[{"data":1,"prerenderedAt":37},["ShallowReactive",2],{"topic-en-theoretical-mechanics\u002Fstatics\u002Ffriction\u002Frolling-resistance":3},{"topic":4,"trail":18,"children":32,"tasks":33,"alternates":34},{"id":5,"name":6,"locale":7,"path":8,"seo_title":9,"seo_description":10,"seo_text":11,"content_html":12,"content_chunks":13},196,"Rolling Resistance","en","theoretical-mechanics\u002Fstatics\u002Ffriction\u002Frolling-resistance","Rolling Resistance — Engineering Statics","Rolling resistance in engineering statics: physical origin, resistance moment and equilibrium conditions for wheels and cylindrical bodies.","This topic explains rolling resistance and how it differs from sliding friction. It introduces the resistance moment and its use in equilibrium problems involving wheels and cylindrical bodies.","\u003Cp>\u003Cstrong>Rolling resistance\u003C\u002Fstrong> occurs when a wheel, cylinder, or other rounded body rolls over a real surface. Unlike ideal point contact, the contact region deforms, so the resultant normal reaction may be offset from the geometric vertical through the body center and produce a moment opposing rolling.\u003C\u002Fp>\u003Ch2>Resistance-moment model\u003C\u002Fh2>\u003Cp>In a simple rolling-resistance model, the limiting resistance moment is proportional to the normal reaction:\u003C\u002Fp>\u003Cp>$$M_{rr}=N\\delta,$$\u003C\u002Fp>\u003Cp>where $\\delta$ is the coefficient of rolling resistance with dimensions of length. The model represents the offset of the resultant normal reaction caused by deformation in the contact region.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003Cp>The coefficient $\\delta$ in this model has units of length, such as metres or millimetres. This is fundamentally different from the dimensionless sliding-friction coefficient $\\mu$.\u003C\u002Fp>\u003Ch2>Physical meaning\u003C\u002Fh2>\u003Cp>For a perfectly rigid wheel on a perfectly rigid surface, idealized rolling resistance is absent. In a real contact, deformation of the wheel and supporting surface, material hysteresis, and other losses create resistance. A simple statics model replaces these effects by a resistance moment or an equivalent offset of the normal reaction.\u003C\u002Fp>\u003Ch2>Condition for the onset of rolling\u003C\u002Fh2>\u003Cp>If external forces create a driving moment about the wheel center, rolling begins when that moment exceeds the maximum available rolling-resistance moment in the adopted model. The no-slip condition must be checked separately when dry friction is also included in the problem.\u003C\u002Fp>\u003Ch2>Rolling versus sliding\u003C\u002Fh2>\u003Cp>Rolling resistance and sliding friction are different phenomena. Contact friction may be required for rolling without slipping, whereas rolling resistance describes losses that oppose the rolling motion itself. The coefficients $\\mu$ and $\\delta$ are therefore not interchangeable.\u003C\u002Fp>\u003Ch2>Example\u003C\u002Fh2>\u003Cp>For a wheel with normal reaction $N=2$ kN and rolling-resistance coefficient $\\delta=5$ mm, $M_{rr}=2000\\cdot0.005=10$ N·m. In the simplified model, the applied driving moment must overcome this resistance for rolling to begin.\u003C\u002Fp>\u003Ch2>Common mistakes\u003C\u002Fh2>\u003Cul>\u003Cli>treating $\\delta$ as dimensionless;\u003C\u002Fli>\u003Cli>confusing rolling resistance with the sliding-friction force $\\mu N$;\u003C\u002Fli>\u003Cli>failing to convert millimetres to metres when calculating a moment in N·m;\u003C\u002Fli>\u003Cli>ignoring the possibility of slipping while analyzing rolling;\u003C\u002Fli>\u003Cli>using the simple model $M_{rr}=N\\delta$ without checking which rolling-resistance model the problem specifies.\u003C\u002Fli>\u003C\u002Ful>",[14],{"id":15,"code":16,"type":17,"locale":7},167,"statics-rolling-resistance-moment","formula",[19,23,27,31],{"id":20,"name":21,"path":22},81,"Theoretical Mechanics","theoretical-mechanics",{"id":24,"name":25,"path":26},136,"Statics","theoretical-mechanics\u002Fstatics",{"id":28,"name":29,"path":30},277,"Friction","theoretical-mechanics\u002Fstatics\u002Ffriction",{"id":5,"name":6,"path":8},[],[],{"en":35,"uk":36},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Ftopics\u002Ftheoretical-mechanics\u002Fstatics\u002Ffriction\u002Frolling-resistance","https:\u002F\u002Fmechclassroom.com\u002Ftopics\u002Fteoretychna-mekhanika\u002Fstatyka\u002Ftertia\u002Ftertia-kochennia",1787712535861]