# On Unintentional Demagnetization Effect of Switched Flux Hybrid Magnet Memory Machine

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## Abstract

**:**

## 1. Introduction

## 2. Unintentional Demagnetization Effects of SF-HMMM

#### 2.1. SF-HMMM Structure

#### 2.2. Description of UD Effect

_{q}= 14.14 A) are shown in Figure 2. The corresponding variations of radial flux densities of three typical points in the LCF PM are shown in Figure 3. The whole process, reflecting the UD effect, includes three periods. The first and third electrical periods refer to the open-circuit states, while the middle one is the on-load state, which are described as follows.

#### 2.2.1. Rotor Position (0°~360°): Self-Demagnetization

#### 2.2.2. Rotor Position (360°~720°): Coupling Demagnetization

#### 2.2.3. Rotor Position (720°~1080°): Post-Demagnetization

_{emf}, which refers to the reduction ratio of the back-EMF fundamental magnitudes, is defined as [23]

_{m}

_{1}and E

_{m}

_{2}are fundamental back-EMF magnitudes, before and after q-axis current excitation, respectively.

_{emf}as a function of armature current magnitudes and current angles is shown in Figure 5. It indicates that the LCF magnets are highly sensitive to the armature current magnitude instead of the current angle.

_{emf}resulting from various q-axis current excitations when the LCF PM with coercive force of −120 kA/m is employed are shown in Figure 6. It can be seen that the UD effect is aggravated with the increase in the armature current value, which is mainly attributed to the cross-coupling effect of PM excitation and armature fields. In addition, the flux-linkage and back-EMF diminutions will result in the discrepancy of the reference look-up table of EMF versus magnetizing current at the open-circuit state. Consequently, the precise online MS manipulation control becomes difficult.

#### 2.3. Analytical Investigation for the UD Phenomenon

_{mag}is the magnetizing MMF.

_{g3}is assumed to be infinite. Consequently, the maximum open-circuit air-gap flux Φ

_{δ}

_{+}can be obtained by synthesizing individual magnet excited cases, based on the superimposition method, namely:

_{m}

_{1}and F

_{m}

_{2}are the equivalent magneto-motive force (MMF) of NdFeB PM and LCF PM, respectively; R

_{m}

_{1}, and R

_{m}

_{2}are the magnetic reluctances of NdFeB PM and LCF PM, respectively; R

_{y}, R

_{st}, and R

_{r}are the magnetic reluctances of stator yoke, stator tooth and rotor pole, respectively.

_{m1}and h

_{m2}are the thicknesses of NdFeB PM and LCF PM, respectively; H

_{c}

_{1}and H

_{c}

_{2}are the coercivities of NdFeB PM and LCF PM, respectively; A

_{m}

_{1}and A

_{m}

_{2}are the cross-sectional areas of NdFeB PM and LCF PM, respectively; μ

_{0}is the vacuum permeability; H

_{c}

_{1}and H

_{c}

_{2}are the relative permeabilities of NdFeB PM and LCF PM, respectively; and both R

_{g}

_{1}and R

_{g}

_{2}are the air-gap magnetic reluctances.

_{1}and R

_{2}are defined as follows:

_{a}should be considered, and consequently, (9) can be rewritten as:

_{δ}

_{+}’ are the maximum on-load air-gap flux, the slope of the load line, and the horizontal intercept of the load line and:

_{4}is added in the open-circuit case. In addition, the horizontal intercept △Φ

_{δ}

_{2+}is higher in comparison to the open-circuit one. As a result, it is theoretically identified that the on-load UD tends to be more severe than the open-circuit case.

#### 2.3.1. Self-Demagnetization

_{1}. In this case, the self-demagnetization will occur, as shown in Figure 8a.

#### 2.3.2. Coupling Demagnetization

_{a}will increase, resulting in the increment of ΔΦ

_{δ}

_{2+}. Consequently, the load line will shift along the negative horizontal axis, and the working points drop to a lower recoil line. This means that the coupling demagnetization will happen, as illustrated in Figure 8b.

_{m}

_{1}can be designed lower, and the magnetic saturation of the stator core should be reduced, with decreasing R

_{1}to R

_{4}. Alternatively, when the coercive force of the LCF PM increases, the load line is located on the linear region, as illustrated in Figure 8c. As a whole, the underlying causes for the UD effect have been analytically identified and explained.

## 3. Demagnetization Type Identification

_{rknee}, and H

_{knee}are the knee point of the hysteresis model of the LCF PM and the knee point coercivity of LCF PM, namely.

_{ref}is defined as the fundamental back-EMF obtained by the VLHC model.

_{ref}and E

_{m}

_{1}are equal, the initial working points are located on the upper limit recoil line. In other words, the self-demagnetization can be prevented. Furthermore, by comparing E

_{m}

_{1}and E

_{m}

_{2}, if they are equal, the UD effect can be avoided. Otherwise (E

_{m}

_{1}> E

_{m}

_{2}), only the coupling UD effect occurs, and the working points of the LCF PMs will shift to the lower recoil lines during the on-load operation.

_{ref}> E

_{m}

_{1}, both UD types possibly occur, and the situations can be analogously subdivided into two cases, according to the relation between E

_{m}

_{1}and E

_{m}

_{2}. First, if E

_{m}

_{1}and E

_{m}

_{2}are equal, only the self-demagnetization occurs. Otherwise, both kinds of UDs simultaneously exist.

## 4. LCF PM Design Guidelines for Elimination of UD Effect

_{remf}is utilized to indicate whether the self-demagnetization occurs prior to the load current excitation, which is defined as:

_{remf}and k

_{emf}with H

_{c}

_{2}and h

_{m}

_{2}are shown in Figure 12.

_{m}

_{2}= 3.2 mm and coercivity H

_{c}

_{2}= −240 kA/m” are selected for the final design, which can well prevent both the coupling and self-demagnetizations. The overall design process of the sizing and grade of the LCF PM is illustrated in Figure 13.

## 5. Experimental Validation

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Illustration of on-load UD effect: open-circuit field distributions (

**a**) before or (

**b**) after the q-axis current excitation (I

_{q}= 14.14 A).

**Figure 3.**Variation of the working point of PM elements subject to one electrical period of q-axis current excitation (I

_{q}= 14.14A).

**Figure 4.**On-load demagnetization effect: field distributions excited by (

**a**) NdFeB only and (

**b**) armature reaction only.

**Figure 7.**Simplified magnetic circuit model of the SF-HMMM when the rotor aligns with d-axis position.

**Figure 8.**Illustration of the different UD cases by hysteresis curves of LCF PMs with different coercive forces. (

**a**) Self-demagnetization. (

**b**) On-load coupling demagnetization. (

**c**) Prevention of the UD effect.

**Figure 11.**Influences of various excited sources on the working points of the LCF PM under rated load.

**Figure 14.**SF-HMMM prototype and test rig. (

**a**) Stator. (

**b**) Rotor. (

**c**) The drive and magnetizing control board. (

**d**) Test platform.

**Figure 15.**FE-predicted and measured open-circuit back-EMF characteristics before and after I

_{q}excitation, 400 r/min. (

**a**) Waveforms. (

**b**) Variation in fundamental magnitudes with applied q-axis current. (

**c**) Comparison in fundamental magnitudes with applied q-axis current.

**Figure 16.**Measured terminal voltage transient response to a current pulse of I

_{q}excitation of 5A, 400 r/min. (The magnetizing current and the d-axis armature current values are both set as zero).

Conditions | Open-Circuit | Armature + LCF PM | Resultant |
---|---|---|---|

Before I_{q} = 14.14 A | 0.388 | 0.776 | 0.234 |

After I_{q} = 14.14 A | 0.470 | 0.860 | 0.412 |

Demag. values | 0.083 | 0.084 | 0.179 |

Items | Parameters |
---|---|

Rated speed (r/min) | 400 |

Rated torque (Nm) | 2.67 |

Rated current (Arms) | 10 |

Rated current density (A/mm^{2}) | 6.5 |

Rated supply voltage (V) | 18 |

Rated efficiency (%) | 83.6 |

Outer diameter of stator (mm) | 90 |

Split ratio | 0.6 |

Air-gap length (mm) | 0.5 |

Active stack length (mm) | 25 |

Stator tooth width (mm) | 3.2 |

Ratio of rotor pole to pitch | 0.43 |

Turns of winding per phase | 84 |

Turns of per magnetizing coil | 100 |

LCF magnet thickness (mm) | 3.2 |

LCF PM width (degree) | 20 |

NdFeB/LCF PM grades | N35SH/SB12B |

NdFeB magnet thickness (mm) | 3.5 |

NdFeB PM length (mm) | 9.0 |

LCF magnet coercivity (-kA/m) | 240 |

LCF magnet remanence (T) | 0.8 |

Slot packing factor | 0.5 |

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**MDPI and ACS Style**

Feng, J.; Yang, H.; Ge, Y.; Zhang, W.
On Unintentional Demagnetization Effect of Switched Flux Hybrid Magnet Memory Machine. *World Electr. Veh. J.* **2022**, *13*, 66.
https://doi.org/10.3390/wevj13040066

**AMA Style**

Feng J, Yang H, Ge Y, Zhang W.
On Unintentional Demagnetization Effect of Switched Flux Hybrid Magnet Memory Machine. *World Electric Vehicle Journal*. 2022; 13(4):66.
https://doi.org/10.3390/wevj13040066

**Chicago/Turabian Style**

Feng, Jingjing, Hui Yang, Yongsheng Ge, and Wei Zhang.
2022. "On Unintentional Demagnetization Effect of Switched Flux Hybrid Magnet Memory Machine" *World Electric Vehicle Journal* 13, no. 4: 66.
https://doi.org/10.3390/wevj13040066