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If I know the torque and rpm that the shaft need to operate at, can I calculate the diameter of the shaft?

A motor operating at 60 rpm applying 1,000 Nm of force on a shaft that has a modulus of rigidity of 50 GPa and is 10 cm in length.

Can I calculate the diameter of the shaft so that it would not fail?

The tensile strength is:

Tensile Strength, Ultimate  686 MPa 
Tensile Strength, Yield     490 MPa

This will be a horizontal shaft, the length isn't final yet but I am estimating that it will be 2,000 mm long and supported at 200 mm from each end.

There shouldn't be any unforseen shocks being applied to the shaft. It will be transmitting the power from a 15 HP motor that's connected via a coupling on one end.

Air
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user1610950
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2 Answers2

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The elastic modulus would give you how much it would twist in use, you would need the tensile strength: taken from engineering toolbox http://www.engineeringtoolbox.com/torsion-shafts-d_947.html :

τ = T r / J                              (1)

where

τ = shear stress (Pa, psi)

T = twisting moment (Nm, in lb)

r = distance from center to stressed surface in the given position (m, in)

J = Polar Moment of Inertia of Area (m4, in4)

Diameter of a Solid Shaft
Diameter of a solid shaft can calculated by the formula

D = 1.72 (Tmax / τmax)^1/3                            (4)

this should answer your question with regard to the minimum theoretical value, but of course in real work applications you would need to consider safety factors and deflection (which you can find calculations for on the aforementioned link).

L Selter
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Given:

$T\ =\ 1000\ Nm^2$, $G\ =\ 50 GPa$, $L\ =\ 10\ cm\ =\ 100\ mm$

The torque has the wrong units, please double check.

To answer your question, a simple google check gives this link about torsion mechanics.

Jem Eripol
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