Hopf Bifurcation Characteristics of Dual-Front Axle Self-Excited Shimmy System for Heavy Truck considering Dry Friction

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/sv/volume-2015/839801/figures/839801.fig.0013a.svgz" name="839801.fig.0013a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Effect of the first transition rod stiffness <svg height="12.449pt" id="M407" style="vertical-align:-3.16067pt" version="1.1" viewbox="-0.0498162 -9.28833 14.7922 12.449" width="14.7922pt" 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="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z" id="g50-108"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="509" vert-adv-y="509"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.552,3.001)"><path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z" id="g50-117"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="347" vert-adv-y="347"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.71,3.001)"><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" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> on shimmy characteristics</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/sv/volume-2015/839801/figures/839801.fig.0013b.svgz" name="839801.fig.0013b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Effect of the second transition rod stiffness <svg height="12.449pt" id="M408" style="vertical-align:-3.16067pt" version="1.1" viewbox="-0.0498162 -9.28833 14.7922 12.449" width="14.7922pt" 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="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z" id="g50-108"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="509" vert-adv-y="509"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.552,3.001)"><path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z" id="g50-117"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="347" vert-adv-y="347"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.71,3.001)"><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" id="g50-51"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> on shimmy characteristics</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/sv/volume-2015/839801/figures/839801.fig.0013c.svgz" name="839801.fig.0013c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Effect of the pneumatic trail <svg height="6.20645pt" id="M409" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -6.00005 5.60619 6.20645" width="5.60619pt" 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="M398 365C398 411 356 451 297 451C250 451 198 430 151 397C65 336 24 230 24 139C24 14 97 -12 148 -12C198 -12 284 7 373 104L355 130C306 84 246 53 198 53C132 53 111 109 111 163V189C209 211 398 261 398 365ZM317 351C317 308 273 262 117 225C134 338 189 383 221 399C230 404 249 407 263 407C295 407 317 389 317 351Z" id="g50-102"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="422" vert-adv-y="422"></glyph.data></g></svg> on shimmy characteristics</td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/sv/volume-2015/839801/figures/839801.fig.0013d.svgz" name="839801.fig.0013d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Effect of caster angle on shimmy characteristics</td></tr></table>

<div>Influence of system parameters.</div>

Shock and Vibration

fig13

Figure 13

Figure 13: Hopf Bifurcation Characteristics of Dual-Front Axle Self-Excited Shimmy System for Heavy Truck considering Dry Friction 