A Hollow Shaft External Diameter Calculation
Calculating the External Diameter of a Hollow Shaft
A hollow shaft is a mechanical component used to transmit power in machines. In this case, we have a hollow shaft with an internal diameter 40% of its external diameter, transmitting 562.5 kW power at 100 r.p.m. We are tasked to determine the external diameter of the shaft given that the shear stress should not exceed 60 N/mm² and the twist in a length of 2.5m should not exceed 1.3 degrees. Additionally, we assume that the maximum torque is 1.25 times the mean torque, and the modulus of rigidity is 9 * 10^3 N/mm².
Calculations and Solution
To determine the external diameter of the hollow shaft, we need to consider the power transmitted, shear stress, and twist.
Explanation:To find the external diameter of the hollow shaft, we need to consider the power transmitted, shear stress, and twist. Let's start by determining the torque using the power and speed:
Torque = (Power × 60) / (2π × Speed)
With the torque value, we can calculate the external diameter using the maximum shear stress formula and the given internal diameter:
Maximum Shear Stress = (16 × Torque × Radius) / (π × External Diameter^3 - Internal Diameter^3)
Finally, we can check the twist using the twist formula:
Twist = (TL / (G × J)) × Length
Where TL is the total torque, G is the modulus of rigidity, J is the polar moment of inertia, and Length is the length of the shaft.
Final answer: The external diameter of the hollow shaft can be determined using the calculations mentioned above.
A hollow shaft having an internal diameter 40% of its external diameter, transmits 562.5 kW power at 100 r.p.m. Determine the external diameter of the shaft if the shear stress is not to exceed 60 N/mm² and the twist in a length of 2.5m should not exceed 1.3 degrees. Assume maximum torque = 1.25 mean torque and modulus of rigidity = 9*10* N/mm². To determine the external diameter of the hollow shaft, we need to consider the power transmitted, shear stress, and twist. By calculating the torque, maximum shear stress, and twist, we can find the required external diameter of the hollow shaft.