Numerical and Experimental Dynamic Analysis of IC Engine Test Beds Equipped with Highly Flexible Couplings

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2"><span style="width: 10.8371ptpx;"><svg height="9.25202pt" id="M115" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 10.8371 9.25202" width="10.8371pt" 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="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="502" vert-adv-y="502" xpluscharwidth="6.526"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.461,3.132)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z" id="g50-100"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="411" vert-adv-y="411" xpluscharwidth="10.20108767"></glyph.data></g></svg></span></td><td class="align_center" colspan="2">45 Sh</td><td class="align_center" colspan="2">70 Sh</td></tr><tr class="thead"><td class="align_center"><svg height="11.9316pt" id="M116" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 43.1652 11.9316" width="43.1652pt" 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="M600 0V24L339 665L311 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descent="-369" horiz-adv-x="484" vert-adv-y="484" xpluscharwidth="40.24638548"></glyph.data></g></svg>  <br/><svg height="12.4177pt" id="M117" style="vertical-align:-3.12937pt" version="1.1" viewbox="-0.0498162 -9.28833 31.4427 12.4177" width="31.4427pt" 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="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" xpluscharwidth="4.485"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g121-112"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371" xpluscharwidth="9.308"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.438,0)"><path d="M169 380V459C122 440 66 423 24 416V392C86 384 90 382 90 317V-135C90 -201 81 -207 17 -213V-240H253V-213C176 -207 169 -201 169 -125V6C182 -1 208 -11 238 -12C368 12 487 109 487 260C487 358 421 449 310 449C298 449 279 444 261 433L169 380ZM169 346C196 367 237 389 269 389C341 389 403 329 403 221C403 109 347 37 263 37C228 37 191 53 169 76V346Z" id="g121-110"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="524" vert-adv-y="524" xpluscharwidth="16.25"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,16.094,0)"><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" id="g121-107"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="819" vert-adv-y="819" xpluscharwidth="26.741"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.741,0)"><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" xpluscharwidth="31.226"></glyph.data></g></svg></td><td class="align_center">IR  <br/><svg height="11.439pt" id="M118" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 18.9681 11.439" width="18.9681pt" 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="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" xpluscharwidth="4.485"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><path d="M594 629L561 652L159 -9L190 -32L594 629ZM194 635C92 635 49 534 49 453C49 374 92 272 193 272C295 272 338 374 338 454S295 635 194 635ZM193 605C257 605 265 504 265 453C265 405 257 302 194 302C133 302 122 403 122 454S133 605 193 605ZM567 351C465 351 421 250 421 169C421 90 465 -12 566 -12S710 90 710 170S667 351 567 351ZM566 322C628 322 637 221 637 169C637 121 628 18 567 18S494 119 494 170C494 223 506 322 566 322Z" id="g121-35"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="756" vert-adv-y="756" xpluscharwidth="14.312999999999999"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.313,0)"><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" xpluscharwidth="18.798000000000002"></glyph.data></g></svg></td><td class="align_center"><svg height="11.9316pt" id="M119" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 40.9861 11.9316" width="40.9861pt" 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="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z" id="g113-133"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="641" vert-adv-y="641" xpluscharwidth="8.333"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.327,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 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523V129C130 45 122 38 38 33V0H306V33C225 38 216 45 216 129V282H249C302 282 319 270 336 243C365 195 401 132 436 84C483 18 525 -5 597 -8C610 -9 622 -9 635 -9L639 21ZM216 319V559C216 586 219 596 227 603S250 613 281 613C356 613 429 576 429 469C429 416 413 379 374 348C349 327 316 319 265 319H216Z" id="g58-80"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="632" vert-adv-y="632" xpluscharwidth="27.57018104"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,27.634,3.132)"><path d="M871 0V33C783 41 780 45 777 152L768 506C765 610 771 609 860 617V650H683L453 157L228 650H59V617C150 609 154 606 146 481L132 275C124 170 117 125 112 93C105 50 84 39 27 34V0H267V34C200 39 176 48 173 93C170 130 171 172 176 256L190 540H192L414 8H438L682 554H685L689 152C689 45 686 41 604 33V0H871Z" id="g58-75"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="902" vert-adv-y="902" xpluscharwidth="35.84217294"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,35.842,3.132)"><path d="M416 501L399 642C356 655 314 665 271 665C140 665 63 582 63 486C63 372 163 325 229 290C304 250 359 217 359 142C359 70 316 25 240 25C138 25 94 125 78 186L44 178C52 123 64 45 72 21C81 16 96 8 121 0S179 -15 220 -15C353 -15 445 68 445 176C445 289 350 335 270 375C191 414 143 449 143 520C143 572 177 627 253 627C340 627 366 556 382 495L416 501Z" id="g58-81"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="484" vert-adv-y="484" xpluscharwidth="40.24638548"></glyph.data></g></svg>  <br/><svg height="12.4177pt" id="M120" style="vertical-align:-3.12937pt" version="1.1" viewbox="-0.0498162 -9.28833 31.4427 12.4177" width="31.4427pt" 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="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" xpluscharwidth="4.485"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g121-112"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371" xpluscharwidth="9.308"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,9.438,0)"><path d="M169 380V459C122 440 66 423 24 416V392C86 384 90 382 90 317V-135C90 -201 81 -207 17 -213V-240H253V-213C176 -207 169 -201 169 -125V6C182 -1 208 -11 238 -12C368 12 487 109 487 260C487 358 421 449 310 449C298 449 279 444 261 433L169 380ZM169 346C196 367 237 389 269 389C341 389 403 329 403 221C403 109 347 37 263 37C228 37 191 53 169 76V346Z" id="g121-110"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="524" vert-adv-y="524" xpluscharwidth="16.25"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,16.094,0)"><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" id="g121-107"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="819" vert-adv-y="819" xpluscharwidth="26.741"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,26.741,0)"><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" xpluscharwidth="31.226"></glyph.data></g></svg></td><td class="align_center">IR  <br/><svg height="11.439pt" id="M121" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 18.9681 11.439" width="18.9681pt" 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="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" xpluscharwidth="4.485"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><path d="M594 629L561 652L159 -9L190 -32L594 629ZM194 635C92 635 49 534 49 453C49 374 92 272 193 272C295 272 338 374 338 454S295 635 194 635ZM193 605C257 605 265 504 265 453C265 405 257 302 194 302C133 302 122 403 122 454S133 605 193 605ZM567 351C465 351 421 250 421 169C421 90 465 -12 566 -12S710 90 710 170S667 351 567 351ZM566 322C628 322 637 221 637 169C637 121 628 18 567 18S494 119 494 170C494 223 506 322 566 322Z" id="g121-35"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="756" vert-adv-y="756" xpluscharwidth="14.312999999999999"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.313,0)"><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" xpluscharwidth="18.798000000000002"></glyph.data></g></svg></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">Regime A</td><td class="align_center">177</td><td class="align_center">7.8</td><td class="align_center">239</td><td class="align_center">10.6</td></tr><tr><td class="align_left">Regime B</td><td class="align_center">153</td><td class="align_center">6.0</td><td class="align_center">205</td><td class="align_center">7.8</td></tr><tr><td class="align_left">Regime C</td><td class="align_center">193</td><td class="align_center">7.0</td><td class="align_center">182</td><td class="align_center">6.2</td></tr><tr><td class="align_left">Regime D</td><td class="align_center">187</td><td class="align_center">6.4</td><td class="align_center">159</td><td class="align_center">4.8</td></tr><tr><td class="align_left">Regime E</td><td class="align_center">176</td><td class="align_center">5.0</td><td class="align_center">144</td><td class="align_center">4.0</td></tr><tr><td class="align_left">Regime F</td><td class="align_center">144</td><td class="align_center">3.6</td><td class="align_center">139</td><td class="align_center">3.2</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Crankshaft velocity oscillations RMS value, <svg height="11.927pt" id="M114" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 19.2013 11.927" width="19.2013pt" 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="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z" id="g113-133"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="641" vert-adv-y="641" xpluscharwidth="8.333"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,8.327,0)"><path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="502" vert-adv-y="502" xpluscharwidth="14.853"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.788,3.132)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z" id="g50-100"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="411" vert-adv-y="411" xpluscharwidth="18.52808767"></glyph.data></g></svg>, and Irregularity Ratio, IR, computed for the stationary tests performed with the two highly flexible couplings.

Shock and Vibration

tab3

Table 3

Table 3: Numerical and Experimental Dynamic Analysis of IC Engine Test Beds Equipped with Highly Flexible Couplings 