# Transmission Shafts: Problem Solving

JoVE 핵심
Mechanical Engineering
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JoVE 핵심 Mechanical Engineering
Transmission Shafts: Problem Solving
##### Previous Video24.2: Design of Transmission Shafts – Stress Analysis

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'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.

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.