# In-Process Monitoring of Changing Dynamics of a Thin-Walled Component During Milling Operation by Ball Shooter Excitation

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Blade Profile—Test Case

#### 2.2. Analytical Approach

#### 2.3. FEA Analysis

## 3. Results

#### 3.1. Measurement

#### 3.1.1. Impulse Excitation with a Ball Shooter

#### 3.1.2. Analysis of Impact Spectrum with Finite Element Simulations

#### 3.2. Measured Impulse Responses

#### 3.3. Improved FE Model

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The machined final blade profile with the excitation (P

_{1}, P

_{2}) and sensing point (P

_{3}) together with the small sized accelerometer. (

**b**) The CAD model of the blade.

**Figure 2.**Different clamping surfaces of the turbine blade: the raw surface in the left, flattened in the middle and the structured surface in the right column. (

**a**) The top row shows the picture of the surface contours created by a light test, (

**b**) the middle row shows the picture of the clamped surface sections and (

**c**) the bottom row shows the (non-scaled) schematic drawing of the cross-sections.

**Figure 3.**Schematic representation of the coupled beam model (

**a**) and the two separated components (

**b**,

**c**). The assumed deformation is represented by blue and green curves in the raw and the blade parts, respectively.

**Figure 4.**The fluctuation of the natural frequencies in the function of the blade height calculated by the simplified analytical model. Thick curves present the frequency fluctuations of the coupled part while thin curves represent the decomposed models. (

**a**) bending vibration along the x axis (

**b**) bending vibration along the y axis.

**Figure 5.**The fluctuation of the natural frequencies in the function of the blade height for both x and y directional bending modes calculated by the simplified analytical model.

**Figure 6.**The natural frequencies as a function of the blade height calculated by the FEA for ideally rigid constraints at the flattened (black) and the structured (red) clamping surfaces.

**Figure 7.**The mode shapes of the first 4 natural frequencies at different blade heights for the ideally fixed flattened geometry.

**Figure 8.**The measurement setup with the ball shooter and the clamped workpiece at the final stage of the machining of the blade profile ($s=50$ mm).

**Figure 9.**The top panel (

**a**) represents the spectrum of the measured acceleration responses induced by the ball shooter at P${}_{1}$ (black) and the micro hammer at P${}_{1}$ (red) and P${}_{2}$ (blue) (three responses for each impulse), while the bottom panel (

**b**) presents the spectrum of the applied excitation force by the micro modal hammer at blade height $s=8$ mm.

**Figure 10.**(

**a**) The applied FE model with maximal deformation and stresses for $v=30\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}/\mathrm{s}$, (

**b**) the impact force characteristics and (

**c**) the impact force spectrum and the limit corresponding to $-3\phantom{\rule{3.33333pt}{0ex}}\mathrm{dB}$ for $v=15,\phantom{\rule{0.166667em}{0ex}}20,\phantom{\rule{0.166667em}{0ex}}25,\phantom{\rule{0.166667em}{0ex}}30\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}/\mathrm{s}$.

**Figure 11.**Typical Frequency Responses Functions for the micro hammer excitation at points P${}_{1}$ (red) & P${}_{2}$ (blue) and for the ball shooter excitation at P${}_{1}$ (black) considering a constant force spetrum at blade height s = 8 mm.

**Figure 12.**The measured averaged Frequency Response Function in the function of the blade height presented as a waterfall diagram. The colour scale denotes the logarithmic amplitude of the averaged FRF, the red crosses denote all the fitted natural frequencies by means of the ISD method for each excitation and the blue circles denote the consistent fitted natural frequencies.

**Figure 14.**The natural frequencies of the FE model with the artificial elastic layer (black lines) and the measured averaged Frequency Response Function in the function of the blade height presented as a waterfall diagram. The colour scale denotes the logarithmic amplitude of the averaged FRF, the red crosses denote all the fitted natural frequencies by means of the ISD method for each excitation and the blue circles denote the consistent fitted natural frequencies.

Name | Unit | Value |
---|---|---|

Density | kg/m${}^{3}$ | 2700 |

Young’s modulus | GPa | 70 |

Poisson’s ratio | 1 | 0.35 |

Name | Unit | Raw Secion | Blade Secion |
---|---|---|---|

Area | mm${}^{2}$ | 800 | 137.7 |

second moment of area to axis x | mm${}^{4}$ | 26,666 | 1500 |

second moment of area to axis y | mm${}^{4}$ | 106,666 | 12,330 |

Parameter | Unit | Airsoft Ball | Wall |
---|---|---|---|

Density | [kg/m${}^{3}$] | 3900 | 2700 |

Elastic modulus | [GPa] | 2.31 | 70 |

Poisson’s ratio | [1] | 0.25 | 0.35 |

Initial yield stress | [MPa] | 23.71 | 324 |

Plastic hardening | [MPa] | 1659.72 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Bachrathy, D.; Kiss, A.K.; Kossa, A.; Berezvai, S.; Hajdu, D.; Stepan, G. In-Process Monitoring of Changing Dynamics of a Thin-Walled Component During Milling Operation by Ball Shooter Excitation. *J. Manuf. Mater. Process.* **2020**, *4*, 78.
https://doi.org/10.3390/jmmp4030078

**AMA Style**

Bachrathy D, Kiss AK, Kossa A, Berezvai S, Hajdu D, Stepan G. In-Process Monitoring of Changing Dynamics of a Thin-Walled Component During Milling Operation by Ball Shooter Excitation. *Journal of Manufacturing and Materials Processing*. 2020; 4(3):78.
https://doi.org/10.3390/jmmp4030078

**Chicago/Turabian Style**

Bachrathy, Daniel, Adam K. Kiss, Attila Kossa, Szabolcs Berezvai, David Hajdu, and Gabor Stepan. 2020. "In-Process Monitoring of Changing Dynamics of a Thin-Walled Component During Milling Operation by Ball Shooter Excitation" *Journal of Manufacturing and Materials Processing* 4, no. 3: 78.
https://doi.org/10.3390/jmmp4030078