Analytical Investigation of the Magnetic-Field Distribution in an Axial Magnetic-Field-Modulated Brushless Double-Rotor Machine
Abstract
:1. Introduction
2. Analytical Modeling
- (1)
- The soft-magnetic material (iron) has infinite magnetic permeability μ → ∞;
- (2)
- The PMs are axially magnetized with relative permeability μr = 1.
3. Analytical Solution
3.1. Governing Partial Differential Equations
3.2. Boundary Conditions
3.2.1. At the Interface z = 0
3.2.2. At the Interface z = z1
3.2.3. At the Interface z = z2
3.2.4. At the Interface z = z3
3.2.5. At the Interface z = z4
3.2.6. At the Interface z = z5
3.2.7. At the Interface θ = θi and θ = θi + β
3.2.8. At the Interface θ = θj and θ = θj + α
3.3. General Solutions
3.4. Magnetic-Field Distribution in Two Air Gaps
3.5. No-Load Back Electromotive Force
3.6. Torque and Axial Force
4. Analytical Method Evaluation
4.1. Magnetic-Field Distribution
4.2. Electromagnetic Performance Prediction
4.3. Saturation Effect
4.4. End Effect
4.5. Influence of Key Parameters on the Performance
4.6. Application Scope
4.7. Computing Time Evaluation
5. Conclusions
- (1)
- The analytical expressions for open-circuit and armature reaction field distribution by considering the stator slotting and modulation effect have been derived from a set of Laplace’s or Poisson’s equations with corresponding boundary conditions. The magnetic-field predictions show good consistency with 3-D FEM results.
- (2)
- The no-load back EMF, torque and axial force have been obtained by adopting the predicted flux density at the mean radius instead of the actual 3-D distribution of the magnetic field. The 2-D analytical method overestimates the machine performance by less than 11%. The discrepancy is mainly due to the fact that the analytical method assumes unsaturation of the soft-magnetic material and no end effect.
- (3)
- As the analytical and 3-D FEM computation follow the same trend in evaluating the torque with less calculation time and more flexibility, it can be used as an effective tool for the initial design procedure of the axial MFM-BDRM with open slot.
- (4)
- Though the proposed method could not capture the fluctuation in torque with the change of slot-opening width, it can be used for performance prediction of the open-slot or the semi-closed-slot machine with high precision.
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix
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Symbol | Quantity | Value |
---|---|---|
Ri | inner radius | 64 mm |
Ro | outer radius | 114 mm |
z1 | PM thickness | 4 mm |
z2 − z1 | inner air-gap thickness | 1 mm |
z3 − z2 | FB thickness | 11 mm |
z4 − z3 | outer air-gap thickness | 1 mm |
Q | pole number of FB | 23 |
pp | pole-pair number of PM rotor | 20 |
ps | pole-pair number of stator | 3 |
S | slot number | 18 |
hs | height of slot | 11 mm |
ws | width of slot | 19.3 mm |
αp | pole-arc coefficient of PM rotor | 1 |
αf | arc ratio of FB | 0.5 |
Nt | number of conductors per slot | 13 |
wt | width of tooth at the mean radius | 11.8 mm |
Br | Remanent flux density of PM | 1.26 T |
I | Root mean square value of one-phase current | 30 A |
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Tong, C.; Song, Z.; Bai, J.; Liu, J.; Zheng, P. Analytical Investigation of the Magnetic-Field Distribution in an Axial Magnetic-Field-Modulated Brushless Double-Rotor Machine. Energies 2016, 9, 589. https://doi.org/10.3390/en9080589
Tong C, Song Z, Bai J, Liu J, Zheng P. Analytical Investigation of the Magnetic-Field Distribution in an Axial Magnetic-Field-Modulated Brushless Double-Rotor Machine. Energies. 2016; 9(8):589. https://doi.org/10.3390/en9080589
Chicago/Turabian StyleTong, Chengde, Zhiyi Song, Jingang Bai, Jiaqi Liu, and Ping Zheng. 2016. "Analytical Investigation of the Magnetic-Field Distribution in an Axial Magnetic-Field-Modulated Brushless Double-Rotor Machine" Energies 9, no. 8: 589. https://doi.org/10.3390/en9080589