3D-FEM Approach of AISI-52100 Hard Turning: Modelling of Cutting Forces and Cutting Condition Optimization
Abstract
:1. Introduction
2. Materials and Methods
2.1. CAD-Based Setup of the Machining Process
2.2. Pre-Processing of the Numerical Model
2.2.1. Analysis Interface Specifications
2.2.2. Material Modelling
3. Results and Discussion
3.1. FEM-Based Evaluation of the Resultant Cutting Force
3.2. Mathematical Modelling of the Resultant Cutting Force
3.3. Analysis and Validation of Mathematical Model
3.4. Investigation of the Cutting Parameters’ Influence
3.5. Optimization Process
3.6. Confirmation of Mathematical Model
4. Conclusions
- Both the established FE model and the mathematical one can predict the generated cutting forces with acceptable errors. The relative error found for the comparison between the numerical and the experimental results ranged between −1.7% and 16.7%, whereas the numerical and the statistical results ranged between −7.9% and 11.3%.
- Especially with the use of the mathematical model, future experimental testing can be skipped and instant results can be delivered for Fresultant within the range of the investigated parameters.
- It was revealed that both depth of cut and feed increasingly act on the generated force, especially depth of cut. The increase percentage when shifting from level one value to level three for feed and depth of cut, is close to 35% and 78%, respectively. Tool nose radius also seems to have an increasing effect, but of no significance, at least compared to the other two parameters. On the other hand, cutting speed seems to lower the produced forces by a small, but not negligible, amount.
- Finally, the optimal cutting conditions were found for three different cutting inserts. Namely, 175.76 m/min cutting speed, 0.097 mm/rev feed and 0.20 mm depth of cut for the 0.80 mm tool, 177.78 m/min cutting speed, 0.098 mm/rev feed and 0.20 mm depth of cut for the 1.20 mm tool and, lastly, 199.73 m/min cutting speed, 0.082 mm/rev feed and 0.20 mm depth of cut for the 1.60 mm tool.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Level | Vc [m/min] | f [mm/rev] | ap [mm] | rε [mm] |
---|---|---|---|---|
−1 | 100 | 0.08 | 0.20 | 0.80 |
0 | 150 | 0.11 | 0.30 | 1.20 |
+1 | 200 | 0.14 | 0.40 | 1.60 |
Mechanical Properties | AISI-52100 | Ceramic |
---|---|---|
Young’s Modulus [GPa] | 210 | 415 |
Density [kg/m3] | 7850 | 3500 |
Poisson’s ratio | 0.30 | 0.22 |
Thermal properties | AISI-52100 | Ceramic |
Heat capacity [J/kgK] | 278 at 93 °C | 334 |
324 at 316 °C | ||
579 at 649 °C | ||
718 at 871 °C | ||
Thermal expansion [μm/mK] | 11.9 | 8.4 |
Thermal conductivity [W/mK] | 24.57 at 149 °C | 7.5 |
24.4 at 349 °C | ||
24.23 at 477 °C | ||
24.75 at 604 °C |
Input | Output | ||||||
---|---|---|---|---|---|---|---|
Standard Order | Vc (m/min) | f (mm/rev) | rε (mm) | ap (mm) | Experimental Fresultant (N) | Numerical Fresultant (N) | Relative Error (%) |
1 | 100 | 0.08 | 0.80 | 0.25 | 127.1 | 132.8 | 4.5 |
2 | 100 | 0.14 | 0.80 | 0.25 | 187.2 | 203.1 | 8.5 |
3 | 200 | 0.08 | 0.80 | 0.25 | 119.9 | 126.6 | 5.6 |
4 | 200 | 0.14 | 0.80 | 0.25 | 171.7 | 183.3 | 6.8 |
5 | 150 | 0.11 | 1.20 | 0.25 | 141.4 | 139.0 | −1.7 |
6 | 100 | 0.08 | 1.60 | 0.25 | 146.0 | 161.0 | 10.3 |
7 | 100 | 0.14 | 1.60 | 0.25 | 191.6 | 212.4 | 10.8 |
8 | 200 | 0.08 | 1.60 | 0.25 | 128.3 | 126.9 | −1.1 |
9 | 200 | 0.14 | 1.60 | 0.25 | 183.7 | 214.4 | 16.7 |
Input | Output | ||||||
---|---|---|---|---|---|---|---|
Run | Vc (m/min) | f (mm/rev) | ap (mm) | rε (mm) | Numerical Fresultant (N) | Statistical Fresultant (N) | Relative Error (%) |
1 | 100 | 0.11 | 0.3 | 1.2 | 203.2 | 209.6 | −3.0 |
2 | 150 | 0.11 | 0.3 | 1.2 | 199.8 | 199.1 | 0.4 |
3 | 150 | 0.11 | 0.3 | 1.6 | 210.6 | 199.3 | 5.6 |
4 | 150 | 0.11 | 0.3 | 1.2 | 203.5 | 199.1 | 2.2 |
5 | 150 | 0.11 | 0.4 | 1.2 | 227.7 | 230.8 | −1.3 |
6 | 150 | 0.11 | 0.2 | 1.2 | 127.9 | 120.5 | 6.2 |
7 | 150 | 0.11 | 0.3 | 0.8 | 177.1 | 184.0 | −3.7 |
8 | 200 | 0.11 | 0.3 | 1.2 | 207.3 | 196.5 | 5.5 |
9 | 150 | 0.08 | 0.3 | 1.2 | 217.4 | 195.3 | 11.3 |
10 | 150 | 0.14 | 0.3 | 1.2 | 239.2 | 256.9 | −6.9 |
11 | 200 | 0.14 | 0.2 | 1.6 | 165.4 | 165.5 | 0.1 |
12 | 200 | 0.08 | 0.4 | 1.6 | 206.5 | 216.1 | −4.4 |
13 | 100 | 0.14 | 0.4 | 1.6 | 307.8 | 311.1 | −1.0 |
14 | 200 | 0.14 | 0.4 | 0.8 | 276.6 | 278.8 | −0.8 |
15 | 150 | 0.11 | 0.3 | 1.2 | 200.6 | 199.1 | 0.8 |
16 | 100 | 0.08 | 0.4 | 0.8 | 206.0 | 212.0 | −2.8 |
17 | 100 | 0.08 | 0.2 | 1.6 | 131.4 | 135.3 | −2.9 |
18 | 100 | 0.08 | 0.2 | 0.8 | 114.4 | 119.1 | −3.9 |
19 | 100 | 0.08 | 0.4 | 1.6 | 235.2 | 234.8 | 0.2 |
20 | 150 | 0.11 | 0.3 | 1.2 | 186.6 | 199.1 | −6.3 |
21 | 200 | 0.08 | 0.2 | 0.8 | 108.0 | 110.8 | −2.5 |
22 | 200 | 0.08 | 0.2 | 1.6 | 115.5 | 125.4 | −7.9 |
23 | 200 | 0.08 | 0.4 | 0.8 | 193.8 | 194.7 | −0.5 |
24 | 200 | 0.14 | 0.4 | 1.6 | 295.4 | 293.4 | 0.7 |
25 | 150 | 0.11 | 0.3 | 1.2 | 201.4 | 199.1 | 1.2 |
26 | 200 | 0.14 | 0.2 | 0.8 | 154.5 | 157.6 | −2.0 |
27 | 100 | 0.14 | 0.2 | 0.8 | 168.5 | 165.0 | 2.1 |
28 | 150 | 0.11 | 0.3 | 1.2 | 198.7 | 199.1 | −0.2 |
29 | 100 | 0.14 | 0.2 | 1.6 | 172.5 | 174.3 | −1.0 |
30 | 100 | 0.14 | 0.4 | 0.8 | 302.3 | 295.0 | 2.5 |
Source | Degree of Freedom | Sum of Squares | Mean Square | f-Value | p-Value |
---|---|---|---|---|---|
Model | 15 | 78,097.5 | 5206.5 | 45.63 | 0.000 |
Error | 14 | 1597.4 | 114.1 | ||
Total | 29 | 79,694.9 | |||
R-sq (adj) = 95.85% | |||||
Term | |||||
Blocks | 1 | 76.4 | 76.4 | 0.67 | 0.427 |
Vc | 1 | 779.3 | 779.3 | 6.83 | 0.020 |
f | 1 | 17,054.7 | 17,054.7 | 149.47 | 0.000 |
ap | 1 | 54,800.3 | 54,800.3 | 480.28 | 0.000 |
rε | 1 | 1074.1 | 1074.1 | 9.41 | 0.008 |
Vc2 | 1 | 40.4 | 40.4 | 0.35 | 0.561 |
f2 | 1 | 1857.9 | 1875.9 | 16.28 | 0.001 |
ap2 | 1 | 1391.0 | 1391.0 | 12.19 | 0.004 |
rε2 | 1 | 139.5 | 139.5 | 1.22 | 0.287 |
Vc × f | 1 | 1.0 | 1.0 | 0.01 | 0.926 |
Vc × ap | 1 | 79.2 | 79.2 | 0.69 | 0.419 |
Vc × rε | 1 | 2.0 | 2.0 | 0.02 | 0.896 |
f × ap | 1 | 1389.4 | 1389.4 | 12.18 | 0.004 |
f × rε | 1 | 46.2 | 46.2 | 0.40 | 0.535 |
ap × rε | 1 | 45.4 | 45.4 | 0.40 | 0.538 |
Lack of fit | 10 | 1597.4 | 144.7 | 3.86 | 0.102 |
Pure error | 4 | 1447.4 | 37.5 |
Factor | Goal | Lower Limt | Upper Limit |
---|---|---|---|
Vc (m/min) | In range | 100 | 200 |
f (mm/rev) | In range | 0.08 | 0.14 |
ap (mm) | In range | 0.20 | 0.40 |
rε (mm) | In range | 0.80 | 1.60 |
Fresultant (N) | Minimize | 108.0 | 307.8 |
Solution | Vc (m/min) | f (mm/rev) | ap (mm) | rε (mm) | Fresultant (N) | Desirability |
---|---|---|---|---|---|---|
1 | 175.76 | 0.097 | 0.20 | 0.80 | 101.0 | 1.000 |
2 | 177.78 | 0.098 | 0.20 | 1.20 | 115.0 | 0.965 |
3 | 199.73 | 0.082 | 0.20 | 1.60 | 123.4 | 0.923 |
Test | Vc (m/min) | f (mm/rev) | ap (mm) | rε (mm) | Simulated Fresultant (N) | Predicted Fresultant (N) | Relative Error (%) |
---|---|---|---|---|---|---|---|
1 | 175.75 | 0.097 | 0.20 | 0.80 | 113.7 | 101.0 | 12.5 |
2 | 120 | 0.10 | 0.25 | 0.80 | 139.5 | 149.6 | −6.8 |
3 | 160 | 0.10 | 0.25 | 1.20 | 141.6 | 159.0 | −10.9 |
4 | 160 | 0.12 | 0.25 | 1.60 | 183.1 | 175.2 | 4.5 |
5 | 120 | 0.10 | 0.35 | 0.80 | 190.5 | 201.4 | −5.4 |
6 | 160 | 0.10 | 0.35 | 1.20 | 229.4 | 210.6 | 8.9 |
7 | 160 | 0.12 | 0.35 | 1.60 | 261.7 | 234.7 | 11.5 |
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Tzotzis, A.; Tapoglou, N.; Verma, R.K.; Kyratsis, P. 3D-FEM Approach of AISI-52100 Hard Turning: Modelling of Cutting Forces and Cutting Condition Optimization. Machines 2022, 10, 74. https://doi.org/10.3390/machines10020074
Tzotzis A, Tapoglou N, Verma RK, Kyratsis P. 3D-FEM Approach of AISI-52100 Hard Turning: Modelling of Cutting Forces and Cutting Condition Optimization. Machines. 2022; 10(2):74. https://doi.org/10.3390/machines10020074
Chicago/Turabian StyleTzotzis, Anastasios, Nikolaos Tapoglou, Rajesh Kumar Verma, and Panagiotis Kyratsis. 2022. "3D-FEM Approach of AISI-52100 Hard Turning: Modelling of Cutting Forces and Cutting Condition Optimization" Machines 10, no. 2: 74. https://doi.org/10.3390/machines10020074