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

Weźmy pod uwagę oponę toczącą się ze stałą prędkością. Działające na niego siły to jego waga i siła normalna.
Powierzchnie kontaktowe ulegają deformacji, tworząc skończoną powierzchnię kontaktu. Powoduje to rozkład sił normalnych w każdym punkcie styku.
Przednia część tego obszaru ulega deformacji, co opóźnia ruch toczenia.
Natomiast tylna część przechodzi stosunkowo mniejszą renowację, która popycha oponę do przodu.
Wynikowa siła normalna działająca na A jest sumą tych sił.
Aby opona toczyła się ze stałą prędkością i zrównoważyć moment ciężaru około A, do środka opony należy przyłożyć poziomą siłę napędową. Tutaj wszystkie siły muszą być współbieżne.
Warunek równowagi momentów w punkcie A określa siłę napędową pod względem współczynnika oporu toczenia.
Ciężar pomnożony przez współczynnik oporu toczenia na promieniu jest zwykle mniejszy niż współczynnik tarcia kinetycznego pomnożony przez masę.
Tak więc siła tarcia tocznego jest mniejsza niż siła poślizgu.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. str. 452 \u2012 439.</li>
	<li>Meriam, J.L.; Kraige, L.G. i Bolton, J.N. (2020). Mechanika inżynierska \u2012 Statyka. Hoboken, New Jersey: John Wiley. str. 372.</li>
	<li>Piwo, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, PJ i Self, BP (2019). Mechanika wektorowa dla inżynierów \u2012 Statyka i dynamika. Nowy Jork: McGraw-Hill. str. 469.</li>
</ol>

opór toczenia

Kiedy stały cylinder toczy się równomiernie po sztywnej powierzchni, siła normalna stosowana przez powierzchnię na cylinder jest prostopadła do stycznej w punkcie kontaktu. Jednakże, ponieważ żadne materiały nie są całkowicie sztywne, reakcja powierzchni na cylinder obejmuje zakres normalnych ciśnień.

Na przykład, wyobraź sobie twardy cylinder toczący się po stosunkowo miękkiej powierzchni. Waga cylindra spręża powierzchnię pod nim. Gdy cylinder się porusza, materiał przed nim zwalnia ze względu na odkształcenie, podczas gdy materiał za nim powraca do swojego odkształconego stanu, popychając cylinder do przodu. Normalne ciśnienia działające na cylinder w ten sposób są przedstawiane przez ich wynikające siły, Nd i Nr. Siła odkształcenia (Nd) i jej składowa pozioma są zawsze większe od siły odtwarzania (Nr), co wymaga wywierania siły napędowej w kierunku poziomym na cylinder, aby utrzymać jego ruch.

Opór toczenia występuje głównie z powodu tego efektu, chociaż wpływa na niego również w mniejszym stopniu, przez przyczepność powierzchni i względne mikro tarcie między powierzchniami kontaktowymi.

Aby dalej wyjaśnić ten temat, rozważ oponę toczącą się z stałą prędkością. Główne siły działające na nią to jej waga, działająca pionowo w dół, i siła normalna wywierana przez podłoże, działająca pionowo w górę. Podczas toczenia opony, przednia część obszaru kontaktu ulega odkształceniu, co opóźnia ruch toczącej się opony. W przeciwieństwie do tego, tylna część przechodzi względnie mniejsze odtwarzanie, które popycha oponę do przodu. Efektem netto jest, że wynikająca siła normalna działająca w punkcie A (środek obszaru kontaktu) jest sumą tych przeciwnych sił.

<img alt="Figure 1" src="/files/ftp_upload/14328/14328_Figure_1v2.svg" style="text-align: center; height: 350px;" />

Aby utrzymać oponę w stałej prędkości i zrównoważyć moment ciężaru względem punktu A, do środka opony musi być stosowana siła napędowa (F). Dla równowagi, wszystkie siły działające na oponę muszą być skoncentrowane. Używając warunku równowagi momentu w punkcie A, możemy określić wymaganą siłę napędową potrzebną do utrzymania stałej prędkości w zależności od współczynnika oporu toczenia (a).

<img alt="Equation 1" src="/files/ftp_upload/14328/14328_Equation_1v2.svg" style="text-align: center; height: 28px;" />

Ta siła napędowa jest zazwyczaj mniejsza od iloczynu współczynnika tarcia kinetycznego i ciężaru opony.

<img alt="Equation 2" src="/files/ftp_upload/14328/14328_Equation_2v2.svg" style="text-align: center; height: 28px;" />

Ta relacja oznacza, że siła tarcia toczenia jest zwykle mniejsza od siły ślizgania, którą odczuwa opona podczas poślizgu po powierzchni. W rezultacie, opór toczenia jest zwykle mniej szkodliwy dla wydajności pojazdu niż tarcie ślizgowe.

Opór toczenia

Gdy solidny cylinder toczy się stabilnie po sztywnej powierzchni, normalna siła przyłożona przez powierzchnię do cylindra jest prostopadła do stycznej na ...

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Kluczowe terminy i pojęcia

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

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