Internal and external diameters - solid shaft, Mechanical Engineering

Internal and external diameters - solid shaft:

Two shafts are of the similar material, length & weight. One is solid & of 100 mm diameter, the outer is hollow. If hollow shaft is to be store 25% more energy than the solid shaft while transmitting torque, what should be its internal & external diameters? Consider the similar maximum shear stress in both the shafts.

Solution

Consider A is the solid shaft of diameter Da & B is the hollow shaft with external diameter Db & internal diameter db. As both of the shafts are to be the similar material and of equal weight, their volumes must be equal.

Therefore,

2055_Internal and external diameters.png

or

798_Internal and external diameters1.png

As the maximum shear stress is the similar for both the shafts, we have,

                                 τa  = τb

                           Ta Da  /2J a = Tb Db/2J B   ( since τ = T × r/ J = T × D/2J )

Therefore,

Ta/ Tb  = Db/ Da  × J a/ Jb

But it is also given that the strain energy of B = 1.25 × strain energy of A.

Thus,

471_Internal and external diameters2.png

From the relationship, this reduces to

1379_Internal and external diameters3.png

After that,  ∴

2345_Internal and external diameters4.png

1158_Internal and external diameters5.png

Therefore, the internal & external diameters of the hollow tube are 57.74 mm & 115.47 mm, respectively.

Posted Date: 1/21/2013 6:28:12 AM | Location : United States







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