Analytical Calculation of Air Gap Magnetic Field of SPMSM with Eccentrically Cut Poles Based on Magnetic Pole Division
Abstract
:1. Introduction
2. Analytical Solution Process of Air Gap Magnetic Field
- (1)
- The magnetic permeability of the ferromagnetic material is set to infinity.
- (2)
- The magnetic permeability of the air gap between the magnetic poles is the same as that of the permanent magnet.
- (3)
- The stator slot type is a radial fan-shaped open slot with a regular shape.
- (4)
- Neglecting the end effect, the model is solved in the two-dimensional region.
2.1. The Model of the Eccentrically Cut Permanent Magnet and Its Equal-Area Integral Block
2.2. General Solution of Each Subdomain
2.2.1. Subdomain 1—Slot
2.2.2. Subdomain 2—Air Gap
2.2.3. Subdomain 3—Permanent Magnet
2.3. Harmonic Coefficient Solution
2.3.1. The Interface between Air Gap and Permanent Magnet
2.3.2. The Interface between Air Gap and Stator Slot
2.4. Air Gap Magnetic Density Distribution
2.5. Calculation of No-Load back Electromotive Force
3. Model Calculation and FEM Verification
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Center of the inner arc of the magnetic pole | |
Center of the outer arc of the magnetic pole | |
Radius of the inner arc of the magnetic pole | |
Radius of the outer arc of the magnetic pole | |
Radius at the top of the slot | |
Radius at the bottom of the slot | |
Radius of the magnetic block | |
Central angle of the magnetic pole of block | |
Central angle of the inner arc of the magnetic pole | |
Central angle of the outer arc of the magnetic pole | |
Pole block number | |
Pairs of poles | |
Total number of blocks for half a magnetic pole | |
Number of stator slots | |
Slot number | |
Harmonic order in slot | |
Harmonic orders in permanent magnet and air gap | |
Relative permeability of permanent magnet | |
Vacuum permeability | |
Central angle corresponding to the slot | |
Position angle of the center of the slot | |
Starting position of the slot | |
Pole distance | |
Core axial length(mm) | |
Pole arc coefficient | |
Fundamental frequency | |
Total number of turns in series for each phase | |
Winding coefficient of the harmonic |
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Parameter | Value | Parameter | Value |
---|---|---|---|
Phase m | 3 | Stator outer diameter D1/mm | 290 |
Rated voltage UN/V | 234 | Stator inner diameter Di1/mm | 180 |
Pairs of poles P | 4 | Rotor outer diameter D2/mm | 176 |
Rated speed n1/rpm | 750 | Rotor inner diameter Di2/mm | 80 |
Permanent magnet material | SmCo30 | Core Axial Length l/mm | 88 |
Pole arc coefficient αp | 0.978 | Number of stator slots Ns | 72 |
Items | Analytical Method | FEM |
---|---|---|
CPU | Intel(R) Core(TM) i7-10750 H CPU @ 2.60 GHz | |
Number of equations/matrixes | 1792 | 36,118 |
Mesh accuracy | - | 1 mm |
Number of subdomains/triangles | 3 | 18,124 |
Elapsed time | 8.7 s | 249 s |
Harmonic Order | Analytical Method | FEA |
---|---|---|
1 | 0.8391 T | 0.8338 T |
3 | 0.0516 T | 0.0591 T |
5 | 0.0118 T | 0.0125 T |
7 | 0.0078 T | 0.0077 T |
9 | 0.0032 T | 0.0026 T |
11 | 0.0002 T | 0.0002 T |
17 | 0.0666 T | 0.0646 T |
19 | 0.0635 T | 0.0612 T |
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Zhang, J.; Hu, J.; Gu, G.; Du, F. Analytical Calculation of Air Gap Magnetic Field of SPMSM with Eccentrically Cut Poles Based on Magnetic Pole Division. Energies 2023, 16, 4450. https://doi.org/10.3390/en16114450
Zhang J, Hu J, Gu G, Du F. Analytical Calculation of Air Gap Magnetic Field of SPMSM with Eccentrically Cut Poles Based on Magnetic Pole Division. Energies. 2023; 16(11):4450. https://doi.org/10.3390/en16114450
Chicago/Turabian StyleZhang, Jiahe, Jiapei Hu, Guobiao Gu, and Fangmian Du. 2023. "Analytical Calculation of Air Gap Magnetic Field of SPMSM with Eccentrically Cut Poles Based on Magnetic Pole Division" Energies 16, no. 11: 4450. https://doi.org/10.3390/en16114450