Three-Dimensional Free Vibration Analysis of Gears with Variable Thickness Using the Chebyshev–Ritz Method

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94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g></svg></span></td><td class="align_center"><span style="width: 9.02594ptpx;"><svg height="10.9562pt" id="M208" style="vertical-align:-3.18152pt" version="1.1" viewbox="-0.0498162 -7.77468 9.02594 10.9562" width="9.02594pt" 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="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,3.965,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg></span></td><td class="align_center"><span style="width: 9.02594ptpx;"><svg height="10.9562pt" id="M209" style="vertical-align:-3.18152pt" version="1.1" viewbox="-0.0498162 -7.77468 9.02594 10.9562" width="9.02594pt" 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="M298 36L289 62C276 55 253 45 228 45C202 45 169 60 169 141V397H276C289 405 292 426 282 437H169V574L155 576L90 509V437H45L17 408L21 397H90V107C90 28 125 -12 188 -12C198 -12 213 -8 230 1L298 36Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,3.965,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="8"><hr/></td></tr><tr><td class="align_left">Gear</td><td class="align_center">100</td><td class="align_center">2.25</td><td class="align_center">19</td><td class="align_center">28</td><td class="align_center">96</td><td class="align_center">20</td><td class="align_center">12</td></tr><tr class="table-tr"><td colspan="8"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab6

Table 6

Table 6: Three-Dimensional Free Vibration Analysis of Gears with Variable Thickness Using the Chebyshev–Ritz Method 