Problem on Calculation of External Diameter of Hollow Shaft

TL;DR

This content explains how to calculate the external diameter of a hollow shaft based on power transmission and the condition that shear stress does not exceed a certain value.

Transcript

let's take the next question question number three a hollow shaft having an internal diameter 40 percent of its external diameter transmits 562.5 kilowatts at 100 rpm full stop determine the external diameter of the shaft if shear stress is not to exceed 1.3 degrees full stop assume t max is equal to 1.25 times t mean capital g is 9 into 10 raised ... Read More

Key Insights

• ✊ The relation between power, torque, and rotational speed is crucial in determining the mean torque in the problem.
• 💁 The maximum torque is found to be 1.25 times the mean torque based on the given information.
• 📶 The strength criteria and rigidity criteria equations help determine the external diameter of the hollow shaft.

Questions & Answers

Q: How is the mean torque calculated in this problem?

The mean torque is calculated using the formula T = (P x 60) / (2 x π x N), where P is the power transmitted in watts, and N is the speed in rpm. In this case, the calculated mean torque is 53.72 x 10^3 Nm.

Q: How is the maximum torque related to the mean torque in this problem?

The maximum torque is given as 1.25 times the mean torque. Therefore, the calculated maximum torque is 67.14 x 10^3 Nm.

Q: How is the external diameter of the hollow shaft determined using the strength criteria?

Using the equation T_max / J = τ_max / r, where T_max is the maximum torque, J is the polar moment of inertia, τ_max is the maximum shear stress, and r is the radius of the external diameter, the external diameter is calculated to be 180 mm.

Q: How is the external diameter of the hollow shaft determined using the rigidity criteria?

Using the equation T / J = Gθ / L, where G is the modulus of rigidity, θ is the twist angle, and L is the length of the shaft, the external diameter is calculated to be 171.2 mm.

Summary & Key Takeaways

• The question involves a hollow shaft with an internal diameter of 40% of its external diameter, transmitting a power of 562.5 kilowatts at 100 rpm. The goal is to determine the external diameter of the shaft without exceeding a specific shear stress value.

• The formula for finding the mean torque is derived and used to calculate the maximum torque. The maximum torque is found to be 67.14 x 10^3 Nm.

• Using the strength criteria, the equation relating torque, internal and external diameters, and shear stress is derived. By substituting given values and solving the equation, the external diameter is found to be 180 mm.

• Applying the rigidity criteria, another equation relating torque, internal and external diameters, rigidity modulus, twist angle, and length is derived. By substituting given values and solving the equation, the external diameter is found to be 171.2 mm.

• Comparing the results obtained from both criteria, the maximum value of 180 mm is selected as the answer.