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

一条平带缠绕在两个带轮A和B上，其半径分别为30 cm和10 cm。
在滑轮处，皮带与水平面之间的夹角为20度。
滑轮 B 顺时针旋转并带动滑轮 A，使皮带一端产生张力 T2&#160;，另一端产生张力 T1。
已知最大允许张力 T2 为 1000 N，且皮带与带轮之间的静摩擦系数为 0.4，求带轮 A 上的最大力矩？
根据系统的几何结构计算，带与表面的接触角为140度。
将皮带与表面接触角的弧度值以及静摩擦系数代入皮带张力表达式，以求得 T1。
当滑轮 B 顺时针旋转时，滑轮 B 处产生的张力差会在滑轮 A 上生成一个力矩。
绘制滑轮 A 的受力分析图，并应用力矩平衡条件。
将半径和张力值代入以获得最大力矩。

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	<li>梅里亚姆，JL;Kraige， LG 和 Bolton， JN （2020）。工程力学 \u2012 静力学。新泽西州霍博肯:约翰·威利。第 372 页。</li>
	<li>比尔，F.P.;约翰斯顿，ER;马祖克，DF;克伦威尔，PJ 和塞尔夫，BP（2019 年）。工程师的矢量力学 \u2012 静力学和动力学。纽约:麦格劳-希尔。第 469-470 页。</li>
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扁平带：问题求解

Flat Belts: Problem Solving

扁平带在许多工业应用中至关重要，因为它们能够将功率从一个滑轮传输到另一个滑轮。使用力和力矩的概念来确定滑轮上的最大力矩。例如，假设有一个包裹在半径分别为30厘米和10厘米的两个滑轮A和B上的扁平带。扁平带与水平线之间的夹角在滑轮处为20度。当滑轮B进行顺时针旋转并驱动滑轮A时，扁平带的一端能够产生张力T2，而另一端则会产生张力T1。 <img alt="Figure 1" src="/files/ftp_upload/14323/14323_PT_Fig_1v2.svg" style="text-align: center; height: 250px;"> 必须计算扁平带与表面接触的角度β以确定其最大力矩。从系统的几何形状中可以得到这个角度为140度。因此，将扁平带与表面所接触的角度（以弧度表示）以及静摩擦系数的值0.4代入到扁平带张力的表达式中。 <img alt="Equation 1" src="/files/ftp_upload/14323/14323_PT_Equation_1v2.svg" style="text-align: center; height: 35px;"> 假设最大允许的张力T2为1000N，通过计算可以得到T1的值为376.93N。当滑轮B进行顺时针旋转时，在滑轮B处可以产生一个张力差，在滑轮A处能够产生一个力矩。对滑轮A的受力分析图进行分析，可以得出应用力矩的平衡条件。 <img alt="Equation 2" src="/files/ftp_upload/14323/14323_PT_Equation_2v2.svg" style="text-align: center; height: 13px;"> 然后，将半径和张力值代入到方程中，可以得出最大的力矩为186.921N·m。

平带在许多工业应用中至关重要，因为它们有助于将动力从一个带轮传递到另一个带轮。力与力矩的概念被用于……

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Friction

摩擦

KEY TERMS AND CONCEPTS

关键术语与概念

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

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Flat Belt Forces and Pulley Moment

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