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

A flat belt wraps around two pulleys, A and B, with radii of 30 cm and 10 cm , respectively.
The angle between the belt and the horizontal is 20 degrees at the pulleys.
Pulley B rotates clockwise and drives Pulley A, causing tension T2&#160; at one end of the belt and tension T1 at the other.
Given that the maximum allowable tension T2 is 1000 N and the coefficient of static friction between the belt and pulleys is 0.4, what is the maximum moment on pulley A?
The belt-to-surface contact angle, calculated from the system&#39;s geometry, is 140 degrees.
The belt-to-surface contact angle in radians and the coefficient of static friction values are substituted into the expression for belt tensions to obtain T1.
As pulley B rotates clockwise, a tension difference created at pulley B generates a moment at pulley A.
A free-body diagram for pulley A is drawn, and the moment equilibrium condition is applied.
The radius and tension values are substituted to obtain the maximum moment.

flat belts: problem solving

Flat Belts: Problem Solving

Flat belts are crucial in many industrial applications as they help transmit power from one pulley to another. The concept of forces and moments is used to determine the maximum moment on a pulley. For instance, consider a flat belt that wraps around two pulleys, A and B, with radii of 30 cm and 10 cm, respectively. The angle between the belt and the horizontal is 20 degrees at the pulleys. As pulley B rotates clockwise and drives pulley A, tension T2 is caused at one end of the belt, while tension T1 is created at the other.
<img alt="Belt-drive tension diagram with pulley radii \(r_A, r_B\), angles, and forces \(T_1, T_2\)." src="/files/ftp_upload/14323/14323_PT_Fig_1v2.svg" style="text-align: center; height: 250px;" data-altupdatedat="1761830439000" data-alt="Figure 1">
The belt-to-surface contact angle, β,  must be calculated to determine the maximum moment. This angle is obtained from the system's geometry and found to be 140 degrees. As a result, the belt-to-surface contact angle in radians, along with the coefficient of static friction value, 0.4, is substituted into the expression for belt tensions.
<img alt="Thermodynamic equation T1=T2/e^µsβ; formula representation; educational use." src="/files/ftp_upload/14323/14323_PT_Equation_1v2.svg" style="text-align: center; height: 35px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
Considering that the maximum allowable tension T2 is 1000 N, the calculated value of T1 is 376.93 N. As pulley B rotates clockwise, a tension difference is created at pulley B, generating a moment at pulley A. Considering a free-body diagram for pulley A, the moment equilibrium condition can be applied.
<img alt="Static equilibrium formula, \(M_A - (T_2)(r_A) + (T_1)(r_A) = 0\), equation diagram." src="/files/ftp_upload/14323/14323_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1761830439000" data-alt="Equation 2">
The radius and tension values are then substituted to obtain the maximum moment as 186.921 N.m.

Flat belts are crucial in many industrial applications as they help transmit power from one pulley to another. The concept of forces and moments is used ...

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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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Flat Belt Forces and Pulley Moment

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