Name: shaft torsion between pulleys b and c
Uploaded: 2024-05-23T12:59:41.000Z
Duration: 1 min 13 s
Channel: JoVE

The electric motor exerts a 700 N-m torque on an aluminium shaft, causing it to rotate at a constant speed. Pulleys B and C experience torques of 300 N-m and 400 N-m, respectively. The modulus of rigidity is given as 25 GPa. If the length and diameter of each section are known, calculate the angle of twist between the pulleys B and C.
First, a cut is made between pulleys B and C, and a free-body diagram of the cut cross-section is considered.
The torque acting on the pulley B is anticlockwise. So, using the principle of equilibrium, the torque at the cut cross-section of the shaft will be equal and opposite to the torque at pulley B.
Next, the polar moment of inertia at the cut cross-section, which is proportional to the fourth power of the radius of the shaft, is calculated.
By substituting all the known parameters, the angle of twist between pulleys B and C is determined. The angle obtained is in radians and can be converted to degrees.

angle of twist: problem solving

An electric motor applies a torque of 700 N&#183;m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N&#183;m and 400 N&#183;m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the torque exerted on pulley B is in an anticlockwise direction, the equilibrium principle dictates that the torque at the cut cross-section of the shaft should match this but in the opposite direction.
The polar moment of inertia is then calculated at the cut cross-section. This value is proportional to the radius of the shaft raised to the fourth power. Then, by inserting all the known parameters into the equation for calculating the angle of twist, it is possible to determine the twist angle between pulleys B and C.
<img alt="Torsional shear flow equation in engineering analysis. Formula: &#966;&#60;sub&#62;B/C&#60;/sub&#62; = (T&#60;sub&#62;BC&#60;/sub&#62;L&#60;sub&#62;BC&#60;/sub&#62;)/(GJ&#60;sub&#62;BC&#60;/sub&#62;)." src="/files/ftp_upload/15616/15616_Equation_1.svg" style="text-align: center; height: 42px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
The result is initially in radians but can be converted into degrees for easier interpretation. This process allows for understanding the system's mechanical behavior under the applied torques.

Angle of Twist: Problem Solving

The electric motor exerts a 700 N-m torque on an aluminium shaft, causing it to rotate at a constant speed. Pulleys B and C experience torques of 300 N-m ...

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Torsion

KEY TERMS AND CONCEPTS

shaft torsion between pulleys b and c

Shaft torsion between pulleys B and C is found by analyzing how torque twists an aluminum shaft. An electric motor applies 700 N·m of torque and produces stable rotation. The shaft carries pulleys B and C, which experience torques of 300 N·m and 400 N·m.

The calculation starts with a section cut between pulleys B and C. A free-body diagram is used to study the cut cross-section. Because pulley B has an anticlockwise torque, the torque at the cut must balance it in the opposite direction. The modulus of rigidity is 25 GPa, and the length and diameter of each shaft segment are known.

Next, the polar moment of inertia is calculated at the cut cross-section. This value depends on the shaft radius raised to the fourth power. Then all known values are placed into the angle-of-twist equation. The twist angle between pulleys B and C is found first in radians. It can then be converted into degrees for easier interpretation. This process shows how the shaft responds to the applied torques.

Shaft Torsion Between Pulleys B and C

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Shaft torsion between pulleys B and C is found by analyzing how torque twists an aluminum shaft. An electric motor applies 700 N·m of torque and produces stable rotation. The shaft carries pulleys B and C, which experience torques of 300 N·m and 400 N·m. The calculation starts with a section cut between pulleys B and C. A free-body diagram is used to study the cut cross-section. Because pulley B has an anticlockwise torque, the torque at the cut must balance it in the opposite direction. The...

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key terms and concepts

Calculate the twist angle in an aluminum shaft using torque, a free-body diagram, polar moment of inertia, and the modulus of rigidity between pulleys B and C.

Shaft Torsion Between Pulleys B and C | JoVE K12

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Shaft Torsion Between Pulleys B and C

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