Bending Vibration Analysis of Tensioned Ball Screw under Nonuniform Stress during the Cutting Process

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Order</td><td class="align_center" colspan="3">Frequency (Hz)</td></tr><tr class="thead"><td class="align_center">Nonstress</td><td class="align_center">Prestretching <svg height="11.786pt" id="M114" style="vertical-align:-0.3499002pt" version="1.1" viewbox="-0.0498162 -11.4361 92.0354 11.786" width="92.0354pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.185,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.886,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.422,0)"><path d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.239,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,46.502,0)"><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><g transform="matrix(.013,0,0,-0.013,52.742,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,55.706,0)"><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><g transform="matrix(.013,0,0,-0.013,61.946,0)"><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,-0.013,70.362,0)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z"></path></g><g transform="matrix(.013,0,0,-0.013,81.008,0)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z"></path></g></svg></td><td class="align_center">Difference</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">1</td><td class="align_center">94.16</td><td class="align_center">95.99</td><td class="align_center">1.83</td></tr><tr><td class="align_left">2</td><td class="align_center">259.55</td><td class="align_center">262.05</td><td class="align_center">2.5</td></tr><tr><td class="align_left">3</td><td class="align_center">508.83</td><td class="align_center">511.57</td><td class="align_center">2.74</td></tr><tr><td class="align_left">4</td><td class="align_center">841.12</td><td class="align_center">844</td><td class="align_center">2.88</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Natural frequencies of ball screw with predeformation.</div>

Shock and Vibration

tab3

Table 3

Table 3: Bending Vibration Analysis of Tensioned Ball Screw under Nonuniform Stress during the Cutting Process 