# A Novel Ultrasonic Trepanning Method for Nomex Honeycomb Core

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## Abstract

**:**

## 1. Introduction

## 2. Ultrasonic Trepanning Process

#### 2.1. Ultrasonic Trepanning Strategy

#### 2.1.1. The Ultrasonic Trepanning Method

#### 2.1.2. Kinematics Analysis of Ultrasonic Trepanning

_{f}is the feed rate, A is the ultrasonic vibration amplitude of the tool, f is the ultrasonic vibration frequency and t is the time.

_{f}= 25 mm/s, A = 20 μm, f = 20 kHz. The motion direction of the cutting edge in ultrasonic trepanning changes periodically, which demonstrates that the cutting edge alternately cuts into and exits the honeycomb core material. Therefore, ultrasonic vibration transforms the conventional continuous cutting into intermittent cutting with ultrasonic frequency.

#### 2.2. Ultrasonic Trepanning Tool

#### 2.2.1. Design of Ultrasonic Trepanning Tool

#### 2.2.2. Finite Element Simulation Analysis

#### 2.2.3. Ultrasonic Vibration Performance Test of Trepanning Tool

## 3. Theoretical Analysis of Ultrasonic Trepanning Quality

#### 3.1. Dimensional Error in Trepanning

#### 3.1.1. Theoretical Analysis of Dimensional Error in Trepanning

_{I}of the internal arc vertical surface in trepanning and the residual height h

_{E}of the external arc vertical surface in trepanning can be expressed as follows:

_{S}of the straight vertical surface in trepanning can be expressed as

#### 3.1.2. The Influence of Process Parameters on Dimensional Error

_{I}are demonstrated in Figure 12, where the radius of the internal arc vertical surface to be machined is 40, 60, 80 and 100 mm, respectively. It can be seen that the residual height increases with the increase in the trepanning step length, when using different sizes of trepanning tools. The use of a larger radius trepanning tool at the same step length can also effectively reduce the residual height. When the radius of the internal arc vertical surface is small, trepanning tools of different sizes have a significant impact on the residual height under the same step length. However, as the size of the internal arc vertical surface increases to more than 80 mm, the effectiveness of the increase in the tool radius on the decrease in the trepanning step length is no longer significant.

_{E}is demonstrated in Figure 13, where the radius of the external arc vertical surface to be machined is 40, 60, 80 and 100 mm, respectively. The relationship between the residual height of the external arc vertical surface and the process parameters is similar to that of the internal arc vertical surface. However, in the trepanning of the external arc vertical surface, when the radius of the trepanning tool increases to more than 20 mm, the residual height does not decrease significantly as the radius of the tool continues to increase when the step length is the same.

#### 3.2. Theoretical Analysis on the Quality of Trepanning Incision

_{t}is the cutting thrust force.

_{c}is the time for the trepanning tool to cut the material in one vibration cycle.

_{1}. In the next vibration cycle, from t

_{1}to t

_{2}, the tool exits the cutting area and is farthest away from the cutting area at t

_{2}. After that, the cutting tool moves towards the cutting area again, the cutting tool reaches the deepest point in the previous vibration cycle at t

_{3}. From t

_{3}to t

_{4}, the trepanning tool cuts into the honeycomb core, and cuts into the deepest part of the honeycomb core at t

_{4}, at the same time, the cutting tool is ready to exit the cutting area.

_{3}and t

_{4}. Therefore, t

_{c}can be expressed as follows:

_{4}and the direction of the tool motion changes in the next moment of t

_{4}, therefore, the speed of the cutting tool along the feed direction at t

_{4}is zero:

_{3}to t

_{4}in a vibration cycle, the cutting depth in a vibration cycle is the distance between the corresponding positions of the tool at t

_{3}and t

_{4}, which can be expressed as follows:

_{f}·T:

_{3}can be obtained by substituting t

_{4}obtained by solving Equation (14) into Equation (17). Combined with Equation (12), t

_{c}can be obtained.

_{f}= 50 mm/s, n = 1500 r/min, the time for the trepanning tool to cut the material in one vibration cycle is t

_{c}= 0.0000038 s and the vibration cycle T = 0.00005 s. Under these processing parameters, the equivalent elastic constant is 13 times of that of the Nomex honeycomb core material. In the ultrasonic trepanning processing, ultrasonic vibration significantly improves the equivalent elastic constant of the honeycomb core material in the cutting area along the in-plane direction, suppresses the deformation of the honeycomb core material, and is better for obtaining higher quality trepanning incisions.

## 4. Ultrasonic Trepanning Experiment

## 5. Result and Discussion

#### 5.1. Dimensional Error of Vertical Surface

_{I}is the distance between the highest peak of the actual residual unremoved part and the theoretical internal arc vertical surface.

#### 5.2. Trepanning Incision Quality of Nomex Honeycomb Core

#### 5.2.1. Typical Characteristics of Trepanning Incision

_{f}= 1000 mm/min. It is found by comparison that the size of the entrance defect in the ultrasonic trepanning is smaller, the ultrasonic trepanning incision is straighter and there is no processing defects such as burrs. The introduction of ultrasonic vibration, under the same processing parameters, significantly improves the quality of the trepanning incision on the Nomex honeycomb core.

#### 5.2.2. The Influence of Process Parameters on Trepanning Incision Quality

_{PT}is shown in Figure 22.

_{PT}values with or without ultrasonic vibration at different feed rates are shown in Figure 23. The L

_{PT}of the ultrasonic trepanning with a vibration amplitude of 20 μm was reduced by 40% compared with non-ultrasonic trepanning, and the L

_{PT}of the ultrasonic trepanning with a vibration amplitude of 10 μm was reduced by 30% on average. Ultrasonic vibration significantly reduces the L

_{PT}of trepanning incision, improves the quality of the trepanning incision of the Nomex honeycomb core, and the effectiveness is significant at a different feed rate. With the increase in feed rate from 1000 to 3000 mm/min, the L

_{PT}of traditional non-ultrasonic trepanning increases by 52%, the L

_{PT}of ultrasonic trepanning with a vibration amplitude of 10 μm increases by 46%, and the L

_{PT}of ultrasonic trepanning with a vibration amplitude of 20 μm increases by 38%. Compared with the traditional non-ultrasonic trepanning, ultrasonic vibration suppresses the deterioration of trepanning quality when the feed rate increases.

_{PT}with or without ultrasonic vibration at different rotating speeds are shown in Figure 24. With the increase in rotating speed from 500 r/min to 1500 r/min, the L

_{PT}of ultrasonic trepanning with vibration amplitude of 20 μm decreases by 49%, the L

_{PT}of the ultrasonic trepanning with a vibration amplitude of 10 μm decreases by 55%, and the L

_{PT}of traditional non-ultrasonic trepanning decreases by 50%. The L

_{PT}of trepanning incision with or without ultrasonic vibration decreases similarly with the increase in rotating speed of tool. At different rotating speed, the L

_{PT}of the ultrasonic trepanning with a vibration amplitude of 20 μm is reduced by 38% compared with non-ultrasonic trepanning, and the L

_{PT}of ultrasonic trepanning with a vibration amplitude of 10 μm is reduced by 30% on average. The ultrasonic vibration significantly reduces the L

_{PT}of the trepanning incision at a different rotating speed, and improves the quality of trepanning incision.

## 6. Conclusions

- (1)
- Ultrasonic trepanning is a high-quality machining method for the vertical surface of the Nomex honeycomb core. The introduction of the ultrasonic vibration improves the quality of the trepanning incision significantly.
- (2)
- The trepanning dimensional error of the vertical surface is influenced by the tool size, step length and feature size of machined vertical surface. Moreover, the trepanning dimensional error experiment verifies that the theoretical value is consistent with the actual value, and the theoretical model can be used to predict the actual trepanning dimensional error.
- (3)
- The actual trepanning incision of the vertical surface is a curve incision with regular wavy characteristics. However, it can be found by comparison that the ultrasonic trepanning incision is straighter and there are no processing defects such as burrs.
- (4)
- The characteristic size of the actual wavy incision is used, as the evaluation parameter, to quantitatively analyze the quality of the trepanning incision. The quantitatively analytical result demonstrates that the quality of the ultrasonic trepanning incision with a vibration amplitude of 20 μm is optimized by about 40% on average, compared with traditional trepanning.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Typical vertical surface: (

**a**) internal arc vertical surface; (

**b**) external arc vertical surface; and (

**c**) straight vertical surface.

**Figure 2.**Ultrasonic trepanning of internal arc vertical surface. (

**a**) Principle of ultrasonic trepanning; (

**b**) Trepanning method.

**Figure 6.**Relationship between the tool size and resonance frequency. (

**a**) Tool length; (

**b**) Tool diameter.

**Figure 7.**Relationship between the tool angle and resonance frequency. (

**a**) Rake angle; (

**b**) Relief angle.

**Figure 8.**Ultrasonic vibration performance test. (

**a**) Test device; (

**b**) Result of ultrasonic vibration performance test.

**Figure 10.**Dimensional error in trepanning: (

**a**) internal arc vertical surface; (

**b**) external arc vertical surface; (

**c**) straight vertical surface.

**Figure 12.**Curve chart of h

_{I}change with the step length: (

**a**) R = 40 mm; (

**b**) R =60 mm; (

**c**) R = 80 mm; and (

**d**) R = 100 mm.

**Figure 13.**Curve chart of the h

_{E}change with step length: (

**a**) R= 40 mm; (

**b**) R = 60 mm; (

**c**) R = 80 mm; and (

**d**) R = 100 mm.

**Figure 16.**Ultrasonic trepanning of the Nomex honeycomb core: (

**a**) the ultrasonic trepanning experiment setup; and (

**b**) the enlarged view of the marked area.

**Figure 21.**Comparison of trepanning incision: (

**a**) ultrasonic trepanning incision; and (

**b**) non-ultrasonic trepanning incision.

Material | Elastic Modulus | Density | Poisson’s Ratio |
---|---|---|---|

(GPa) | (Kg/m^{3}) | ||

W9Mo3Cr4V | 221.9 | 7930 | 0.3 |

Radius of Internal Arc | Step Length | Rotating Speed | Feed Rate |
---|---|---|---|

R /mm | θ/deg | n/(r/min) | v_{f}/(mm/min) |

100 | 5, 6, 7, 8, 9, 10 | 1500 | 500 |

Number | Ultrasonic Amplitude | Rotating Speed | Feed Rate |
---|---|---|---|

A/μm | n/(r/min) | v_{f}/(mm/min) | |

1 | Non-ultrasonic | 500 | 2000 |

2 | 1000 | 2000 | |

3 | 1500 | 2000 | |

4 | 1500 | 1000 | |

5 | 1500 | 3000 | |

6 | 10 | 500 | 2000 |

7 | 1000 | 2000 | |

8 | 1500 | 2000 | |

9 | 1500 | 1000 | |

10 | 1500 | 3000 | |

11 | 20 | 500 | 2000 |

12 | 1000 | 2000 | |

13 | 1500 | 2000 | |

14 | 1500 | 1000 | |

15 | 1500 | 3000 |

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## Share and Cite

**MDPI and ACS Style**

Sun, D.; Kang, R.; Wang, Y.; Guo, J.; Dong, Z.
A Novel Ultrasonic Trepanning Method for Nomex Honeycomb Core. *Appl. Sci.* **2021**, *11*, 354.
https://doi.org/10.3390/app11010354

**AMA Style**

Sun D, Kang R, Wang Y, Guo J, Dong Z.
A Novel Ultrasonic Trepanning Method for Nomex Honeycomb Core. *Applied Sciences*. 2021; 11(1):354.
https://doi.org/10.3390/app11010354

**Chicago/Turabian Style**

Sun, Dingyi, Renke Kang, Yidan Wang, Jialin Guo, and Zhigang Dong.
2021. "A Novel Ultrasonic Trepanning Method for Nomex Honeycomb Core" *Applied Sciences* 11, no. 1: 354.
https://doi.org/10.3390/app11010354