Efficiency Optimization of the Electroerosive Process in µ-WEDM of Steel MS1 Sintered Using DMLS Technology
Abstract
:1. Introduction
2. Materials and Methods
2.1. Mathematical Modeling and Optimization of the µ-WEDM Process Efficiency
2.2. Identification of MTP in Relation to MRR and Roughness Parameter Rz in the µ-WEDM Process
2.3. Conditions of the Experiment
3. Results and Discussion
3.1. DoE Statistical Analysis of Experimentally Measured MRR and Rz Data at µ-WEDM
3.2. Design and Validation of the MSC Model for the Prediction of MRR and Rz at µ-WEDM
3.3. Optimization of Process Efficiency in µ-WEDM Maraging Steel MS1
5.0 ≤ Pulse-on time duration ton (μs) ≤ 40.0
3.0 ≤ Pulse-off time duration toff (μs) ≤ 15.0
70.0 ≤ Voltage of discharge U (V) ≤ 90.0
4. Conclusions
- ▪
- It was found that in terms of the four considered input factors of the electroerosive process, maximum peak current I with a weight of 37.513%, pulse-on time duration ton with a weight of 11.306%, pulse-off time duration toff with a weight of 9.51%, and voltage of discharge U with a weight of 5.18% have the main influence on MRR;
- ▪
- It was also found that in terms of the four considered input factors of the electroerosive process, maximum peak current I with a weight of 41.466%, pulse-on time duration ton with a weight of 20.814%, pulse-off time duration toff with a weight of 12.76%, and voltage of discharge U with a weight of 7.42% have the main influence on Rz;
- ▪
- It was found that with increasing values of the input parameters of the electrical discharge process I and ton, the cutting performance of MRR increases but the quality of the machined surface decreases in terms of the surface roughness parameter Rz. The highest value of the MRR parameter = 0.190 mm3·min−1 was obtained for the combination of MTP: I = 8.0 A, ton = 40 μs, toff = 3 μs, and U = 70 V;
- ▪
- At the same time, it was found that with increasing values of the input parameters of the electrical discharge process toff and U, the cutting performance of the MRR decreases but the quality of the machined surface increases in terms of the surface roughness parameter Rz. The lowest value of the Rz parameter = 0.09 μm was obtained for the combination of MTP: I = 2.5 A, ton = 3 μs, toff = 15 μs, and U = 90 V;
- ▪
- It was found that the aforementioned pairs of MTP input parameters in the electrical discharge process behave oppositely in relation to MRR and Rz;
- ▪
- For the given reasons, it was necessary to search for an appropriate ratio of the MTP input parameters in the electrical discharge process to achieve the optimum value of the process output performance parameter MRR and the quality parameter of the machined surface Rz;
- ▪
- Optimization was performed with respect to maximizing the output parameter of the MRR and minimizing the quality parameter of the machined surface in terms of the surface roughness parameter Rz for µ-WEDM maraging steel MS1. Through the optimization, a local maximum of 0.159 mm3·min−1 of the MRR parameter can be achieved at with MTP settings of I = 5.5 A, ton = 21.5 µs, toff = 5.5 µs, and U = 75 V. Conversely, through optimization a local minimum of 1.051 µm of the Rz parameter can be achieved at MTP settings of I = 3.014 A, ton = 3.0 µs, toff = 3.0 µs, and U = 70 V;
- ▪
- The performed optimization of the electrical discharge process can generally achieve an increase in the overall efficiency of µ-WEDM in the machining of maraging steel MS1.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
CDA | Confirmatory Data Analysis |
DOE | Design of Experiments |
DMLS | Direct Metal Laser Sintering |
D | Total required functionality |
EDA | Exploratory Data Analysis |
I | Maximum peak current (A) |
IPM | Interior Point Method |
MSC | Mathematical-Statistical Computational |
MTP | Main Technological Parameters |
MRR | Material Removal Rate |
NLP | Non-Linear Programming |
QNM | Quasi-Newton Methods |
Rz | Ten-point Mean Roughness (µm) |
SDM | Steepest Descent Method |
SQP | Sequential Quadratic Programming |
ton | Pulse-on time duration (µs) |
toff | Pulse-off time duration (µs) |
U | Voltage of discharge (V) |
y | Desired value function |
ymin/max | Lower/upper response limit values |
µ-WEDM | micro-Wire Electrical Discharge Machining |
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MTP | µ-WEDM Operation | Setting Range | Influence of MTP on Rz | Influence of MTP on MRR |
---|---|---|---|---|
Maximum peak current I (A) | roughing | 6.0–8.0 | As the value of parameter I increases, the surface roughness deteriorates [13]. | As the value of parameter I increases, the MRR increases [22]. |
semifinishing | 4.0–6.0 | |||
finishing | 2.0–4.0 | |||
Pulse-on time duration ton (μs) | roughing | 20.0–40.0 | As the value of the parameter ton increases, the surface roughness deteriorates [14]. | As the value of the parameter ton increases, the MRR increases [22]. |
semifinishing | 10.0–20.0 | |||
finishing | 5.0–10.0 | |||
Pulse-off time duration toff (μs) | roughing | 9.0–15.0 | As the value of the parameter toff increases, the surface roughness improves [23]. | As the value of the parameter toff increases, the MRR decreases [23]. |
semifinishing | 6.0–9.0 | |||
finishing | 3.0–6.0 | |||
Voltage of discharge U (V) | roughing | 85–90 | As the value of parameter U increases, the surface roughness improves [40]. | As the value of the parameter U increases, the MRR decreases [51]. |
semifinishing | 75–80 | |||
finishing | 70–75 |
Fe | Ni | Co | Mo | Ti | Al | Cr | C | Mn, Si | P, S |
---|---|---|---|---|---|---|---|---|---|
Zb. | 17–19% | 8.5–9.5% | 4.5–5.2% | 0.6–0.8% | 0.05–0.15% | ≤0.5 | ≤0.03 | each ≤ 0.1% | each ≤ 0.01% |
Mechanical properties of maraging steel MS1 | ||
Parameter | As built | After age hardening |
Tensile strength (MPa) | 1200 ± 100 | 1950 ± 100 |
Yield strength Rp 0.2% (MPa) | 1100 ± 100 | 1900 ± 100 |
Elongation at break (%) | 8 ± 3 | 2 ± 1 |
Hardness (HRC) | 33–37 | 50–54 |
Ductility (J) | 45 ± 10 | 11 ± 4 |
Modulus of elasticity (GPa) | 150 ± 25 | |
Physical properties of maraging steel MS1 | ||
Density (g·cm−3) | 8.0–8.1 | |
Electrical conductivity (Siemens·m·mm−2) | 2.25 | |
Thermal conductivity (W·m−1·°C) | 15 ± 0.8 | |
Specific heat capacity (J·kg−1·°C) | 450 ± 20 | |
Melting temperature (°C) | 1370–1400 |
Source | DF | Sum of Squares | Mean Square | F Ratio | Prob > F |
---|---|---|---|---|---|
Model | DFModel = a − 1 | SModel | MSModel = SModel/DFModel | F = MSModel/MSError | pM |
Error | DFError = N − a | SError | MSError = SError/DFError | ||
C.Total | DFC.Total = N − 1 | SC.Total | MSC.Total = SC.Total/DFC.Total |
Term for MRR | Estimate | Std Error | t-Ratio | Prob > |t| |
Intercept (x0) | −0.010813 | 0.020121 | −0.54 | 0.5929 |
x1 | 0.0165482 | 0.000279 | 59.26 | 0.0001 * |
x2 | 0.0012834 | 7.19 × 10−5 | 17.86 | 0.0001 * |
x3 | −0.001947 | 0.00014 | −13.94 | 0.0001 * |
x4 | 0.0008016 | 0.000237 | 3.38 | 0.0013 * |
(x1 − 5)⋯(x1 − 5) | 0.0128791 | 0.003127 | 4.12 | 0.0001 * |
(x1 − 5)⋯(x2 − 22.8767) | −0.000387 | 0.000016 | −24.17 | 0.0001 * |
(x2 − 22.8767)⋯(x2 − 22.8767) | −0.000275 | 8.03 × 10−5 | −3.42 | 0.0011 * |
(x2 − 22.8767)⋯(x3 − 9) | 0.0000673 | 0.000008 | 8.40 | 0.0001 * |
(x2 − 22.8767)⋯(x4 − 80) | 0.0000419 | 4.70 × 10−6 | 8.93 | 0.0001 * |
(x1 − 5)⋯(x1 − 5)⋯(x4 − 80) | −0.000165 | 2.62 × 10−5 | −6.32 | 0.0001 * |
(x1 − 5)⋯(x1 − 5)⋯(x1 − 5)⋯(x1 − 5) | −0.000438 | 5.73 × 10−5 | −7.63 | 0.0001 * |
Term for Rz | Estimate | Std Error | t-Ratio | Prob > |t| |
Intercept (x0) | 4.312305 | 0.462060 | 9.33 | <0.0001 * |
x1 | 1.263985 | 0.017863 | 70.76 | <0.0001 * |
x2 | 0.108301 | 0.003054 | 35.46 | <0.0001 * |
x3 | −0.115140 | 0.009508 | −12.11 | <0.0001 * |
x4 | −0.025370 | 0.005077 | −5.00 | <0.0001 * |
(x1 − 5)⋯(x1 − 5) | −0.459620 | 0.148820 | −3.09 | 0.0030 * |
(x1 − 5)⋯(x2 − 22.8767) | −0.025260 | 0.001029 | −24.55 | <0.0001 * |
(x1 − 5)⋯(x3 − 9) | 0.113915 | 0.035306 | 3.23 | 0.0020 * |
(x2 − 22,8767)⋯(x3 − 9) | −0.031130 | 0.011999 | −2.59 | 0.0119 * |
(x2 − 22,8767)⋯(x4 − 80) | −0.009710 | 0.003622 | −2.68 | 0.0094 * |
(x1 − 5)⋯(x1 − 5)⋯(x1 − 5)⋯(x1 − 5) | 0.051696 | 0.016525 | 3.13 | 0.0027 * |
(x1 − 5)⋯(x1 − 5)⋯(x1 − 5)⋯(x4 − 80) | 0.013128 | 0.004660 | 2.82 | 0.0065 * |
Parameter for MRR | Value |
RSquare | 0.998175 |
RSquare Adj | 0.997846 |
Root Mean Square Error | 0.002675 |
Mean of Response | 0.136644 |
Observations (or Sum Wgts) | 73 |
Parameter for Rz | Value |
RSquare | 0.998773 |
RSquare Adj | 0.998528 |
Root Mean Square Error | 0.164369 |
Mean of Response | 9.332192 |
Observations (or Sum Wgts) | 73 |
SourceforMRR | DF | Sum of Squares | Mean Square | F-Ratio | Prob > F |
Model | 11 | 0.2387703 | 0.021706 | 3033.879 | 0.0001 * |
Error | 61 | 0.0004364 | 7.16 × 10−6 | ||
C. Total | 72 | 0.2392067 | |||
Source for Rz | DF | Sum of Squares | Mean Square | F-Ratio | Prob > F |
Model | 12 | 1319.781 | 109.982 | 4070.833 | 0.0001 * |
Error | 60 | 1.621 | 0.027 | ||
C. Total | 72 | 1321.402 |
Source | DF | Sum of Squares | Mean Square | F Ratio | Prob > F |
Lack of Fit | 7 | 0.0001104 | 0.000016 | 2.6133 | 0.0513 |
Pure Error | 54 | 0.000326 | 6.04 × 10−6 | ||
Total Error | 61 | 0.0004364 | |||
Source | DF | Sum of Squares | Mean Square | F Ratio | Prob > F |
Lack of Fit | 6 | 1.588221 | 0.264703 | 435.7923 | 0.0677 |
Pure Error | 54 | 0.0328 | 0.000607 | ||
Total Error | 60 | 1.621021 |
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Straka, Ľ.; Gombár, M.; Vagaská, A.; Kuchta, P. Efficiency Optimization of the Electroerosive Process in µ-WEDM of Steel MS1 Sintered Using DMLS Technology. Micromachines 2022, 13, 1446. https://doi.org/10.3390/mi13091446
Straka Ľ, Gombár M, Vagaská A, Kuchta P. Efficiency Optimization of the Electroerosive Process in µ-WEDM of Steel MS1 Sintered Using DMLS Technology. Micromachines. 2022; 13(9):1446. https://doi.org/10.3390/mi13091446
Chicago/Turabian StyleStraka, Ľuboslav, Miroslav Gombár, Alena Vagaská, and Patrik Kuchta. 2022. "Efficiency Optimization of the Electroerosive Process in µ-WEDM of Steel MS1 Sintered Using DMLS Technology" Micromachines 13, no. 9: 1446. https://doi.org/10.3390/mi13091446