A Model of the Transient Behavior of Tractive Rolling Contacts

A Model for the Transient Behavior of Tractive Rolling Contacts

<div class="xml-content"><hr><p>(1) In [<a href="#B1">1</a>, equation (35), page 6],
<span class="equation" id="eq1"><svg height="28.9625" id="M1" preserveAspectRatio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewBox="0 0 700.9375 28.9625" width="700.9375" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(1.25,0,0,-1.25,0,28.9625)"><g transform="translate(72,-48.83)"><text transform="matrix(1,0,0,-1,162.02,52.37)"><tspan style="font-size: 12.50px; " x="0" y="0"></tspan><tspan style="font-size: 12.50px; " x="7.3699999" y="-4.9200001">𝑝</tspan></text><text transform="matrix(1,0,0,-1,175.5,54.16)"><tspan style="font-size: 8.75px; " x="0" y="0">𝑥</tspan></text><text transform="matrix(1,0,0,-1,180.81,57.29)"><tspan style="font-size: 12.50px; " x="0" y="0">,</tspan><tspan style="font-size: 12.50px; " x="5.2012482" y="0">𝑝</tspan></text><text transform="matrix(1,0,0,-1,192.14,54.16)"><tspan style="font-size: 8.75px; " x="0" y="0">𝑦</tspan></text><text transform="matrix(1,0,0,-1,196.97,52.37)"><tspan style="font-size: 12.50px; " x="0" y="0"></tspan><tspan style="font-size: 12.50px; " x="11.08" y="-4.9200001">=</tspan><tspan style="font-size: 12.50px; " x="23.107885" y="-4.9200001">𝐿</tspan><tspan style="font-size: 12.50px; " x="31.960011" y="-4.9200001">(</tspan><tspan style="font-size: 12.50px; " x="36.123508" y="-4.9200001">𝑢</tspan><tspan style="font-size: 12.50px; " x="42.049931" y="-4.9200001">,</tspan><tspan style="font-size: 12.50px; " x="47.263683" y="-4.9200001">𝑣</tspan><tspan style="font-size: 12.50px; " x="53.590199" y="-4.9200001">)</tspan><tspan style="font-size: 12.50px; " x="277.14999" y="-4.9200001">(</tspan><tspan style="font-size: 12.50px; " x="281.31351" y="-4.9200001">1</tspan><tspan style="font-size: 12.50px; " x="287.565" y="-4.9200001">)</tspan></text></g></g></svg></span> should be replaced by
<span class="equation" id="eq2"><svg height="30.700001" id="M2" preserveAspectRatio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewBox="0 0 700.9375 30.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(1.25,0,0,-1.25,0,30.7)"><g transform="translate(72,-47.44)"><text transform="matrix(1,0,0,-1,159.26,51.33)"><tspan style="font-size: 12.50px; " x="0" y="0"></tspan><tspan style="font-size: 12.50px; " x="7.3699999" y="-4.9200001">𝑝</tspan></text><text transform="matrix(1,0,0,-1,172.74,53.12)"><tspan style="font-size: 8.75px; " x="0" y="0">𝑥</tspan></text><text transform="matrix(1,0,0,-1,178.05,56.25)"><tspan style="font-size: 12.50px; " x="0" y="0">,</tspan><tspan style="font-size: 12.50px; " x="5.2012482" y="0">𝑝</tspan></text><text transform="matrix(1,0,0,-1,189.38,53.12)"><tspan style="font-size: 8.75px; " x="0" y="0">𝑦</tspan></text><text transform="matrix(1,0,0,-1,194.22,51.33)"><tspan style="font-size: 12.50px; " x="0" y="0"></tspan><tspan style="font-size: 12.50px; " x="11.07" y="-4.9200001">=</tspan><tspan style="font-size: 12.50px; " x="25.6" y="-12.17">1</tspan></text><g><path d="m 218.52,59.37 8.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path></g><text transform="matrix(1,0,0,-1,218.52,47.49)"><tspan style="font-size: 12.50px; " x="0" y="0">𝐿</tspan><tspan style="font-size: 12.50px; " x="10.05" y="-8.7600002">(</tspan><tspan style="font-size: 12.50px; " x="14.213499" y="-8.7600002">𝑢</tspan><tspan style="font-size: 12.50px; " x="20.139921" y="-8.7600002">,</tspan><tspan style="font-size: 12.50px; " x="25.341169" y="-8.7600002">𝑣</tspan><tspan style="font-size: 12.50px; " x="31.667686" y="-8.7600002">)</tspan><tspan style="font-size: 12.50px; " x="35.831184" y="-8.7600002">.</tspan><tspan style="font-size: 12.50px; " x="255.60001" y="-8.7600002">(</tspan><tspan style="font-size: 12.50px; " x="259.76349" y="-8.7600002">2</tspan><tspan style="font-size: 12.50px; " x="266.01498" y="-8.7600002">)</tspan></text></g></g></svg></span> (2) In [<a href="#B1">1</a>, equation (36), page 7],
<span class="equation" id="eq3"><svg height="45.325001" id="M3" preserveAspectRatio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewBox="0 0 700.9375 45.325001" width="700.9375" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(1.25,0,0,-1.25,0,45.325)"><g transform="translate(72,-35.74)"><text transform="matrix(1,0,0,-1,135.82,55.27)"><tspan style="font-size: 12.50px; " x="0" y="0">(</tspan><tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝑢</tspan><tspan style="font-size: 12.50px; " x="10.089921" y="0">,</tspan><tspan style="font-size: 12.50px; " x="15.291169" y="0">𝑣</tspan><tspan style="font-size: 12.50px; " x="21.617687" y="0">)</tspan></text><text transform="matrix(1,0,0,-1,161.61,52.15)"><tspan style="font-size: 8.75px; " x="0" y="0">n</tspan><tspan style="font-size: 8.75px; " x="4.3759999" y="0">e</tspan><tspan style="font-size: 8.75px; " x="8.104352" y="0">w</tspan></text><text transform="matrix(1,0,0,-1,180,55.27)"><tspan style="font-size: 12.50px; " x="0" y="0">=</tspan><tspan style="font-size: 12.50px; " x="13.23" y="-9.2600002">𝜇</tspan><tspan style="font-size: 12.50px; " x="20.844328" y="-9.2600002">𝑝</tspan></text><text transform="matrix(1,0,0,-1,206.96,61.41)"><tspan style="font-size: 8.75px; " x="0" y="0">𝑧</tspan></text><g><path d="m 193.23,58.4 18.6,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path></g><text transform="matrix(1,0,0,-1,198.1,46.52)"><tspan style="font-size: 12.50px; " x="0" y="0">𝐿</tspan><tspan style="font-size: 12.50px; " x="14.92" y="-3.8299999"></tspan><tspan style="font-size: 12.50px; " x="30.02" y="-16.98">(</tspan><tspan style="font-size: 12.50px; " x="34.183498" y="-16.98">𝑢</tspan><tspan style="font-size: 12.50px; " x="40.109921" y="-16.98">,</tspan><tspan style="font-size: 12.50px; " x="45.311169" y="-16.98">𝑣</tspan><tspan style="font-size: 12.50px; " x="51.637688" y="-16.98">)</tspan></text><g><path d="m 221.58,58.4 38.87,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path></g><text transform="matrix(1,0,0,-1,221.58,45.93)"><tspan style="font-size: 12.50px; " x="0" y="0">‖</tspan><tspan style="font-size: 12.50px; " x="0" y="6.3000002">‖</tspan><tspan style="font-size: 12.50px; " x="32.330002" y="0">‖</tspan><tspan style="font-size: 12.50px; " x="32.330002" y="6.3000002">‖</tspan><tspan style="font-size: 12.50px; " x="40.060001" y="-4.4200001"></tspan><tspan style="font-size: 12.50px; " x="6.54" y="3.1500001">(</tspan><tspan style="font-size: 12.50px; " x="10.703499" y="3.1500001">𝑢</tspan><tspan style="font-size: 12.50px; " x="16.629921" y="3.1500001">,</tspan><tspan style="font-size: 12.50px; " x="21.831169" y="3.1500001">𝑣</tspan><tspan style="font-size: 12.50px; " x="28.157686" y="3.1500001">)</tspan></text><text transform="matrix(1,0,0,-1,269.25,35.87)"><tspan style="font-size: 8.75px; " x="0" y="0">o</tspan><tspan style="font-size: 8.75px; " x="4.3759999" y="0">l</tspan><tspan style="font-size: 8.75px; " x="6.8090558" y="0">d</tspan></text><text transform="matrix(1,0,0,-1,474.12,55.27)"><tspan style="font-size: 12.50px; " x="0" y="0">(</tspan><tspan style="font-size: 12.50px; " x="4.1634989" y="0">3</tspan><tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan></text></g></g></svg></span> should be replaced by
<span class="equation" id="eq4"><svg height="45.325001" id="M4" preserveAspectRatio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewBox="0 0 700.9375 45.325001" width="700.9375" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(1.25,0,0,-1.25,0,45.325)"><g transform="translate(72,-35.74)"><text transform="matrix(1,0,0,-1,131.03,55.27)"><tspan style="font-size: 12.50px; " x="0" y="0">(</tspan><tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝑢</tspan><tspan style="font-size: 12.50px; " x="10.089921" y="0">,</tspan><tspan style="font-size: 12.50px; " x="15.291169" y="0">𝑣</tspan><tspan style="font-size: 12.50px; " x="21.617687" y="0">)</tspan></text><text transform="matrix(1,0,0,-1,156.82,52.15)"><tspan style="font-size: 8.75px; " x="0" y="0">n</tspan><tspan style="font-size: 8.75px; " x="4.3759999" y="0">e</tspan><tspan style="font-size: 8.75px; " x="8.0956001" y="0">w</tspan></text><text transform="matrix(1,0,0,-1,175.2,55.27)"><tspan style="font-size: 12.50px; " x="0" y="0">=</tspan><tspan style="font-size: 12.50px; " x="12.040389" y="0">𝜇</tspan><tspan style="font-size: 12.50px; " x="19.654716" y="0">𝑝</tspan></text><text transform="matrix(1,0,0,-1,200.97,52.15)"><tspan style="font-size: 8.75px; " x="0" y="0">𝑧</tspan></text><text transform="matrix(1,0,0,-1,205.84,55.27)"><tspan style="font-size: 12.50px; " x="0" y="0">𝐿</tspan><tspan style="font-size: 12.50px; " x="8.8500004" y="4.9200001"></tspan><tspan style="font-size: 12.50px; " x="23.950001" y="-8.2299995">(</tspan><tspan style="font-size: 12.50px; " x="28.113499" y="-8.2299995">𝑢</tspan><tspan style="font-size: 12.50px; " x="34.039921" y="-8.2299995">,</tspan><tspan style="font-size: 12.50px; " x="39.241169" y="-8.2299995">𝑣</tspan><tspan style="font-size: 12.50px; " x="45.567688" y="-8.2299995">)</tspan></text><g><path d="m 223.25,58.4 38.87,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path></g><text transform="matrix(1,0,0,-1,223.25,45.93)"><tspan style="font-size: 12.50px; " x="0" y="0">‖</tspan><tspan style="font-size: 12.50px; " x="0" y="6.3000002">‖</tspan><tspan style="font-size: 12.50px; " x="32.330002" y="0">‖</tspan><tspan style="font-size: 12.50px; " x="32.330002" y="6.3000002">‖</tspan><tspan style="font-size: 12.50px; " x="40.060001" y="-4.4200001"></tspan><tspan style="font-size: 12.50px; " x="6.54" y="3.1500001">(</tspan><tspan style="font-size: 12.50px; " x="10.703499" y="3.1500001">𝑢</tspan><tspan style="font-size: 12.50px; " x="16.629921" y="3.1500001">,</tspan><tspan style="font-size: 12.50px; " x="21.831169" y="3.1500001">𝑣</tspan><tspan style="font-size: 12.50px; " x="28.157686" y="3.1500001">)</tspan></text><text transform="matrix(1,0,0,-1,270.91,35.87)"><tspan style="font-size: 8.75px; " x="0" y="0">o</tspan><tspan style="font-size: 8.75px; " x="4.3759999" y="0">l</tspan><tspan style="font-size: 8.75px; " x="6.8090558" y="0">d</tspan></text><text transform="matrix(1,0,0,-1,282.6,55.27)"><tspan style="font-size: 12.50px; " x="0" y="0">.</tspan><tspan style="font-size: 12.50px; " x="191.52" y="0">(</tspan><tspan style="font-size: 12.50px; " x="195.6835" y="0">4</tspan><tspan style="font-size: 12.50px; " x="201.935" y="0">)</tspan></text></g></g></svg></span></p></div>

Advances in Tribology

Farid Al-Bender and Kris De Moerlooze, “A model of the transient behavior of tractive rolling contacts,” <i>Advances in Tribology</i>, vol. 2008, Article ID 214894, 17 pages, 2008.

Advances in Tribology

A Model for the Transient Behavior of Tractive Rolling Contacts

References

Copyright