Feature Extraction of Faulty Rolling Element Bearing under Variable Rotational Speed and Gear Interferences Conditions

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Parameters</td><td align="center">Value</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">Length of the signal</td><td align="center">8 s</td></tr><tr><td align="left">Length of <svg height="12.7178pt" id="M97" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 21.9563 12.7178" width="21.9563pt" 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="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.352,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.85,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,17.283,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg></td><td align="center">5 Hz–25 Hz</td></tr><tr><td align="left">Length of <svg height="14.8173pt" id="M98" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 26.1028 14.8173" width="26.1028pt" 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="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.721,3.132)"><path d="M554 433L549 437C539 437 513 441 503 443C481 447 456 451 436 451C354 451 268 415 216 368C150 308 99 205 99 106C99 24 136 -12 165 -12C196 -12 243 14 268 33C318 70 374 118 415 181H419L395 39C374 -84 332 -149 295 -175C269 -193 245 -197 212 -197C137 -197 93 -156 76 -102C71 -87 61 -87 51 -96C36 -110 24 -130 24 -147C24 -183 76 -257 171 -257C226 -257 285 -227 323 -200C387 -155 455 -76 480 94C499 225 538 391 554 433ZM460 386C457 361 438 287 426 254C408 218 373 176 332 133C294 93 246 61 217 61C198 61 186 80 186 122C186 167 206 250 231 294C262 349 288 375 317 387C334 394 358 400 381 400C413 400 439 393 460 386Z" id="g50-104"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="578" vert-adv-y="578"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.499,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,16.997,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,21.43,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg></td><td align="center">6 Hz–30 Hz</td></tr><tr><td align="left">Sampling rate <svg height="12.7178pt" id="M99" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 10.824 12.7178" width="10.824pt" 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="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.721,3.132)"><path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z" id="g50-116"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="381" vert-adv-y="381"></glyph.data></g></svg></td><td align="center">20000 Hz</td></tr><tr><td align="left">Fault characteristic coefficient</td><td align="center">3</td></tr><tr><td align="left">Bearing resonance frequency  <svg height="9.25202pt" id="M100" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 13.4625 9.25202" width="13.4625pt" 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="M689 332C689 394 670 448 646 448C620 448 597 421 597 396C597 386 600 381 608 372C619 359 620 334 620 315C620 150 538 45 454 45C414 45 386 67 386 122C386 138 388 158 394 180L457 426L452 432L377 416L315 156C302 100 259 45 216 45C176 45 148 67 148 122C148 133 152 158 156 180C162 212 173 259 194 332C201 357 206 384 206 405C206 430 198 448 174 448C125 448 66 406 23 342L43 319C84 368 110 383 121 383C126 383 128 382 128 377C128 370 127 359 122 343C99 268 84 204 77 156C74 137 70 111 70 104C70 25 125 -12 180 -12C228 -12 276 12 319 50C338 8 378 -12 418 -12C549 -12 689 166 689 332Z" id="g113-120"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="712" vert-adv-y="712"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.931,3.132)"><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" id="g50-115"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="427" vert-adv-y="427"></glyph.data></g></svg></td><td align="center">5000 Hz</td></tr><tr><td align="left">Number of teeth <i>L </i></td><td align="center">18</td></tr><tr><td align="left">Rotating frequency ratio <svg height="6.1673pt" id="M101" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.40217 6.1673" width="6.40217pt" 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="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z" id="g113-241"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="483" vert-adv-y="483"></glyph.data></g></svg></td><td align="center">1.2</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Parameters of mixed bearing and gear simulation model under time-varying rotational speed.

Shock and Vibration

tab1

Table 1

Table 1: Feature Extraction of Faulty Rolling Element Bearing under Variable Rotational Speed and Gear Interferences Conditions 