# Investigation on the Surface Quality Obtained during Trochoidal Milling of 6082 Aluminum Alloy

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Experimental Results Regarding Ra and Rz

_{trad,tt}(t) = R

_{tool}cos(ω

_{1}t) + v

_{f}t

_{trad,tt}(t) = R

_{tool}sin(ω

_{1}t)

_{tool}is the radius of the cutting tool, v

_{f}is the feed rate equal to N × z × f

_{z}, N is the spindle speed, z the number of flutes of the cutting tool and ω

_{1}is the angular speed of the cutting tool.

_{troch,tc}(t) = R

_{tc}sin(ω

_{2}t)

_{tc}is the trochoidal radius, and ω

_{2}is the angular speed of the trochoidal movement of the cutting tool center. In order to define a constant feed rate, equal to v

_{f}, the ω

_{2}angular speed should be variable [26]. As there is no analytical solution for the determination of ω

_{2}, it can be approximated in terms of v

_{f}and L

_{troch}, which represent the length of the trochoidal path for one revolution [26]:

_{2}is also called the nutation rate. The trajectory of the tool tip in this case is given by the following parametric equations [14,27,28]:

_{troch, tt}= R

_{tc}cos(ω

_{2}t) + R

_{tt}cos(ω

_{1}t) + v

_{f}t

_{troch,tt}= R

_{tc}sin(ω

_{2}t) + R

_{tt}sin(ω

_{1}t)

_{c}+ 11.400f

_{z}

_{c}+ 52.700f

_{z}

^{2}values for the two equations were 0.8047 and 0.7788, respectively, which are not acceptable values, as the variance of the responses for which the model does not account for is relatively high. Thus, non-linear regression models are created based on a power law function:

_{c}

^{−0.498}f

_{z}

^{0.541}

_{c}

^{−0.413}f

_{z}

^{0.449}

^{2}values are 0.9648 and 0.9028. From these results, it can be concluded that the predicted values from the power law models model are significantly closer to the experimental ones than the results using the linear model. Thus, the power law model can be used in order to predict the expected surface roughness values with low computational cost and high accuracy. This observation is directly related to the results displayed in Figure 4, as in most cases, the predicted Ra and Rz values from the power law model are closer to the experimental ones than in the ones obtained from the linear model.

_{c}+ 20.700f

_{z}

_{c}+ 89.500f

_{z}

_{c}

^{−0.298}f

_{z}

^{0.687}

_{c}

^{−0.091}f

_{z}

^{0.591}

^{2}values are 0.889 and 0.949, respectively, and in the case of Rz, 0.862 and 0.905, respectively. Thus, also in this case, the power law model is clearly superior to the linear one. These findings have an obvious relation with the results displayed in Figure 5, as the results obtained with the power law model are usually closer to the experimental ones than those obtained with the linear model.

_{z}increases by a factor of 8, whereas the increase in surface roughness in the cases with the highest cutting speed is only almost twofold for the same increase in f

_{z}. Similar results are observed in the case of Rz, as its values increased with an increase in f

_{z}, but the increase was significantly lower in the cases with the higher cutting speed. However, regarding both Ra and Rz, it can be observed that in the cases with a cutting speed of 200 m/min, the surface roughness values remain almost constant above an f

_{z}value of 0.04 mm/tooth.

_{z}values over 0.02 mm/tooth.

_{z}values is clearer in comparison to the trochoidal milling. Moreover, the surface roughness values decrease almost in every case with a higher cutting speed. For Rz, similar trends are observed. Regarding the comparison between the trochoidal milling strategy and traditional slot milling, it can be seen from Figure 7a,b that in most cases, especially for f

_{z}values over 0.01 mm/tooth, the surface roughness values obtained from trochoidal milling are lower than the values obtained from traditional milling, and the difference between them increases considerably with increasing f

_{z}. Thus, it is confirmed that, from the perspective of surface quality, the trochoidal milling strategy enables the use of higher feeds and cutting speeds, increasing the productivity of the process.

#### 3.2. Experimental Results Regarding Skewness and Kurtosis of Surface Roughness Profile

#### 3.3. Effect of Depth of Cut, Coolant and Trochoidal Stepover on Surface Roughness

## 4. Conclusions

^{2}values than the simple linear models.

_{z}values. Thus, it is possible to use larger feed values while maintaining surface quality at acceptable levels.

## Author Contributions

## Funding

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The machine tool used for the experiments; (

**b**) the cutting tool and workpiece used for the experiments.

**Figure 3.**Images from the machined surfaces of experiments: (

**a**) no.4 (trochoidal milling), (

**b**) no.8 (trochoidal milling), (

**c**) no.14 (traditional milling) and (

**d**) no. 18 (traditional milling).

**Figure 4.**Comparison of experimental and predicted results for the cases of trochoidal milling regarding: (

**a**) Ra and (

**b**) Rz.

**Figure 5.**Comparison of experimental and predicted results for the cases of traditional milling regarding: (

**a**) Ra and (

**b**) Rz.

Parameter | Values |
---|---|

depth of cut (a_{p}) | 0.2, 0.5, 0.8, 1.1, 1.4 mm |

slot width (w) | 6 mm |

cutting tool diameter (d) | 6 mm (traditional milling) 4 mm (trochoidal milling) |

cutting speed (v_{c}) | 80 m/min, 200 m/min |

feed (f_{z}) | 0.01, 0.02, 0.04, 0.06, 0.08 mm/tooth |

trochoidal step (P_{troch}) | 0.1, 0.3, 0.4, 0.5, 0.7 mm |

cutting length (L) | 60 mm |

Al (%) | Si (%) | Fe (%) | Cu (%) | Mn (%) | Mg (%) | Cr (%) | Zn (%) | Ti (%) |
---|---|---|---|---|---|---|---|---|

Bal. | 0.7–1.3 | 0.45–0.55 | 0.08–0.12 | 0.4–1.0 | 0.6–1.2 | 0.23–0.27 | 0.18–0.22 | 0.08–0.12 |

No | Milling Strategy | v_{c} (m/min) | f_{z} (mm/tooth) | Ra (μm) | Rz (μm) |
---|---|---|---|---|---|

1 | Trochoidal | 80 | 0.01 | 0.412 | 2.508 |

2 | Trochoidal | 80 | 0.02 | 0.656 | 3.673 |

3 | Trochoidal | 80 | 0.04 | 1.048 | 5.443 |

4 | Trochoidal | 80 | 0.06 | 1.304 | 7.589 |

5 | Trochoidal | 80 | 0.08 | 1.652 | 7.732 |

6 | Trochoidal | 200 | 0.01 | 0.4 | 2.517 |

7 | Trochoidal | 200 | 0.02 | 0.602 | 3.472 |

8 | Trochoidal | 200 | 0.04 | 0.824 | 4.662 |

9 | Trochoidal | 200 | 0.06 | 0.788 | 4.159 |

10 | Trochoidal | 200 | 0.08 | 0.836 | 4.701 |

11 | Traditional | 80 | 0.01 | 0.377 | 2.757 |

12 | Traditional | 80 | 0.02 | 0.687 | 4.313 |

13 | Traditional | 80 | 0.04 | 1.462 | 6.975 |

14 | Traditional | 80 | 0.06 | 1.914 | 7.625 |

15 | Traditional | 80 | 0.08 | 2.021 | 8.194 |

16 | Traditional | 200 | 0.01 | 0.297 | 3.624 |

17 | Traditional | 200 | 0.02 | 0.661 | 4.864 |

18 | Traditional | 200 | 0.04 | 1.255 | 5.96 |

19 | Traditional | 200 | 0.06 | 1.303 | 6.457 |

20 | Traditional | 200 | 0.08 | 1.52 | 8.124 |

No | Trochoidal Stepover (mm) | Coolant | Depth of Cut (mm) | v_{c} (m/min) | f_{z} (mm/tooth) | Ra (μm) | Rz (μm) |
---|---|---|---|---|---|---|---|

21 | 0.1 | No | 0.8 | 200 | 0.04 | 0.485 | 2.531 |

22 | 0.4 | No | 0.8 | 200 | 0.04 | 0.792 | 4.444 |

23 | 0.5 | No | 0.8 | 200 | 0.04 | 0.79 | 4.666 |

24 | 0.7 | No | 0.8 | 200 | 0.04 | 0.876 | 5.146 |

25 | 0.3 | No | 0.2 | 200 | 0.04 | 0.511 | 3.04 |

26 | 0.3 | No | 0.5 | 200 | 0.04 | 0.643 | 3.62 |

27 | 0.3 | No | 1.1 | 200 | 0.04 | 1.057 | 5.55 |

28 | 0.3 | No | 1.4 | 200 | 0.04 | 1.37 | 6.199 |

29 | 0.3 | Yes | 0.8 | 200 | 0.01 | 0.285 | 2.091 |

30 | 0.3 | Yes | 0.8 | 200 | 0.02 | 0.435 | 2.998 |

31 | 0.3 | Yes | 0.8 | 200 | 0.04 | 0.665 | 4.277 |

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**MDPI and ACS Style**

Karkalos, N.E.; Karmiris-Obratański, P.; Kurpiel, S.; Zagórski, K.; Markopoulos, A.P.
Investigation on the Surface Quality Obtained during Trochoidal Milling of 6082 Aluminum Alloy. *Machines* **2021**, *9*, 75.
https://doi.org/10.3390/machines9040075

**AMA Style**

Karkalos NE, Karmiris-Obratański P, Kurpiel S, Zagórski K, Markopoulos AP.
Investigation on the Surface Quality Obtained during Trochoidal Milling of 6082 Aluminum Alloy. *Machines*. 2021; 9(4):75.
https://doi.org/10.3390/machines9040075

**Chicago/Turabian Style**

Karkalos, Nikolaos E., Panagiotis Karmiris-Obratański, Szymon Kurpiel, Krzysztof Zagórski, and Angelos P. Markopoulos.
2021. "Investigation on the Surface Quality Obtained during Trochoidal Milling of 6082 Aluminum Alloy" *Machines* 9, no. 4: 75.
https://doi.org/10.3390/machines9040075