# Reconstruction of Process Forces in a Five-Axis Milling Center with a LSTM Neural Network in Comparison to a Model-Based Approach

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup

#### 2.2. Model-Based Force Reconstruction

#### 2.3. Neural Network Based Force Reconstruction

_{f}, depth of cut a

_{p}, and width of cut a

_{e}. Table 1 gives a full overview of the variations of the process parameters for the training data. Based on the tool manufacturer’s data, these variations where determined by preliminary tests.

## 3. Results

#### 3.1. Model-Based Force Reconstruction

#### 3.2. LSTM

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Stribeck curve: (

**a**) fitted for the X-axis of the HSC30; (

**b**) fitted for the Y-axis of the HSC30.

**Figure 4.**Comparison between measured process forces and the model-based approach during milling of a diagonal groove: (

**a**) force acting in X-direction (root mean square error (RMSE) = 36.22 N); (

**b**) force acting in Y-direction (RMSE = 28.25 N).

**Figure 5.**Comparison between measured process forces and the model-based approach during milling of a diagonal groove: (

**a**) force acting in X-direction (RMSE = 30.74 N); (

**b**) force acting in Y-direction (RMSE = 33.49 N).

**Figure 6.**Comparison between measured process forces and the model-based approach during milling of a circular pocket: (

**a**) force acting in X-direction (RMSE = 104.4 N); (

**b**) force acting in Y-direction (RMSE = 149.1 N).

**Figure 7.**Comparison between measured process forces and the result of the LSTM during milling of a circular pocket: (

**a**) force acting in X-direction; (

**b**) force acting in Y-direction.

**Figure 8.**Comparison between measured process forces and the result of the LSTM during side milling in negative X-direction: (

**a**) force acting in X-direction; (

**b**) force acting in Y-direction.

**Figure 9.**Comparison between measured process forces and the result of the LSTM during ramp milling in negative Y-direction and positive Z-direction: (

**a**) force acting in X-direction; (

**b**) force acting in Y-direction.

Parameter | Unit | Variations |
---|---|---|

a_{p} | (mm) | {1, 2, 3, 4} |

a_{e} | (mm) | {1, 2, 4, 5, 7, 10} |

v_{f} | (mm/min) | {300, 400, 500, 700, 800} |

n | (1/min) | {2600, 3500, 4500, 5400, 6000} |

Feed Direction | a_{e} | a_{p} | f | n | ANN | Model | Max. |F_{me}| |
---|---|---|---|---|---|---|---|

x|y | x|y | x|y | |||||

(mm) | (mm) | (mm/min) | (1/min) | (N) | (N) | (N) | |

+x | 5 | 2 | 800 | 5400 | 33.9|12.0 | 18.9|132.8 | 238.7|117.6 |

+x | 5 | 2 | 800 | 6000 | 36.6|33.2 | 68.8|29.5 | 222.6|144.6 |

+x | 5 | 5 | 800 | 5400 | 146.0|58.6 | 128.9|772.7 | 448.5|146.1 |

+x | 7 | 2 | 400 | 2600 | 77.9|101.3 | 53.6|536.0 | 1016.7|740.5 |

+x | 7 | 2 | 800 | 5400 | 36.8|29.2 | 31.5|225.1 | 372.6|208.3 |

+x | 7 | 2 | 800 | 5400 | 33.8|25.4 | 30.1|127.0 | 241.1|166.8 |

+x | 10 | 1 | 700 | 5000 | 35.6|54.8 | 23.3|129.4 | 375.0|317.8 |

−x | 5 | 2 | 600 | 5400 | 30.1|22.6 | 45.0|51.5 | 80.8|212.3 |

−x | 5 | 3 | 800 | 6000 | 42.7|27.7 | 32.8|30.3 | 100.4|320.9 |

−x | 10 | 3 | 800 | 5000 | 34.3|19.5 | 12.9|26.8 | 268.5|536.9 |

−y | 5 | 5 | 600 | 5400 | 48.7|88.6 | 99.0|245.3 | 478.8|281.5 |

−y | 10 | 1 | 300 | 2600 | 48.5|74.1 | 157.4|179.0 | 579.6|634.4 |

−y | 10 | 1 | 500 | 3500 | 42.5|81.1 | 90.5|172.4 | 836.0|709.6 |

+x/−y | 5 | 2 | 600 | 4500 | 38.9|23.1 | 12.0|153.7 | 205.4|458.0 |

+x/−y | 5 | 4 | 800 | 5400 | 36.9|31.1 | 30.7|33.5 | 261.3|314.25 |

+x/−y | 10 | 1 | 600 | 5400 | 32.6|26.2 | 23.9|67.2 | 99.3|208.6 |

−x/+y | 5 | 3 | 600 | 4500 | 68.6|26.6 | 157.1|26.3 | 324.9|544.3 |

−x/+y | 5 | 4 | 800 | 6000 | 36.5|21.5 | 64.4|54.4 | 297.4|246.0 |

−x/+y | 10 | 2 | 600 | 5400 | 35.0|32.1 | 47.7|163.4 | 156.6|321.5 |

−y/+z | 10 | 0 to 2 | 600 | 5000 | 28.1|21.4 | 50.6|18.2 | 206.2|115.5 |

ccw | 2 | 2 | 600 | 4500 | 49.8|38.3 | 104.4|149.1 | 247.5|437.0 |

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**MDPI and ACS Style**

Denkena, B.; Bergmann, B.; Stoppel, D. Reconstruction of Process Forces in a Five-Axis Milling Center with a LSTM Neural Network in Comparison to a Model-Based Approach. *J. Manuf. Mater. Process.* **2020**, *4*, 62.
https://doi.org/10.3390/jmmp4030062

**AMA Style**

Denkena B, Bergmann B, Stoppel D. Reconstruction of Process Forces in a Five-Axis Milling Center with a LSTM Neural Network in Comparison to a Model-Based Approach. *Journal of Manufacturing and Materials Processing*. 2020; 4(3):62.
https://doi.org/10.3390/jmmp4030062

**Chicago/Turabian Style**

Denkena, Berend, Benjamin Bergmann, and Dennis Stoppel. 2020. "Reconstruction of Process Forces in a Five-Axis Milling Center with a LSTM Neural Network in Comparison to a Model-Based Approach" *Journal of Manufacturing and Materials Processing* 4, no. 3: 62.
https://doi.org/10.3390/jmmp4030062