Name: flat belt forces and pulley moment
Uploaded: 2023-09-22T11:49:30.000Z
Duration: 1 min 28 s
Channel: JoVE

フラットベルトが2つのプーリーAとBを包み込み、半径はそれぞれ30cmと10cmです。
ベルトと水平の間の角度は、プーリーで20度です。
プーリーBは時計回りに回転してプーリーAを駆動し、ベルトの一方の端に張力T2、もう一方の端に張力T1を引き起こします。
最大許容張力 T2 が 1000 N で、ベルトとプーリーの間の静摩擦係数が 0.4 であるとすると、プーリー A の最大モーメントはどれくらいですか?
システムの形状から計算されるベルトと表面の接触角は 140 度です。
ベルトと表面の接触角(ラジアン)と静摩擦値の係数をベルト張力の式に代入して、T1を求めます。
プーリ B が時計回りに回転すると、プーリ B で生じる張力差がプーリ A でモーメントを生成します。
プーリーAの自由体線図を描き、モーメント平衡条件を適用します。
半径と張力の値は、最大モーメントを取得するために代入されます。

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	<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。469-470ページ。</li>
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フラットベルト：問題解決

Flat Belts: Problem Solving

フラットベルトは、パワーをプーリーから別のプーリーに伝達するために多くの産業アプリケーションで重要です。力とモーメントの概念は、プーリー上の最大モーメントを決定するために使用されます。例えば、半径がそれぞれ30 cmと10 cmの2つのプーリー、AとB、に巻かれたフラットベルトを考えてみましょう。ベルトと水平線の間の角度は、プーリーで20度です。プーリーBが時計回りに回転し、プーリーAを駆動すると、ベルトの片側で張力T2が生じ、もう片側で張力T1が生じます。

<img alt="Figure 1" src="/files/ftp_upload/14323/14323_PT_Fig_1v2.svg" style="text-align: center; height: 250px;" />

ベルト-表面接触角βを計算して、最大モーメントを決定する必要があります。この角度はシステムの幾何学から得られ、140度となります。結果として、ベルト-表面接触角（ラジアン）と静止摩擦係数の値0.4がベルトテンションの式に代入されます。

<img alt="Equation 1" src="/files/ftp_upload/14323/14323_PT_Equation_1v2.svg" style="text-align: center; height: 35px;" />

T2の最大許容テンションが1000 Nであると考えると、T1の計算値は376.93 Nとなります。プーリーBが時計回りに回転すると、プーリーBでテンション差が生じ、プーリーAでモーメントが発生します。プーリーAの自由物体図を考慮すると、モーメントの平衡条件が適用されます。

<img alt="Equation 2" src="/files/ftp_upload/14323/14323_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

半径とテンションの値を代入して、最大モーメントは186.921 N.mとなります。

フラットベルトは、1つのプーリーから別のプーリーに動力を伝達するのに役立つため、多くの産業用途で重要です。力とモーメントの概念が使われています...

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

flat belt forces and pulley moment

Flat belts transmit power from one pulley to another, and the forces on the belt help determine the moment on a pulley. In this example, a belt wraps around pulleys A and B, with radii of 30 cm and 10 cm. The belt meets the pulleys at a 20 degree angle from the horizontal, which sets up the force balance in the system.

As pulley B rotates clockwise, it drives pulley A. That motion creates tension T2 on one side of the belt and tension T1 on the other side. The belt-to-surface contact angle, β, is needed to find the maximum moment, so it is first found from the geometry of the setup. The angle is 140 degrees.

Next, the contact angle in radians and the coefficient of static friction, 0.4, are used in the belt tension equation. With the maximum allowable tension T2 set to 1000 N, the value of T1 is calculated as 376.93 N. A free-body diagram for pulley A then helps apply moment equilibrium. Using the pulley radius and the belt tensions, the maximum moment is found to be 186.921 N.m.

Flat Belt Forces and Pulley Moment

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key terms and concepts

Learn how belt tension, friction, and pulley radius are used to calculate the maximum moment in a flat belt drive system with two pulleys.

Flat Belt Forces and Pulley Moment | JoVE K12

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mechanical engineering

Flat Belt Forces and Pulley Moment

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