WEDM-Generated Slot Width Variation Modeling
Abstract
:1. Background
2. Materials and Methods
2.1. Theoretical Considerations
- (a)
- Characteristics of electric discharges (voltage, current, pulse shape, pulse-on time, pulse-off time, filling factor, etc.)
- (b)
- Some physical-mechanical properties that define the behavior of the test sample material under the action of electric discharges (density, melting temperature, vaporization temperatures, etc.)
- (c)
- The characteristics of the dielectric liquid (density, fluidity, etc.) and its way of circulation in the working gap
- (d)
- The test sample thickness
- (e)
- The tension force of the wire electrode
- (f)
- The speed of movement of the wire electrode along its axis.
2.2. Experimental Conditions
- a—the width of the slot in the lower part of the test sample, where the wire electrode enters the test sample
- b—the width of the slot in the upper area of the test sample, where the wire electrode comes out of the test sample
- m—the width of the slot corresponding approximately to the middle of the thickness H of the test sample.
- -
- test sample thickness H1 = 1 mm and H2 = 20 mm
- -
- pulse-on time Ton 1 = 2 µs and Ton 2 = 12 µs
- -
- pulse-off time Toff 1 = 7 µs and Toff 2 = 30 µs
- -
- average current intensity I1 = 3.1 A and I2 = 3.8 A
- -
- tension force F1 = 2.45 N and F2 = 10.54 N
- -
- wire movement speed along with its axis v1 = 500 mm/min and v2 = 2500 mm/min
- -
- average voltage U1 = 135 V and U2 = 160 V.
3. Results
4. Discussion
- -
- for which Gauss’s criterion has the value SG = 2354.82
- -
- for the slot width amed:
- -
- for the slot width mmed:
- -
- for the slot width bmed:
- -
- for which the Gauss’s criterion has the value SG = 2359.49
5. Conclusions
- The width of the slot generated by WEDM can be taken into account in the area of entry of the wire electrode into the test sample, in the area of exit of the wire electrode from the test sample, and respectively in the area corresponding to the middle of the thickness of the test sample.
- Distinct factors influence the slot width values in the three distinct areas mentioned. A factorial experiment was designed and materialized, with six independent variables at two levels of variation and one variable at four levels of variation; The seven independent variables considered were the thickness of the test sample, the pulse-on time, the pulse-off time, the average current, the wire electrode tension force, the wire traveling speed, and the average voltage.
- By mathematically processing the experimental results, empirical models of power type were established for the three widths of the slot. Empirical mathematical models highlight the variation of slot widths and the intensity of the influence exerted by the seven factors taken into account on the values of slot widths.
- The values of the exponents attached to the input factors in the WEDM process were examined, providing information on the intensity of the influence exerted by each of the input factors in the WEDM process on the width of the slot in the three areas.
- It was found that the strongest influence on the width of the slot is exerted by the average current, followed by the average voltage and the tension force of the wire. The other factors exert a low or negligible influence on the variation of the slot width generated by WEDM.
- In the future, there is the intention to perform experimental tests on test samples made of other materials, following the influence of the seven factors on other output parameters of the WEDM process, such as the roughness of the machined surface, the wear of the wire electrode, and the material removal rate.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Input Factors | Output Parameters | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Experiment No. | H, mm | Ton, μs | Toff, μs | I, A | F, N | v, mm/min | U, V | Measured Values for b, μm | bmed, μm | Measured Values for m, μm | mmed, μm | Measured Values for a, μm | amed, µm |
Column1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
1 | 1 | 2 | 7 | 3.1 | 2.45 | 500 | 135 | 281,282,287 | 283 | 281,282,287 | 283 | 281,282,287 | 283 |
2 | 1 | 2 | 7 | 3.8 | 10.54 | 2500 | 135 | 270,273,269 | 270 | 270,273,269 | 270 | 270,273,269 | 270 |
3 | 1 | 2 | 30 | 3.1 | 2.45 | 2500 | 135 | 265,261,271 | 265 | 265,261,271 | 265 | 265,261,271 | 265 |
4 | 1 | 2 | 30 | 3.8 | 10.54 | 500 | 135 | 287,281,283 | 283 | 287,281,283 | 283 | 287,281,283 | 283 |
5 | 1 | 12 | 7 | 3.8 | 2.45 | 2500 | 135 | 315,289,298 | 300 | 315,289,298 | 300 | 315,289,298 | 300 |
6 | 1 | 12 | 7 | 3.1 | 10.54 | 500 | 135 | 254,259,258 | 257 | 254,259,258 | 257 | 254,259,258 | 257 |
7 | 1 | 12 | 30 | 3.1 | 2.45 | 500 | 135 | 312,306,320 | 312 | 312,306,320 | 312 | 312,306,320 | 312 |
8 | 1 | 12 | 30 | 3.8 | 10.54 | 2500 | 135 | 268,273,269 | 270 | 268,273,269 | 270 | 268,273,269 | 270 |
9 | 20 | 2 | 7 | 3.1 | 2.45 | 2500 | 135 | 280,291,288 | 286 | 294,288,293 | 291 | 304,282,285 | 290 |
10 | 20 | 2 | 7 | 3.8 | 10.54 | 500 | 135 | 302,298,300 | 300 | 300,306,311 | 305 | 302,303,309 | 304 |
11 | 20 | 2 | 30 | 3.1 | 2.45 | 500 | 135 | 296,291,293 | 293 | 302,297,299 | 299 | 288,290,315 | 297 |
12 | 20 | 2 | 30 | 3.8 | 10.54 | 2500 | 135 | 250,255,252 | 252 | 259,254,261 | 258 | 254,249,267 | 256 |
13 | 20 | 12 | 7 | 3.8 | 2.45 | 500 | 135 | 381,395,375 | 383 | 393,387,389 | 389 | 388,380,396 | 388 |
14 | 20 | 12 | 7 | 3.1 | 10.54 | 2500 | 135 | 258,251,250 | 253 | 256,259,260 | 258 | 257,254,260 | 257 |
15 | 20 | 12 | 30 | 3.1 | 2.45 | 2500 | 135 | 356,351,351 | 352 | 353,359,363 | 358 | 357,356,358 | 357 |
16 | 20 | 12 | 30 | 3.8 | 10.54 | 500 | 135 | 230,234,242 | 235 | 245,238,239 | 240 | 236,248,235 | 239 |
17 | 20 | 2 | 7 | 3.1 | 2.45 | 500 | 160 | 300,301,307 | 302 | 310,315,314 | 313 | 311,304,312 | 309 |
18 | 20 | 2 | 7 | 3.8 | 10.54 | 2500 | 160 | 332,330,328 | 330 | 338,343,340 | 340 | 332,339,340 | 337 |
19 | 20 | 2 | 30 | 3.1 | 2.45 | 2500 | 160 | 301,306,305 | 304 | 315,311,316 | 314 | 305,315,310 | 310 |
20 | 20 | 2 | 30 | 3.8 | 10.54 | 500 | 160 | 278,272,272 | 274 | 282,284,286 | 284 | 284,273,286 | 281 |
21 | 20 | 12 | 7 | 3.8 | 2.45 | 2500 | 160 | 405,400,398 | 401 | 415,410,412 | 412 | 400,416,408 | 408 |
22 | 20 | 12 | 7 | 3.1 | 10.54 | 500 | 160 | 287,292,291 | 290 | 302,299,298 | 299 | 293,283,315 | 297 |
23 | 20 | 12 | 30 | 3.1 | 2.45 | 500 | 160 | 381,384,384 | 383 | 392,396,394 | 394 | 391,386,393 | 390 |
24 | 20 | 12 | 30 | 3.8 | 10.54 | 2500 | 160 | 269,267,267 | 267 | 279,278,276 | 277 | 271,278,273 | 274 |
25 | 40 | 2 | 7 | 3.1 | 2.45 | 2500 | 160 | 316,312,306 | 311 | 325,323,322 | 323 | 326,314,320 | 320 |
26 | 40 | 2 | 7 | 3.8 | 10.54 | 500 | 160 | 328,327,325 | 326 | 336,339,341 | 338 | 324,338,346 | 336 |
27 | 40 | 2 | 30 | 3.1 | 2.45 | 500 | 160 | 308,311,315 | 311 | 320,326,325 | 323 | 312,326,322 | 320 |
28 | 40 | 2 | 30 | 3.8 | 10.54 | 2500 | 160 | 239,242,242 | 241 | 256,252,252 | 253 | 249,253,248 | 250 |
29 | 40 | 12 | 7 | 3.8 | 2.45 | 500 | 160 | 431,428,427 | 428 | 441,442,443 | 442 | 427,440,447 | 438 |
30 | 40 | 12 | 7 | 3.1 | 10.54 | 2500 | 160 | 245,240,239 | 241 | 250,252,259 | 253 | 253,247,250 | 250 |
31 | 40 | 12 | 30 | 3.1 | 2.45 | 2500 | 160 | 411,409,407 | 409 | 423,422,418 | 421 | 423,414,417 | 418 |
32 | 40 | 12 | 30 | 3.8 | 10.54 | 500 | 160 | 236,232,231 | 233 | 246,243,244 | 244 | 239,247,240 | 242 |
33 | 40 | 2 | 7 | 3.1 | 2.45 | 500 | 190 | 310,308,306 | 308 | 329,326,325 | 326 | 326,316,318 | 320 |
34 | 40 | 2 | 7 | 3.8 | 10.54 | 2500 | 190 | 364,364,367 | 365 | 384,385,382 | 383 | 376,381,377 | 378 |
35 | 40 | 2 | 30 | 3.1 | 2.45 | 2500 | 190 | 339,340,337 | 338 | 356,354,360 | 356 | 356,342,352 | 350 |
36 | 40 | 2 | 30 | 3.8 | 10.54 | 500 | 190 | 335,339,337 | 337 | 352,355,357 | 354 | 359,342,349 | 350 |
37 | 40 | 12 | 7 | 3.8 | 2.45 | 2500 | 190 | 446,448,447 | 447 | 464,469,468 | 467 | 467,453,460 | 460 |
38 | 40 | 12 | 7 | 3.1 | 10.54 | 500 | 190 | 316,313,310 | 313 | 333,334,324 | 330 | 326,319,333 | 326 |
39 | 40 | 12 | 30 | 3.1 | 2.45 | 500 | 190 | 390,386,385 | 387 | 408,408,404 | 406 | 396,405,399 | 400 |
40 | 40 | 12 | 30 | 3.8 | 10.54 | 2500 | 190 | 263,266,267 | 265 | 281,283,285 | 283 | 274,268,289 | 277 |
41 | 60 | 2 | 7 | 3.1 | 2.45 | 2500 | 190 | 387,385,383 | 385 | 401,405,414 | 406 | 406,397,400 | 401 |
42 | 60 | 2 | 7 | 3.8 | 10.54 | 500 | 190 | 370,374,367 | 370 | 393,392,391 | 392 | 395,381,388 | 388 |
43 | 60 | 2 | 30 | 3.1 | 2.45 | 500 | 190 | 330,325,329 | 328 | 350,351,349 | 350 | 339,350,343 | 344 |
44 | 60 | 2 | 30 | 3.8 | 10.54 | 2500 | 190 | 234,230,226 | 230 | 256,252,249 | 252 | 249,240,252 | 247 |
45 | 60 | 12 | 7 | 3.8 | 2.45 | 500 | 190 | 474,471,470 | 471 | 492,496,497 | 495 | 487,492,488 | 489 |
46 | 60 | 12 | 7 | 3.1 | 10.54 | 2500 | 190 | 225,228,222 | 225 | 246,248,246 | 246 | 245,238,240 | 241 |
47 | 60 | 12 | 30 | 3.1 | 2.45 | 2500 | 190 | 460,464,466 | 463 | 486,485,483 | 484 | 485,476,479 | 480 |
48 | 60 | 12 | 30 | 3.8 | 10.54 | 500 | 190 | 233,229,226 | 229 | 251,248,250 | 249 | 249,240,249 | 246 |
49 | 60 | 2 | 7 | 3.1 | 2.45 | 500 | 215 | 320,325,318 | 321 | 349,352,349 | 350 | 343,338,339 | 340 |
50 | 60 | 2 | 7 | 3.8 | 10.54 | 2500 | 215 | 410,419,413 | 414 | 440,447,439 | 442 | 430,433,439 | 434 |
51 | 60 | 2 | 30 | 3.1 | 2.45 | 2500 | 215 | 370,373,373 | 372 | 406,399,395 | 400 | 394,387,389 | 390 |
52 | 60 | 2 | 30 | 3.8 | 10.54 | 500 | 215 | 380,373,381 | 378 | 400,397,417 | 404 | 396,399,399 | 398 |
53 | 60 | 12 | 7 | 3.8 | 2.45 | 2500 | 215 | 515,518,521 | 518 | 547,542,558 | 549 | 539,542,536 | 539 |
54 | 60 | 12 | 7 | 3.1 | 10.54 | 500 | 215 | 342,349,335 | 342 | 362,369,374 | 368 | 360,365,361 | 362 |
55 | 60 | 12 | 30 | 3.1 | 2.45 | 500 | 215 | 389,395,407 | 397 | 419,427,434 | 426 | 413,419,419 | 417 |
56 | 60 | 12 | 30 | 3.8 | 10.54 | 2500 | 215 | 263,269,254 | 262 | 293,288,286 | 289 | 284,277,279 | 280 |
57 | 80 | 2 | 7 | 3.1 | 2.45 | 2500 | 215 | 340,337,328 | 335 | 369,366,369 | 368 | 364,358,358 | 360 |
58 | 80 | 2 | 7 | 3.8 | 10.54 | 500 | 215 | 330,339,330 | 333 | 361,365,370 | 365 | 363,359,358 | 360 |
59 | 80 | 2 | 30 | 3.1 | 2.45 | 500 | 215 | 345,348,342 | 345 | 372,379,385 | 378 | 367,374,369 | 370 |
60 | 80 | 2 | 30 | 3.8 | 10.54 | 2500 | 215 | 226,220,226 | 224 | 259,258,255 | 257 | 252,248,250 | 250 |
61 | 80 | 12 | 7 | 3.8 | 2.45 | 500 | 215 | 508,516,509 | 511 | 543,547,550 | 546 | 536,541,537 | 538 |
62 | 80 | 12 | 7 | 3.1 | 10.54 | 2500 | 215 | 325,329,321 | 325 | 353,359,362 | 358 | 352,346,352 | 350 |
63 | 80 | 12 | 30 | 3.1 | 2.45 | 2500 | 215 | 510,518,520 | 516 | 546,549,551 | 548 | 544,539,543 | 542 |
64 | 80 | 12 | 30 | 3.8 | 10.54 | 500 | 215 | 228,221,223 | 224 | 251,257,256 | 254 | 253,247,250 | 250 |
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Dodun, O.; Slătineanu, L.; Nagîț, G.; Hrițuc, A.; Mihalache, A.M.; Beșliu-Băncescu, I. WEDM-Generated Slot Width Variation Modeling. Micromachines 2022, 13, 1231. https://doi.org/10.3390/mi13081231
Dodun O, Slătineanu L, Nagîț G, Hrițuc A, Mihalache AM, Beșliu-Băncescu I. WEDM-Generated Slot Width Variation Modeling. Micromachines. 2022; 13(8):1231. https://doi.org/10.3390/mi13081231
Chicago/Turabian StyleDodun, Oana, Laurențiu Slătineanu, Gheorghe Nagîț, Adelina Hrițuc, Andrei Marius Mihalache, and Irina Beșliu-Băncescu. 2022. "WEDM-Generated Slot Width Variation Modeling" Micromachines 13, no. 8: 1231. https://doi.org/10.3390/mi13081231