Semi-Empirical Prediction of Turned Surface Residual Stress for Inconel 718 Grounded in Experiments and Finite Element Simulations
Abstract
:1. Introduction
2. Methods
2.1. Three-Dimensional FEM Simulation
2.2. Turning Experiments and Measuring Residual Stresses
2.3. FEM Validation
2.4. Simulation Planning
3. Results and Discussion
3.1. Analysis of Cutting Forces
3.2. Analysis of Cutting Temperatures
3.3. Analysis of Surface Residual Stress
4. Establishment of Prediction Model
4.1. Introduction of Cutting Tool Angles
4.2. Prediction Model and Determination of Parameters
4.3. How to Use the Model
- γ0 and λs cannot be zero at the same time.
- When κr equals 45° or 135°, |γ0| ≠ |λs|.
5. Conclusions
- The distributions of residual stress in two experiments of turning Inconel 718 were consistent with that in the simulations. Furthermore, under the 24 parameters studied in the simulations, the circumferential cutting force, the radial cutting force, and the axial cutting force rose with the growing feed, no matter at high speed or low speed. With the increasing cutting depth, cutting forces rose more obviously. The cutting forces were lower at high cutting speed than at low cutting speed. The cutting temperature had an upward trend with the growth of the feed rate. The cutting temperature at high speed was slightly higher than that at low speed. The circumferential residual stress climbed with the rising feed rate within 0.075~0.15 mm/rev.
- A novel empirical residual stress prediction equation was proposed. In this equation, κr, γ0, and λs were introduced for the first time. Further, the optimization objective function was established according to the residual stress prediction equation, and the undetermined coefficients in the equation were obtained by using the genetic algorithm in MATLAB.
- Comparing the predicted, the simulated, and the measured stress, the results show that this prediction equation is accurate in predicting turned surface residual stress for Inconel 718 material within the feed rate of 0.075~0.15 mm/rev. The R value between the predicted and simulated stress was 0.9624 using the Pearson correlation analysis, and the average absolute error (AARE) was 13.40%, which further shows the accuracy of the prediction equation.
- When Equation (10) was applied, there were two restrictions: the rake angle and the inclination angle cannot be zero at the same time, and |γ0| cannot equal |λs| when κr is 45° or 135°. Therefore, future studies can be carried out based on the present work.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
vc | Cutting speed (m/min) | vf | Direction of feed motion |
ap, DA(CB) | Depth of cut (mm) | A | Yield strength (MPa) |
f, CH(DG) | Feed rate (mm/rev) | B | Strain hardening coefficient (MPa) |
FEM | Finite element model | C | Strain rate hardening coefficient |
F | Cutting force (N) | m | Thermal softening exponent |
Fc | Circumferential force (N) | n | Strain hardening exponent |
Fr | Radial force (N) | S1 | Projection area of chip and rake face contact surfaces on the base plane |
Fa | Axial force (N) | S2 | Projection area of chip and rake face contact surfaces on the working plane |
Pr, ADGE | Base plane | S3 | Projection area of chip and rake face contact surfaces on the back plane |
Ps, | Cutting plane | T | Temperature (°C) |
Po, | Orthogonal plane | Troom | Room temperature (°C) |
Pp, ABCD | Back plane | Tmelt | Melting temperature (°C) |
Pf, CDGH | Working plane | B0 | Coefficient of temperature and cutting speed term |
3D | Three-dimensional | ||
κr | Tool cutting-edge angle (°) | B1~B3 | Coefficients of cutting forces, cutting, and tool parameters’ terms |
γ0 | Rake angle (°) | m1, m2 | Exponents of temperature and cutting speed terms |
λs | Inclination angle (°) | n1~n6 | Exponents of cutting forces, cutting, and tool parameters’ terms |
γp, ∠MDA | Back-rake angle (°) | N | Total of simulations (N = 24) |
γf, ∠NDG | Side-rake angle (°) | i | The ith simulation (I = 1, 2, ⋯, N.) |
R | Correlation coefficient | AARE | Absolute average error |
Equivalent plastic strain | Equivalent plastic stress (MPa) | ||
Equivalent plastic strain rate () | Reference equivalent plastic strain rate () | ||
Surface residual stress | Stress component caused by Fc applying to S1 | ||
Stress component caused by Fr applying to S2 | Stress component caused by Fa applying to S3 | ||
Stress component relevant to thermal effect | Part of surface residual stress relevant to cutting temperature and cutting speed | ||
Mean of all 24 simulated residual stresses on the surface | Part of surface residual stress relevant to cutting force, feed, cutting depth, and tool angle | ||
The ith simulated residual stress on the surface | The predicted residual stress on the surface for the ith simulation | ||
Optimization objective | Mean of all 24 predicted residual stresses on the surface |
Appendix A
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Thermal Conductivity (W/(m·K)) | Specific Heat (J/(kg·K)) | Thermal Expansion Coefficient (10−6/K) | Melting Temperature (K) |
---|---|---|---|
10.53 (293 K) | 435 (293 K) | 11.8 (293–373 K) | 1573 |
14.7 (373 K) | 481.4 (573 K) | 13 (293–573 K) | |
17.8 (573 K) | 514.8 (773 K) | 14.1 (293–673 K) | |
19.6 (773 K) | 573.4 (973 K) | 14.8 (573–873 K) |
Tool Parameters | Values |
---|---|
Rake angle (degree) | −6 |
Relief angle (degree) | 6 |
Lead angle (degree) | −17.5 |
Inclination angle (degree) | −7 |
Coating (thickness) | TiAlN (0.002 mm) |
Turning Experiments | Cutting Speed (m/min) | Depth of Cut (mm) | Feed Rate (mm/rev) |
---|---|---|---|
1 | 60 | 0.4 | 0.1 |
2 | 120 | 0.8 |
Elements | Ni | Fe | Cr | Nb | Mo | Ti |
---|---|---|---|---|---|---|
Weight | 52.86% | 19.15% | 19.085% | 5.085% | 3.105% | 0.71% |
Test No. | Feed Rate (mm/rev) | Depth of Cut (mm) | Cutting Speed (m/min) |
---|---|---|---|
1 | 0.075 | 0.4 | 60, 120 |
2 | 0.10 | ||
3 | 0.125 | ||
4 | 0.15 | ||
5 | 0.075 | 0.6 | |
6 | 0.10 | ||
7 | 0.125 | ||
8 | 0.15 | ||
9 | 0.075 | 0.8 | |
10 | 0.10 | ||
11 | 0.125 | ||
12 | 0.15 |
Parameters | B0 | m1 | m2 | B1 | n1 | n2 | B2 | n3 | n4 | B3 | n5 | n6 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Value | 15.332 | 0.732 | 0.118 | 0.444 | 0.133 | 1.096 | 1.736 | 0.543 | 0.555 | 3.998 | 2.13 | 0.289 |
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Peng, H.; Tang, W.; Xing, Y.; Zhou, X. Semi-Empirical Prediction of Turned Surface Residual Stress for Inconel 718 Grounded in Experiments and Finite Element Simulations. Materials 2021, 14, 3937. https://doi.org/10.3390/ma14143937
Peng H, Tang W, Xing Y, Zhou X. Semi-Empirical Prediction of Turned Surface Residual Stress for Inconel 718 Grounded in Experiments and Finite Element Simulations. Materials. 2021; 14(14):3937. https://doi.org/10.3390/ma14143937
Chicago/Turabian StylePeng, Huachen, Wencheng Tang, Yan Xing, and Xin Zhou. 2021. "Semi-Empirical Prediction of Turned Surface Residual Stress for Inconel 718 Grounded in Experiments and Finite Element Simulations" Materials 14, no. 14: 3937. https://doi.org/10.3390/ma14143937