Discharge Energy as a Key Contributing Factor Determining Microgeometry of Aluminum Samples Created by Electrical Discharge Machining
Abstract
:1. Introduction
2. Materials and Methods
2.1. Sample Preparation
2.2. Measurements and Filtration
- dataset leveling—in this operation non-measured points and their neighboring areas were excluded from the calculation of the least square polynomial surface of 1st degree. There was no form-removal step since the samples were manufactured as a flat surface and form deviation would not clearly manifest itself in the relatively small measurement area;
- thresholding—this operation generally aids in the next step of software-driven outliers removal, which does not always remove larger spikes, and plateau-like artifacts, which are characteristic of FVM measurements [44]. Generally, for other surface morphologies, this step would be omitted and only outliers removal procedure would be performed [45];
- outliers removal—the built-in software operation was used to remove the outliers, i.e., spikes, vertical slopes, etc.;
- filling in non-measured points—in this operation non-measured points were replaced with a smooth shape calculated from the neighbors. In order to avoid the reappearance of previously present artifacts, non-measured zones were dilated by 1.5 µm. None of the measured surfaces contained significantly large (>15 µm in diameter) non-measured areas.
2.3. Surface Characterization Methods
2.3.1. Standard Analysis with ISO Parameters (MM)
2.3.2. Length-Scale and Area-Scale Analyses
2.3.3. Multiscale Curvature Analysis
2.4. Discrimination Analysis
3. Results
3.1. Measurements of Surface Topographies
3.2. Standard Analysis with ISO Parameters
3.3. Length- and Area-Scale Analyses
3.4. Curvature
4. Discussion
5. Conclusions
- Strong correlations (R2 > 0.9) were found between the electrical discharge energy values and the topographic parameters of the surface:
- ○
- Rel, Lsfc for scales >90 µm, RelA, Asfc for scales ranging between 2400 and 138,000 µm
- ○
- Curvature statistical measures (apart from κ2a) starting from scales between 36 a 41 µm.
- The highest coefficients of determination were noted generally for the coarse scales of observation in which geometrical properties of large size morphological features are best characterized. The strongest coefficients of determination R2 > 0.9 were noted for linear (0.993 for Ka at scale = 41 µm, 0.951 for Rel at scale = 111.38 µm) and exponential regressions (0.957 for Rel at scale 51.49 µm);
- Length- and area-scale analyses performed the best at discriminating the surfaces. A similar observation was made for curvature, apart from standard deviations of both signed and signed maximum curvature was considered, which failed at finest scales (<11 µm);
- The convergence of the results obtained by the considered multiscale methods is high for intermediate scales although the definition of scale differs depending on the method;
- Apart from average mean curvature (Ha), characterizations of fine-scale features do not correlate strongly with the energy of electrical discharges using the proposed linear, logarithmic, and exponential models (as R2 < 0.9), although surfaces can be confidently discriminated at those corresponding scales. A more complex statistical model should be considered in those cases;
- Conventional surface characterization parameters generally do not correlate well with the discharge weakly. Some exceptions were found for Sv, Spc, Shv, and Spar for which R2 was found to be greater than 0.9;
- The effect of the discharge energy is shown in the magnitude of the surface principal curvatures and their combinations. This relationship is evident mainly for the three mean measures: κ1a, Ha, and Ka and occurs starting from the intermediate scales (between 36 and 41 µm).
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
Appendix A
Abbrevation | Full Name |
---|---|
Sq | Root-mean-square height |
Ssk | Skewness |
Sku | Kurtosis |
Sp | Maximum peak height |
Sv | Maximum pit height |
Sz | Maximum height |
Sa | Arithmetic mean height |
Smr | Areal material ratio |
Smc | Inverse areal material ratio |
Sxp | Extreme peak height |
Sal | Autocorrelation length |
Str | Texture-aspect ratio |
Std | Texture direction |
Sdq | Root-mean-square gradient |
Sdr | Developed interfacial area ratio |
Vm | Material volume |
Vv | Void volume |
Vmp | Peak material volume |
Vmc | Core material volume |
Vvc | Core void volume |
Vvv | Pit void volume |
Spd | Density of peaks |
Spc | Arithmetic mean peak curvature |
S10z | Ten point height |
S5p | Five point peak height |
S5v | Five point pit height |
Sda | Mean dale area |
Sha | Mean hill area |
Sdv | Mean dale volume |
Shv | Mean hill volume |
Sbi | Surface bearing index |
Sci | Core fluid retention index |
Svi | Valley fluid retention index |
Smean | Mean height in absolute |
Sdar | Developed area |
Spar | Projected area |
Rel | Relative length |
RelA | Relative area |
Lsfc | Length-scale fractal complexity |
Asfc | Area-scale fractal complexity |
κ1a | Average maximum curvature |
κ1q | Standard deviation of maximum curvature |
κ2a | Average minimum curvature |
κ2q | Standard deviation of minimum curvature |
Ha | Average mean curvature |
Hq | Standard deviation of mean curvature |
Ka | Average Gaussian curvature |
Kq | Standard deviation of Gaussian curvature |
κ1aabs | Average absolute maximum curvature |
κ1qabs | Standard deviation of absolute maximum curvature |
κ2aabs | Average absolute minimum curvature |
κ2qabs | Standard deviation of absolute minimum curvature |
Haabs | Average absolute mean curvature |
Hqabs | Standard deviation of absolute mean curvature |
Kaabs | Average absolute Gaussian curvature |
Kqabs | Standard deviation of absolute Gaussian curvature |
Parameter | R2 Linear Regression | R2 Logarithmic Regression | R2 Exponential Regression |
---|---|---|---|
Sq | 0.833 | 0.776 | 0.577 |
Ssk | 0.238 | 0.593 | N/A |
Sku | 0.000 | 0.010 | 0.001 |
Sp | 0.732 | 0.826 | 0.500 |
Sv | 0.900 | 0.655 | 0.718 |
Sz | 0.827 | 0.773 | 0.599 |
Sa | 0.826 | 0.779 | 0.568 |
Smr (c = 1 µm under the highest peak) | 0.392 | 0.355 | 0.755 |
Smc (p = 10%) | 0.838 | 0.784 | 0.573 |
Sxp (p = 50%, q = 97.5%) | 0.857 | 0.698 | 0.620 |
Sal (s = 0.2) | 0.700 | 0.733 | 0.629 |
Str (s = 0.2) | 0.060 | 0.336 | 0.046 |
Std (Reference angle = 0°) | 0.006 | 0.046 | 0.006 |
Sdq | 0.794 | 0.842 | 0.558 |
Sdr | 0.732 | 0.857 | 0.461 |
Vm (p = 10%) | 0.801 | 0.808 | 0.532 |
Vv (p = 10%) | 0.836 | 0.785 | 0.571 |
Vmp (p = 10%) | 0.801 | 0.808 | 0.532 |
Vmc (p = 10%, q = 80%) | 0.802 | 0.784 | 0.548 |
Vvc (p = 10%, q = 80%) | 0.830 | 0.793 | 0.563 |
Vvv (p = 80%) | 0.889 | 0.623 | 0.676 |
Spd (pruning = 2.5%) | 0.320 | 0.393 | 0.572 |
Spc (pruning = 2.5%) | 0.925 | 0.592 | 0.869 |
S10z (pruning = 2.5%) | 0.809 | 0.776 | 0.585 |
S5p (pruning = 2.5%) | 0.732 | 0.820 | 0.494 |
S5v (pruning = 2.5%) | 0.883 | 0.648 | 0.727 |
Sda (pruning = 2.5%) | 0.874 | 0.731 | 0.638 |
Sha (pruning = 2.5%) | 0.779 | 0.698 | 0.534 |
Sdv (pruning = 2.5%) | 0.899 | 0.775 | 0.508 |
Shv (pruning = 2.5%) | 0.947 | 0.623 | 0.594 |
Sbi | 0.196 | 0.004 | 0.165 |
Sci | 0.394 | 0.723 | 0.374 |
Svi | 0.118 | 0.497 | 0.113 |
Smean | 0.780 | 0.429 | N/A |
Sdar | 0.738 | 0.855 | 0.693 |
Spar | 0.909 | 0.262 | 0.826 |
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Al | Si | Fe | Cu | Mn | Mg | Cr | Zn | Ti |
---|---|---|---|---|---|---|---|---|
rest | 0.3–0.6 | 0.1–0.3 | max. 0.1 | max. 0.1 | 0.35–0.6 | max. 0.05 | max. 0.15 | max. 0.1 |
Surface | Voltage, V | Current, A | Single Pulse Time, µs | Break between Pulses, µs | Single Discharge Energy, mJ | Theoretical VDI Class | Theoretical Roughness Ra, µm |
---|---|---|---|---|---|---|---|
S1 | 150 | 1.2 | 2.7 | 15 | 0.486 | 15 | 0.56 |
S2 | 160 | 1.8 | 8.7 | 15 | 2.506 | 18 | 0.8 |
S3 | 180 | 2.4 | 11.5 | 15 | 4.968 | 21 | 1.12 |
S4 | 180 | 3.2 | 17.8 | 18 | 10.253 | 24 | 1.6 |
S5 | 180 | 4.4 | 20.5 | 27 | 16.236 | 27 | 2.24 |
S6 | 100 | 6.2 | 23.7 | 37 | 14.694 | 30 | 3.15 |
S7 | 100 | 10 | 31.6 | 49 | 31.600 | 33 | 4.5 |
S8 | 100 | 13 | 86.6 | 49 | 112.580 | 36 | 6.3 |
S9 | 100 | 21 | 133.4 | 49 | 280.140 | 39 | 9 |
S10 | 100 | 29 | 237.1 | 49 | 687.590 | 42 | 12.5 |
S11 | 100 | 39 | 356.2 | 49 | 1,389.180 | 45 | 18 |
Parameter | Unit | Value |
---|---|---|
Magnification | – | 50× |
Area size | μm | 900 × 900 |
Estimated vertical resolution | μm | 0.022 |
Estimated lateral resolution | μm | 1.500 |
Lateral sampling intervals | μm | 0.176 |
Standard | Parameter Group | Parameter Symbol |
---|---|---|
ISO 25178 | Height | Sq, Ssk, Sku, Sp, Sv, Sz, Sa |
Functional | Smr, Smc, Sxp | |
Spatial | Sal, Str, Std | |
Hybrid | Sdq, Sdr | |
Functional (Volume) | Vm, Vv, Vmp, Vmc, Vvc, Vvv | |
Feature | Spd, Spc, S10z, S5p, S5v, Sda, Sha, Sdv, Shv | |
EUR 15178N | Functional Indices | Sbi, Sci, Svi |
- | Other | Smean, Sdar, Spar |
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Peta, K.; Mendak, M.; Bartkowiak, T. Discharge Energy as a Key Contributing Factor Determining Microgeometry of Aluminum Samples Created by Electrical Discharge Machining. Crystals 2021, 11, 1371. https://doi.org/10.3390/cryst11111371
Peta K, Mendak M, Bartkowiak T. Discharge Energy as a Key Contributing Factor Determining Microgeometry of Aluminum Samples Created by Electrical Discharge Machining. Crystals. 2021; 11(11):1371. https://doi.org/10.3390/cryst11111371
Chicago/Turabian StylePeta, Katarzyna, Michał Mendak, and Tomasz Bartkowiak. 2021. "Discharge Energy as a Key Contributing Factor Determining Microgeometry of Aluminum Samples Created by Electrical Discharge Machining" Crystals 11, no. 11: 1371. https://doi.org/10.3390/cryst11111371