# Cutting Energy Consumption Modelling of End Milling Cutter Coated with AlTiCrN

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## Abstract

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## 1. Introduction

_{f}= 300, a

_{p}= 2 and a

_{e}= 0.3. The last part summarizes the full paper. The structure of this paper is shown in Figure 2.

## 2. Modelling of Cutting Energy Consumption

_{t}is the instantaneous power, and E is the energy consumption of time t

_{1}to t

_{2}. Therefore, the cutting energy consumption is analyzed from the two factors of cutting power and machining time.

#### 2.1. Cutting Power Model of Machine Tool

_{p}. In the second deformation zone, the chip is further squeezed by the rake face when it is discharged along the rake face, resulting in friction. The power consumed in this stage is the friction power P

_{fr}of the rake face. In the third deformation zone, the machined surface is subjected to the extrusion, friction, and spring back of the cutting edge and the flank face. The power consumed in this stage is the friction power of the flank face P

_{ff}. Other energies involved in the cutting process are chip kinetic energy, surface energy, and elastic deformation energy P

_{e}.

_{p}. The second part is the friction power consumed at contact zone of cutting tool and workpiece P

_{f}, which including friction power consumed at rake face in second deformation zone P

_{fr}and friction power consumed at flank face in third deformation zone P

_{ff}. The third part is kinetic energy of chip, surface energy of workpiece, and elastic deformation power P

_{e}.

_{c}is expressed by Equation (2).

#### 2.2. Power Model of Plastic Deformation of Workpiece

_{p}is the cutting depth, a

_{e}is the cutting width, v

_{f}is the feed rate, t

_{pro}is the cutting time. Substituting Equation (2), the plastic deformation power consumed in the cutting process ${P}_{p}$ can be expressed as

#### 2.3. Friction Power Model of Rake Face

_{c}on the rake face, the average friction stress on the rake face is set to ${\overline{\tau}}_{c}$. Therefore, the friction force consumed on the rake face tool-chip contact surface is ${\overline{\tau}}_{c}A$. The friction work per unit time can be expressed by Equation (5).

_{chip}is the velocity of the chip flowing out along the rake face of the tool, which can be expressed by Equation (6).

_{c}is the ratio of the actual contact zone to the apparent contact zone, which is generally 0.8.

_{f}, where b is the cutting width, and l

_{fr}is the theoretical cutting tool–chip contact length. The relationship between the theoretical contact length and the actual contact length l

_{c}can be expressed by Equation (7).

_{m}is the ratio of the actual contact length to the theoretical contact length, which is generally 2.0, and h is the thickness of the workpiece to be cut.

#### 2.4. Friction Power Model of Flank Face

_{ff}, and the average friction stress of the contact zone is ${\tau}_{cf}$. Then the friction force acting on the contact zone is ${\tau}_{cf}{l}_{ff}b$, and the friction work consumed per unit time can be expressed by Equation (9).

_{e}, and the workpiece thickness h is regarded as a

_{p}. Therefore, the cutting power with the sharp cutting edge can be calculated by Equation (11).

#### 2.5. Machining Time Model

_{l}= l/v

_{f}. The rough milling time t

_{cr}can be expressed as

_{cf}can be expressed as

_{m}, the maximum acceleration and maximum deceleration are equal to a

_{m}, and the maximum operating speed of the machine tool is v

_{m}. According to the acceleration change, it can be divided into seven stages: jerk, uniform acceleration, decelerated acceleration, uniform velocity, accelerated deceleration, uniform deceleration, and decelerated deceleration. The operation time of each stage is recorded as t

_{1}, t

_{2}, t

_{3}, t

_{4}, t

_{5}, t

_{6}, and t

_{7}. The feed rate calculation formula is shown in Equation (14). According to the above piecewise function, the machining time of each stage can be determined from t

_{1}to t

_{7}. At the corner, the change of feed rate is shown in Figure 6.

## 3. Experimental Setup

_{cal}is the predicted value of energy consumption, which is calculated by the energy consumption model, E

_{mea}is the measured value of energy consumption, which is obtained by experiment, and AE is the prediction error.

## 4. Analysis of the Influence of Cutting Parameters on Cutting Energy Consumption

_{f}< 300 mm/min, the unit pressure of the rake face is small with the increase in the feed rate, and the friction coefficient is constant. Therefore, the cutting power changes slightly. When v

_{f}> 300 mm/min, the cutting power increases with the feed rate continuing to increase. As the feed rate increases, the cutting zone increases, and the friction energy increases. Therefore, reducing the cutting power of the machine tool by changing cutting width or the cutting depth is more effective than changing feed rate and spindle speed.

_{f}= 300, a

_{p}= 2, and a

_{e}= 0.3 is the smallest combination out of 81 groups of cutting power values.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 10.**Comparison of calculated and measured values of cutting energy: (

**a**) Cutting width; (

**b**) Cutting depth.

Type of Cutter | Particle Size | Hardness | Coating | Helix Angle | Number of Edges | Material |
---|---|---|---|---|---|---|

End milling cutter | 0.6μm | ≤65° | AlTiCrN | 35° | 2 | Tungsten steel |

Material | Yield Strength (MPa) | Ultimate Strength (MPa) | Elongation (%) | Vickers Hardness (HV) | Density (gr/cm ^{3}) |
---|---|---|---|---|---|

Al 6061 | 286 | 318 | 5.44 | 106 | 2.7 |

Experiment Number | a_{e}(mm) | a_{p}(mm) | E_{cal}(J) | E_{mea}(J) | Prediction Error (%) |
---|---|---|---|---|---|

1 | 5 | 5 | 5896 | 6397 | 8.50 |

2 | 5.2 | 5 | 6132 | 5940 | 3.13 |

3 | 5.4 | 5 | 6368 | 6949 | 9.12 |

4 | 5.6 | 5 | 6603 | 6995 | 5.94 |

5 | 5.8 | 5 | 6840 | 6863 | 0.34 |

6 | 5 | 5 | 5896 | 6397 | 8.50 |

7 | 5 | 5.5 | 6486 | 6971 | 7.48 |

8 | 5 | 6 | 7075 | 8319 | 17.58 |

9 | 5 | 6.5 | 7665 | 8443 | 10.15 |

10 | 5 | 7 | 8254 | 8641 | 4.69 |

Experiment Number | n (rpm) | v_{f}(mm/min) | a_{p}(mm) | a_{e}(mm) | P_{c}(W) | E (J) |
---|---|---|---|---|---|---|

1 | 2500 | 200 | 2 | 0.3 | 7.05 | 530.16 |

2 | 2500 | 300 | 4 | 0.6 | 15.51 | 775.50 |

3 | 2500 | 400 | 6 | 0.9 | 39.36 | 1472.06 |

4 | 3000 | 200 | 4 | 0.9 | 21.56 | 1621.31 |

5 | 3000 | 300 | 6 | 0.3 | 14.41 | 720.50 |

6 | 3000 | 400 | 2 | 0.6 | 14.62 | 546.79 |

7 | 3500 | 200 | 6 | 0.6 | 20.26 | 1523.55 |

8 | 3500 | 300 | 2 | 0.9 | 17.77 | 888.5 |

9 | 3500 | 400 | 4 | 0.3 | 14.55 | 544.17 |

Experiment Number | n (rpm) | v_{f}(mm/min) | a_{p}(mm) | a_{e}(mm) |
---|---|---|---|---|

1 | 20.65 | 16.29 | 13.15 | 12.01 |

2 | 16.87 | 15.90 | 17.21 | 16.80 |

3 | 17.53 | 22.85 | 24.68 | 26.24 |

Calculation rank | 3.78 | 6.95 | 11.54 | 14.23 |

Rank | ${a}_{e}>{a}_{p}>{v}_{f}>n$ |

Experiment Number | n (rpm) | v_{f}(mm/min) | a_{p}(mm) | a_{e}(mm) |
---|---|---|---|---|

1 | 925.9 | 1225.0 | 655.1 | 598.3 |

2 | 962.9 | 794.8 | 980.3 | 948.6 |

3 | 985.4 | 854.3 | 1238.7 | 1327.3 |

Calculation rank | 59.5 | 430.2 | 583.6 | 729.0 |

Rank | ${a}_{e}>{a}_{p}>{v}_{f}>n$ |

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**MDPI and ACS Style**

Meng, Y.; Sun, X.; Dong, S.; Wang, Y.; Liu, X. Cutting Energy Consumption Modelling of End Milling Cutter Coated with AlTiCrN. *Coatings* **2023**, *13*, 679.
https://doi.org/10.3390/coatings13040679

**AMA Style**

Meng Y, Sun X, Dong S, Wang Y, Liu X. Cutting Energy Consumption Modelling of End Milling Cutter Coated with AlTiCrN. *Coatings*. 2023; 13(4):679.
https://doi.org/10.3390/coatings13040679

**Chicago/Turabian Style**

Meng, Yue, Xinsheng Sun, Shengming Dong, Yue Wang, and Xianli Liu. 2023. "Cutting Energy Consumption Modelling of End Milling Cutter Coated with AlTiCrN" *Coatings* 13, no. 4: 679.
https://doi.org/10.3390/coatings13040679