Analytical Investigation of Magnetic Scalar Potentials Oscillation in Spoke PM Flux Modulation Machines
Abstract
:1. Introduction
2. Characteristic Equations Considering Magnetic Potential Oscillation
2.1. Generalized Equivalent Circuit Model of a Spoke-Array PM Machine
2.2. Analytical Expressions of Scalar Magnetic Potential
2.3. Air Gap Magneto-Motive Force
2.4. Air Gap Flux Density and Back EMF
2.5. Suppression Characteristics of Modulation Flux Due to Magnetic Potential’s Oscillation
3. Potentials Oscillation Behavior in Various Spoke PM Machines
3.1. Conventional Spoke PM Machine
3.2. Spoke PM Vernier Machine
3.3. Flux Switching PM Machine
4. Validation with Case Studies
4.1. Analysis Models
4.2. Procedure for Verification with FEM
4.2.1. Vernier Machine
4.2.2. Flux Switching Machine
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Number of slots | |
PMs/Number of iron core pieces | |
PM Pole pairs | |
Modulation pole pair | |
Air gap length | |
Radius of air gap | |
Stack length | |
PM magneto magneto-motive force | |
Magnetic reluctance | |
Leakage reluctance | |
Scalar magnetic potential | |
Average/fixed potential value | |
Oscillating potential value | |
Air gap flux | |
Flux from PM | |
Leakage flux | |
Lumped permeance connected to kth core piece. | |
Average value Lumped permeance | |
Harmonic permeance | |
Permeance function of upper side | |
Permeance function of lower side | |
Permeance′ coefficient | |
Stationary axis | |
Mover position in the air gap | |
Angle in mover reference | |
Winding factor | |
Mechanical angular span of coil | |
Gear ratio of vernier machine | |
Gear ratio of FSPM machine | |
Ratio of slots and PMs | |
Suppression ratio | |
FSC | Fractional slot oncentrate winding |
IS | Integral slot winding |
P. O | Potential oscillation |
Appendix A
Appendix B
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Parameters | Vernier Spoke PM Machine (Figure 4a,b) | Flux Switching Spoke PM Machine (Figure 4c,d) | ||
---|---|---|---|---|
Gear ratio | ||||
Winding type | FSC | IS | FSC | IS |
Air-gap radius | 100 mm | |||
Stack length | 50 mm | |||
Air-gap length | 1 mm | |||
Magnet height | 44.8 mm | 28.5 mm | 52.5 mm | 35 mm |
Magnet width | 8.9 mm | 5.7 mm | 10.5 mm | 6.9 mm |
No. of slots, ZU | 9 | 12 | 10 | 10 |
PM poles, ZL | 14 | 22 | 12 | 18 |
Rotational speed | 600 rpm | |||
Turns per Phase | 200 | |||
γz (=ZU/ZL) | 0.64 | 0.54 | 0.833 | 0.56 |
Suppression ratio (%) | = 58% | = 89% | = 15%, −23%, −15% | = 84%, −15%, −13% |
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Ur Rahman, L.; Rehman, A.; Kim, B. Analytical Investigation of Magnetic Scalar Potentials Oscillation in Spoke PM Flux Modulation Machines. Energies 2023, 16, 3658. https://doi.org/10.3390/en16093658
Ur Rahman L, Rehman A, Kim B. Analytical Investigation of Magnetic Scalar Potentials Oscillation in Spoke PM Flux Modulation Machines. Energies. 2023; 16(9):3658. https://doi.org/10.3390/en16093658
Chicago/Turabian StyleUr Rahman, Lutf, Abdur Rehman, and Byungtaek Kim. 2023. "Analytical Investigation of Magnetic Scalar Potentials Oscillation in Spoke PM Flux Modulation Machines" Energies 16, no. 9: 3658. https://doi.org/10.3390/en16093658