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# Design of Shaft, Hub and Key

Design of Shaft, Hub and Key

The diameter of shaft for flywheel is obtained from the maximum torque transmitted. We know that the maximum torque transmitted,

Tmax = π/16 × τ (d1)^3

where d1 = Diameter of the shaft, and
τ = Allowable shear stress for the material of the shaft.

The hub is designed as a hollow shaft, for the maximum torque transmitted. We know that the maximum torque transmitted,

Tmax =  π/16 × τ [(d^4 – d1^4) / d]

where d = Outer diameter of hub, and
d1 = Inner diameter of hub or diameter of shaft.

The diameter of hub is usually taken as twice the diameter of shaft and length from 2 to 2.5 times the shaft diameter. It is generally taken equal to width of the rim.

A standard sunk key is used for the shaft and hub. The length of key is obtained by considering the failure of key in shearing. We know that torque transmitted by shaft,

Tmax = L × w × τ × d1/2

where L = Length of the key,
τ = Shear stress for the key material, and
d1 = Diameter of shaft.

Reference A Textbook of Machine Design by R.S.Khurmi and J.K.Gupta

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