# Thermomechanical Rotor Fatigue of an Interior Permanent Magnet Synchronous Motor

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## Abstract

**:**

## 1. Introduction

## 2. Rotor Stress Due to Electromagnetic, Thermal, and Mechanical Loads

#### 2.1. Loads and Boundary Conditions

#### 2.2. Stress Analysis Results

#### 2.2.1. Individual Load Cases

#### 2.2.2. Combined Load Cases

## 3. Drive Cycle Design for Thermomechanical Fatigue Analysis of a Rotor

## 4. Motor Thermal Management and Temperature Profile Estimation for a Drive Cycle

## 5. Accelerated Fatigue Life Approach

## 6. Rotor Stress Analysis for a Drive Cycle

## 7. Thermomechanical Fatigue Analysis

#### 7.1. Stress-Life Curve Generation

#### 7.2. Fatigue Analysis Results

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

IPMSM | Interior permanent magnet synchronous motor |

EVs | Electric vehicles |

LPTN | Lumped parameter thermal network |

E-N | Strain-life |

S-N | Stress-life |

RPM | Revolutions per minute |

EM | Electromagnetic |

UDDS | Urban Dynamometer Driving Schedule |

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**Figure 2.**Effect of interference fit on von Mises rotor stress at Hotspot 3 in Figure 1 under various rotor speeds.

**Figure 3.**Normalized rotor stress under combined centrifugal load, thermal load, and interference fit; (

**a**) von Mises stress; (

**b**) maximum principal stress.

**Figure 4.**Maximum principal stress at hotspots in Figure 1 under combined load and under various rotor speeds.

**Figure 10.**Depiction of von Mises stress for linear material and von Mises stress and plastic strain for nonlinear material.

**Figure 11.**True stress–true plastic strain curve for electrical steel 27PNX1350 at room tempertaure and at 150 °C.

**Figure 12.**Depiction of von Mises stress at Hotspot 1 and Hotspot 3 for the daily rotor speed profile.

**Figure 14.**Fatigue life for rotor lamination, accounting for varying loads, a temperature-dependent median S-N curve, and the Goodman mean stress correction factor.

Parameters | Values | Units |
---|---|---|

Base speed | 3750 | RPM |

Nominal DC voltage | 350 | V |

Maximum rotor speed | 18,000 | RPM |

Peak/continuous torque | 438/193 | Nm |

Stator outer diameter | 220 | mm |

Rotor outer diameter | 150 | mm |

Axial length | 150 | mm |

Number of poles | 8 | - |

Rotor and stator lamination material | 20SW1200 | - |

Magnet material | G48UH | - |

Shaft material | Hot rolled steel | - |

Load Case | Normalized Stress Values | Hotspot Location |
---|---|---|

Electromagnetic load at peak torque | 0.03 | Hotspot 1 |

Thermal load at 150 °C | 0.23 | Hotspot 2 |

0.2 | Hotspot 3 | |

Interference fit at 25 °C | 1.18 | Hotspot 3 |

0.82 | Hotspot 2 | |

Centrifugal load at 18,000 RPM and 25 °C | 1.7 | Hotspot 3 |

0.99 | Hotspot 1 | |

0.98 | Hotspot 4 | |

0.96 | Hotspot 5 |

Parameter | Value | Temperature |
---|---|---|

Stress amplitude intercept (${{S}^{\prime}}_{f}$) | 1502.3 (MPa) | RT |

Slope 1 ($b1$) | −0.12 | RT |

Slope 2 ($b2$) | −0.06383 | RT |

Endurance strength (${S}_{e}$) | 286.2 (MPa) | RT |

Stress at fatigue cut-off limit | 8.4 (MPa) | RT |

Stress amplitude intercept (${{S}^{\prime}}_{f}$) | 1236.7 (MPa) | 150 °C |

Slope 1 ($b1$) | −0.112 | 150 °C |

Slope 2 ($b2$) | −0.05932 | 150 °C |

Endurance strength (${S}_{e}$) | 263.2 (MPa) | 150 °C |

Stress at fatigue cut-off limit | 9.9 (MPa) | 150 °C |

Parameter | Value | Temperature |
---|---|---|

Stress amplitude intercept (${{S}^{\prime}}_{f}$) | 1224 (MPa) | RT |

Endurance strength (${S}_{e}$) | 192.5 (MPa) | RT |

Stress at fatigue cutoff limit | 3.7 (MPa) | RT |

Stress amplitude intercept (${{S}^{\prime}}_{f}$) | 1195.7 (MPa) | 150 °C |

Endurance strength (${S}_{e}$) | 188.2 (MPa) | 150 °C |

Stress at fatigue cutoff limit | 3.6 (MPa) | 150 °C |

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**MDPI and ACS Style**

Sahu, A.K.; Haddad, R.Z.; Al-Ani, D.; Bilgin, B.
Thermomechanical Rotor Fatigue of an Interior Permanent Magnet Synchronous Motor. *Machines* **2024**, *12*, 158.
https://doi.org/10.3390/machines12030158

**AMA Style**

Sahu AK, Haddad RZ, Al-Ani D, Bilgin B.
Thermomechanical Rotor Fatigue of an Interior Permanent Magnet Synchronous Motor. *Machines*. 2024; 12(3):158.
https://doi.org/10.3390/machines12030158

**Chicago/Turabian Style**

Sahu, Ashish Kumar, Reemon Z. Haddad, Dhafar Al-Ani, and Berker Bilgin.
2024. "Thermomechanical Rotor Fatigue of an Interior Permanent Magnet Synchronous Motor" *Machines* 12, no. 3: 158.
https://doi.org/10.3390/machines12030158