Name: tire deformation and rolling resistance
Uploaded: 2023-09-22T11:49:30.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS.P3

HS.P3U2.7

Rolling Resistance

Considérons un pneu qui roule à une vitesse constante. Les forces qui agissent sur lui sont son poids et la force normale.
Les surfaces de contact se déforment, créant une zone de contact finie. Il en résulte une répartition des forces normales à chaque point de contact.
La section avant de cette zone subit une déformation, ce qui retarde le mouvement de roulement.
En revanche, la section arrière subit une restauration relativement plus petite qui pousse le pneu vers l’avant.
La force normale résultante agissant en A est la somme de ces forces.
Pour maintenir le pneu roulant à une vitesse constante et équilibrer le moment du poids autour de A, une force motrice horizontale doit être appliquée au centre du pneu. Ici, toutes les forces doivent être concurrentes.
La condition d’équilibre de moment au point A donne la force motrice en termes de coefficient de résistance au roulement.
Le poids multiplié par le coefficient de résistance au roulement sur le rayon est généralement inférieur au coefficient de frottement cinétique multiplié par le poids.
Ainsi, la force de frottement de roulement est inférieure à la force de glissement.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. pp 452 à 439.</li>
	<li>Meriam, J.L. ; Kraige, L.G. et Bolton, J.N. (2020). Génie mécanique \u2012 Statique. Hoboken, New Jersey : John Wiley. p. 372.</li>
	<li>Bière, F.P. ; Johnston, E.R. ; Mazurek, D.F ; Cromwell, P.J. et Self, B.P. (2019). Mécanique vectorielle pour les ingénieurs \u2012 Statique et dynamique. New York : McGraw-Hill. p. 469.</li>
</ol>

résistance au roulement

Lorsqu'un cylindre solide roule de manière régulière sur une surface rigide, la force normale appliquée par la surface sur le cylindre est perpendiculaire à la tangente au point de contact. Cependant, étant donné que aucun matériau n'est totalement rigide, la réaction de la surface au cylindre implique une gamme de pressions normales. Par exemple, imaginez un cylindre dur roulant sur une surface relativement souple. Le poids du cylindre comprime la surface en dessous. Lorsque le cylindre avance, le matériau devant lui ralentit en raison de la déformation, tandis que le matériau derrière lui retrouve son état initial déformé, poussant le cylindre vers l'avant. Les pressions normales agissant sur le cylindre de cette manière sont représentées par leurs forces résultantes, Nd et Nr. La force de déformation (Nd) et sa composante horizontale sont consubstantiellement supérieures à la force de restauration (Nr), ce qui nécessite l'application d'une force horizontale pour maintenir le mouvement du cylindre. La résistance au roulement se produit principalement en raison de cet effet, bien qu'elle soit également influencée, dans une moindre mesure, par l'adhérence de la surface et le micro-glissement relatif entre les surfaces de contact. Pour expliquer davantage ce concept, considérez un pneu roulant à vitesse constante. Les principales forces qui agissent sur lui sont son poids, agissant verticalement vers le bas, et la force normale exercée par le sol, agissant verticalement vers le haut. Lorsque le pneu roule, la section avant de la zone de contact subit une déformation, ce qui retarde le mouvement de roulement du pneu. En revanche, la section arrière subit une restitution relativement plus petite qui pousse le pneu vers l'avant. L'effet net est que la force normale résultante agissant au point A (le centre de la zone de contact) est la somme de ces forces opposées. <img alt="Figure 1" src="/files/ftp_upload/14328/14328_Figure_1v2.svg" style="text-align: center; height: 350px;"> Pour maintenir le pneu en mouvement à vitesse constante et équilibrer le moment du poids autour du point A, une force horizontale (F) doit être appliquée au centre du pneu. Pour l'équilibre, toutes les forces agissant sur le pneu doivent être concourantes. En utilisant la condition d'équilibre des moments au point A, nous pouvons déterminer la force d'entraînement nécessaire pour maintenir une vitesse constante en fonction du coefficient de résistance au roulement (a). <img alt="Equation 1" src="/files/ftp_upload/14328/14328_Equation_1v2.svg" style="text-align: center; height: 28px;"> Cette force d'entraînement est généralement inférieure au produit du coefficient de frottement cinétique et du poids du pneu. <img alt="Equation 2" src="/files/ftp_upload/14328/14328_Equation_2v2.svg" style="text-align: center; height: 28px;"> Cette relation implique que la force de frottement de roulement est généralement inférieure à la force de glissement éprouvée lorsqu'un pneu dérape sur une surface. Par conséquent, la résistance au roulement est généralement moins préjudiciable aux performances d'un véhicule que le frottement de glissement.

Résistance au roulement

Lorsqu’un cylindre solide roule régulièrement sur une surface rigide, la force normale appliquée par la surface sur le cylindre est perpendiculaire à la tangente au ...

Education

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Mechanical Engineering

Génie mécanique

Unit 1

Unité 1

Friction

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tire deformation and rolling resistance

Tire deformation and rolling resistance explain why a rolling wheel still needs a driving force. When a solid cylinder or tire rolls on a rigid surface, the normal force is perpendicular to the surface at the contact point. But real materials are not perfectly rigid, so the surface pushes back with a spread of normal pressures instead of one single force.

A hard cylinder on a softer surface compresses the material under it. As the cylinder moves forward, the material in front of the contact area slows because it is being deformed. The material behind the cylinder begins to recover, and that recovery pushes the cylinder forward.

These effects are often shown as two resultants, N d for the deformation force and N r for the restoration force. The deformation force and its horizontal component are larger than the restoration force. Because of that imbalance, a horizontal driving force must be applied to keep the cylinder moving.

The same idea applies to a tire rolling at constant speed. Its weight acts downward, and the ground provides an upward normal force. The front of the contact patch deforms and slows the tire, while the rear part restores more weakly and pushes it forward. The resultant normal force at point A is the sum of these opposing effects.

To keep the tire in equilibrium and maintain constant speed, a horizontal driving force F must act at the center of the tire. Using moment equilibrium about point A, the needed driving force can be written in terms of the rolling resistance coefficient a. This force is usually smaller than the force from kinetic friction, so rolling resistance is less harmful than sliding when a tire skids.

Rolling resistance is mainly caused by surface deformation, but adhesion and small-scale sliding between surfaces can also play a smaller role. These effects help explain why rolling wheels still lose some energy even when they do not appear to slip.

Tire Deformation and Rolling Resistance

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Tire deformation and rolling resistance explain why a rolling wheel still needs a driving force. When a solid cylinder or tire rolls on a rigid surface, the normal force is perpendicular to the surface at the contact point. But real materials are not perfectly rigid, so the surface pushes back with a spread of normal pressures instead of one single force. A hard cylinder on a softer surface compresses the material under it. As the cylinder moves forward, the material in front of the contact...

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key terms and concepts

Learn how tire deformation creates rolling resistance, why a driving force is needed, and how it compares with sliding friction in moving wheels.

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Tire Deformation and Rolling Resistance

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