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Saturday, 16 September 2017

POWER TRANSMITTED BY SOLID CIRCULAR SHAFT


Now we are going further to start a new topic i.e. Power transmitted by a circular solid shaft with the help of this post. We recommend to first review the recent post “Torsion or twisting moment” for having basic information about the concept of torsion or twisting moment.

So, what is torsion or twisting moment?

A shaft will said to be in torsion, if it will be subjected with two equal and opposite torques applied at its two ends.

When a shaft will be subjected to torsion or twisting moment, there will be developed shear stress and shear strain in the shaft material.

We will discuss here one case of circular shaft which will be subjected to torsion and we will secure here the expression for power transmitted by a circular solid shaft.
We have following information from above figure

R = Radius of the circular shaft
D = Diameter of the circular shaft
dr = Thickness of small elementary circular ring
r = Radius of the small elementary of circular ring
q = Shear stress at a radius r from the centre of the circular shaft
τ = Shear stress at outer surface of shaft
dA = Area of the small elementary of circular ring
dA = 2П x r x dr

Shear stress, at a radius r from the centre, could be determined as mentioned here
q/r = τ /R
q = τ x r/R

Turning force due to shear stress at a radius r from the centre could be determined as mentioned here
dF = q x dA
dF = τ x r/R x 2П x r x dr
dF = τ/R x 2П r2dr

Twisting moment at the circular elementary ring could be determined as mentioned here
dT = Turning force x r
dT = τ/R x 2П r3dr

Total torque could be easily determined by integrating the above equation between limits 0 and R
Therefore total torque transmitted by a circular solid shaft

T = (П/16) τ D3

Let us consider that N is the R.P.M of the shaft and ω is the angular velocity of the shaft. We have already secured here the torque transmitted by circular solid shaft and it is mentioned above. Now we will find here the expression for power transmitted by solid circular shaft as mentioned here.

Do you have suggestions? Please write in comment box.

We will now discuss the topic, Power transmitted by a hollow circular shaft, in the category of strength of material, in our next post.

Reference:

Strength of material, By R. K. Bansal
Image Courtesy: Google

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