# Experimental Validations of Hybrid Excited Linear Flux Switching Machine

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## Abstract

**:**

## 1. Introduction

## 2. Targeted Applications

## 3. Topology and Working Principle

#### 3.1. Topology

#### 3.2. Working Principle

## 4. Optimization and Comparisons

#### 4.1. Optimization of Proposed HELFSM

#### 4.1.1. Split Ratio Optimization

#### 4.1.2. Slot Area Dimensions Optimization

#### 4.1.3. PM Dimensions Optimization

#### 4.1.4. Unequal Primary Tooth Width Optimization

#### 4.1.5. Stator Segment Tip Width Optimization

#### 4.1.6. Stator Segment Base Width Optimization

#### 4.2. Comparison of Initial and Optimized HELFSM

#### 4.2.1. No-Load Flux Linkage

#### 4.2.2. Detent Force

#### 4.2.3. Thrust Force and TFRR

## 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 1.**Existing and proposed schemes of targeted applications: (

**a**) existing electric train, (

**b**) proposed electric train, (

**c**) existing vertical lifting, and (

**d**) proposed rope-less elevator.

**Figure 5.**Magnetic circuit based working principle, (

**a**) Positive max. flux linkage, and (

**b**) Negative max. flux linkage.

**Figure 6.**Optimization of HELFSM: (

**a**) split ratio, (

**b**) slot area dimensions, (

**c**) PM dimensions, (

**d**) unequal tooth width, (

**e**) stator segment tip width, and (

**f**) stator segment base width.

**Figure 7.**On-load magnetic flux lines: (

**a**) equal primary tooth width and (

**b**) unequal primary tooth width.

Symbol | Parameter (Unit) | Initial Value | Optimized Value |
---|---|---|---|

${\tau}_{s}$ | Stator pole pitch (mm) | 30 | |

${\tau}_{m}$ | Mover pole pitch (mm) | 35 | |

${h}_{m}$ | Mover height (mm) | 85 | 91 |

${w}_{DCt}$ | Mover DC tooth width (mm) | 7.5 | 9.5 |

${h}_{s}$ | Stator height (mm) | 25 | 19 |

${w}_{slot}$ | Slot width (mm) | 10 | 8.5 |

${w}_{ACt}$ | Mover AC tooth width (mm) | 7.5 | 8.5 |

${h}_{slot}$ | Slot height (mm) | 17.5 | 20.6 |

${h}_{y}$ | Mover yoke height (mm) | 15 | 8.6 |

${w}_{PM}$ | PM width (mm) | 5 | 7 |

${h}_{PM}$ | PM height (mm) | 5 | 3.5 |

${V}_{PM}$ | PM volume (grams) | 45.5 | 45.5 |

${w}_{sst}$ | Stator segment tip width (mm) | 24 | 28.5 |

${h}_{ss}$ | Stator segment height (mm) | 12.5 | 9.5 |

${w}_{ssb}$ | Stator segment base width (mm) | 12 | 12.825 |

L | Stack length (mm) | 10 | |

g | Air-gap height (mm) | 2 | |

v | Mover velocity (m/s) | 1.5 | |

${J}_{DC}$ | DC current density (A/mm${}^{2}$) | 4.52 | |

${J}_{AC}$ | AC current density (A/mm${}^{2}$) | 4.57 | |

${N}_{AC/DC}$ | Number of AC and DC coil turns | 40 |

Coefficients (Symbol) | Definition | Initial Value | Constraints | Optimized Value |
---|---|---|---|---|

Split Ratio | $\frac{{h}_{s}+2\xb7g}{{h}_{s}+2\xb7g+{h}_{m}}$ | 0.254 | (0.20–0.34) | 0.201 |

$(S.R)$ | ||||

Slot area | $\frac{{w}_{\mathrm{slot}\phantom{\rule{4.pt}{0ex}}}}{{h}_{\mathrm{slot}\phantom{\rule{4.pt}{0ex}}}}$ | 0.571 | (0.36–0.82) | 0.412 |

dimensions | ||||

$\left({K}_{slotdim}\right)$ | ||||

PM dimensions | $\frac{{w}_{PM}}{{h}_{PM}}$ | 1.0 | (0.16–2.0) | 2.0 |

$\left(P{M}_{dim}\right)$ | ||||

Unequal tooth | $\frac{{w}_{ACt}}{{w}_{DCt}}$ | 1.0 | (0.71–1.0) | 0.894 |

width | ||||

$\left({U}_{T-Width}\right)$ | ||||

Stator segment | $\frac{{w}_{sst}}{{\tau}_{s}}$ | 0.8 | (0.60–0.95) | 0.95 |

tip width | ||||

$\left({K}_{SSTW}\right)$ | ||||

Stator segment | $\frac{{w}_{ssb}}{{w}_{sst}}$ | 0.5 | (0–0.50) | 0.45 |

base width | ||||

$\left({K}_{SSBW}\right)$ |

Performance Indicator (Unit) | Excitation | Initial Value | Optimized Value |
---|---|---|---|

Flux Linkage${}_{p-p}$ | PM | 4.88 | 7.41 |

(mWb) | |||

THD $(\%)$ | 8.62 | 1.48 | |

Detent Force${}_{p-p}$ | 1739.05 | 1359.34 | |

(N) | |||

Thrust Force${}_{avg}$ | 4472.19 | 6915.87 | |

(N) | |||

TFRR $(\%)$ | 40.94 | 19.27 | |

Flux Linkage${}_{p-p}$ | FEC | 3.20 | 3.45 |

(mWb) | |||

THD $(\%)$ | 2.03 | 1.88 | |

Detent Force${}_{p-p}$ | 133.32 | 216.61 | |

(N) | |||

Thrust Force${}_{avg}$ | 3202.39 | 3483.92 | |

(N) | |||

TFRR $(\%)$ | 10.85 | 13.87 | |

Flux Linkage${}_{p-p}$ | PM+FEC | 8.10 | 10.90 |

(mWb) | |||

THD $(\%)$ | 4.76 | 1.17 | |

Detent Force${}_{p-p}$ | 2338.65 | 1028.83 | |

(N) | |||

Thrust Force${}_{avg}$ | 7581.32 | 10111.13 | |

(N) | |||

TFRR $(\%)$ | 30.71 | 9.15 |

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**MDPI and ACS Style**

Ullah, N.; Khan, F.; Basit, A.; Shahzad, M. Experimental Validations of Hybrid Excited Linear Flux Switching Machine. *Energies* **2021**, *14*, 7274.
https://doi.org/10.3390/en14217274

**AMA Style**

Ullah N, Khan F, Basit A, Shahzad M. Experimental Validations of Hybrid Excited Linear Flux Switching Machine. *Energies*. 2021; 14(21):7274.
https://doi.org/10.3390/en14217274

**Chicago/Turabian Style**

Ullah, Noman, Faisal Khan, Abdul Basit, and Mohsin Shahzad. 2021. "Experimental Validations of Hybrid Excited Linear Flux Switching Machine" *Energies* 14, no. 21: 7274.
https://doi.org/10.3390/en14217274