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

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HS.P3U2.7

Rolling Resistance

Stellen Sie sich einen Reifen vor, der mit konstanter Geschwindigkeit rollt. Die Kräfte, die auf ihn wirken, sind sein Gewicht und die Normalkraft.
Die Kontaktflächen verformen sich, wodurch eine endliche Kontaktfläche entsteht. Daraus ergibt sich eine Verteilung der Normalkräfte an jedem Kontaktpunkt.
Der vordere Teil dieses Bereichs verformt sich, was die Abrollbewegung verlangsamt.
Im Gegensatz dazu erfährt die hintere Partie eine relativ kleinere Restauration, die den Reifen nach vorne schiebt.
Die resultierende Normalkraft, die bei A wirkt, ist die Summe dieser Kräfte.
Um den Reifen mit einer konstanten Geschwindigkeit rollen zu lassen und das Moment des Gewichts um A auszugleichen, muss eine horizontale Antriebskraft auf die Mitte des Reifens ausgeübt werden. Hier müssen alle Kräfte gleichzeitig sein.
Die Momentengleichgewichtsbedingung an Punkt A gibt die treibende Kraft in Bezug auf den Rollwiderstandskoeffizienten an.
Das Gewicht multipliziert mit dem Koeffizienten des Rollwiderstands auf dem Radius ist in der Regel kleiner als der Koeffizient der kinetischen Reibung multipliziert mit dem Gewicht.
Die Rollreibungskraft ist also kleiner als die Gleitkraft.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. S. 452 \u2012 439.</li>
	<li>Meriam, J.L.; Kraige, L.G. und Bolton, J.N. (2020). Technische Mechanik \u2012 Statik. Hoboken, New Jersey: John Wiley. Seite 372.</li>
	<li>Bier, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. und Self, B.P. (2019). Vektormechanik für Ingenieure \u2012 Statik und Dynamik. New York: McGraw-Hill. S. 469.</li>
</ol>

rollwiderstand

Wenn ein fester Zylinder gleichmäßig auf einer starren Oberfläche rollt, ist die Normalkraft, die von der Oberfläche auf den Zylinder ausgeübt wird, senkrecht zum Tangentenpunkt. Da jedoch keine Materialien vollständig starr sind, beinhaltet die Reaktion der Oberfläche auf den Zylinder eine Reihe von Normalkräften.
Stellen Sie sich zum Beispiel vor, ein harter Zylinder rollt auf einer vergleichsweise weichen Oberfläche. Das Gewicht des Zylinders komprimiert die Oberfläche darunter. Wenn sich der Zylinder bewegt, verlangsamt sich das Material vor ihm aufgrund von Verformungen, während sich das Material hinter ihm von seinem verformten Zustand erholt und den Zylinder nach vorne schiebt. Die auf den Zylinder wirkenden Normalkräfte werden durch ihre resultierenden Kräfte, N_d und N_r, dargestellt. Die Verformungskraft (N_d) und ihre horizontale Komponente sind konsequent größer als die Wiederherstellungskraft (N_r), wodurch eine horizontale Antriebskraft auf den Zylinder ausgeübt werden muss, um seine Bewegung aufrechtzuerhalten.
Rollwiderstand tritt hauptsächlich aufgrund dieses Effekts auf, obwohl er auch in geringerem Maße von der Oberflächenhaftung und dem relativen Mikrogleiten zwischen den Kontaktflächen beeinflusst wird.
Um dieses Konzept weiter zu erklären, betrachten Sie einen Reifen, der mit konstanter Geschwindigkeit rollt. Die Hauptkräfte, die auf ihn wirken, sind sein Gewicht, das vertikal nach unten wirkt, und die Normalkraft, die vom Boden nach oben ausgeübt wird. Wenn der Reifen rollt, erfährt der vordere Teil des Kontaktbereichs eine Verformung, die die Rollbewegung des Reifens verlangsamt. Im Gegensatz dazu erfolgt im hinteren Bereich eine relativ kleinere Wiederherstellung, die den Reifen nach vorne schiebt. Der Nettoeffekt besteht darin, dass die resultierende Normalkraft, die am Punkt A (dem Mittelpunkt des Kontaktbereichs) wirkt, die Summe dieser entgegengesetzten Kräfte ist.
<img alt="Figure 1" src="/files/ftp_upload/14328/14328_Figure_1v2.svg" style="text-align: center; height: 350px;" />
Um den Reifen mit konstanter Geschwindigkeit zu rollen und das Gewicht um den Punkt A auszugleichen, muss eine horizontale Antriebskraft (F) auf die Mitte des Reifens ausgeübt werden. Für das Gleichgewicht müssen alle auf den Reifen wirkenden Kräfte zusammenfallen. Mit Hilfe der Momentengleichgewichtsbedingung am Punkt A können wir die benötigte Antriebskraft zur Aufrechterhaltung der konstanten Geschwindigkeit in Bezug auf den Rollwiderstandsbeiwert a bestimmen.
<img alt="Equation 1" src="/files/ftp_upload/14328/14328_Equation_1v2.svg" style="text-align: center; height: 28px;" />
Diese Antriebskraft ist normalerweise kleiner als das Produkt aus dem Beiwert der kinetischen Reibung und dem Gewicht des Reifens.
<img alt="Equation 2" src="/files/ftp_upload/14328/14328_Equation_2v2.svg" style="text-align: center; height: 28px;" />
Dieses Verhältnis impliziert, dass die Rollreibungskraft typischerweise kleiner ist als die Gleitkraft, die auftritt, wenn ein Reifen auf einer Oberfläche schleudert. Als Folge davon ist der Rollwiderstand in der Regel weniger nachteilig für die Leistung eines Fahrzeugs als die Gleitreibung.

Rollwiderstand

Wenn ein massiver Zylinder gleichmäßig auf einer starren Oberfläche rollt, ist die Normalkraft, die von der Oberfläche auf den Zylinder ausgeübt wird, senkrecht zur Tangente an der ...

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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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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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