Optimization Method of Tool Parameters and Cutting Parameters Considering Dynamic Change of Performance Indicators
Abstract
:1. Introduction
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
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
2.2.2. Setting Performance Indicators
2.3. Finite Element Simulation Results
3. Dynamic Evaluation Method Based on Gain Horizontal Excitation
3.1. Dynamic Evaluation Method Based on Gain Level Excitation
3.2. Comprehensive Evaluation of Each Stage Based on Grey-Fuzzy Analytic Hierarchy Process
3.3. Parameter Level Optimization Based on Dynamic Evaluation Method
3.4. Comprehensive Evaluation of Parameter Level in Each Stage
3.5. Dynamic Evaluation of Parameter 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 |
ε0 | The reference plastic strain rate |
T | The absolute temperature |
Tr | The ambient temperature |
Tm | 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 |
vf | The feed speed |
d | The cutter diameter |
ap | The cutting depth |
ae | The cutting width |
fz | The feed per tooth |
fz | The feed per tooth |
z | The number of teeth |
WAdhesion wear | The adhesion wear |
σn | The positive pressure |
vc | The chip slip speed |
T | The celsius |
Aw | The wear characteristic constant |
Bw | The wear characteristic constant |
lk | The kth phase |
tk | The period k |
n | The number of evaluated objects |
si | The ith object to be evaluated |
m | The number of performance indicators |
T | The number of time periods |
xj | The jth performance indicator |
xij(tk) | The value of the ith evaluated object about the jth indicator at the time tk |
Bk | The static evaluation matrix of the kth period |
yi(tk) | The static evaluation value of the ith evaluated object in the kth period |
Y | The static comprehensive evaluation matrix |
ηmax | The mean maximum gain |
ηmin | The mean minimum gain |
The average gain | |
η+ | The optimal gain level |
η− | The inferior gain level |
yi+(tk) | The optimal excitation point of the ith evaluated object at time tk |
yi−(tk) | The inferior excitation point of the ith evaluated object at time tk |
υi+(tk) | The optimal excitation quantity obtained by the ith evaluated object at time tk |
υi−(tk) | The inferior excitation obtained by the ith evaluated object at time tk |
zi(tk) | The dynamic comprehensive evaluation value of the ith evaluated object at tk 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 |
τk | The time factor |
zi | The total dynamic comprehensive evaluation value of the ith evaluated object |
Ujh | The weight ratio of the jth performance indicator to the hth performance indicator |
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A (MPa) | B (MPa) | C | m | n | (s−1) | Tm (°C) | Tr (°C) |
---|---|---|---|---|---|---|---|
875 | 793 | 0.01 | 0.71 | 0.386 | 1 | 1560 | 20 |
Material Parameter | YG6 | Ti6Al4V |
---|---|---|
Density (g/cm3) | 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 (l1) | The Second Stage (l2) | The Third Stage (l3) | The Fourth Stage (l4) | |||||
---|---|---|---|---|---|---|---|---|
Wear Rate (mm/s) | V (mm3/s) | Wear Rate (mm/s) | V (mm3/s) | Wear Rate (mm/s) | V (mm3/s) | Wear Rate (mm/s) | V (mm3/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 |
t1 | t2 | … | tT | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
x1 | x2 | … | xm | x1 | x2 | … | xm | … | x1 | x2 | … | xm | |
s1 | x11(t1) | x12(t1) | … | x1m(t1) | x11(t2) | x12(t2) | … | x1m(t2) | … | x11(tT) | x12(tT) | … | x1m(tT) |
s2 | x21(t1) | x22(t1) | … | x2m(t1) | x21(t2) | x22(t2) | … | x2m(t2) | … | x21(tT) | x22(tT) | … | x2m(tT) |
… | … | … | … | … | … | … | … | … | … | … | … | … | … |
sn | xn1(t1) | xn2(t1) | … | xnm(t1) | xn1(T2) | xn2(t2) | … | xnm(t2) | … | xn1(tT) | xn2(tT) | … | xnm(tT) |
xj/xh | x1/x2 | x2/x2 |
---|---|---|
Ujh | 1.5 | 1.0 |
The First Stage (l1) | The Second Stage (l2) | The Third Stage (l3) | The Fourth Stage (l4) | |||||
---|---|---|---|---|---|---|---|---|
Wear Rate (mm/s) | V (mm3/s) | Wear Rate (mm/s) | V (mm3/s) | Wear Rate (mm/s) | V (mm3/s) | Wear Rate (mm/s) | V (mm3/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 |
l1 | l2 | l3 | l4 | ||||
---|---|---|---|---|---|---|---|
yi(l1) | yi+(l2) | yi−(l2) | yi+(l3) | yi−(l3) | yi+(l4) | yi−(l4) | |
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 |
l1 | l2 | l3 | l4 | |||||
---|---|---|---|---|---|---|---|---|
υi+(l1) | υi−(l1) | υi+(l2) | υi−(l2) | υi+(l3) | υi−(l3) | υi+(l4) | υi−(l4) | |
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 |
z(l1) | z(l2) | z(l3) | z(l4) | 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 |
zHelix angle | zFeed per tooth | zCutting 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 |
Wear Rate (mm/s) | V (mm3/s) | |||
---|---|---|---|---|
l1 | l2 | l3 | l4 | |
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) | |
---|---|---|---|
Fx | 31.40 | 313.613 | 266.791 |
37.68 | 634.243 | 510.750 | |
47.10 | 577.552 | 462.902 | |
Fy | 31.40 | 358.606 | 289.408 |
37.68 | 532.094 | 466.600 | |
47.10 | 503.908 | 415.483 | |
Fz | 31.40 | 234.752 | 188.069 |
37.68 | 168.884 | 135.653 | |
47.10 | 191.216 | 153.299 |
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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
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 StyleYue, 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