# Practical and Rapid Motor Sizing Technique Using Existing Electrical Motor

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## Abstract

**:**

## 1. Introduction

_{s}), inductance (L

_{s}), and back EMF constant (K

_{e}).

## 2. Description of Analysis Model

## 3. Sizing Theories and Procedure

#### 3.1. Magnet Flux Loss

#### 3.2. Back EMF Constant (${K}_{e}$)

#### 3.3. Motor Inductance

#### 3.4. Current Density

^{2}at the maximum current condition is generally appropriate for this design, which operates in an instantaneous condition.

#### 3.5. Winding Feasibility Study

#### 3.6. Resistance

#### 3.7. Torque Constant Saturation, Torque Ripple, and Demagnetization

#### 3.8. Torque–Speed Performance

_{e}), resistance, and inductance, which are the fundamental parameters of the motor described previously, the required torque and speed characteristics can be calculated within the given constraints such as input voltage and current limits.

#### 3.9. Sizing Procedure

_{e}matrix and inductance matrix for the stack length and series turns, respectively, based on the reference model as explained in Section 3.2 to Section 3.3. Next, the stack length for each turn that satisfies the requirements is selected from the calculated ${K}_{e}$ and inductance results.

## 4. Verification

#### 4.1. Study Case 1

#### 4.2. Study Case 2

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Demag. | Demagnetization |

EPS | Electric power steering |

FEM | Finite element method |

NdFeB | Neodymium iron boron |

PM | Permanent magnet |

PMSM | Permanent magnet synchronous motor |

SPMSM | Surface permanent magnet synchronous motor |

S/W | Software |

## References

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**Figure 6.**Back EMF constant (K

_{e}) matrix calculated for different turn and stack length combinations.

**Figure 17.**Magnetic flux line and density distribution for FEM analysis model at 154 Apk, Current Angle 0, and Elec.Deg.

Parameters | Values | Unit |
---|---|---|

Resistance | 11.8 | mOhm |

Synchronous Inductance | 53.1 | µH |

Back EMF Constant | 0.0384 | V-s/rad |

Stack Length | 37.5 | mm |

Stator Outer Diameter | 85 | mm |

Rotor Outer Diameter | 39.2 | mm |

Air-Gap | 0.9 | mm |

Wire Diameter | 2 | mm |

Series Turns | 18 | Turns |

Residual Flux Density of PM | 1.37 | Tesla |

Coercivity of PM | 1030 | kA/m |

Surface Treatment | Thickness [µm] |
---|---|

Phosphate | 0.1–0.5 |

Nickel or Copper | 10–20 |

Zinc | 8–20 |

Epoxy | 15–20 |

Parameters | Values | Unit |
---|---|---|

Resistance | Max 14 | mOhm |

Synchronous Inductance | 57–63 | µH |

Back EMF Constant (${K}_{e}$) | 0.04–0.044 | V-s/rad |

Max Phase Current | 109 | Arms |

Current Density | 10–25 | A/mm |

Demag. Current | 167.4 | A |

Demag. Temperature | 130 | °C |

Demag. Ratio | Max 5 | % |

Kt Saturation | Max 5 | % |

Torque Ripple | Max 4 | % |

Rated Torque @30 rpm | Min 5 | Nm |

Parameters | Unit | Sizing Result | FEM Analysis | Test Result |
---|---|---|---|---|

Wire Diameter | mm | 2.0 | 2.0 | 2.0 |

Series Turns | Turns | 18 | 18 | 18 |

Stack Length | mm | 40.5 | 40.5 | 40.5 |

Resistance | mOhm | 11.32 | 11.32 | 11.9 (5%) |

Inductance | µH | 57.4 | 58.5 (2%) | 59 (3%) |

${K}_{e}$ | V-s/rad | 0.0416 | 0.0415 (0%) | 0.0415 (0%) |

Demag. Ratio | % | 3.37 | 3.5 (4%) | 3.21 (5%) |

Torque Ripple | % | 2.57 | 2.31 (10%) | 2.91 (13%) |

Torque @30 rpm | Nm | 5.26 | 5.13 (2%) | 5.18 (2%) |

Torque @3900 rpm | Nm | 2.05 | 2.29 (12%) | 2.23 (9%) |

Total Calculation Time | - | <1 s | around 1.5 h | - |

Parameters | Values | Unit |
---|---|---|

Resistance | Max 18 | mOhm |

Synchronous Inductance | 80–90 | µH |

Back EMF Constant (${K}_{e}$) | 0.067–0.074 | V-s/rad |

Max Phase Current | 103 | Arms |

Current Density | 10–25 | A/mm |

Demag. Current | 176 | A |

Demag. Temperature | 130 | Deg.C |

Demag. Ratio | Max 5 | % |

Kt Saturation | Max 5 | % |

Torque Ripple | Max 4 | % |

Rated Torque @30 rpm | Min 8.7 | Nm |

Parameters | Unit | Sizing Result | FEM Analysis | Test Result |
---|---|---|---|---|

Wire Diameter | mm | 2.2 | 2.2 | 2.2 |

Series Turns | Turns | 16 | 16 | 16 |

Stack Length | mm | 73.5 | 73.5 | 73.5 |

Resistance | mOhm | 15.1 | 15.1 (0%) | 15.5 (5%) |

Inductance | µH | 83.8 | 82.6 (1%) | 81 (3%) |

${K}_{e}$ | V-s/rad | 0.0675 | 0.0675 (0%) | 0.0675 (0%) |

Demag. Ratio | % | 1.58 | 1.4 (11%) | 1.2 (23%) |

Torque Ripple | % | 2.2 | 2.4 (9%) | 2.7 (23%) |

Torque @30 rpm | Nm | 8.93 | 8.85 (1%) | 8.91 (0%) |

Torque @2000 rpm | Nm | 3.34 | 3.6 (8%) | 3.71 (11%) |

Total Calculation Time | - | <1 s | around 1.5 h | - |

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**MDPI and ACS Style**

Kim, Y.-C.; Han, J.-H.; Lee, J.
Practical and Rapid Motor Sizing Technique Using Existing Electrical Motor. *Actuators* **2023**, *12*, 430.
https://doi.org/10.3390/act12120430

**AMA Style**

Kim Y-C, Han J-H, Lee J.
Practical and Rapid Motor Sizing Technique Using Existing Electrical Motor. *Actuators*. 2023; 12(12):430.
https://doi.org/10.3390/act12120430

**Chicago/Turabian Style**

Kim, Yong-Chul, Jung-Ho Han, and Ju Lee.
2023. "Practical and Rapid Motor Sizing Technique Using Existing Electrical Motor" *Actuators* 12, no. 12: 430.
https://doi.org/10.3390/act12120430