# Simple max shaft torque calculation

1. Jan 30, 2014

### AQUAPOP

Hello.

I'm trying to add a mechanical (pneumatic or electrical) brake to a shaft.

I have a 2" diameter shaft rotating at 8 rpm's max.

The shaft has and 60" diameter, 6500lb. cylinder attached to it axially.

How do I calculate the maximum torque of the shaft?

Frank

2. Jan 30, 2014

### Q_Goest

Rotating shafts generally fail from fatigue. Do you know how to calculate stresses and predict fatigue?

3. Jan 30, 2014

### AQUAPOP

At this point I'm not really concerned with the shaft failing.

I had a grossly undersized gear reducer fail a few times on this application,
so i'm trying to add a brake, and then find a more appropriate gear reducer.

thanks for the quick reply. :)

4. Jan 30, 2014

### Q_Goest

Sorry, I think I get you now. You're trying to figure out how much torque this 60" diameter, 6500 pound cylinder requires to stop or start it moving at 8 RPM? If that's correct, do you have dimensions on it and do you know how to calculate the rotational moment of inertia? I presume also that there are rolling element bearings supporting this shaft so that friction can be neglected?

5. Jan 30, 2014

### AQUAPOP

You are correct.
I have steel cylinders (heat exchangers) on a horizontal rotisserie.
Both ends are supported on shafts in bearings.
The cylinders vary in diameter and length, and internal structure.
Another wrinkle is because of varying internal structure some rotate 2" offset from their center of gravity.

6. Jan 30, 2014

### Q_Goest

The torque required to start or stop the shaft is a function of it's rotational inertia. Imagine a car and you have to push it. The lighter the car is, the easier it is to accelerate it from a dead stop by pushing it. The torsional analogue of that is what you're interested in. Just as the car has some mass which resists accelerating, the shaft with the attached cylinder has rotational resistance due to its rotational inertia. You can calculate the rotational moment of inertia using standard formulas for simple shapes as shown here: https://webspace.utexas.edu/cokerwr/www/index.html/RI.htm [Broken]
or if you can do the math, try a more advanced calculation following the equations provided by Wikipedia here:
http://en.wikipedia.org/wiki/Moment_of_inertia#Example_calculation_of_moment_of_inertia

Once you know the rotational inertia, and you want to find the torque required to change the rotational speed, use the formula for angular acceleration,
http://en.wikipedia.org/wiki/Angular_acceleration
http://hyperphysics.phy-astr.gsu.edu/hbase/n2r.html
http://theory.uwinnipeg.ca/physics/rot/node5.html
I've provided a few different sites but they all say the same thing. Note that angular acceleration is simply the change in angular rotational rate divided by the time taken to change, ie: [PLAIN]http://upload.wikimedia.org/math/f/d/9/fd97cb711276815954e9824fabee8baf.png. [Broken] So for example, if you want to accelerate the cylinder from 0 to 8 RPM in 1 second, that's an acceleration rate of 8/60*2*pi*radians/s2. If it takes longer or shorter than 1 second, divide by the number of seconds.

For the torque exerted by the cylinder being off center by 2", just add an additional torque of the cylinder weight times this 2" moment arm (ie: 6500 lb x 2" = 13,000 lb in). The amplitude of that torque is obviously going to vary sinusoidally but for your purposes (trying to determine the peak torque on the brakes or gearbox) you really don't care about that.

Last edited by a moderator: May 6, 2017