# Optimization Method of Tool Parameters and Cutting Parameters Considering Dynamic Change of Performance Indicators

^{*}

## Abstract

**:**

## 1. Introduction

_{4}C mass fraction was obtained by grey-fuzzy comprehensive evaluation method.

## 2. Establishment and Verification of Finite Element Simulation of Milling Process

#### 2.1. Establishment of Finite Element Simulation Model for Milling Process

#### 2.1.1. Finite Element Simulation Model Establishment Process

#### 2.1.2. Material Constitutive Model

_{0}are equivalent flow stress, equivalent plastic strain rate, and reference plastic strain rate, respectively. T, T

_{r}, and T

_{m}denote the absolute temperature, ambient temperature and melting temperature of the workpiece material, respectively. A, B, C, m, and n are the yield strength, hardening modulus, strain rate sensitivity coefficient, heat softening coefficient, and strain hardening index, respectively. J-C parameters of the Ti6Al4V constitutive model are presented in Table 1.

#### 2.1.3. Material Parameters

#### 2.1.4. D Model Establishment, Import and Grid Division

#### 2.1.5. Setting of Tool Wear Model in Finite Element Simulation Software

#### 2.2. Simulation Parameter Selection and Performance Indicator Setting

#### 2.2.1. Simulation Parameter Selection

_{25}(5

^{4}) orthogonal test was obtained as shown in Table 5 and Table 6 was the orthogonal simulation test table corresponding to Table 5.

#### 2.2.2. Setting Performance Indicators

_{f}is feed speed, v

_{c}is cutting speed, f

_{z}is feed per tooth, z is the number of teeth, d is cutter diameter, a

_{p}is cutting depth, a

_{e}is cutting width.

_{n}is the positive pressure, v

_{c}is the chip slip velocity, T is the celsius temperature, and A

_{w}and B

_{w}are the wear characteristic constants, which can be obtained by tool wear test. According to reference [33] and reference [34], A

_{w}= 0.0004, B

_{w}= 7000, in which the values of A

_{w}and B

_{w}need to be input into Deform-3D software.

#### 2.3. Finite Element Simulation Results

_{1}phase, l

_{2}phase, l

_{3}phase, l

_{4}phase. According to Equation (2), the material removal rate of titanium alloy processed by end milling cutter is obtained. Table 7 shows the data table of tool wear rate and material removal rate under different combinations of tool parameters and cutting parameters in each stage.

## 3. Dynamic Evaluation Method Based on Gain Horizontal Excitation

#### 3.1. Dynamic Evaluation Method Based on Gain Level Excitation

_{1}to obtain the comprehensive evaluation value of each evaluated object at that time, and the same method is applied at other times. Then, the evaluation values of each evaluation object at different times are unified together, and the dynamic evaluation values of each evaluated object are obtained according to the dynamic evaluation method.

#### 3.2. Comprehensive Evaluation of Each Stage Based on Grey-Fuzzy Analytic Hierarchy Process

_{i}is the ith level of this parameter, m performance indicators, x

_{ij}(t

_{k}) is the ith (i = 1, 2, …, n) evaluated objects at t

_{k}(k = 1, 2, …, T) about the indicator x

_{j}(j = 1, 2, …, m) observed value.

_{k}of the evaluated object at the t

_{k}moment is obtained, and its expression is shown in Equation (4).

_{i}(t

_{k}) (y

_{i}(t

_{k}) ∈ [0,1]) is the comprehensive evaluation value of the ith evaluated object at the t

_{k}moment.

#### 3.3. Parameter Level Optimization Based on Dynamic Evaluation Method

_{k}of the evaluated object at the t

_{k}moment is obtained through the grey-fuzzy analytic hierarchy process, and all the comprehensive evaluation matrix B

_{k}is combined into the comprehensive evaluation matrix Y, as shown in Equation (5).

_{i}(t

_{k}) is the comprehensive evaluation value of the ith evaluated object at the t

_{k}moment.

**Definition**

**1.**

^{max}, η

^{min}, and$\overline{\eta}$evaluated object, respectively. Its calculation formula is shown in Equation (6).

**Definition**

**2.**

^{+}and η

^{−}are the good and bad gain levels of the evaluated object, and their calculation formula is shown in Equation (7).

^{+}and k

^{−}are corresponding floating coefficients, k

^{+}and k

^{−}∈ (0,1]. Floating coefficients k

^{+}and k

^{−}are used to describe the decision maker’s psychological expectation of the overall development of the evaluated object.

^{+}and η

^{−}are obtained, they are substituted into the following Equation (8),

_{i}

^{+}(t

_{k}) and y

_{i}

^{−}(t

_{k}) of the ith evaluated object at the t

_{k}moment are obtained by Equation (8).

_{i}

^{+}(t

_{k}) and y

_{i}

^{−}(t

_{k}) are substituted into Equation (9).

_{i}

^{+}(t

_{k}) and υ

_{i}

^{−}(t

_{k}) are the excellent and bad excitation quantities obtained by the ith evaluated object at the t

_{k}stage, respectively. In addition, in the case outside the value range, the superior and inferior excitation quantities are 0. υ

_{i}

^{+}(t

_{k}) = υ

_{i}

^{−}(t

_{k}) = 0 is set at the initial t

_{k}stage without any excitation. Figure 8 is the geometric visual representation of the excellent and bad excitation points. In Figure 8, t

_{k}, t

_{k+1}and t

_{k+2}stages respectively represent the three situations in which the evaluated object obtains the excellent excitation, does not obtain the bad excitation and obtains the good excitation.

_{i}(t

_{k}) be the dynamic comprehensive evaluation value of the ith evaluated object in the t

_{k}stage, then the calculation formula of z

_{i}(t

_{k}) is shown in Equation (10).

^{+}, h

^{−}(h

^{+}, h

^{−}> 0) are superior and inferior excitation factors respectively; h

^{+}υ

_{i}

^{+}(t

_{k}) and h

^{−}υ

_{i}

^{−}(t

_{k}) are the optimal and the inferior excitation values respectively. In addition, according to Equation (9), any t

_{k}(k = 1, 2, …, T) in the moment, υ

_{i}

^{+}(t

_{k}) × υ

_{i}

^{−}(t

_{k}) = 0, that is, h

^{+}υ

_{i}

^{+}(t

_{k}), h

^{−}υ

_{i}

^{−}(t

_{k}) cannot be obtained at the same time.

^{+}) is the proportion relation between the total amount of excellent incentives and the total amount of bad incentives, which is a reflection of the decision intention of the evaluator. When r > 1, indicates that the total amount of excellent excitation is greater than the total amount of bad excitation; When r < 1, indicates that the total amount of excellent excitation is less than the total amount of bad excitation; When r = 1, it means that the total amount of excellent excitation is equal to the total amount of bad excitation.

^{+}and h

^{−}is 1.

^{+}and h

^{−}can be obtained through Equations (11) and (12).

_{i}(t

_{k}) of the ith evaluated object at the t

_{k}stage is obtained through the above steps. Then the total dynamic comprehensive evaluation value z

_{i}of the ith evaluated object at all times is shown in Equation (13).

_{k}is the time factor, {τ

_{k}} is usually taken as a series of increasing type. If there is no specific requirement and time preference can be ignored, τ

_{k}= 1.

#### 3.4. Comprehensive Evaluation of Parameter Level in Each Stage

_{1}, x

_{2}}. Among them, x

_{1}is tool wear rate, and x

_{2}is material removal rate. First of all, weight distribution was carried out for each performance indicator. In order to highlight the importance of tool life, it was necessary to increase the weight value of tool wear rate, as shown in Table 9. Then, according to reference [36], the weight value of tool wear rate is 0.6, the weight value of material removal rate is 0.4, and the indicator weight matrix P = [0.6, 0.4].

_{k}was used instead of moment t

_{k}to represent the dynamic nodes in the cutting process. The values shown in Table 10 are the average values of the sum of the performance indicator values of the clearance angle at the same level obtained in Table 7 at different stages. And according to the weight matrix of performance indicators and the grey-fuzzy evaluation method, the comprehensive evaluation matrix B

_{1}, B

_{2}, B

_{3}, and B

_{4}of four stages are obtained, among which the coefficients required by the grey-fuzzy evaluation method can be obtained from reference [37].

#### 3.5. Dynamic Evaluation of Parameter Level

_{1}, B

_{2}, B

_{3}, and B

_{4}of each stage obtained in 3.4 were transformed and combined to obtain the comprehensive evaluation matrix Y of five levels about the clearance angle.

^{max}= 0.01092, average minimum gain η

^{min}= −0.07892, average gain $\overline{\eta}$ = −0.015588 were obtained for the comprehensive evaluation matrix Y.

^{+}and k

^{−}as 0.3, the optimal gain level η

^{+}= −0.00764 and the inferior gain level η

^{−}= −0.03459 of the comprehensive evaluation matrix Y were obtained according to Equation (7).

_{i}

^{+}(t

_{k}) and the inferior excitation points y

_{i}

^{−}(t

_{k}) of each level of the clearance angle in Table 11 at different stages were obtained.

_{i}

^{+}(l

_{k}) and the inferior excitation quantities υ

_{i}

^{−}(l

_{k}) at different stages of each level of the clearance angle in Table 12 were obtained.

^{+}= 0.47894 and the inferior excitation factor h

^{−}= 0.52106 can be obtained.

_{k}) of each level of the clearance angle in Table 13 at different stages is obtained. Set τ

_{k}= 1 and obtain the total dynamic comprehensive evaluation value z for each level of the rear Angle according to Equation (13). According to the total dynamic comprehensive evaluation value z of each level of the clearance angle in the last column in Table 13, 9° clearance angle is selected as the best level.

#### 3.6. Comparison between Parameter Combinations

## 4. Validation of the Finite Element Model

#### 4.1. Setting of Experimental Parameters

#### 4.2. The Experimental Device

#### 4.3. Reliability Verification of Simulation Model

## 5. Conclusions and Prospects

- In this paper, the dynamic evaluation method based on gain horizontal excitation was used to optimize the tool parameters and cutting parameters in the process of milling titanium alloy with milling cutter side, and the optimal matching combination of tool parameters and cutting parameters on the tool wear rate and material removal rate was obtained.
- When the rake angle is 8°, the cutting speed is 37.68 m/min, and the cutting width is 0.2 mm, the machining effect of the clearance angle is 9°, the helix angle is 30°, the feed per tooth is 0.15 mm/z, and the cutting depth is 2.5 mm achieves the best, which can simultaneously meet the requirements of long tool life and high machining efficiency. In addition, the reliability of simulation model is verified, and the optimization results are also reliable.
- The comparison between the optimized parameters by finite element method and the parameter combination in Table 6 shows that the optimized parameter combination has higher comprehensive performance.
- In this paper, the performance indicator value is obtained by simulation, but there is some error between simulation value and experimental value. Therefore, in the future, under the condition of sufficient time and funding, the required numerical value of tool wear rate and material removal rate will be obtained through experiments to make the optimization results more accurate.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Notation | |

CNC | Computerized Numerical Control |

PVD | Physical Vapor Deposition |

Symbol | |

σ | The equivalent flow stress |

ε | The equivalent plastic strain rate |

ε_{0} | The reference plastic strain rate |

T | The absolute temperature |

T_{r} | The ambient temperature |

T_{m} | The melting temperature |

A | the yield strength |

B | The hardening modulus |

C | The strain rate sensitivity coefficient |

m | The heat softening coefficient |

n | The strain hardening index |

V | The material removal rate |

v_{f} | The feed speed |

d | The cutter diameter |

a_{p} | The cutting depth |

a_{e} | The cutting width |

f_{z} | The feed per tooth |

f_{z} | The feed per tooth |

z | The number of teeth |

W_{Adhesion wear} | The adhesion wear |

σ_{n} | The positive pressure |

v_{c} | The chip slip speed |

T | The celsius |

A_{w} | The wear characteristic constant |

B_{w} | The wear characteristic constant |

l_{k} | The kth phase |

t_{k} | The period k |

n | The number of evaluated objects |

s_{i} | The ith object to be evaluated |

m | The number of performance indicators |

T | The number of time periods |

x_{j} | The jth performance indicator |

x_{ij}(t_{k}) | The value of the ith evaluated object about the jth indicator at the time t_{k} |

B_{k} | The static evaluation matrix of the kth period |

y_{i}(t_{k}) | The static evaluation value of the ith evaluated object in the kth period |

Y | The static comprehensive evaluation matrix |

η^{max} | The mean maximum gain |

η^{min} | The mean minimum gain |

$\overline{\eta}$ | The average gain |

η^{+} | The optimal gain level |

η^{−} | The inferior gain level |

y_{i}^{+}(t_{k}) | The optimal excitation point of the ith evaluated object at time t_{k} |

y_{i}^{−}(t_{k}) | The inferior excitation point of the ith evaluated object at time t_{k} |

υ_{i}^{+}(t_{k}) | The optimal excitation quantity obtained by the ith evaluated object at time t_{k} |

υ_{i}^{−}(t_{k}) | The inferior excitation obtained by the ith evaluated object at time t_{k} |

z_{i}(t_{k}) | The dynamic comprehensive evaluation value of the ith evaluated object at t_{k} moment |

h^{+} | The optimal excitation factor |

h^{−} | The inferior excitation factor |

r | The proportional relationship between the total amount of the optimal excitation quantity and the total amount of bad incentives |

τ_{k} | The time factor |

z_{i} | The total dynamic comprehensive evaluation value of the ith evaluated object |

U_{jh} | The weight ratio of the jth performance indicator to the hth performance indicator |

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**Figure 2.**Simulation model of the side milling process: (

**a**) End milling cutter model, (

**b**) Workpiece model, (

**c**) 3D models in simulation software and (

**d**) The simulation model.

**Figure 6.**Flow chart of dynamic comprehensive evaluation method based on gain horizontal excitation.

**Figure 8.**Geometric representation of excellent and bad excitation points and excitation quantities.

**Figure 9.**Simulation diagram of tool wear rate at each stage: (

**a**) the first-stage wear rate value (

**b**) the second-stage wear rate value (

**c**) the third-stage wear rate value and (

**d**) the fourth-stage wear rate value.

**Figure 10.**Experimental instruments and equipment used in the experiment (

**a**) CNC milling machine and (

**b**) cutting force measuring equipment.

**Figure 11.**The simulation value of cutting force is compared with the experimental value: (

**a**) x-direction (

**b**) y-direction and (

**c**) z-direction.

**Table 1.**J-C parameters for Ti-6Al-4V alloy [27].

A (MPa) | B (MPa) | C | m | n | $\overline{{\mathbf{\epsilon}}_{\mathbf{0}}}$ (s^{−1}) | T_{m} (°C) | T_{r} (°C) |
---|---|---|---|---|---|---|---|

875 | 793 | 0.01 | 0.71 | 0.386 | 1 | 1560 | 20 |

**Table 2.**Material parameter [28].

Material Parameter | YG6 | Ti6Al4V |
---|---|---|

Density (g/cm^{3}) | 14.85 | 4.44 |

Young’s modulus (GPa) | 640 | 112 |

Poission’s Ratio | 0.22 | 0.34 |

Expansion (/°C) | 4.7 × 10^{−6} | 9.4 × 10^{−6} |

Conductivity (W/m·K) | 79.6 | 6.8 |

Specific heat (J/(kg·°C)) | 176 | 565 |

Num. | Parameter | Value |
---|---|---|

1 | The blade number | 4 |

2 | The cutter diameter | 10 (mm) |

3 | The rake angle | 8 (°) |

4 | The width of rake face | 1.0 (mm) |

5 | The first clearance angle | 12 (°) |

6 | The second clearance angle | 23 (°) |

7 | The width of the first flank face | 0.7 (mm) |

8 | The width of the second flank face | 0.8 (mm) |

9 | The helix angle | 35 (°) |

10 | The core diameter | 6.2 (mm) |

Rake Angle (°) | Cutting Speed (m/min) | Cutting Width (mm) |
---|---|---|

8 | 37.68 | 0.2 |

Clearance Angle (°) | Helix Angle (°) | Feed Per Tooth (mm/z) | Cutting Depth (mm) | |
---|---|---|---|---|

1 | 8.00 | 30.00 | 0.05 | 1.00 |

2 | 9.00 | 32.00 | 0.10 | 1.50 |

3 | 10.00 | 33.00 | 0.15 | 2.00 |

4 | 11.00 | 34.00 | 0.20 | 2.50 |

5 | 12.00 | 35.00 | 0.25 | 3.00 |

Clearance Angle (°) | Helix Angle (°) | Feed Per Tooth (mm/z) | Cutting Depth (mm) | |
---|---|---|---|---|

1 | 9.00 | 32.00 | 0.20 | 1.50 |

2 | 12.00 | 30.00 | 0.10 | 1.50 |

3 | 11.00 | 30.00 | 0.15 | 2.00 |

4 | 8.00 | 32.00 | 0.25 | 2.00 |

5 | 10.00 | 30.00 | 0.20 | 2.50 |

6 | 9.00 | 33.00 | 0.15 | 2.50 |

7 | 11.00 | 32.00 | 0.10 | 3.00 |

8 | 12.00 | 32.00 | 0.05 | 2.50 |

9 | 12.00 | 34.00 | 0.20 | 2.00 |

10 | 11.00 | 34.00 | 0.25 | 2.50 |

11 | 10.00 | 34.00 | 0.05 | 3.00 |

12 | 9.00 | 34.00 | 0.10 | 1.00 |

13 | 9.00 | 30.00 | 0.25 | 3.00 |

14 | 11.00 | 33.00 | 0.05 | 1.50 |

15 | 8.00 | 33.00 | 0.20 | 3.00 |

16 | 8.00 | 30.00 | 0.05 | 1.00 |

17 | 10.00 | 32.00 | 0.15 | 1.00 |

18 | 12.00 | 35.00 | 0.15 | 3.00 |

19 | 8.00 | 34.00 | 0.15 | 1.50 |

20 | 10.00 | 35.00 | 0.25 | 1.50 |

21 | 9.00 | 35.00 | 0.05 | 2.00 |

22 | 11.00 | 35.00 | 0.20 | 1.00 |

23 | 12.00 | 33.00 | 0.25 | 1.00 |

24 | 8.00 | 35.00 | 0.10 | 2.50 |

25 | 10.00 | 33.00 | 0.10 | 2.00 |

The First Stage (l_{1}) | The Second Stage (l_{2}) | The Third Stage (l_{3}) | The Fourth Stage (l_{4}) | |||||
---|---|---|---|---|---|---|---|---|

Wear Rate (mm/s) | V (mm ^{3}/s) | Wear Rate (mm/s) | V (mm ^{3}/s) | Wear Rate (mm/s) | V (mm ^{3}/s) | Wear Rate (mm/s) | V (mm ^{3}/s) | |

1 | 0.00934 | 4.8 | 0.00547 | 4.8 | 0.00156 | 4.8 | 0.02260 | 4.8 |

2 | 0.07030 | 2.4 | 0.04810 | 2.4 | 0.06770 | 2.4 | 0.13100 | 2.4 |

3 | 0.01680 | 4.8 | 0.01240 | 4.8 | 0.00945 | 4.8 | 0.02470 | 4.8 |

4 | 0.00623 | 8.0 | 0.01920 | 8.0 | 0.01110 | 8.0 | 0.13000 | 8.0 |

5 | 0.03900 | 8.0 | 0.14100 | 8.0 | 0.03130 | 8.0 | 0.02760 | 8.0 |

6 | 0.00718 | 6.0 | 0.03550 | 6.0 | 0.00378 | 6.0 | 0.01050 | 6.0 |

7 | 0.00168 | 4.8 | 0.00718 | 4.8 | 0.11400 | 4.8 | 0.01590 | 4.8 |

8 | 0.02320 | 2.0 | 0.01390 | 2.0 | 0.01760 | 2.0 | 0.01180 | 2.0 |

9 | 0.00508 | 6.4 | 0.03820 | 6.4 | 0.04800 | 6.4 | 0.10500 | 6.4 |

10 | 0.01030 | 10.0 | 0.02150 | 10.0 | 0.00221 | 10.0 | 0.00834 | 10.0 |

11 | 0.00338 | 2.4 | 0.22500 | 2.4 | 0.00802 | 2.4 | 0.05170 | 2.4 |

12 | 0.06360 | 1.6 | 0.11400 | 1.6 | 0.04850 | 1.6 | 0.05840 | 1.6 |

13 | 0.00747 | 12.0 | 0.05300 | 12.0 | 0.09910 | 12.0 | 0.06970 | 12.0 |

14 | 0.01660 | 1.2 | 0.04650 | 1.2 | 0.01180 | 1.2 | 0.07540 | 1.2 |

15 | 0.05810 | 9.6 | 0.02610 | 9.6 | 0.05140 | 9.6 | 0.01940 | 9.6 |

16 | 0.01460 | 0.8 | 0.03630 | 0.8 | 0.07520 | 0.8 | 0.04940 | 0.8 |

17 | 0.00944 | 2.4 | 0.03190 | 2.4 | 0.07750 | 2.4 | 0.00726 | 2.4 |

18 | 0.02010 | 6.4 | 0.00564 | 6.4 | 0.06460 | 6.4 | 0.01400 | 6.4 |

19 | 0.00544 | 3.2 | 0.00826 | 3.2 | 0.00757 | 3.2 | 0.01910 | 3.2 |

20 | 0.03630 | 6.0 | 0.09990 | 6.0 | 0.03680 | 6.0 | 0.03020 | 6.0 |

21 | 0.01550 | 1.6 | 0.00282 | 1.6 | 0.01850 | 1.6 | 0.00993 | 1.6 |

22 | 0.01930 | 3.2 | 0.01340 | 3.2 | 0.02070 | 3.2 | 0.01630 | 3.2 |

23 | 0.01380 | 4.0 | 0.03740 | 4.0 | 0.01010 | 4.0 | 0.00943 | 4.0 |

24 | 0.04980 | 4.0 | 0.01570 | 4.0 | 0.02950 | 4.0 | 0.03220 | 4.0 |

25 | 0.01970 | 3.2 | 0.01060 | 3.2 | 0.04600 | 3.2 | 0.02340 | 3.2 |

t_{1} | t_{2} | … | t_{T} | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

x_{1} | x_{2} | … | x_{m} | x_{1} | x_{2} | … | x_{m} | … | x_{1} | x_{2} | … | x_{m} | |

s_{1} | x_{11}(t_{1}) | x_{12}(t_{1}) | … | x_{1m}(t_{1}) | x_{11}(t_{2}) | x_{12}(t_{2}) | … | x_{1m}(t_{2}) | … | x_{11}(t_{T}) | x_{12}(t_{T}) | … | x_{1m}(t_{T}) |

s_{2} | x_{21}(t_{1}) | x_{22}(t_{1}) | … | x_{2m}(t_{1}) | x_{21}(t_{2}) | x_{22}(t_{2}) | … | x_{2m}(t_{2}) | … | x_{21}(t_{T}) | x_{22}(t_{T}) | … | x_{2m}(t_{T}) |

… | … | … | … | … | … | … | … | … | … | … | … | … | … |

s_{n} | x_{n1}(t_{1}) | x_{n2}(t_{1}) | … | x_{nm}(t_{1}) | x_{n1}(T_{2}) | x_{n2}(t_{2}) | … | x_{nm}(t_{2}) | … | x_{n1}(t_{T}) | x_{n2}(t_{T}) | … | x_{nm}(t_{T}) |

x_{j}/x_{h} | x_{1}/x_{2} | x_{2}/x_{2} |
---|---|---|

U_{jh} | 1.5 | 1.0 |

The First Stage (l_{1}) | The Second Stage (l_{2}) | The Third Stage (l_{3}) | The Fourth Stage (l_{4}) | |||||
---|---|---|---|---|---|---|---|---|

Wear Rate (mm/s) | V (mm ^{3}/s) | Wear Rate (mm/s) | V (mm ^{3}/s) | Wear Rate (mm/s) | V (mm ^{3}/s) | Wear Rate (mm/s) | V (mm ^{3}/s) | |

1 | 0.02683 | 5.12 | 0.02111 | 5.12 | 0.03495 | 5.12 | 0.05002 | 5.12 |

2 | 0.02062 | 5.20 | 0.04216 | 5.20 | 0.03429 | 5.20 | 0.03427 | 5.20 |

3 | 0.09176 | 4.40 | 0.10168 | 4.40 | 0.03992 | 4.40 | 0.02803 | 4.40 |

4 | 0.01150 | 5.04 | 0.01728 | 5.04 | 0.04477 | 5.04 | 0.01450 | 5.04 |

5 | 0.02650 | 4.24 | 0.02865 | 4.24 | 0.04160 | 4.24 | 0.26369 | 4.24 |

**Table 11.**The excellent and bad excitation points of each level of the clearance angle at different stages.

l_{1} | l_{2} | l_{3} | l_{4} | ||||
---|---|---|---|---|---|---|---|

y_{i}(l_{1})
| y_{i}^{+}(l_{2})
| y_{i}^{−}(l_{2})
| y_{i}^{+}(l_{3})
| y_{i}^{−}(l_{3})
| y_{i}^{+}(l_{4})
| y_{i}^{−}(l_{4})
| |

1 | 0.77701 | 0.76937 | 0.74242 | 0.88793 | 0.86098 | 0.86810 | 0.84115 |

2 | 0.88889 | 0.88125 | 0.85430 | 0.77800 | 0.75105 | 0.99236 | 0.96541 |

3 | 0.75000 | 0.74236 | 0.71541 | 0.74236 | 0.71541 | 0.43160 | 0.40465 |

4 | 0.90000 | 0.89236 | 0.86541 | 0.89236 | 0.86541 | 0.49236 | 0.46541 |

5 | 0.57008 | 0.56244 | 0.53549 | 0.60416 | 0.57721 | 0.37621 | 0.34926 |

l_{1} | l_{2} | l_{3} | l_{4} | |||||
---|---|---|---|---|---|---|---|---|

υ_{i}^{+}(l_{1})
| υ_{i}^{−}(l_{1})
| υ_{i}^{+}(l_{2})
| υ_{i}^{−}(l_{2})
| υ_{i}^{+}(l_{3})
| υ_{i}^{−}(l_{3})
| υ_{i}^{+}(l_{4})
| υ_{i}^{−}(l_{4})
| |

1 | 0 | 0 | 0.12640 | 0 | 0 | 0 | 0 | 0.03139 |

2 | 0 | 0 | 0 | 0.06866 | 0.22800 | 0 | 0 | 0.04758 |

3 | 0 | 0 | 0.00764 | 0 | 0 | 0.27617 | 0.25963 | 0 |

4 | 0 | 0 | 0.00764 | 0 | 0 | 0.36541 | 0.40764 | 0 |

5 | 0 | 0 | 0.04936 | 0 | 0 | 0.19336 | 0 | 0.01593 |

**Table 13.**The dynamic comprehensive evaluation table of each level of the clearance angle and the total dynamic comprehensive evaluation table.

z(l_{1})
| z(l_{2})
| z(l_{3})
| z(l_{4})
| z | |
---|---|---|---|---|---|

1 | 0.77701 | 0.95611 | 0.87574 | 0.79340 | 3.40295 |

2 | 0.88889 | 0.74986 | 1.10920 | 0.89304 | 3.65099 |

3 | 0.75000 | 0.75366 | 0.29534 | 0.70366 | 2.50266 |

4 | 0.9000 | 0.90366 | 0.30960 | 1.09524 | 3.20850 |

5 | 0.57008 | 0.63544 | 0.28310 | 0.32503 | 1.81365 |

z_{Helix angle} | z_{Feed per tooth} | z_{Cutting depth} | |
---|---|---|---|

1 | 2.44285 | 1.99773 | 1.75018 |

2 | 2.20450 | 1.62204 | 1.77147 |

3 | 2.31967 | 3.05105 | 2.48153 |

4 | 2.04067 | 2.39639 | 2.93874 |

5 | 2.06289 | 2.95389 | 2.67173 |

**Table 15.**The numerical table of tool wear rate and material removal rate corresponding to the optimal parameters.

Wear Rate (mm/s) | V (mm^{3}/s) | |||
---|---|---|---|---|

l_{1} | l_{2} | l_{3} | l_{4} | |

0.00645 | 0.0459 | 0.00947 | 0.0103 | 6.0 |

Cutting Speed (m/min) | Feed Speed (mm/min) | Cutting Depth (mm) | Cutting Width (mm) |
---|---|---|---|

31.40 | 400 | 3 | 0.8 |

37.68 | 400 | 3 | 0.8 |

47.10 | 400 | 3 | 0.8 |

Cutting Speed (m/min) | Simulation (N) | Experiment (N) | |
---|---|---|---|

F_{x} | 31.40 | 313.613 | 266.791 |

37.68 | 634.243 | 510.750 | |

47.10 | 577.552 | 462.902 | |

F_{y} | 31.40 | 358.606 | 289.408 |

37.68 | 532.094 | 466.600 | |

47.10 | 503.908 | 415.483 | |

F_{z} | 31.40 | 234.752 | 188.069 |

37.68 | 168.884 | 135.653 | |

47.10 | 191.216 | 153.299 |

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## Share and Cite

**MDPI and ACS Style**

Yue, D.; Zhang, A.; Yue, C.; Liu, X.; Li, M.; Hu, D.
Optimization Method of Tool Parameters and Cutting Parameters Considering Dynamic Change of Performance Indicators. *Materials* **2021**, *14*, 6181.
https://doi.org/10.3390/ma14206181

**AMA Style**

Yue D, Zhang A, Yue C, Liu X, Li M, Hu D.
Optimization Method of Tool Parameters and Cutting Parameters Considering Dynamic Change of Performance Indicators. *Materials*. 2021; 14(20):6181.
https://doi.org/10.3390/ma14206181

**Chicago/Turabian Style**

Yue, Daxun, Anshan Zhang, Caixu Yue, Xianli Liu, Mingxing Li, and Desheng Hu.
2021. "Optimization Method of Tool Parameters and Cutting Parameters Considering Dynamic Change of Performance Indicators" *Materials* 14, no. 20: 6181.
https://doi.org/10.3390/ma14206181