Name: transmission shaft bending and torsion
Uploaded: 2024-05-23T12:59:58.000Z
Duration: 1 min 15 s
Channel: JoVE

The design of a transmission shaft involves understanding the stresses due to bending moments and torques.
When power is transferred through gears, the forces exerted equate to force-couple systems applied at cross-section centers, which subject the shaft to both transverse and torsional loading.
Although shearing stresses from transverse loads are smaller than those produced by torques and often neglected, the considerable normal stresses from transverse loads contribute significantly to the maximum shearing stress.
The normal stress exerted on the section is computed by examining a shaft&#39;s cross-section at a specific point and accounting for both the torque and bending couples.
The maximum normal stress occurs at the end of the diameter perpendicular to the resultant of the bending moment couple.
The minimum allowable polar moment ratio for the cross-section is determined by considering both the maximum resultant bending moment and torque in the shaft, along with the allowable shearing stress.
This approach facilitates the design of both solid and hollow circular shafts.

design of transmission shafts - stress analysis

Design of Transmission Shafts - Stress Analysis

Designing a transmission shaft requires a thorough understanding of the stresses induced by bending moments and torques, especially in systems where power is transferred through gears. These forces create force-couple systems at the centers of the shaft's cross-sections, leading to both transverse and torsional loading. Although shearing stresses from transverse loads are typically smaller than those from torques and are often overlooked, the significant normal stresses from these loads contribute to the maximum shearing stress.
<img alt="Shear stress formula &#964;_max=sqrt((&#963;_m/2)^2+(&#964;_m)^2), stress analysis equation." src="/files/ftp_upload/15663/15663_Equation_1.svg" style="text-align: center; height: 48px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
Calculating the normal stress exerted on a shaft section involves examining the shaft's cross-section at a specific point, considering both the torque and bending couples. The maximum normal stress typically occurs at the ends of the diameter perpendicular to the resultant of the bending moment couple. Determining the cross-section's minimum allowable polar moment ratio J/c is essential to ensure the shaft's integrity and functionality.
<img alt="Static equilibrium equation &#931;Fx=0, formula diagram, stress analysis method." src="/files/ftp_upload/15663/15663_Equation_2.svg" style="text-align: center; height: 38px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
This ratio is vital as it accounts for both the maximum resultant bending moment and torque on the shaft, in addition to the allowable shearing stress. This analytical approach is fundamental in designing both solid and hollow circular shafts, enabling the creation of optimized shaft configurations that can reliably withstand operational stresses. Such methodology ensures that the designed shafts are robust, efficient, and tailored to their specific applications, guaranteeing mechanical systems' safety and functionality.

The design of a transmission shaft involves understanding the stresses due to bending moments and torques.
When power is transferred through gears, the ...

design-of-transmission-shafts-stress-analysis

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Principal Stresses under a Given Loading

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transmission shaft bending and torsion

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 stress, the shaft section is examined at a specific point, and both the torque and the bending couples are considered.

The highest normal stress often appears at the ends of the diameter that is perpendicular to the resultant bending moment couple. Designers then determine the minimum allowable ratio of J/c for the cross-section. Here, J is the polar moment of inertia and c is the outer radius, and this ratio helps keep the shaft strong enough for the load.

This calculation uses the maximum resultant bending moment, the torque, and the allowable shearing stress. It applies to both solid and hollow circular shafts. The result is a shaft design that is efficient, reliable, and able to handle operational stress in mechanical systems.

Transmission Shaft Bending and Torsion

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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...

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...

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key terms and concepts

Learn how transmission shafts handle bending moment and torque, and how engineers use J/c to design solid and hollow shafts that resist stress.

Transmission Shaft Bending and Torsion | 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.

Transmission Shaft Bending and Torsion

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