Optimization of AL6061-T6 Tube End Forming Process Using Response Surface Method

<div>Contour plots for (a) <svg height="14.8173pt" id="M204" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 13.6569 14.8173" width="13.6569pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"><path d="M620 667C620 684 593 710 552 710C515 710 459 687 409 634C360 582 334 506 320 433H247L215 400L220 388H310L259 80C224 -129 199 -161 185 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transform="matrix(.0091,0,0,-0.0091,6.786,3.132)"><path d="M636 22C611 29 589 38 560 74C536 104 518 134 495 173L430 300C518 328 592 392 592 492C592 555 563 594 528 618C491 643 435 650 377 650H140L131 618C222 610 223 601 208 518L137 136C121 43 116 40 27 32L18 0H295L300 32C212 40 206 42 223 138L248 279H296C334 279 350 272 369 230C393 174 413 140 441 94C482 24 523 1 626 -8L636 22ZM497 480C497 422 468 374 417 343C387 324 353 315 304 315H255L298 556C303 583 309 598 319 603C331 610 348 613 367 613C448 613 497 573 497 480Z"></path></g></svg> against roller inclination angle and contact depth, while holding the other input variable [<svg height="11.6399pt" id="M206" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -8.34882 40.3202 11.6399" width="40.3202pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 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transform="matrix(.013,0,0,-0.013,16.384,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,27.647,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.887,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g></svg> mm, <svg height="12.5794pt" id="M207" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 45.3883 12.5794" width="45.3883pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"><path d="M397 380C406 395 404 411 396 425S369 451 350 451C302 451 239 372 192 294H189L199 338C214 407 207 451 180 451C152 451 83 405 30 345L48 318C87 354 117 372 125 372S135 362 127 324L55 -5L61 -12C87 -5 117 3 139 5C154 87 168 162 179 207C198 250 240 310 260 332C281 355 297 366 307 366C321 366 333 360 347 346C351 342 360 342 369 348C379 355 389 366 397 380Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.18,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.443,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.683,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.923,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g></svg> mm, and <svg height="8.8423pt" id="M208" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 44.761 8.8423" width="44.761pt" 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Modelling and Simulation in Engineering

fig18

Figure 18

Figure 18: Optimization of AL6061-T6 Tube End Forming Process Using Response Surface Method 