Electromagnetic–Mechanical Coupling Optimization of an IPM Synchronous Machine with Multi Flux Barriers
Abstract
:1. Introduction
2. Machine Structure and Stress Analysis
3. Electromagnetic–Mechanical Coupling Optimization
3.1. Optimization Strategy
3.2. Objectives, Objective Functions, and Constraints
3.2.1. Maximum Stress Coupling Optimization Zone
3.2.2. Maximum Deformation Coupling Optimization Zone
3.3. Boundary Conditions, Loads, and Solution
3.4. Optimization Step 1
3.5. Optimization Step 2
4. Performance Analysis
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
Trel | Reluctance torque |
T | Maximum stress |
Tripple | Torque ripple |
Rib1 | Bridge width |
h1 | Low barrier thickness |
βpo | Starting angle of arc PM |
R | Proportion coefficient of minor and major axis |
a | Length of the major axis of the elliptical barrier |
y/f(x) | Optimization objective |
S(xi) | Sensitivity index |
ξ | Saliency ratio |
ψ | Flux linkage |
γ | Maximum deformation |
Rib2 | Rid width |
h2 | Upper barrier thickness |
βpm | Radian of the PM in barrier |
xi | Optimization variable |
Tout | Output torque |
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Parameters | Values | Parameters | Values |
---|---|---|---|
Rated power | 5.5 kW | Inner diameter | 116 mm |
Rated speed | 1200 rpm | Stack length | 65 mm |
Maximum speed | 10,000 rpm | Air gap | 0.5 mm |
Rated torque | 40 Nm | Number of turns | 16 |
Outside diameter | 195 mm | PM property | NdFeB (1.2T) |
Materials | Density | Young’s Modulus | Poisson’s Ratio |
---|---|---|---|
kg/m3 | GPa | / | |
PM | 7400 | 150 | 0.23 |
Rotor core | 7650 | 200 | 0.3 |
Steps | Objectives | Variables and Variation Ranges |
---|---|---|
1 | Reluctance torque (Trel) Saliency ratio (ξ) Maximum stress (τ) | Rib1:0.5–2.0 mm Rib2:0.5–2.0 mm h1:1.5–3.5 mm h2:1.5–3.5 mm |
2 | Flux linkage (ψ) Torque ripple (Tripple) Maximum deformation (γ) | βpm: 14–28° βpo: 5–30° R: 0.2–0.5 a: 2.0–6.0 mm |
Variables/Objectives | Initial Value | Optimal Value |
---|---|---|
a (mm) | 4.0 | 4.8 |
R | 0.4 | 0.45 |
βpm (°) | 24 | 20 |
Βpo (°) | 20 | 16.2 |
Tripple (Nm) | 11.8 | 7.2 |
γ (μm) | 3.4 | 2.9 |
ψ (Wb) | 0.091 | 0.082 |
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Wu, W.; Chen, Q.; Zhu, X.; Zhao, F.; Xiang, Z. Electromagnetic–Mechanical Coupling Optimization of an IPM Synchronous Machine with Multi Flux Barriers. Energies 2020, 13, 1819. https://doi.org/10.3390/en13071819
Wu W, Chen Q, Zhu X, Zhao F, Xiang Z. Electromagnetic–Mechanical Coupling Optimization of an IPM Synchronous Machine with Multi Flux Barriers. Energies. 2020; 13(7):1819. https://doi.org/10.3390/en13071819
Chicago/Turabian StyleWu, Wenye, Qingzhang Chen, Xiaoyong Zhu, Fuzhou Zhao, and Zixuan Xiang. 2020. "Electromagnetic–Mechanical Coupling Optimization of an IPM Synchronous Machine with Multi Flux Barriers" Energies 13, no. 7: 1819. https://doi.org/10.3390/en13071819