24.3: 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.
