Prediction of Nonlinear Micro-Milling Force with a Novel Minimum Uncut Chip Thickness Model
Abstract
:1. Introduction
2. Prerequisite Knowledge and Related Works
3. Novel Minimum Uncut Chip Thickness Model
4. Micro-Milling Force Prediction with the Novel MUCT Model
4.1. Uncut Chip Thickness Model
4.2. Nonlinear Cutting Force Coefficient Function
4.3. Micro-Milling Force Model Embed with the Novel MUCT
5. Parameters Estimation
6. Experimental Validation
6.1. Experimental Setup
6.2. Parameters Estimation Results
6.3. Force Prediction Results
6.4. Discussion on the Advantages of the Model
7. Conclusions
- Compared to the maximum shear stress principle, the minimum cutting energy principle is more reasonable to model the cutting force in the shear region on the round edge.
- Under the proposed equilibrium normal force assumption, the stagnant angle corresponding to the MUCT is constantly greater than the friction angle, resulting in an integrable stress distribution function and a stable cutting force model.
- Embedded with a more flexible and stable MUCT model, the proposed nonlinear micro-milling force model is more accurate than the conventional models. The prediction accuracy of the proposed model is improved by 5%–10% compared to the traditional models.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Minimum uncut chip thickness () | |
Stagnant angle (rad) | |
Friction angle (rad) | |
Ploughing coefficient (Gpa) | |
Friction stress in ploughing region (Gpa) | |
Shear stress (Gpa) | |
Cutting edge radius () | |
Length of tool runout () | |
Angle of tool runout (rad) | |
Shear-ploughing coefficient function in tangential direction (Gpa) | |
Shear-ploughing coefficient function in radial direction (Gpa) |
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The Type of Parameters | Parameters | Notation | Unit |
---|---|---|---|
mechanical parameters | shear stress | Gpa | |
friction angle | rad | ||
ploughing coefficient | Gpa | ||
friction stress in ploughing region | Gpa | ||
parameters related to cutting trajectory | runout length | ||
runout angle | rad | ||
starting point. | -- |
Cutting Condition | Spindle Speed (rpm) | Cutting SPEED (m/min) | Axial Cutting Depth (μm) | Feed Speed (mm/min) | Feed Speed per Tooth (μm/tooth) |
---|---|---|---|---|---|
C1 | 18,000 | 45.24 | 60 | 72 | 2 |
C2 | 18,000 | 45.24 | 80 | 144 | 4 |
C3 | 18,000 | 45.24 | 100 | 216 | 6 |
C4 | 24,000 | 60.32 | 80 | 288 | 6 |
C5 | 30,000 | 75.40 | 60 | 360 | 6 |
C6 | 24,000 | 60.32 | 60 | 192 | 4 |
C7 | 24,000 | 60.32 | 100 | 96 | 2 |
C8 | 30,000 | 75.40 | 80 | 120 | 2 |
C9 | 30,000 | 75.40 | 100 | 240 | 4 |
Cutting Condition | |||||||
---|---|---|---|---|---|---|---|
C1 | 30 | 1.01 | 2.07 | 0.52 (29.91°) | 25.00 | 16.00 | 0.98 |
C2 | 29 | 1.02 | 2.05 | 0.56 (31.91°) | 27.00 | 26.00 | 1.02 |
C3 | 35 | 0.09 | 1.43 | 0.53 (30.19°) | 23.00 | 11.00 | 0.98 |
C4 | 124 | 0.92 | 0.86 | 0.50 (28.71°) | 23.00 | 11.00 | 0.95 |
C5 | 22 | 0.76 | 2.16 | 0.51 (29.45°) | 24.00 | 17.00 | 1.02 |
C6 | 38 | 1.17 | 2.68 | 0.57 (32.77°) | 32.00 | 21.00 | 1.04 |
C7 | 123 | 0.32 | 0.95 | 0.44 (25.25°) | 24.00 | 12.00 | 1.04 |
C8 | 29 | 0.21 | 1.69 | 0.45 (24.98°) | 29.00 | 14.00 | 1.05 |
C9 | 23 | 0.36 | 1.08 | 0.60 (34.38°) | 35.00 | 19.00 | 1.07 |
C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | |
---|---|---|---|---|---|---|---|---|---|
48.45° | 49.74° | 49.68° | 48.62° | 48.42° | 48.96° | 43.74° | 41.53° | 49.80° | |
0.673 | 0.7073 | 0.7061 | 0.6780 | 0.6725 | 0.6868 | 0.5550 | 0.5029 | 0.7092 | |
0.3367 | 0.3537 | 0.3530 | 0.3390 | 0.3363 | 0.3434 | 0.2775 | 0.2514 | 0.3546 |
Cutting Condition | Malekian’s Model (Average Rake Angle) | Malekian’s Model (Partial Rake Angle) | Son’s Model under | Our Model |
---|---|---|---|---|
C1 | 36.19% | 35.46% | 29.36% | 26.90% |
C2 | 34.64% | 33.55% | 26.95% | 23.29% |
C3 | 20.78% | 21.05% | 17.92% | 10.16% |
C4 | 24.32% | 26.79% | 22.45% | 15.38% |
C5 | 33.31% | 30.95% | 24.53% | 21.18% |
C6 | 30.09% | 29.30% | 26.64% | 21.17% |
C7 | 26.32% | 27.15% | 23.77% | 18.04% |
C8 | 32.50% | 33.76% | 26.40% | 22.14% |
C9 | 32.88% | 31.24% | 25.23% | 20.81% |
Average of C1–C9 | 30.11% | 29.92% | 24.81% | 19.10% |
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Liu, T.; Zhang, K.; Wang, G.; Wang, C. Prediction of Nonlinear Micro-Milling Force with a Novel Minimum Uncut Chip Thickness Model. Micromachines 2021, 12, 1495. https://doi.org/10.3390/mi12121495
Liu T, Zhang K, Wang G, Wang C. Prediction of Nonlinear Micro-Milling Force with a Novel Minimum Uncut Chip Thickness Model. Micromachines. 2021; 12(12):1495. https://doi.org/10.3390/mi12121495
Chicago/Turabian StyleLiu, Tongshun, Kedong Zhang, Gang Wang, and Chengdong Wang. 2021. "Prediction of Nonlinear Micro-Milling Force with a Novel Minimum Uncut Chip Thickness Model" Micromachines 12, no. 12: 1495. https://doi.org/10.3390/mi12121495