Name: sizing a solid power transmission shaft
Uploaded: 2024-05-23T12:59:58.000Z
Duration: 1 min 9 s
Channel: JoVE

A solid shaft rotates, transmitting power from the motor to a machine tool connected to the gear. Given the allowable shearing stress, calculate the smallest possible diameter of the solid shaft.
First, calculate the torque exerted on the gear using the shaft revolution and power transmission values.
The corresponding tangential forces acting on the gears are computed using the torque.
The bending moment diagrams determine the bending moment values for forces acting on the horizontal and vertical planes.
At all potentially critical transverse sections, calculate the square root of the sum of squares of bending moments, and torsion.
Obtain the polar moment ratio by substituting the known and computed values into the relation that equates shearing stress with the polar moment ratio and the maximum value derived from the square root of the sum of the squares of bending moments and torsion.
Finally, determine the shaft&#39;s radius and the smallest permissible diameter using the polar moment ratio value.

transmission shafts: problem solving

Designing a solid shaft that transmits power from a motor to a machine tool involves a series of calculations to ensure the shaft can withstand the stresses applied by bending moments and torques. First, calculate the torque exerted on the gear, considering the power transmitted by the shaft and its rotational speed. Following this, compute the tangential forces acting on the gears, which directly relate to the torque and the gear radius.
Next, use bending moment diagrams for the shaft to identify the bending moment values due to forces acting in horizontal and vertical planes. At potentially critical transverse sections of the shaft, determine the combined stresses from these bending moments and torsion by calculating the square root of the sum of the squares of these values. This analysis helps assess whether the shaft can handle the stress without failing. Then, calculate the polar moment of inertia, which is crucial for linking shearing stress with torsion and bending moments.
<img alt="Stress analysis formula; mechanical engineering; static equilibrium; equations; educational use." src="/files/ftp_upload/15664/15664_Equation_1.svg" style="text-align: center; height: 58px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
This calculation verifies the shaft's capacity to endure the applied forces. Finally, calculate the shaft's minimum required diameter based on the polar moment of inertia, ensuring it can withstand the calculated stresses with minimal material use while meeting safety and performance standards.

Transmission Shafts: Problem Solving

A solid shaft rotates, transmitting power from the motor to a machine tool connected to the gear. Given the allowable shearing stress, calculate the ...

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sizing a solid power transmission shaft

A solid power transmission shaft must be sized so it can carry both torque and bending loads. In this problem, the shaft connects a motor to a machine tool through a gear, so the design must resist the stress created by rotation and force transfer.

The first step is to calculate the torque on the gear. This uses the power carried by the shaft and its rotational speed. The tangential force on the gear is then found from the torque and the gear radius.

Next, bending moment diagrams are used for the shaft. These diagrams show the bending moments produced by forces in the horizontal and vertical planes. At critical transverse sections of the shaft, the bending and torsional stresses are combined by taking the square root of the sum of the squares of these values.

That combined-stress check helps show whether the shaft can resist failure under the applied loading. The polar moment of inertia is then calculated. This value links shear stress with torsion and bending moments and is used to verify the shaft’s strength.

The final step is to find the minimum required shaft diameter from the polar moment of inertia. This gives a solid shaft size that can handle the calculated stresses while using as little material as possible. The design must still meet safety and performance standards.

Sizing a Solid Power Transmission Shaft

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Beam stress patterns under transverse load depend on both bending and shear. In a prismatic beam, these two effects work together to shape how stress is distributed across the cross-section and to help engineers judge structural integrity. The largest normal, or bending, stress appears at the outer fibers of the beam. It drops in a straight line to zero at the neutral axis, which is the line in the cross-section where bending stress changes direction. Shear stress behaves differently. It is...

design of transmission shafts - stress analysis

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Transmission shafts carry power while facing both bending and torsion. In gear systems, these loads create force-couple systems at the center of the shaft cross-section. That means the shaft must be checked for transverse loading and twisting at the same time. The transverse loads create shearing stress, but it is usually smaller than the stress from torque and is often ignored. Even so, the normal stress from these loads can add to the maximum shearing stress in the shaft. To find that normal...

A solid power transmission shaft must be sized so it can carry both torque and bending loads. In this problem, the shaft connects a motor to a machine tool through a gear, so the design must resist the stress created by rotation and force transfer. The first step is to calculate the torque on the gear. This uses the power carried by the shaft and its rotational speed. The tangential force on the gear is then found from the torque and the gear radius. Next, bending moment diagrams are used for...

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key terms and concepts

Learn how a solid transmission shaft is sized by calculating torque, tangential force, bending moments, combined stress, and minimum diameter for safe design.

Sizing a Solid Power Transmission Shaft | 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.

Sizing a Solid Power Transmission Shaft

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