Finite Element Analysis and Statistical Optimization of End-Burr in Turning AA2024
Abstract
:1. Introduction
2. Finite Element Model for Cutting Simulation
2.1. Geometrical Model and Boundary Conditions
2.2. Constitutive Model and Chip Separation
2.3. Finite Element Formulation
2.4. Thermal Aspects
2.5. Friction Law
3. FEA Results and Discussion
3.1. Effect of Feed on End-Burr Formation (at Section Z = 0)
3.2. Effect of Rake Angle on End-Burr (at Section Z = 0)
3.3. Effect of Speed on End-Burr (at Section Z = 0)
3.4. Burr Formation on Workpiece Edges (at Section Z = ±2)
4. Statistical Analysis and Optimization
- Which process parameters (VC, f and γ) have a major/minor effect in producing pronounced end-burr.
- What is the optimum combination of process parameters to minimize the burr lengths?
- Which of the previously discussed phenomena including temperature, cutting force evolution, pivot-point appearance time, pivot-point location, etc., have direct or more conspicuous relation with the burr formation process?
- Can a functional relationship between response (burr length) and process parameters be established?
4.1. Burr Optimization Using Taguchi’s Methodology
4.2. RSM Based Statistical Analysis
5. Conclusions
- End-burr is the only type of burr produced on the exit edge in the middle sections of the workpiece. While additionally, poisson-burr is generated on the corner sections of the workpiece.
- As tool advances and approaches near workpiece end, negative shear zone appears at the workpiece exit edge and continuously propagates to meet the primary shear zone. The shear zone widened and material continuously flows towards the workpiece edges (due to tool advancement) to eventually produce end-burr.
- Numerical simulations and statistical analyses for various combinations of cutting speed, feed, and tool-rake angle are made. Optimum cutting parameters (within the tested range of parameters) to minimize burr are identified. It has been figured out that the lower feed, larger rake angle (more positive rake angle), and higher cutting speeds helps to decrease burr. Feed is found to be the most influential factor (contribution: 82%), while speed has the least effect (contribution: 2%) in producing burr. Whereas, rake angle has a 13% contribution in generating burr.
- As feed increases, the pivot-point (large deformation point in negative shear zone) appears earlier in the cutting process and far below the workpiece surface and longer burr lengths are produced.
- To predict burr lengths in machining of AA2024, a multiple regression model with acceptable accuracy (multiple correlation factor, R2 = 97.8%) has been proposed.
Author Contributions
Funding
Conflicts of Interest
Notations
A | Initial yield stress (MPa) |
aP | Cutting depth or axial depth of cut (mm) |
B | Hardening modulus (MPa) |
C | Strain rate dependency coefficient |
Cp | Specific heat (J·kg−1·°C−1) |
Difference between current and the exact solution | |
D | damage evolution parameter |
D1…D5 | Coefficients of Johnson-Cook material shear failure initiation criterion |
E | Young’s modulus (MPa) |
f | Feed rate (mm/rev) |
FN | Force component conjugate to the Nth variable, N |
FN after ith iteration | |
F | Body force per unit volume N/m3 |
fT | Transpose of f |
Gf | Fracture energy (N/m) |
KC I, II | Fracture toughness () for failure mode I and mode II |
Jacobian matrix | |
m | Thermal softening coefficient |
n | Work-hardening exponent |
NN | Interpolation functions |
Transpose of NN | |
P | Hydrostatic pressure (MPa) |
Heat generation rate due to plastic deformation W/m3 | |
Heat generation rate due to friction W/m3 | |
S | Surface bounding volume V, m2 |
Г | Surface traction per unit area, N/m2 |
ГT | Transpose of Г |
T | Temperature at a given calculation instant (°C) |
Tm | Melting temperature (°C) |
Tr | Room temperature (°C) |
Equivalent plastic displacement (mm) | |
Equivalent plastic displacement at failure (mm) | |
uM | Value of the Mth variable |
VC | Cutting speed (m/min) |
V | Volume occupied by body m3 |
V0 | Reference Volume m3 |
Stress, MPa | |
Johnson-Cook equivalent stress (MPa) | |
Yield stress (MPa) | |
τc | Material stress, MPa |
Stress triaxiality | |
Equivalent plastic strain | |
Plastic strain rate (s−1) | |
Reference strain rate (10−3 s−1) | |
Equivalent plastic strain at failure | |
Equivalent plastic strain increment | |
Plastic strain at damage initiation | |
δD | Virtual strain rate (s−1) |
δu | Virtual velocity field (m/sec) |
βN | Strain variation |
Inelastic heat fraction | |
Frictional work conversion factor | |
ω | Damage initiation criterion |
ν | Poisson’s ratio |
α | Expansion coefficient (µm·m−1°C−1) |
λ | Thermal conductivity (W·m−1°C−1) |
ρ | Density (kg/m3) |
γ | Rake angle (degrees) |
ANOVA | Analysis of variance |
DOE | Design of experiment |
RSM | Response surface methodology |
DF | Degrees of freedom |
MS | Mean squares (variance) |
SS | Sum of squares |
PP | Percent contribution |
P-value | Probability of significance |
F-value | Fisher coefficient (variance ratio) |
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Parameters | Workpiece (AA2024-T351) | Insert (Tungsten Carbide) |
---|---|---|
Density, ρ | 2700 | 11,900 |
Young’s modulus, E | 73,000 | 534,000 |
Poisson’s ratio, ν | 0.33 | 0.22 |
Fracture energy, Gf | 20 × 103 | X |
Specific heat, Cp | 0.557 T + 877.6 | 400 |
Expansion Coefficient, αd | 8.91−3 T + 22.2 | X |
Thermal conductivity, λ | 25 ≤ T ≤ 300: λ = 0.247T + 114.4 300 ≤ T ≤ Tm: λ = −0.125T + 226 | 50 |
Meting temperature, Tm | 520 | X |
Room temperature, Tr | 25 | 25 |
Fracture toughness (KIC and KIIC) | 26 and 37 | X |
A | B | n | C | m | D1 | D2 | D3 | D4 | D5 |
---|---|---|---|---|---|---|---|---|---|
352 | 440 | 0.42 | 0.0083 | 1 | 0.13 | 0.13 | −1.5 | 0.011 | 0 |
Feed Rate, f (mm/rev) | Cutting Force, FC (N) | |
---|---|---|
Experimental [24] | Numerical | |
0.3 | 769 | 718 |
0.4 | 976 | 933 |
Test Number | Cutting Parameters | Burr Length along x-axis at Z = 0 | ||
---|---|---|---|---|
Cutting Speed (VC) | Feed Rate (f) | Rake Angle (γ) | ||
1 | 800 | 0.3 | 17.5 | 0.0743 |
2 | 800 | 0.3 | 5 | 0.08944 |
3 | 1000 | 0.3 | 17.5 | 0.0723 |
4 | 1000 | 0.3 | 5 | 0.08344 |
5 | 800 | 0.4 | 17.5 | 0.1226 |
6 | 800 | 0.4 | 5 | 0.149 |
7 | 1000 | 0.4 | 17.5 | 0.11 |
8 | 1000 | 0.4 | 5 | 0.137 |
Level | Factor (Speed) | Factor (Feed) | Factor (Rake Angle) |
---|---|---|---|
1 | 19.57901329 | 21.98483401 | 19.08593539 |
2 | 20.20687077 | 17.80105005 | 20.69994867 |
Difference | 0.627857489 | 4.183783969 | 1.614013276 |
Rank | 3 | 1 | 2 |
Source | DF | SS | MS | F-value | P-value | PP (%) | Remarks |
---|---|---|---|---|---|---|---|
Model | 3 | 0.005882 | 0.001960 | 60.11 | 0.00087 | - | Significant |
Speed | 1 | 0.000132 | 0.000132 | 4.07 | 0.11374 | 2.208548 | Insignificant |
Feed | 1 | 0.004956 | 0.004956 | 151.94 | 0.00024 | 82.42308 | Significant |
Angle | 1 | 0.000793 | 0.000793 | 24.33 | 0.00785 | 13.19807 | Significant |
Error | 4 | 0.000130 | 0.000032 | - | - | 2.170298 | - |
Total | 7 | 0.006013 | - | - | - | 100 |
Source | DF | SS | MS | F-value | P-value | PP (%) | Remarks |
---|---|---|---|---|---|---|---|
Speed | 1 | 180.5 | 180.5 | 288.8 | <0.0001 | 14.37 | Significant |
Feed | 1 | 760.5 | 760.5 | 1216.8 | <0.0001 | 60.54 | Significant |
Angle | 1 | 312.5 | 312.5 | 500 | <0.0001 | 24.88 | Significant |
Error | 4 | 2.5 | 0.63 | - | - | 0.2 | - |
Total | 7 | 1256 | - | - | - | 100 | - |
Source | DF | SS | MS | F-value | P-value | PP (%) | Remarks |
---|---|---|---|---|---|---|---|
Speed | 1 | 3 | 3 | 0.03 | 0.867 | 0.002 | Insignificant |
Feed | 1 | 98790 | 98790 | 1001.67 | <0.0001 | 79.42 | Significant |
Angle | 1 | 25200 | 25200 | 255.51 | <0.0001 | 20.25 | Significant |
Error | 4 | 394 | 99 | - | - | 0.3 | - |
Total | 7 | 124388 | - | - | - | 100 | - |
Source | DF | SS | MS | F-value | P-value | PP (%) | Remarks |
---|---|---|---|---|---|---|---|
Speed | 1 | 0.0000231 | 0.0000231 | 0.14 | 0.723 | 0.09 | Insignificant |
Feed | 1 | 0.006072 | 0.006072 | 37.93 | 0.004 | 25.9 | Significant |
Angle | 1 | 0.0167079 | 0.0167079 | 104.38 | 0.001 | 71.26 | Significant |
Error | 4 | 0.0006403 | 0.0001601 | - | - | 2.73 | - |
Total | 7 | 0.0234433 | - | - | - | 100 | - |
Source | DF | SS | MS | F-value | P-value | PP (%) | Remarks |
---|---|---|---|---|---|---|---|
Speed | 1 | 0.000025 | 0.000025 | 0.05 | 0.831 | 0.02 | Insignificant |
Feed | 1 | 0.091164 | 0.091164 | 191.94 | <0.0001 | 85.7 | Significant |
Angle | 1 | 0.013284 | 0.013284 | 27.97 | 0.006 | 12.48 | Significant |
Error | 4 | 0.0019 | 0.000475 | - | - | 1.78 | - |
Total | 7 | 0.106373 | - | - | - | 100 | - |
Source | DF | SS | MS | F-value | P-value | PP (%) | Remarks |
---|---|---|---|---|---|---|---|
Speed | 1 | 0.000365 | 0.000365 | 0.74 | 0.438 | 0.48 | Insignificant |
Feed | 1 | 0.043512 | 0.043512 | 88.42 | 0.001 | 57.73 | Significant |
Angle | 1 | 0.029525 | 0.029525 | 59.99 | 0.001 | 39.17 | Significant |
Error | 4 | 0.001968 | 0.000492 | - | - | 2.61 | - |
Total | 7 | 0.07537 | - | - | - | 100 | - |
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Asad, M.; Ijaz, H.; Saleem, W.; Mahfouz, A.S.B.; Ahmad, Z.; Mabrouki, T. Finite Element Analysis and Statistical Optimization of End-Burr in Turning AA2024. Metals 2019, 9, 276. https://doi.org/10.3390/met9030276
Asad M, Ijaz H, Saleem W, Mahfouz ASB, Ahmad Z, Mabrouki T. Finite Element Analysis and Statistical Optimization of End-Burr in Turning AA2024. Metals. 2019; 9(3):276. https://doi.org/10.3390/met9030276
Chicago/Turabian StyleAsad, Muhammad, Hassan Ijaz, Waqas Saleem, Abdullah S.B. Mahfouz, Zeshan Ahmad, and Tarek Mabrouki. 2019. "Finite Element Analysis and Statistical Optimization of End-Burr in Turning AA2024" Metals 9, no. 3: 276. https://doi.org/10.3390/met9030276