
Fig. 1
Experimental setup for ECMM. ECMM, electrochemical micromachining.
Table 1
Experimental details of ECMM setup.
| Parameters | Range |
|---|---|
| Working voltage | 150 V DC |
| Gap voltage | 0–10 V |
| Electrolyte | NaNO3 + Water |
| Magnets | Neodymium 40 × 20 × 10 mm |
| Tool | Copper: ϕ 0.6 mm |
| Workpiece | Ti-6Al-4V: 30 × 10 × 0.1 mm |
| Process parameters | Symbols Levels | |||
|---|---|---|---|---|
| Peak current (mA) | Ip | 1.2 | 1.35 | 1.5 |
| Pulse on time (ms) | Ton | 300 | 400 | 500 |
| Duty factor | DF | 0.5 | 0.6 | 0.7 |
| Concentration of electrolyte (%) | C | 15 | 22 | 5 30 |
[i] ECMM, electrochemical micromachining.

Fig. 2
Magnetic field measurement of magnets using gauss meter.

Fig. 3
Placement of magnets in the machining cycle.
Table 2
Orthogonal array experiment (L27) for magnetic and nonmagnetic field ECMM of Ti-6Al-4V titanium alloy.
| No magnetic force | Attraction magnetic force | Repulsion magnetic force | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| S. No. | Concentration of electrolyte (g/l) | Ip (A) | Ton (μs) | DF | MRR 10−3 (mm3/min) | OC (mm) | MRR 10−3 (mm3/min) | OC (mm) | MRR 10−3 (mm3/min) | OC (mm) |
| 1 | 15 | 1.20 | 300 | 0.5 | 0.59 | 0.32 | 0.66 | 0.25 | 0.72 | 0.21 |
| 2 | 15 | 1.20 | 300 | 0.5 | 0.59 | 0.32 | 0.66 | 0.25 | 0.73 | 0.21 |
| 3 | 15 | 1.20 | 300 | 0.5 | 0.59 | 0.32 | 0.66 | 0.26 | 0.73 | 0.22 |
| 4 | 15 | 1.35 | 400 | 0.6 | 0.97 | 0.35 | 1.48 | 0.31 | 2.22 | 0.28 |
| 5 | 15 | 1.35 | 400 | 0.6 | 0.97 | 0.35 | 1.47 | 0.31 | 2.22 | 0.28 |
| 6 | 15 | 1.35 | 400 | 0.6 | 0.96 | 0.35 | 1.47 | 0.31 | 2.21 | 0.28 |
| 7 | 15 | 1.50 | 500 | 0.7 | 0.72 | 0.33 | 0.88 | 0.28 | 1.46 | 0.24 |
| 8 | 15 | 1.50 | 500 | 0.7 | 0.72 | 0.33 | 0.88 | 0.28 | 1.46 | 0.24 |
| 9 | 15 | 1.50 | 500 | 0.7 | 0.72 | 0.33 | 0.87 | 0.28 | 1.47 | 0.24 |
| 10 | 22.5 | 1.20 | 400 | 0.7 | 0.60 | 0.43 | 0.68 | 0.39 | 0.78 | 0.34 |
| 11 | 22.5 | 1.20 | 400 | 0.7 | 0.59 | 0.43 | 0.68 | 0.39 | 0.79 | 0.35 |
| 12 | 22.5 | 1.20 | 400 | 0.7 | 0.59 | 0.43 | 0.68 | 0.39 | 0.79 | 0.34 |
| 13 | 22.5 | 1.35 | 500 | 0.5 | 0.72 | 0.32 | 0.89 | 0.27 | 1.50 | 0.23 |
| 14 | 22.5 | 1.35 | 500 | 0.5 | 0.73 | 0.32 | 0.87 | 0.27 | 1.52 | 0.24 |
| 15 | 22.5 | 1.35 | 500 | 0.5 | 0.73 | 0.32 | 0.89 | 0.26 | 1.51 | 0.23 |
| 16 | 22.5 | 1.50 | 300 | 0.6 | 0.62 | 0.30 | 0.72 | 0.24 | 0.85 | 0.22 |
| 17 | 22.5 | 1.50 | 300 | 0.6 | 0.62 | 0.30 | 0.72 | 0.24 | 0.85 | 0.22 |
| 18 | 22.5 | 1.50 | 300 | 0.6 | 0.62 | 0.29 | 0.72 | 0.24 | 0.84 | 0.22 |
| 19 | 30 | 1.20 | 500 | 0.6 | 0.76 | 0.34 | 0.97 | 0.29 | 1.60 | 0.26 |
| 20 | 30 | 1.20 | 500 | 0.6 | 0.76 | 0.34 | 0.95 | 0.29 | 1.57 | 0.26 |
| 21 | 30 | 1.20 | 500 | 0.6 | 0.77 | 0.34 | 0.96 | 0.28 | 1.59 | 0.26 |
| 22 | 30 | 1.35 | 300 | 0.7 | 0.64 | 0.37 | 0.78 | 0.34 | 1.00 | 0.30 |
| 23 | 30 | 1.35 | 300 | 0.7 | 0.64 | 0.37 | 0.78 | 0.34 | 0.99 | 0.30 |
| 24 | 30 | 1.35 | 300 | 0.7 | 0.65 | 0.37 | 0.78 | 0.34 | 0.99 | 0.30 |
| 25 | 30 | 1.50 | 400 | 0.5 | 0.62 | 0.35 | 0.70 | 0.31 | 0.82 | 0.26 |
| 26 | 30 | 1.50 | 400 | 0.5 | 0.63 | 0.35 | 0.73 | 0.31 | 0.84 | 0.26 |
| 27 | 30 | 1.50 | 400 | 0.5 | 0.62 | 0.35 | 0.71 | 0.33 | 0.83 | 0.27 |
[i] ECMM, electrochemical micromachining; MRR, material removal rate; OC, overcut.

Fig. 4
Methodology of TOPSIS (close to ideal solution).
Table 3
Computational steps of SIMOS weighting procedure.
| Subset criteria | Number of criteria (variables) | Number of position | Non-normalized weighted matrix | Total (%) |
|---|---|---|---|---|
| MRR | 1 | 1 | 1/2*100 = 50~50 | 50 |
| OC | 1 | 2 | 11/2*100 =50~50 | 50 |
[i] MRR, material removal rate; OC, overcut.
Table 4
TOPSIS evaluation for ECMM of Ti-6Al-4V under nonmagnetic field.
| S. No. | Concentration of electrolyte (g/l) | Ip (A) | Ton (μs) | DF | Weighted matrix | Distance from ideal solution | Closeness coefficient | Rank | ||
|---|---|---|---|---|---|---|---|---|---|---|
| WMRR | WOC | Eij+ | Eij− | CCij | ||||||
| 1 | 15 | 1.20 | 300 | 0.5 | 0.08 | 0.09 | 0.05 | 0.03 | 0.36 | 18 |
| 2 | 15 | 1.20 | 300 | 0.5 | 0.08 | 0.09 | 0.05 | 0.03 | 0.37 | 16 |
| 3 | 15 | 1.20 | 300 | 0.5 | 0.08 | 0.09 | 0.05 | 0.03 | 0.36 | 17 |
| 4 | 15 | 1.35 | 400 | 0.6 | 0.13 | 0.10 | 0.02 | 0.06 | 0.78 | 3 |
| 5 | 15 | 1.35 | 400 | 0.6 | 0.13 | 0.10 | 0.02 | 0.06 | 0.78 | 1 |
| 6 | 15 | 1.35 | 400 | 0.6 | 0.13 | 0.10 | 0.02 | 0.06 | 0.78 | 2 |
| 7 | 15 | 1.50 | 500 | 0.7 | 0.10 | 0.09 | 0.04 | 0.03 | 0.48 | 10 |
| 8 | 15 | 1.50 | 500 | 0.7 | 0.10 | 0.09 | 0.04 | 0.03 | 0.48 | 12 |
| 9 | 15 | 1.50 | 500 | 0.7 | 0.10 | 0.09 | 0.04 | 0.03 | 0.48 | 11 |
| 10 | 22.5 | 1.20 | 400 | 0.7 | 0.08 | 0.12 | 0.06 | 0.00 | 0.03 | 25 |
| 11 | 22.5 | 1.20 | 400 | 0.7 | 0.08 | 0.12 | 0.07 | 0.00 | 0.00 | 27 |
| 12 | 22.5 | 1.20 | 400 | 0.7 | 0.08 | 0.12 | 0.06 | 0.00 | 0.01 | 26 |
| 13 | 22.5 | 1.35 | 500 | 0.5 | 0.10 | 0.09 | 0.04 | 0.04 | 0.50 | 8 |
| 14 | 22.5 | 1.35 | 500 | 0.5 | 0.10 | 0.09 | 0.04 | 0.03 | 0.50 | 9 |
| 15 | 22.5 | 1.35 | 500 | 0.5 | 0.10 | 0.09 | 0.03 | 0.04 | 0.51 | 7 |
| 16 | 22.5 | 1.50 | 300 | 0.6 | 0.08 | 0.08 | 0.05 | 0.04 | 0.43 | 15 |
| 17 | 22.5 | 1.50 | 300 | 0.6 | 0.09 | 0.08 | 0.05 | 0.04 | 0.43 | 14 |
| 18 | 22.5 | 1.50 | 300 | 0.6 | 0.09 | 0.08 | 0.05 | 0.04 | 0.44 | 13 |
| 19 | 30 | 1.20 | 500 | 0.6 | 0.10 | 0.09 | 0.03 | 0.03 | 0.52 | 4 |
| 20 | 30 | 1.20 | 500 | 0.6 | 0.10 | 0.09 | 0.03 | 0.03 | 0.51 | 5 |
| 21 | 30 | 1.20 | 500 | 0.6 | 0.10 | 0.10 | 0.03 | 0.03 | 0.51 | 6 |
| 22 | 30 | 1.35 | 300 | 0.7 | 0.09 | 0.10 | 0.05 | 0.02 | 0.24 | 24 |
| 23 | 30 | 1.35 | 300 | 0.7 | 0.09 | 0.10 | 0.05 | 0.02 | 0.25 | 23 |
| 24 | 30 | 1.35 | 300 | 0.7 | 0.09 | 0.10 | 0.05 | 0.02 | 0.26 | 22 |
| 25 | 30 | 1.50 | 400 | 0.5 | 0.08 | 0.10 | 0.05 | 0.02 | 0.31 | 21 |
| 26 | 30 | 1.50 | 400 | 0.5 | 0.09 | 0.10 | 0.05 | 0.02 | 0.32 | 19 |
| 27 | 30 | 1.50 | 400 | 0.5 | 0.09 | 0.10 | 0.05 | 0.02 | 0.31 | 20 |
[i] ECMM, electrochemical micromachining.
Table 5
TOPSIS evaluation for ECMM of Ti-6Al-4V under magnetic field (attraction).
| S. No. | Concentration of electrolyte (g/l) | Ip (A) | Ton (μs) | DF | Weighted matrix | Distance from ideal solution | Closeness coefficient | Rank | ||
|---|---|---|---|---|---|---|---|---|---|---|
| WMRR | WOC | Eij+ | Eij− | CCij | ||||||
| 1 | 15 | 1.20 | 300 | 0.5 | 0.07 | 0.08 | 0.09 | 0.05 | 0.34 | 16 |
| 2 | 15 | 1.20 | 300 | 0.5 | 0.07 | 0.08 | 0.09 | 0.04 | 0.34 | 17 |
| 3 | 15 | 1.20 | 300 | 0.5 | 0.07 | 0.08 | 0.09 | 0.04 | 0.33 | 18 |
| 4 | 15 | 1.35 | 400 | 0.6 | 0.16 | 0.10 | 0.02 | 0.09 | 0.82 | 1 |
| 5 | 15 | 1.35 | 400 | 0.6 | 0.16 | 0.10 | 0.02 | 0.09 | 0.80 | 3 |
| 6 | 15 | 1.35 | 400 | 0.6 | 0.16 | 0.10 | 0.02 | 0.09 | 0.82 | 2 |
| 7 | 15 | 1.50 | 500 | 0.7 | 0.09 | 0.09 | 0.07 | 0.04 | 0.40 | 10 |
| 8 | 15 | 1.50 | 500 | 0.7 | 0.09 | 0.09 | 0.07 | 0.04 | 0.40 | 11 |
| 9 | 15 | 1.50 | 500 | 0.7 | 0.09 | 0.09 | 0.07 | 0.04 | 0.40 | 12 |
| 10 | 22.5 | 1.20 | 400 | 0.7 | 0.07 | 0.13 | 0.10 | 0.00 | 0.03 | 26 |
| 11 | 22.5 | 1.20 | 400 | 0.7 | 0.07 | 0.13 | 0.10 | 0.00 | 0.03 | 27 |
| 12 | 22.5 | 1.20 | 400 | 0.7 | 0.07 | 0.12 | 0.10 | 0.00 | 0.03 | 25 |
| 13 | 22.5 | 1.35 | 500 | 0.5 | 0.10 | 0.09 | 0.06 | 0.05 | 0.43 | 8 |
| 14 | 22.5 | 1.35 | 500 | 0.5 | 0.09 | 0.09 | 0.07 | 0.05 | 0.41 | 9 |
| 15 | 22.5 | 1.35 | 500 | 0.5 | 0.10 | 0.08 | 0.06 | 0.05 | 0.44 | 6 |
| 16 | 22.5 | 1.50 | 300 | 0.6 | 0.08 | 0.08 | 0.08 | 0.05 | 0.37 | 14 |
| 17 | 22.5 | 1.50 | 300 | 0.6 | 0.08 | 0.08 | 0.08 | 0.05 | 0.37 | 15 |
| 18 | 22.5 | 1.50 | 300 | 0.6 | 0.08 | 0.08 | 0.08 | 0.05 | 0.37 | 13 |
| 19 | 30 | 1.20 | 500 | 0.6 | 0.10 | 0.09 | 0.06 | 0.05 | 0.45 | 5 |
| 20 | 30 | 1.20 | 500 | 0.6 | 0.10 | 0.09 | 0.06 | 0.05 | 0.44 | 7 |
| 21 | 30 | 1.20 | 500 | 0.6 | 0.10 | 0.09 | 0.06 | 0.05 | 0.46 | 4 |
| 22 | 30 | 1.35 | 300 | 0.7 | 0.08 | 0.11 | 0.08 | 0.02 | 0.21 | 22 |
| 23 | 30 | 1.35 | 300 | 0.7 | 0.08 | 0.11 | 0.08 | 0.02 | 0.21 | 23 |
| 24 | 30 | 1.35 | 300 | 0.7 | 0.08 | 0.11 | 0.08 | 0.02 | 0.22 | 21 |
| 25 | 30 | 1.50 | 400 | 0.5 | 0.08 | 0.10 | 0.09 | 0.03 | 0.25 | 20 |
| 26 | 30 | 1.50 | 400 | 0.5 | 0.08 | 0.10 | 0.08 | 0.03 | 0.26 | 19 |
| 27 | 30 | 1.50 | 400 | 0.5 | 0.08 | 0.10 | 0.09 | 0.02 | 0.20 | 24 |
[i] ECMM, electrochemical micromachining.
Table 6
TOPSIS evaluation for ECMM of Ti-6Al-4V under magnetic field (repulsion).
| S. No. | Concentration of electrolyte (g/l) | Ip (A) | Ton (μs) | DF | Weighted matrix | Distance from ideal solution | Closeness coefficient | Rank | ||
|---|---|---|---|---|---|---|---|---|---|---|
| WMRR | WOC | Eij+ | Eij− | CCij | ||||||
| 1 | 15 | 1.20 | 300 | 0.5 | 0.05 | 0.08 | 0.11 | 0.05 | 0.30 | 17 |
| 2 | 15 | 1.20 | 300 | 0.5 | 0.05 | 0.08 | 0.11 | 0.05 | 0.31 | 16 |
| 3 | 15 | 1.20 | 300 | 0.5 | 0.05 | 0.08 | 0.11 | 0.05 | 0.30 | 18 |
| 4 | 15 | 1.35 | 400 | 0.6 | 0.16 | 0.10 | 0.02 | 0.11 | 0.82 | 1 |
| 5 | 15 | 1.35 | 400 | 0.6 | 0.16 | 0.10 | 0.03 | 0.11 | 0.82 | 2 |
| 6 | 15 | 1.35 | 400 | 0.6 | 0.16 | 0.10 | 0.03 | 0.11 | 0.81 | 3 |
| 7 | 15 | 1.50 | 500 | 0.7 | 0.11 | 0.09 | 0.06 | 0.07 | 0.54 | 11 |
| 8 | 15 | 1.50 | 500 | 0.7 | 0.11 | 0.09 | 0.06 | 0.07 | 0.53 | 12 |
| 9 | 15 | 1.50 | 500 | 0.7 | 0.11 | 0.09 | 0.06 | 0.07 | 0.54 | 10 |
| 10 | 22.5 | 1.20 | 400 | 0.7 | 0.06 | 0.12 | 0.11 | 0.01 | 0.05 | 25 |
| 11 | 22.5 | 1.20 | 400 | 0.7 | 0.06 | 0.13 | 0.12 | 0.01 | 0.04 | 27 |
| 12 | 22.5 | 1.20 | 400 | 0.7 | 0.06 | 0.12 | 0.11 | 0.01 | 0.05 | 26 |
| 13 | 22.5 | 1.35 | 500 | 0.5 | 0.11 | 0.08 | 0.05 | 0.07 | 0.57 | 9 |
| 14 | 22.5 | 1.35 | 500 | 0.5 | 0.11 | 0.09 | 0.05 | 0.07 | 0.57 | 8 |
| 15 | 22.5 | 1.35 | 500 | 0.5 | 0.11 | 0.09 | 0.05 | 0.07 | 0.57 | 7 |
| 16 | 22.5 | 1.50 | 300 | 0.6 | 0.06 | 0.08 | 0.10 | 0.05 | 0.32 | 13 |
| 17 | 22.5 | 1.50 | 300 | 0.6 | 0.06 | 0.08 | 0.10 | 0.05 | 0.32 | 15 |
| 18 | 22.5 | 1.50 | 300 | 0.6 | 0.06 | 0.08 | 0.10 | 0.05 | 0.32 | 14 |
| 19 | 30 | 1.20 | 500 | 0.6 | 0.12 | 0.09 | 0.05 | 0.07 | 0.60 | 4 |
| 20 | 30 | 1.20 | 500 | 0.6 | 0.12 | 0.09 | 0.05 | 0.07 | 0.58 | 6 |
| 21 | 30 | 1.20 | 500 | 0.6 | 0.12 | 0.10 | 0.05 | 0.07 | 0.58 | 5 |
| 22 | 30 | 1.35 | 300 | 0.7 | 0.07 | 0.11 | 0.10 | 0.03 | 0.22 | 21 |
| 23 | 30 | 1.35 | 300 | 0.7 | 0.07 | 0.11 | 0.10 | 0.03 | 0.21 | 24 |
| 24 | 30 | 1.35 | 300 | 0.7 | 0.07 | 0.11 | 0.10 | 0.03 | 0.21 | 23 |
| 25 | 30 | 1.50 | 400 | 0.5 | 0.06 | 0.10 | 0.10 | 0.03 | 0.23 | 20 |
| 26 | 30 | 1.50 | 400 | 0.5 | 0.06 | 0.10 | 0.10 | 0.03 | 0.23 | 19 |
| 27 | 30 | 1.50 | 400 | 0.5 | 0.06 | 0.10 | 0.10 | 0.03 | 0.22 | 22 |
[i] ECMM, electrochemical micromachining.
Table 7
Improvement in response factors in presence of magnetic field with respect to nonmagnetic field electrochemical micromachined Ti-6Al-4V.
| % Increase in MRR | % Decrease in OC | |||||||
|---|---|---|---|---|---|---|---|---|
| Concentration of electrolyte (g/l) | Ip(A) | Ton (μs) | DF | Attraction | Repulsion | Concentration of electrolyte (g/l) | Ip(A) | Ton (μs) |
| 15 | 1.20 | 300 | 0.5 | 12.09 | 23.51 | 15 | 1.20 | 300 |
| 15 | 1.20 | 300 | 0.5 | 11.91 | 23.74 | 15 | 1.20 | 300 |
| 15 | 1.20 | 300 | 0.5 | 12.44 | 23.95 | 15 | 1.20 | 300 |
| 15 | 1.35 | 400 | 0.6 | 52.43 | 127.99 | 15 | 1.35 | 400 |
| 15 | 1.35 | 400 | 0.6 | 51.47 | 128.19 | 15 | 1.35 | 400 |
| 15 | 1.35 | 400 | 0.6 | 51.99 | 129.68 | 15 | 1.35 | 400 |
| 15 | 1.50 | 500 | 0.7 | 22.45 | 103.00 | 15 | 1.50 | 500 |
| 15 | 1.50 | 500 | 0.7 | 22.39 | 103.34 | 15 | 1.50 | 500 |
| 15 | 1.50 | 500 | 0.7 | 21.78 | 103.98 | 15 | 1.50 | 500 |
| 22.5 | 1.20 | 400 | 0.7 | 14.05 | 31.28 | 22.5 | 1.20 | 400 |
| 22.5 | 1.20 | 400 | 0.7 | 16.12 | 35.21 | 22.5 | 1.20 | 400 |
| 22.5 | 1.20 | 400 | 0.7 | 14.88 | 33.62 | 22.5 | 1.20 | 400 |
| 22.5 | 1.35 | 500 | 0.5 | 23.30 | 107.71 | 22.5 | 1.35 | 500 |
| 22.5 | 1.35 | 500 | 0.5 | 20.56 | 110.10 | 22.5 | 1.35 | 500 |
| 22.5 | 1.35 | 500 | 0.5 | 20.53 | 106.00 | 22.5 | 1.35 | 500 |
| 22.5 | 1.50 | 300 | 0.6 | 15.51 | 37.78 | 22.5 | 1.50 | 300 |
| 22.5 | 1.50 | 300 | 0.6 | 15.23 | 36.32 | 22.5 | 1.50 | 300 |
| 22.5 | 1.50 | 300 | 0.6 | 16.34 | 35.64 | 22.5 | 1.50 | 300 |
| 30 | 1.20 | 500 | 0.6 | 27.78 | 110.54 | 30 | 1.20 | 500 |
| 30 | 1.20 | 500 | 0.6 | 25.28 | 107.33 | 30 | 1.20 | 500 |
| 30 | 1.20 | 500 | 0.6 | 25.00 | 107.12 | 30 | 1.20 | 500 |
| 30 | 1.35 | 300 | 0.7 | 22.18 | 55.34 | 30 | 1.35 | 300 |
| 30 | 1.35 | 300 | 0.7 | 20.46 | 53.08 | 30 | 1.35 | 300 |
| 30 | 1.35 | 300 | 0.7 | 20.13 | 51.27 | 30 | 1.35 | 300 |
| 30 | 1.50 | 400 | 0.5 | 14.18 | 33.51 | 30 | 1.50 | 400 |
| 30 | 1.50 | 400 | 0.5 | 15.97 | 33.52 | 30 | 1.50 | 400 |
| 30 | 1.50 | 400 | 0.5 | 14.28 | 32.43 | 30 | 1.50 | 400 |
[i] MRR, material removal rate; OC, overcut.

Fig. 5
Improvement in MRR and OC in presence of magnetic field when electrochemical micromachined Ti-6Al-4V. MRR, material removal rate; OC, overcut.

Fig. 6
EDS analysis of electrochemical micromachined Ti-6Al-4V hole profile: (A) without magnetic field and (B) with magnetic field. EDS, energy dispersive X-ray spectroscopy.

Fig. 7
Hole profile of electrochemical micromachined Ti-6Al-4V: (A) without and (B) with magnetic field.

Fig. 8
Atomic force microscopy of electrochemical micromachined Ti-6Al-4V hole profile: (A) without and (B) with magnetic field.
Table 8
Topographical analysis of electrochemical micromachined Ti-6Al-4V hole profile.
| ECMM environment | Hole surface roughness (nm) |
|---|---|
| No magnetic field | 159 |
| Magnetic field | 71 |
[i] ECMM, electrochemical micromachining.
Table 9
Residual stress analysis of electrochemical micromachined Ti-6Al-4V hole profile.
| No magnetic field | Magnetic field | |
|---|---|---|
| Residual stress values (MPa) | 259.62 | 264.89 |

Fig. 9
XRD analysis of electrochemical micromachined Ti-6Al-4V hole profile: (A) Without and (B) With magnetic field. XRD, x-ray diffraction.