}\displaystyle F_{{\beta}}\text{} & =\text{} & \displaystyle F_{r2}-F_{r4}.\end{eqnarray}$ (2) In the above formula: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle F_{r1}=\frac{h{\mu}_{0}}{2}\left\{\frac{1}{l_{0}^{2}}\left[U_{1}\left(1-\frac{1}{2e_{m}}\right)+\frac{l_{m}B_{sat}}{2{\mu}}-\sqrt{\frac{l_{m}^{2}B_{sat}^{2}}{4{\mu}^{2}}+U_{1}\frac{B_{sat}}{e_{m}{\mu}}\left(l-\frac{l_{m}}{2}\right)+\frac{U_{1}^{2}}{4e_{m}^{2}}}\right]^{2}\left(\frac{{\pi}r}{12}-r\left|{\theta}\right|\right)\right.\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \left.\qquad +∼\frac{1}{l_{f1}^{2}}\left[U_{1}\left(1-\frac{1}{2e_{f}}\right)+\frac{l_{f}B_{sat}}{2{\mu}}-\sqrt{\frac{l_{f}^{2}B_{sat}^{2}}{4{\mu}^{2}}+U_{1}\frac{B_{sat}}{e_{f}{\mu}}\left(l-\frac{l_{f}}{2}\right)+\frac{U_{1}^{2}}{4e_{f}^{2}}}\right]^{2}\left(l_{0}+2r\left|{\theta}\right|\right)\right\}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle F_{r3}=\frac{h{\mu}_{0}}{2}\left\{\frac{1}{l_{0}^{2}}\left[U_{3}\left(1-\frac{1}{2e_{m}}\right)+\frac{l_{m}B_{sat}}{2{\mu}}-\sqrt{\frac{l_{m}^{2}B_{sat}^{2}}{4{\mu}^{2}}+U_{3}\frac{B_{sat}}{e_{m}{\mu}}\left(l-\frac{l_{m}}{2}\right)+\frac{U_{3}^{2}}{4e_{m}^{2}}}\right]^{2}\left(\frac{{\pi}r}{12}-r\left|{\theta}\right|\right)\right.\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \left.\qquad +∼\frac{1}{l_{f1}^{2}}\left[U_{3}\left(1-\frac{1}{2e_{f}}\right)+\frac{l_{f}B_{sat}}{2{\mu}}-\sqrt{\frac{l_{f}^{2}B_{sat}^{2}}{4{\mu}^{2}}+U_{3}\frac{B_{sat}}{e_{f}{\mu}}\left(l-\frac{l_{f}}{2}\right)+\frac{U_{3}^{2}}{4e_{f}^{2}}}\right]^{2}\left(l_{0}+2r\left|{\theta}\right|\right)\right\}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle U_{1}=N_{m}I_{m}\pm N_{s}I_{s1}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle U_{3}=N_{m}I_{m}\pm N_{s}I_{s3}\nonumber\end{eqnarray}$

In formula (1)–(2), F _𝛼, F _𝛽 When the stator yoke permanent magnet bearingless switched reluctance motor has two-phase conduction, it is in the rotating coordinate system 𝛼 and 𝛽 Direction radial force. I _m and is are the current of torque winding and suspension winding respectively; μ₀ is the air permeability; μ Is the permeability of the medium; l ₀ is the average air gap length; Bsat is the saturation magnetic density of the material. The meanings of other symbols have been explained in reference [11] and will not be repeated here. It should be noted that i _s1 and i _s3 are the currents of the suspended windings relative to the two stator poles. Since the suspended windings of the two stages are connected in series, the two currents are equal numerically. If the current of the suspended winding of a certain pole is in the same direction as that of the main winding of the same pole, the positive sign will be taken; otherwise, the negative sign will be taken. 𝛽 The radial forces F _r2 and F _r4 in the same direction can be obtained.

3. Static characteristics

3.1. Permanent magnetic field distribution

The presence of a flux leakage branch will affect the magnetic flux density in the air gap, and then affect the electromagnetic characteristics such as permanent magnet flux linkage. Figure 4 shows the no-load magnetic field distribution of the BSRM-PMSY at different rotor position angles. It can be seen that the permanent magnetic circuit flows out of the N pole of the permanent magnet, passes through the stator tooth pole, stator yoke, air gap, rotor pole, air gap, and stator tooth pole, then returning to the S pole of the permanent magnet. For each special position of the rotor, the permanent magnet magnetic circuit is consistent with the theoretical analysis to within an acceptable tolerance.

Fig. 4.

No-load permanent magnetic field distribution.

Air gap length refers to the distance between stator and rotor, and its size must be reasonably selected. If the air gap is too large, the bearing capacity decreases; if the air gap is too small, a more accurate control system is required. Therefore, the determination of air gap length is important. In the design of the test prototype, the air gap length is 0.5 mm. Figure 5(a) corresponds to the rotor position in Fig. 4(a) (θ_r = 0°), Fig. 5(b) corresponds to the rotor position in Fig. 4(b) (θ_r = 45°) showing the distribution of no-load permanent magnetic flux density in air gap when θ_r = 45°. The peak air gap flux density occurs at rotor position θ_r = 0° can reach 0.8 T and at θ_r = 45° can reach 0.9 T, which is far less than the peak value of air gap magnetic flux density when using a traditional single-winding BSRM (about 2T), which proves that the magnetic load on the BSRM-PMSY is much less than that on the single-winding BSRM. Due to the salient pole structure characteristics of the proposed BSRM-PMSY device, the harmonic content of air gap permeance is rich, causing significant distortion of the magnetic density waveform. This also shows that the motor may be classified as a harmonic modulation motor, that is, the motor has multiple harmonics involved in the generation of torque.

Fig. 5.

No-load air gap flux density distribution.

3.2. Permanent magnet flux linkage

The BSRM-PMSY single-phase no-load permanent magnet flux linkage is illustrated in Fig. 6, so only A1 and A2 coils are taken as examples in the figure. Since the permanent magnet flux linkage of the turn chain in coil A1 is the same as that in coil A2, and the flux linkage waveforms coincide, it is verified that the flux linkage of armature coils A1 and A2 is consistent and complementary, and can offset the even harmonics of armature coil permanent magnet flux linkage and induced potential, improving the sinusoidal degree of each phase of permanent magnet flux linkage and induced potential.

Fig. 6.

Coil flux linkage and single-phase flux linkage.

Figure 7 shows the harmonic distribution of no-load permanent magnet flux linkage of the BSRM-PMSY. Among them, the permanent magnet flux linkage of the turn chain in armature coils A1 and A2 contains even harmonics, and the harmonic content is THD%_A1 = THD%_A2 = 3%. It can be seen from the previous analysis that armature coils A1 and A2 are complementary, and the even harmonics in the permanent magnet flux offset each other. Therefore, in the phase a permanent magnet flux, the even harmonics are almost 0, which improves the symmetry of the permanent magnet flux. Figure 8 illustrates the three-phase permanent magnet flux linkage in an electric cycle, which further illustrates the sinusoidal nature of each phase and its permanent magnet flux linkage.

Fig. 7.

Harmonic distribution of no-load permanent magnet flux linkage.

Fig. 8.

Three-phase no-load permanent magnet flux linkage.

The waveform of the BSRM-PMSY single-phase back EMF is shown in Fig. 9: the influences of the complementary characteristics of the winding on the synthetic single-phase back EMF are evident. In addition, A1 and A2 curves in Fig. 9 coincide. Figure 10 demonstrates the harmonic analysis of the single-coil, and single-phase, back EMF waveforms. Among them, the third harmonic content is the highest in either single-phase back EMF or single-coil back EMF. In armature coils A1 and A2, the amplitude of the second harmonic is almost equal and the phase is opposite. Therefore, after forming a single-phase winding in series, the even harmonics cancel each other.

Fig. 9.

Single-phase back EMF waveform of the BSRM-PMSY.

Fig. 10.

Back EMF harmonic analysis of a BSRM-PMSY.

4. Suspension force analysis

In the conduction section, the unbalanced air gap magnetic density is constructed by asymmetric excitation of two tooth pole windings of the same phase, resulting in a radial suspension force. For example, when the mechanical angle of the motor is within [−90°,90°] and the AB two-phase is on, iam1 = iaf1 = ibm1 = ibf1 = 3A, iam2 = iaf2 = ibm2 = ibf2 = 1a, icm1 = icf1 = icm2 = icf2 = 0A; when phase A is on, iam1 = iaf1 = 3A, iam2 = iaf2 = 1A, ibm1 = ibf1 = ibm2 = ibf2 = icm1 = icf1 = icm2 = icf2 = 0A. The current with subscript m represents the torque current, and the current with subscript f represents the suspension current. The levitation force waveforms under single-phase conduction and two-phase conduction are shown in Fig. 11. The radial levitation force in the X-direction is significantly smaller than that in the case of two-phase conduction, however, in the case of single-phase conduction, the radial levitation force in the Y-direction is significantly larger than that in the case of two-phase conduction. Therefore, single-phase conduction is adopted in the X-direction and the two-phase conduction mode is used in the Y-direction to ensure the tracking of X and Y components of the radial levitation force at any angle.

Fig. 11.

Suspension force simulation waveform of single-phase and two-phase conduction when the current is equal.

5. Conclusion

According to the development requirements imposed by the need for device integration, high speed and high power-density in a motor, a 6/4-pole BSRM-PMSY is investigated, and the topological evolution of its operating process is described. The basic suspension principle of such a BSRM-PMSY is revealed based on the principle of minimum reluctance. Finally, the harmonic analysis of the BSRM-PMSY permanent magnet flux is conducted to verify that the armature winding of the BSRM-PMSY had both “consistency” and “complementarity”, which can offset the even harmonics in the permanent magnet flux and improve the sinusoidal characteristics of the permanent magnet flux and induced EMF. The results of the present research lay a theoretical foundation for research into BSRM-PMSY suspension mechanisms and mathematical models thereof.

Footnotes

Acknowledgements

This work was supported in part by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Project (19KJD470005), and Suzhou Agricultural Science and Technology Innovation Project (SNG2020055).

Author declarations

The authors have no conflicts to disclose.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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