calculate torsion in a diffrent sized shaft

first of i know it seems like a homework assignment but it does not, it is calculations i need to do at work and it has been a long time since i studied this material. so I need help to calculate if a given clutch can handle a given torque but I'm not sure if my calculation are right.

what I did so far

on the left there is a motor on the right is the cluch with a connector.

ive build a FBD:

and ended up with this eq:

$$\tau_{max} = \frac{T*r_1}{J} = \frac{2T*r_1}{\pi*r^3}=\frac{2*2.5}{\pi*(6.05*10^{-3})^3} = 7.2 [MPa]$$

but I don't know if this is the way to calculate and I don't know how to calculate if the point connecting the two diameters is strong enough.

1 Answer

Your calculation is generally correct .

The basic formula is:

$$\tau_{max} = \frac{T*r_1}{J}$$

Although the Torque is constant ($$2.5 [Nm]$$), what changes is the radii and the second moment of area.

• For solid sections $$J_{solid} = \frac{\pi r^4}{4}$$

• For hollow sections $$J_{hollow} = \frac{\pi \left(r_o^4 - r_i^4\right)}{4}$$

where:

• $$r_o$$: the external radius
• $$r_i$$: the internal radius

if you are worried for increases in stress due to the change in diameter, you can look at stress concentrations.