A New Approach for Reliability Life Prediction of Rail Vehicle Axle by Considering Vibration Measurement

<table class="table-group" id="tab9"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left" rowspan="2">Life</td><td align="center" colspan="2">Real life values (Table <a href="../tab1/">1</a>)</td></tr><tr class="thead"><td align="center"><svg height="12.4067pt" id="M100" style="vertical-align:-3.408751pt" version="1.1" viewbox="-0.0498162 -8.99795 27.8011 12.4067" width="27.8011pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 558C744 603 756 619 816 622L822 650Z" id="g113-79"></path><glyph.data ascent="3473" descent="-2876" 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412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z" id="g190-102"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="425" vert-adv-y="425"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,20.492,3.264)"><path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z" id="g190-98"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="439" vert-adv-y="439"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,24.703,3.264)"><path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g190-109"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="253" vert-adv-y="253"></glyph.data></g></svg>  <svg height="11.9171pt" id="M101" style="vertical-align:-2.2392pt" version="1.1" viewbox="-0.0498162 -9.6779 4.79128 11.9171" width="4.79128pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z" id="g113-92"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="345" vert-adv-y="345"></glyph.data></g></svg>load cycle<svg height="11.9171pt" id="M102" style="vertical-align:-2.2392pt" version="1.1" viewbox="-0.0498162 -9.6779 4.79128 11.9171" width="4.79128pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M226 -163V703H56V676C162 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transform="matrix(.0095,0,0,-0.0095,10.486,3.264)"><path d="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z" id="g190-83"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="621" vert-adv-y="621"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,16.404,3.264)"><path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z" id="g190-102"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="425" vert-adv-y="425"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,20.492,3.264)"><path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z" id="g190-98"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="439" vert-adv-y="439"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,24.703,3.264)"><path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g190-109"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="253" vert-adv-y="253"></glyph.data></g></svg>  <svg height="11.9171pt" id="M104" style="vertical-align:-2.2392pt" version="1.1" viewbox="-0.0498162 -9.6779 4.79128 11.9171" width="4.79128pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z" id="g113-92"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="345" vert-adv-y="345"></glyph.data></g></svg>km<svg height="11.9171pt" id="M105" style="vertical-align:-2.2392pt" version="1.1" viewbox="-0.0498162 -9.6779 4.79128 11.9171" width="4.79128pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z" id="g113-94"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="345" vert-adv-y="345"></glyph.data></g></svg></td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left">90% reliability</td><td align="center"> </td><td align="center"> </td></tr><tr><td align="left"> TR</td><td align="center">10<sup>8.2699</sup></td><td align="center">350914</td></tr><tr><td align="left"> TR-LRT</td><td align="center">10<sup>8.6497</sup></td><td align="center">841397</td></tr><tr><td align="left">10% reliability</td><td align="center"> </td><td align="center"> </td></tr><tr><td align="left"> TR</td><td align="center">10<sup>8.5671</sup></td><td align="center">695666</td></tr><tr><td align="left"> TR-LRT</td><td align="center">10<sup>8.8959</sup></td><td align="center">1483204</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab9

Table 9

Table 9: A New Approach for Reliability Life Prediction of Rail Vehicle Axle by Considering Vibration Measurement 