Cutting Force Prediction Models by FEA and RSM When Machining X56 Steel with Single Diamond Grit
Abstract
:1. Introduction
2. Finite Element Modeling
2.1. The Mechanisms of Diamond Grits Cutting
2.2. Modeling of the Single Diamond Grit
2.3. Modeling of the Cutting Force
3. Response Surface Regression Modeling
3.1. Principle of Tribometer and Experiments
3.2. Response Surface Methodology and Design of Experiment
−0.0306B2 − 0.1671C2 − 0.00260ABC − 0.0391A2B − 0.0041 A2C + 0.0039AB2
4. Confirmation Experiment
5. Conclusions
- Two means were used to obtain the equation of the cutting force. In the first approach, AdvantEdge was used to simulate the cutting process, and the virtual experiment data were applied to fit the empirical equation of the cutting force. In the second one, the regression equation of the cutting force and the corresponding response surface was obtained by Design of Experiments.
- Twelve confirmation experiments were conducted, and the results indicate that both derived models can predict the cutting force with fair accuracy. The prediction errors of the developed models and experimental results vary from −11.7% to 10.02%, which are acceptable in engineering. Additionally, the predicted values of the regression model using FEM were generally lower than the experimental results because graphitization was not included in FEM.
- The results of RSM reveal that with increasing depth of cut and coefficient of friction, cutting force shows an increasing trend. High cutting speed increases cutting efficiency while reducing the coefficient of friction. Hence, the cutting speed needs to be restricted to a specified range. The influence of the depth of the cut is the most significant among the three factors. However, high protrusion contributes to less grit–workpiece contact. Therefore, the protrusion heights of the diamond grits deserve first priority when manufacturing diamond beads that serve different purposes.
Author Contributions
Funding
Conflicts of Interest
Appendix A
Num of Experiment | ν (m/min) | f (mm/r) | µ | F (N) |
---|---|---|---|---|
1 | 960 | 0.01 | 0.1 | 0.9178 |
2 | 0.3 | 1.2018 | ||
3 | 0.5 | 1.4041 | ||
4 | 0.7 | 1.4081 | ||
5 | 0.02 | 0.1 | 1.5144 | |
6 | 0.3 | 1.9554 | ||
7 | 0.5 | 2.3423 | ||
8 | 0.7 | 2.3861 | ||
9 | 0.03 | 0.1 | 2.0514 | |
10 | 0.3 | 2.5581 | ||
11 | 0.5 | 3.0224 | ||
12 | 0.7 | 3.0845 | ||
13 | 0.04 | 0.1 | 2.5614 | |
14 | 0.3 | 3.1344 | ||
15 | 0.5 | 3.5284 | ||
16 | 0.7 | 3.6851 | ||
17 | 1140 | 0.01 | 0.1 | 0.8922 |
18 | 0.3 | 1.1736 | ||
19 | 0.5 | 1.3336 | ||
20 | 0.7 | 1.3224 | ||
21 | 0.02 | 0.1 | 1.5044 | |
22 | 0.3 | 1.9422 | ||
23 | 0.5 | 2.2216 | ||
24 | 0.7 | 2.2826 | ||
25 | 0.03 | 0.1 | 2.0472 | |
26 | 0.3 | 2.5521 | ||
27 | 0.5 | 2.9478 | ||
28 | 0.7 | 3.0292 | ||
29 | 0.04 | 0.1 | 2.5468 | |
30 | 0.3 | 3.0598 | ||
31 | 0.5 | 3.4636 | ||
32 | 0.7 | 3.5468 | ||
33 | 1320 | 0.01 | 0.1 | 0.8794 |
34 | 0.3 | 1.1662 | ||
35 | 0.5 | 1.3014 | ||
36 | 0.7 | 1.2626 | ||
37 | 0.02 | 0.1 | 1.4896 | |
38 | 0.3 | 1.9056 | ||
39 | 0.5 | 2.2318 | ||
40 | 0.7 | 2.2416 | ||
41 | 0.03 | 0.1 | 2.0496 | |
42 | 0.3 | 2.5364 | ||
43 | 0.5 | 2.9374 | ||
44 | 0.7 | 2.9072 | ||
45 | 0.04 | 0.1 | 2.5484 | |
46 | 0.3 | 3.0478 | ||
47 | 0.5 | 3.4502 | ||
48 | 0.7 | 3.5606 | ||
49 | 1500 | 0.01 | 0.1 | 0.8728 |
50 | 0.3 | 1.1494 | ||
51 | 0.5 | 1.2626 | ||
52 | 0.7 | 1.2232 | ||
53 | 0.02 | 0.1 | 1.4896 | |
54 | 0.3 | 1.8744 | ||
55 | 0.5 | 2.1764 | ||
56 | 0.7 | 2.2094 | ||
57 | 0.03 | 0.1 | 2.0292 | |
58 | 0.3 | 2.5174 | ||
59 | 0.5 | 2.8846 | ||
60 | 0.7 | 2.9058 | ||
61 | 0.04 | 0.1 | 2.5443 | |
62 | 0.3 | 3.0476 | ||
63 | 0.5 | 3.4006 | ||
64 | 0.7 | 3.5346 |
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Levels Parameters | 1 | 2 | 3 | 4 |
---|---|---|---|---|
Cutting speed (m/min) | 960 | 1140 | 1320 | 1500 |
Depth of cut (mm) | 0.01 | 0.02 | 0.03 | 0.04 |
Coefficient of friction | 0.1 | 0.3 | 0.5 | 0.7 |
Parameters | Level 1 | Level 2 | Level 3 |
---|---|---|---|
Cutting Speed (m/min) | 960 | 1230 | 1500 |
Depth of Cut (mm) | 0.02 | 0.03 | 0.04 |
Coefficient of Friction | 0.1 | 0.4 | 0.7 |
Run Order | Cutting Speed (m/min) | Depth of Cut (mm) | Coefficient of Friction | Cutting Force (N) |
---|---|---|---|---|
1 | 1230 | 0.03 | 0.4 | 2.791 |
2 | 1230 | 0.03 | 0.1 | 2.134 |
3 | 1500 | 0.04 | 0.1 | 2.55 |
4 | 1230 | 0.02 | 0.4 | 2.114 |
5 | 960 | 0.02 | 0.1 | 1.66 |
6 | 960 | 0.04 | 0.7 | 3.892 |
7 | 1230 | 0.03 | 0.4 | 2.791 |
8 | 1500 | 0.02 | 0.1 | 1.593 |
9 | 960 | 0.04 | 0.1 | 2.659 |
10 | 960 | 0.02 | 0.7 | 2.411 |
11 | 1230 | 0.03 | 0.4 | 2.791 |
12 | 1500 | 0.02 | 0.7 | 2.312 |
13 | 1230 | 0.03 | 0.7 | 3.113 |
14 | 1230 | 0.03 | 0.4 | 2.79 |
15 | 1230 | 0.03 | 0.4 | 2.792 |
16 | 1230 | 0.03 | 0.4 | 2.789 |
17 | 960 | 0.03 | 0.4 | 2.857 |
18 | 1500 | 0.03 | 0.4 | 2.74 |
19 | 1500 | 0.04 | 0.7 | 3.73 |
20 | 1230 | 0.04 | 0.4 | 3.406 |
Source | Sum of Squares | DOF | Mean Square | F-Value | p-Value | Significance |
---|---|---|---|---|---|---|
Model | 6.46 | 13 | 0.4965 | 5.566 | <0.0001 | Significant |
A-Cutting Speed | 0.0068 | 1 | 0.0068 | 7672.82 | <0.0001 | - |
B-Depth of cut | 0.8346 | 1 | 0.8346 | 9.356 | <0.0001 | |
C-Coefficient of Friction | 0.4792 | 1 | 0.4792 | 5.372 | <0.0001 | |
AB | 0.0014 | 1 | 0.0014 | 1544.90 | <0.0001 | |
AC | 0.0009 | 1 | 0.0009 | 1012.42 | <0.0001 | |
BC | 0.1112 | 1 | 0.1112 | 1.246 | <0.0001 | |
A2 | 0.0002 | 1 | 0.0002 | 192.84 | <0.0001 | |
B2 | 0.0026 | 1 | 0.0026 | 2884.90 | <0.0001 | |
C2 | 0.0768 | 1 | 0.0768 | 86069.91 | <0.0001 | |
ABC | 0.0001 | 1 | 0.0001 | 61.80 | 0.0002 | |
A2B | 0.0024 | 1 | 0.0024 | 2745.63 | <0.0001 | |
A2C | 0.0000 | 1 | 0.0000 | 30.52 | 0.0015 | |
AB2 | 0.0000 | 1 | 0.0000 | 26.93 | 0.0020 | |
AC2 | 0.0000 | 0 | - | - | - | |
B2C | 0.0000 | 0 | ||||
BC2 | 0.0000 | 0 | ||||
A3 | 0.0000 | 0 | ||||
B3 | 0.0000 | 0 | ||||
C3 | 0.0000 | 0 | ||||
Residual | 5.352 | 6 | 8.920 | |||
Lack of Fit | 1.894 | 1 | 1.894 | 0.0178 | 0.8992 | Not significant |
Pure Error | 5.333 | 5 | 1.067 | - | - | - |
Cor Total | 6.46 | 19 | - |
Numbers of Experiments | Cutting Speed (m/min) | Depth of Cut (mm) | Coefficient of Friction | Cutting Force (N) | RSM Results | Error% | FEM Results | Error% |
---|---|---|---|---|---|---|---|---|
1 | 1300 | 0.02 | 0.5 | 1.796 | 1.996 | 10.02 | 2.096 | −11.7 |
2 | 1000 | 0.03 | 0.21 | 2.211 | 2.102 | 5.19 | 2.411 | −8.3 |
3 | 1100 | 0.04 | 0.51 | 3.11 | 2.83 | 9.89 | 3.51 | −11.4 |
4 | 1500 | 0.02 | 0.52 | 1.983 | 2.203 | −9.99 | 2.083 | −6.9 |
5 | 1150 | 0.03 | 0.48 | 2.611 | 2.761 | −5.43 | 2.811 | −7.11 |
6 | 1240 | 0.04 | 0.37 | 3.001 | 2.801 | 7.14 | 3.251 | −7.69 |
7 | 1340 | 0.02 | 0.61 | 1.825 | 1.985 | −8.06 | 1.675 | −8.96 |
8 | 980 | 0.03 | 0.4 | 2.602 | 2.5 | 4.08 | 2.752 | −6.81 |
9 | 1280 | 0.04 | 0.31 | 2.927 | 2.777 | 5.4 | 3.127 | −6.4 |
10 | 1160 | 0.02 | 0.49 | 1.961 | 1.83 | 7.16 | 2.111 | −7.11 |
11 | 1400 | 0.03 | 0.2 | 2.11 | 2.311 | −8.7 | 2.31 | −8.66 |
12 | 1340 | 0.04 | 0.35 | 2.891 | 3.191 | −9.4 | 3.105 | −9.23 |
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Zhang, L.; Sha, X.; Liu, M.; Wang, L.; Pang, Y. Cutting Force Prediction Models by FEA and RSM When Machining X56 Steel with Single Diamond Grit. Micromachines 2021, 12, 326. https://doi.org/10.3390/mi12030326
Zhang L, Sha X, Liu M, Wang L, Pang Y. Cutting Force Prediction Models by FEA and RSM When Machining X56 Steel with Single Diamond Grit. Micromachines. 2021; 12(3):326. https://doi.org/10.3390/mi12030326
Chicago/Turabian StyleZhang, Lan, Xianbin Sha, Ming Liu, Liquan Wang, and Yongyin Pang. 2021. "Cutting Force Prediction Models by FEA and RSM When Machining X56 Steel with Single Diamond Grit" Micromachines 12, no. 3: 326. https://doi.org/10.3390/mi12030326