# Design, Analysis, and Comparison of Permanent Magnet Claw Pole Motor with Concentrated Winding and Double Stator

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structural Design and Principle Analysis

#### 2.1. Structural Design

#### 2.2. Equivalent Circuit and Equivalent Magnetic Circuit

_{A}, X

_{B}, and X

_{C}represent the equivalent synchronous reactance of the three-phase winding A, B, and C of the outer stator, and R

_{A}, R

_{B}, and R

_{C}represent the equivalent resistance of the three-phase winding A, B, and C of the outer stator, respectively. In Figure 5b, $\dot{{E}_{a0}},\dot{{E}_{b0}},\mathrm{a}\mathrm{n}\mathrm{d}\dot{{E}_{c0}}$ represent the induced electromotive force of the three-phase winding of the inner stator a, b, and c, X

_{a}, X

_{b}, and X

_{c}represent the equivalent synchronous reactance of the three-phase winding of the inner stator a, b, and c, respectively, and R

_{a}, R

_{b}, and R

_{c}represent the equivalent resistance of the three-phase winding of the inner stator a, b, and c.

_{M}represents the amplitude of the induced electromotive force of the three-phase winding of the outer stator, and E

_{m}represents the amplitude of the induced electromotive force of the inner-stator three-phase winding.

_{ABC}and R

_{ABC}, respectively, represent the equivalent synchronous reactance and equivalent resistance of the three-phase winding of the outer stator, and X

_{abc}and R

_{abc}represent the equivalent synchronous reactance and equivalent resistance of the three-phase winding of the inner stator, respectively.

_{M}represents the amplitude of the voltage at the three-phase winding end of the outer stator, and U

_{m}represents the amplitude of the voltage at the three-phase winding end of the inner stator.

_{r}represents the magnetic resistance of the rotor core, R

_{pm}represents the magnetic resistance of the permanent magnet, and R

_{σ1}is the leakage resistance between permanent magnets. R

_{σ2}is the leakage reluctance between the permanent magnet and the rotor core, R

_{g}is the air gap reluctance, R

_{c}

_{t}is the reluctance of the claw pole teeth, R

_{σ3}is the leakage magnetic resistance between the claw pole teeth, R

_{ce}is the wall magnetic resistance of the claw pole, R

_{s}is the equivalent magnetic resistance of the stator yoke, F

_{a}is the equivalent magnetic electromotive force of the armature winding, and F

_{pm}is the excitation magnetic electromotive force of the permanent magnet.

#### 2.3. Analysis of Equivalent Power Equation

_{m}represents the amplitude of the back electromotive force; I

_{m}represents the amplitude of the current.

_{coil}represents the number of winding turns; φ

_{m}represents the maximum permanent magnetic flux.

_{c}represents the current density, A

_{coil}represents the cross-sectional area of the winding, and k

_{sf}represents the slot fill rate.

_{m}

_{_outer}and φ

_{m}

_{_inner}represent the magnetic flux linkage of the inner and outer windings, N

_{m}

_{_outer}and N

_{m}

_{_inner}represent the number of turns of the inner and outer windings, and A

_{m}

_{_outer}and A

_{m}

_{_inner}represent the winding area of the inner and outer windings, respectively, P

_{r}represent the number of pole pairs of the motor.

## 3. Performance Analysis and Comparison

#### 3.1. No-Load Performance Analysis

#### 3.2. Load Performance Analysis

^{2}operating conditions. It can be seen that the torque of the two types of double-stator structure motors is significantly higher than that of TPMCPM. At 6 A/mm

^{2}, the average torque of TPMCPM was 27.8 Nm, and the average torques of PMCPM1 and PMCPM2 were 41.5 Nm and 46.9 Nm, respectively, which increased by 49.3% and 68.7% compared to TPMCPM. However, under the working condition of 6 A/mm

^{2}, the torque ripple of TPMCPM is 14.8%, and the torque ripples of PMCPM1 and PMCPM2 are 16.9% and 22.7%, respectively. The torque ripple increased by 14.2% and 53.4% compared to TPMCPM. As the current density increases, the slope of the change in the torque gradually decreases, which is caused by the large leakage of the stator core of the PMCPM. As shown in Figure 16, the slopes of PMCPM1 and PMCPM2 at different positions are greater than those of TPMCPM, indicating that the overall magnetic leakage of the double-stator motor is smaller than that of TPMCPM.

^{2}, the iron losses of TPMCPM, PMCPM1, and PMCPM2 are 69.6 W, 126.7 W, and 144.1 W, respectively. Due to the addition of an inner stator in the double-stator structure, the inner stator significantly increases the motor’s iron loss. The inner space of PMCPM2 is larger, and the inner stator is much larger than PMCPM1, resulting in a 13.7% increase in motor iron loss compared to PMCPM2.

^{2}, the efficiencies of TPMCPM, PMCPM1, and PMCPM2 are 0.971, 0.970, and 0.969, respectively. The efficiency of the three different structures of PMCPMs is not significantly different. The double-stator structure has little effect on the efficiency of PMCPMs.

## 4. Interference Assembly Analysis

#### 4.1. Stress Analysis of Interference Assembly

#### 4.2. Hybrid Material Magnetic Core Design

^{2}. From Figure 24, it can be seen that the design of the hybrid material magnetic core can slightly improve the electromagnetic performance of the motor, but the improvement is about 1%.

## 5. Experimental Verification

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**TPMCPM structure diagram. (

**a**) Overall structure diagram; (

**b**) A-phase stator structure diagram.

**Figure 5.**Equivalent circuit of double-stator PMCPM. (

**a**) External stator equivalent circuit; (

**b**) internal stator equivalent circuit.

**Figure 9.**Comparison of no-load permanent magnet flux linkage. (

**a**) Outer stator winding; (

**b**) inner stator winding.

**Figure 10.**Comparison of no-load electromotive force between the outer stator coil of PMCPM1 and PMCPM2. (

**a**) No-load electromotive force; (

**b**) FFT of no-load electromotive force.

**Figure 11.**Comparison of no-load electromotive force between the inner stator coil of PMCPM1 and PMCPM2. (

**a**) No-load electromotive force; (

**b**) FFT of no-load electromotive force.

**Figure 14.**Mutual inductance of inner and outer windings of PMCPM2. (

**a**) Inner and outer mutual inductance; (

**b**) external A-phase and internal three-phase mutual inductance; (

**c**) external B-phase and internal three-phase mutual inductance; (

**d**) external C-phase and internal three-phase mutual inductance.

**Figure 21.**Stress and deformation of PMCPM1 stator. (

**a**) Stress on the outer stator of PMCPM1; (

**b**) strain of the outer stator of PMCPM1; (

**c**) stress on the inner stator of PMCPM1; (

**d**) strain of inner stator of PMCPM1.

**Figure 22.**Stress and strain of hybrid material core PMCPM1. (

**a**) Stress on the outer stator of hybrid material core PMCPM1; (

**b**) strain of the outer stator of hybrid material core PMCPM1; (

**c**) stress on the inner stator of hybrid material core PMCPM1; (

**d**) strain of inner stator of hybrid material core PMCPM1.

**Figure 23.**BH curve and loss curve of silicon steel and SMC materials. (

**a**) BH curves of two materials; (

**b**) loss curves of two materials.

**Figure 24.**Performance comparison and analysis of hybrid material magnetic core structure motors. (

**a**) Comparison of magnetic flux linkage of outer stator winding; (

**b**) comparison of inner stator winding flux linkage; (

**c**) cogging torque; (

**d**) torque at different current densities.

**Figure 25.**Prototype structure diagram. (

**a**) stator claw pole; (

**b**) windings and stator yoke silicon steel laminations; (

**c**) single-phase stator assembly diagram; (

**d**) complete motor assembly diagram.

**Figure 27.**Comparison of experimental and test results. (

**a**) Measured three-phase EMF; (

**b**) calculated three-phase EMF; (

**c**) comparison of calculated and tested of A-phase EMF; (

**d**) comparison of calculated and tested of C-phase of C-phase EMF.

Parameter | Units | TPMCPM | PMCPM1 | PMCPM2 |
---|---|---|---|---|

Rated speed | rpm | 1500 | 1500 | 1500 |

Maximum speed | rpm | 6000 | 6000 | 6000 |

Rated frequency | Hz | 325 | 325 | 325 |

Maximum frequency | Hz | 1300 | 1300 | 1300 |

Rated current | A/mm^{2} | 6 | 6 | 6 |

Maximum current | A/mm^{2} | 10 | 10 | 10 |

Rated output power | kW | 4.36 | 6.52 | 7.37 |

Maximum output power | kW | 26.4 | 36.7 | 40.6 |

Rated torque | Nm | 27.8 | 41.5 | 46.9 |

Maximum torque | Nm | 42.0 | 58.4 | 64.7 |

Coil | A | B | C |
---|---|---|---|

a | 32.8 μ H | 19.4 μ H | 24.6 μ H |

b | 19.4 μ H | 32.8 μ H | 19.4 μ H |

c | 24.6 μ H | 19.4 μ H | 32.8 μ H |

Performance | Operating Conditions | TPMCPM | PMCPM1 | PMCPM2 |
---|---|---|---|---|

Core loss | 1500 rpm 6 A/mm^{2} | 72 W | 137 W | 157 W |

3000 rpm 6 A/mm^{2} | 13 W | 278 W | 289 W | |

6000 rpm 6 A/mm^{2} | 379 W | 765 W | 784 W | |

Efficiency | 1500 rpm 6 A/mm^{2} | 0.702 | 0.693 | 0.697 |

3000 rpm 6 A/mm^{2} | 0.745 | 0.729 | 0.725 | |

6000 rpm 6 A/mm^{2} | 0.725 | 0.695 | 0.683 |

Attribute | Units | Somaloy700HR5P | B27AHV1400 |
---|---|---|---|

Yield strength | Mpa | 15 | 410 |

Vickers hardness | Hv | 160 | 181 |

Density | g/cm^{3} | 7.5 | 7.65 |

Young’s modulus | Mpa | 1.5 × 10^{5} | 1.87 × 10^{5} |

Poisson’s ratio | — | 0.23 | 0.25–0.27 |

Symbol | Describe | Unit | TCPM |
---|---|---|---|

R_{so} | Stator outer diameter | mm | 50 |

R_{si} | Stator inner diameter | mm | 30 |

L_{gap} | Air gap length | mm | 0.85 |

H_{pm} | PM radial length | mm | 3 |

A_{pm} | PM circumferential width | deg | 8.5 |

L_{PM} | PM axial length | mm | 15 |

L_{ry} | Rotor yoke thickness | mm | 9 |

L_{tall} | Shaft length | mm | 15 |

Speed | Rated speed | rpm | 1500 |

Speed_{m} | Maximum speed | rpm | 6000 |

f_{r} | Rated frequency | Hz | 325 |

f_{m} | Maximum frequency | Hz | 1300 |

J_{cr} | Rated current | A/mm^{2} | 6 |

J_{cm} | Maximum current | A/mm^{2} | 10 |

P_{r} | Rated output power | W | 471 |

P_{m} | Maximum output power | kW | 3.14 |

T_{r} | Rated torque | Nm | 3 |

T_{m} | Maximum torque | Nm | 5 |

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## Share and Cite

**MDPI and ACS Style**

Liu, C.; Zhang, H.; Wang, S.; Zhang, S.; Wang, Y.
Design, Analysis, and Comparison of Permanent Magnet Claw Pole Motor with Concentrated Winding and Double Stator. *World Electr. Veh. J.* **2023**, *14*, 237.
https://doi.org/10.3390/wevj14090237

**AMA Style**

Liu C, Zhang H, Wang S, Zhang S, Wang Y.
Design, Analysis, and Comparison of Permanent Magnet Claw Pole Motor with Concentrated Winding and Double Stator. *World Electric Vehicle Journal*. 2023; 14(9):237.
https://doi.org/10.3390/wevj14090237

**Chicago/Turabian Style**

Liu, Chengcheng, Hongming Zhang, Shaoheng Wang, Shiwei Zhang, and Youhua Wang.
2023. "Design, Analysis, and Comparison of Permanent Magnet Claw Pole Motor with Concentrated Winding and Double Stator" *World Electric Vehicle Journal* 14, no. 9: 237.
https://doi.org/10.3390/wevj14090237