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

タイヤが一定の速度で転がっていると考えてください。それに作用する力は、その重量と垂直力です。
接触面が変形し、有限の接触領域が作成されます。これにより、各接触点で垂直抗力が分布します。
この領域のフロントセクションは変形し、ローリングモーションが遅れます。
対照的に、リアセクションは、タイヤを前方に押し出す比較的小さな修復を受けます。
Aに作用する合成法線力は、これらの力の合計です。
タイヤを一定の速度で転がし続け、重量のモーメントをA付近でバランスさせるには、タイヤの中心に水平方向の駆動力を加える必要があります。ここでは、すべての力が同時になければなりません。
点Aでのモーメント平衡状態は、転がり抵抗係数で駆動力を与えます。
半径に対する転がり抵抗係数を掛けた重量は、通常、動摩擦係数に重量を掛けた値よりも小さくなります。
そのため、転がり摩擦力は滑り力よりも小さくなります。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス \u2012 静力学と力学。 ニュージャージー州ホーボーケン:ピアソンプレンティスホール。452 \u2012 439ページ。</li>
	<li>メリアム、J.L.;Kraige、LGおよびBolton、JN(2020)。エンジニアリングメカニクス \u2012 静力学。ニュージャージー州ホーボーケン:ジョン・ワイリー。372ページ。</li>
	<li>ビール、FP;ジョンストン、ER;マズレック、D.F;クロムウェル、PJおよびセルフ、BP(2019)。エンジニアのためのベクトル力学 \u2012 静力学と動力学。ニューヨーク:マグロウヒル。469ページ。</li>
</ol>

転がる時の抵抗

固形の円柱が剛性のある表面上で一定の速度で転がる場合、表面が円柱に対して加える法線力は接点での接線に垂直である。しかしながら、材料は完全に剛性を持つことはないため、表面の反応は様々な法線圧力に影響を受ける。

例えば、硬い円柱が比較的柔らかい表面上で転がる場合を想像してみよう。円柱の重さによってその下の表面が圧縮される。円柱が移動すると、その前方の材料は変形によって遅くなり、一方後方の材料は変形から回復し、円柱を前方に押し出す。このような方法で円柱に作用する法線圧力は、その結果としての力NdとNrによって描かれる。変形力（Nd）およびその水平成分は、回復力（Nr）よりも常に大きくなるため、円柱の運動を維持するためには水平な駆動力が必要である。

転がる時の抵抗は主にこの効果によって発生するが、接触面間の表面付着力と相対微小滑りの影響もあるが、それはそれほど大きくはない。

この概念をさらに説明するために、一定の速度で転がるタイヤを考えてみよう。タイヤに作用する主な力は垂直方向の重さと地面によって加えられる法線力である。タイヤが転がると、接触面の前部では変形が生じ、その結果タイヤの転がり運動が妨げられる。対照的に、後部では比較的小さな回復があり、タイヤを前方に押し出す。その結果、接点A（接触面の中心）で作用する法線力の合力はこれらの相反する力の合計となる。

<img alt="Figure 1" src="/files/ftp_upload/14328/14328_Figure_1v2.svg" style="text-align: center; height: 350px;" />

タイヤを一定の速度で転がし、点A周りの重さのモーメントをバランスさせるためには、水平な駆動力(F)をタイヤの中心に加える必要がある。平衡のためには、タイヤに作用するすべての力が同一の点で作用している必要がある。接点Aにおけるモーメント平衡条件を使用して、一定の速度を維持するために必要な駆動力を転がる時の抵抗係数(a)の形で決定することができる。

<img alt="Equation 1" src="/files/ftp_upload/14328/14328_Equation_1v2.svg" style="text-align: center; height: 28px;" />

この駆動力は通常、動摩擦係数とタイヤの重量の積よりも小さい。

<img alt="Equation 2" src="/files/ftp_upload/14328/14328_Equation_2v2.svg" style="text-align: center; height: 28px;" />

この関係から、転がる時の摩擦力は通常、タイヤが表面上を滑るときに経験する滑り力よりも小さくなることが示される。その結果、転がる時の抵抗は滑り摩擦よりも車両の性能に対して一般的にはより少ない影響を与える。

固体の円柱が硬い表面で着実に転がるとき、円柱の表面によって加えられる垂直な力は、...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Friction

摩擦

KEY TERMS AND CONCEPTS

主要用語と概念

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

dry friction

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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

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Tire Deformation and Rolling Resistance | JoVE K12

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

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Tire Deformation and Rolling Resistance

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