# Evaluation of the Multiaxial Fatigue Life of Electro-Mechanical Actuator for Aircraft Blade Pitch Control Based on Certification Standards

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fatigue Theory

## 3. Methodology

#### 3.1. Mechanical Properties for Calculation

^{4}~10

^{7}cycles) was derived and an S-N curve corresponding to a failure probability of 50% was calculated through Equation (1) [22].

#### 3.2. Multibody Dynamics

_{2}and v

_{2}are the scale factor and velocity of the action element. Here, the scale factor of the action element (c

_{2}) is assumed to be 1, relative to the base element’s scale factor (${\mathrm{c}}_{1}$) and is calculated based on the relative velocity between the base and action elements. The motion velocities of the nut, rollers, and screw were calculated using Equations (5)–(8) [25].

_{2}) calculated from Equations (5)–(8) between the nut and roller and the roller and screw, as well as the joint conditions for each component, are listed in Table 3. As a result, the orbital and spin speeds of the nut for 1 rev/s are 1.60 rev/s and 0.25 rev/s, respectively, and the reciprocating speed of the driving load is 4.71 mm/s.

#### 3.3. Static Analysis

#### 3.4. Fatigue Analysis

## 4. Results

#### 4.1. Multibody Dynamics

#### 4.2. Static Analysis

#### 4.3. Fatigue Analysis

^{7}cycles or more, specified as the requirements, was considered as infinite life. For a conservative analysis, a load history of the actuator completing 7.5 reciprocating cycles was defined as 1 cycle. Nonetheless, in the case of the model#1, the fatigue life of all key components was calculated as 10

^{7}cycles as shown in Figure 17a, confirming structural safety compared to the typically required fatigue life for aircraft components (10

^{6}cycles) [32,33,34,35]. Figure 17b shows the fatigue analysis results for model#2. Specifically, the clevis which showed higher von Mises stress compared to other components in the static analysis, and the conservatively analyzed model#2, both calculated a fatigue life of over 10

^{7}cycles, affirming structural integrity under fatigue loads. Therefore, the MS and fatigue life resulting from the structural analysis of the EMA are listed in Table 5. As presented in Table 5, an MS of 1.9 or higher was calculated, Additionally, a fatigue life of 10

^{7}cycles was determined. Accordingly, all key components of the EMA were found to be structurally safe against ULs and repeated loads (MoS ≥ 0).

## 5. Conclusions

^{7}cycles or more and ensuring both static and fatigue safety. This study thus demonstrates the feasibility of evaluating the structural safety of aircraft components using analytical methods. It is suggested that the structural analysis techniques proposed in this study be considered for future application to substantiate the certification criteria for the structural safety of eVTOL aircraft components using analytical methods.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 11.**The calculation model and the boundary conditions of model#1 used in finite element analysis.

**Figure 12.**The calculation model and the boundary conditions of model#2 used in finite element analysis.

**Figure 14.**Results of multibody dynamics analysis: (

**a**) rotational angular velocity of the roller; (

**b**) revolution angular velocity of the roller; (

**c**) angular velocity of the nut; (

**d**) stroke of the screw.

**Figure 16.**The von Mises stress distribution of the components of the linear actuator obtained from the static analysis.

**Figure 17.**The fatigue life (logarithmic scale) of the components of the linear actuator obtained from the fatigue analysis.

Properties | Materials | ||
---|---|---|---|

Aluminum | Steel#1 | Steel#2 | |

Elastic modulus (GPa) | 69.8 | 193 | 210 |

Poisson’s ratio | 0.33 | 0.29 | 0.30 |

Yield strength (MPa) | 275.8 | 215.0 | 1700 |

Tensile strength (MPa) | 310.3 | 505.0 | 2300 |

Fatigue strength coefficient, ${{\mathsf{\sigma}}^{\prime}}_{\mathrm{f}}$ | 872.1 (P = 50%) 815.2 (P = 1%) | 326.7 (P = 50%) 277.0 (P = 1%) | 701.3 (P = 50%) 689.9 (P = 1%) |

Fatigue strength exponent, $\mathrm{b}$ | −0.145 | −0.063 | −0.054 |

Fatigue strength (10 ^{7} cycles, MPa) | 84.5 (P = 50%) 79.0 (P = 1%) | 118.3 (P = 50%) 100.3 (P = 1%) | 295.9 (P = 50%) 291.1 (P = 1%) |

Parameter Name | Symbol | Value | Unit |
---|---|---|---|

Effective diameter of screw | ${d}_{s}$ | 21 | mm |

Effective diameter of roller | ${d}_{p}$ | 7 | mm |

Effective diameter of nut | ${d}_{n}$ | 35 | mm |

Pitch | p_{z} | 3.333 | mm |

Number of rollers | - | 9 | - |

Type | Base Elements | Action Elements | Boundary Conditions | Remark |
---|---|---|---|---|

Merge | Housing | Rod (4EA) | - | - |

Merge | Housing | Connector (4EA) | - | - |

Merge | Nut | Mount | - | - |

Revolute | Housing | Nut | X-axis rotation | - |

Revolute | Housing | Carrier | X-axis rotation | - |

Revolute | Carrier | Rollers | X-axis rotation | - |

Translate | Housing | Screw | X-axis translation | - |

Coupler | Revolute (nut) | Revolute (carrier) | Scale c _{2} = 1.6 | ${\omega}_{n}$:${\Omega}_{p}$ = 1.60:1 |

Coupler | Revolute (carrier) | Revolute (roller) | Scale c _{2} = 0.25 | ${\Omega}_{p}$:${\omega}_{p}$ = 0.25:1 |

Coupler | Revolute (roller) | Translate (screw) | Scale c _{2} = 4.71 | ${\omega}_{p}$:$\dot{x}$ = 4.71:1 |

Parameter Name | Components | Materials | The Number of Elements and Nodes |
---|---|---|---|

Model#1 | Housings | Aluminum | 975,204/1,336,435 |

Clevis | 79,544/115,990 | ||

Rod | 119,474/169,646 | ||

Bushing | Steel#1 | 108,601/160,171 | |

Screw | 130,280/180,784 | ||

Rollers | 73,120/79,507 | ||

Nut | 97,334/116,358 | ||

Retainer | Steel#2 | 5686/13,372 | |

Carrier | 3240/4761 | ||

Model#2 | Screw | Steel#1 | 283,611/405,910 |

Rollers | 432,119/604,546 | ||

Nut | 606,813/858,098 |

Components | Static Analysis | Fatigue Analysis | |
---|---|---|---|

MS (von Mises Stress) | Fatigue Life (Cycles) | ||

Model#1 | Housings | 3.3 (89.6 MPa) | 10^{7} |

Clevis | 1.9 (132.2 MPa) | ||

Rod | 2.9 (97.8 MPa) | ||

Bushing | 645.3 (2.6 MPa) | ||

Screw | 14.7 (108.1 MPa) | ||

Rollers | 13.1 (120.5 MPa) | ||

Nut | 14.7 (108.2 MPa) | ||

Retainer | 338.3 (1.4 MPa) | ||

Carrier | 1806.6 (0.3 MPa) | ||

Model#2 | Screw | 9.1 (168.6 MPa) | 10^{7} |

Rollers | 13.8 (114.8 MPa) | ||

Nut | 11.8 (132.8 MPa) |

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**MDPI and ACS Style**

Kim, Y.-C.; Kim, D.-H.; Kim, S.-W.
Evaluation of the Multiaxial Fatigue Life of Electro-Mechanical Actuator for Aircraft Blade Pitch Control Based on Certification Standards. *Aerospace* **2024**, *11*, 91.
https://doi.org/10.3390/aerospace11010091

**AMA Style**

Kim Y-C, Kim D-H, Kim S-W.
Evaluation of the Multiaxial Fatigue Life of Electro-Mechanical Actuator for Aircraft Blade Pitch Control Based on Certification Standards. *Aerospace*. 2024; 11(1):91.
https://doi.org/10.3390/aerospace11010091

**Chicago/Turabian Style**

Kim, Young-Cheol, Dong-Hyeop Kim, and Sang-Woo Kim.
2024. "Evaluation of the Multiaxial Fatigue Life of Electro-Mechanical Actuator for Aircraft Blade Pitch Control Based on Certification Standards" *Aerospace* 11, no. 1: 91.
https://doi.org/10.3390/aerospace11010091