Propeller inertia estimation

I am making a very simplified model of offshore propulsion systems (electric motors specifically), and I was wondering if there is any (easy) way to guesstimate weight and/or moment of inertia for propellers ranging from 1.5m to 3m in diameter.

I have very limited data apart from the diameter and number of blades. The weight data seems to include a lot of non-moving parts, and I have no clue what the mass of an actual propeller and shaft might be.

 

If you have access to a 3-D CAM software like Solidworks, Inventor or similar, you can build a 3-D model of a propeller and perform the mass analysis. It will give you the exact values of mass and moment of inertia.
Or, you can download a similar prop from one of many sites for sharing of 3-D models (like grabcad.com), scale it to the size you need and perform the mass analysis.
Cheers

 

This paper at the link below gives some formulas for calculating the weight of a propeller along with the polar moment of inertia of the blades:

http://www.ajol.info/index.php/wajiar/article/viewFile/97540/86843

You can see how accurate it is by comparing its results with data from propeller manufacturers.

As far as shaft weights go, there is no simple formula for calculating shaft weight, except taking the actual dimensions of the shaft and making a weight take-off. Some vessels have long shafts, some short, some don't use conventional shafts and propellers at all (Z-drives are becoming more common for offshore vessels, because of the flexibility in control and because more vessels are adopting dynamic positioning to remain on station.)

 

Do you also wish to include the mass moment of inertia of the propeller shaft, gearbox, and the electric motor itself?

For the propeller I would model it as a hollow cylinder and an offset disk, as follows...

d1 = inside diameter of hub which is also the diameter of the shaft
d2 = outside diameter of the hub
d3 = diameter of the propeller
x1 = length of the propeller hub
m = mass of the propeller
rho = density of the propeller

from the above you should be able to determine the following
m1 = mass of the propeller hub = rho * pi * x1 * 0.25(d2^2 - d2^2)
m2 = mass of the propeller blades = m - m1
x2 = equivalent thickness of propeller disks = m2 / ( rho * pi * 0.25(d3-d2)^2 )
note that x2 isn't really needed but it does provide a bit of a reality check

From all of this the mass moment of inertia of the propeller can be estimated as...

I = [0.125 * m1 * (d2^2 - d1^2) ]
+ [ 0.125 * m2 * (d3-d2)^2 ]
+ [0.0625 * m2 * (d3+d2) ]

perhaps someone can check my work

 

Thanks for the quick and insightful comments!

I have access to autodesk software, but have never used it. Is it possible to use that for inertia calculations with a premade model?

I guess I will need approximate density of the propeller alloys to make the calculations.

 

Autodesk Inventor will do that job for you.
Download the propeller you need (or a similar one) from the Grabcad, import it into Inventor, assign the material to the part and calculate mass properties. As simple as that.
It is sufficient to download a prop which has a shape similar to the one you need. The diameter of the downloaded prop is not important as you can then scale it to the required value.

This is an example of what you get by performing the above steps, it took me 4-5 minutes from scratch to this:



The red marks indicate the mass and the moment of inertia of this 28.5" (0.72 m) bronze prop. This model of the prop is not very accurate (blades thickness not correct), so the resulting mass of 72 kg is pretty big for its size. More accurate models can be found in internet, all that is necessary is some time to find a proper one.

Hope it helps.

 

A quick estimate might be mk^2 where m is the mass and k, the radius of gyration.

k is perhaps 1/6 to 1/4 the diameter depending on how relatively heavy the hub is or how big the hole for the shaft is relative to the mass of the blades. It is always easier to estimate with radius of gyration rather than directly with moment of inertia because you can just guess what radius of ring of the same mass would have the same moment of inertia.

There is also way to measure it by swinging the propeller like a pendulum and working it out from the period of the pendulum, the mass, and the radius you are swinging it from. Fun stuff, if you have the propeller.

I am curious if in practice the water entrained by the propeller adds to its inertia.

 

Usually referred to a "added mass" for objects accelerating/decelerating in water. Typically calculated as a fraction of the displaced mass, and the added mass fraction depends on the shape of the object.

 

This paper can help: http://www.hydrocompinc.com/wp-cont...herson-2007-Estimation-of-Entrained-Water.pdf
The paper treats both axial and torsional added mass of a prop. In this particular case, the torsional component is what interests you.

 

Interesting. Thanks for that.

 

Thanks for the link.

 

Thanks again! Adding the right density was easy, but I do have some trouble halving the size of this to 2m diameter.

 

You have to open a new blank part, hit the "derive" button and choose that prop as a basis for the derived one. There, among the options, you will note the one which allows you to scale the part to the factor you need.
More info here: http://knowledge.autodesk.com/suppo...4F913EDA-57C3-4C3F-ADD7-7129880D0D1A-htm.html