Moment of inertia is calculated incorrectly

[Anonymous]

So I wanted to calculate the moment of inertia matrix about the COM of one of my parts. I decided to do a sanity check by comparing it to the moment of inertia for a cube. From sources I know that the moment of inertia of a cube is diagonal. but I am not obtaining that from Fusion 360. I get the following:

I then decided to compare this with Inventor and I did end up obtaining the diagonal: 

I also compared it with another CAD software and sure enough I got the what I expected

To my best knowledge I modeled this cube the same way in all 3 programs.  So I was wondering if I made a mistake in the modeling or if I am interpreting this data incorrectly. I have attached the Fusion 360 file I used to calculate the moment of inertia as well.

[henderh]

Hi @Anonymous,

I agree the products of inertia should be zero for a symmetrical body. It's logged in our system and sent on to development as ID 55088.

We appreciate you bringing this to our attention, and apologize for the inconvenience this is causing.

Best regards,

[Anonymous]

I don't know if this will also help out.So I believe this is an issue when right clicking on "Bodies" and selecting "Properties". When I right clicked on the "Component" and selected "Properties", I actually did obtain obtain a diagonal matrix. 

[henderh]

Aha!  Thank you for noticing the component properties are correct.
I've added this info to the issue ticket, it may help us diagnose the cause and remediation.

[henderh]

Hi @Anonymous,

Development has arrived at the solution. You'll be able to see the correct behavior in an upcoming Fusion update. However, it won't be for a while...it's looking like it'll be available towards the beginning of the spring season (for those of us in the N. hemisphere).

Thanks again!

Best regards,

[busycleta]

Hello,

@Anonymous  Fusion team, can you confirm, that moment of inertia is calculated 100% correct in current Version?

Thank you

[phoshovsky]

The moment of inertia calculation is not correct. See attached file. The values given for both the plate and circle are wrong. Selecting the properties from either the component or body gives the wrong value.

The Units shown in the dialog box must be in mm^4. It shows mm^2.  check any engineering textbook.

regards

paul

[sharatXNMPE]

I have the same issue of incorrect moment of inertia calculation for simple symmetric geometries. I have attached images with a cube and a sphere which should show MOI only on the principal axes but Fusion shows non-zero product of inertia. 

It doesn't look like this issue is solved. 

[busycleta]

This issue can be resolved with the help of a coding assistant, if I were the product manager, I would just do it

[andreiioan_cheptea]

The issue remains for bodies? The problem seems to be when you move the bodies from the center of mass to the origin, for components it seems that it works just fine. For bodies it calculates the moment of inertia at center of mass a bit wrong but hey it is close to the real value so...

The data copied from clipboard: 

Bodies (1)

Area 6.400E+07 mm^2

Density 0.008 g / mm^3

Mass 1.570E+08 g

Volume 2.000E+10 mm^3

Physical Material Steel

Appearance Steel - Satin

Bounding Box

Length 1000.00 mm

Width 10000.00 mm

Height 2000.00 mm

Center of Mass 0.00 mm, 0.00 mm, 0.00 mm

Moment of Inertia at Center of Mass   (g mm^2)

Ixx = 1.361E+15

Ixy = 0.00

Ixz = 0.00

Iyx = 0.00

Iyy = 6.542E+13

Iyz = 0.00

Izx = 0.00

Izy = 0.00

Izz = 1.321E+15

Moment of Inertia at Origin   (g mm^2)

Ixx = 1.361E+15

Ixy = 0.00

Ixz = 0.00

Iyx = 0.00

Iyy = 6.542E+13

Iyz = 0.00

Izx = 0.00

Izy = 0.00

Izz = 1.321E+15

And the one away from the origin:

Bodies (1)

Area 6.400E+07 mm^2

Density 0.008 g / mm^3

Mass 1.570E+08 g

Volume 2.000E+10 mm^3

Physical Material Steel

Appearance Steel - Satin

Bounding Box

Length 1000.00 mm

Width 10000.00 mm

Height 2000.00 mm

Center of Mass 500.00 mm, 5000.00 mm, 1000.00 mm

Moment of Inertia at Center of Mass   (g mm^2)

Ixx = 1.361E+15

Ixy = 0.048

Ixz = 0.012

Iyx = 0.048

Iyy = 6.542E+13

Iyz = 0.095

Izx = 0.012

Izy = 0.095

Izz = 1.321E+15

Moment of Inertia at Origin   (g mm^2)

Ixx = 5.443E+15

Ixy = -3.925E+14

Ixz = -7.850E+13

Iyx = -3.925E+14

Iyy = 2.617E+14

Iyz = -7.850E+14

Izx = -7.850E+13

Izy = -7.850E+14

Izz = 5.286E+15

[johnsonshiue]

Hi! Many thanks for reporting the issue! I tried it on my machine and I got slightly different measurement. For the box away from the origin, Moment of Inertia at Center of Mass, Ixy, Iyx, Ixz, and Izx are all 0.00, while yours shows some minor deviation.

Please share the f3d file here. I would like to take a look to understand the difference better.

Many thanks! 

[sharatXNMPE]

Update: The problem seems to have been resolved in April. I have consistent results with product of inertia = 0 for symmetric bodies and components as well. Not sure if the fix is universal or not. 

[andreiioan_cheptea]

It might be because I changed the Z axis to be up? Or something else, I don't know for sure.

(just right click on the body for properties, if it still shows 0 then it might be only on my computer- might need a reinstall)

[s190906BH5AJ]

I wanted to use the inertia calculation for a robot and also wrote an AddIn that can scale the inertia according to mass and translate it based on given axis. It was using the properties that Fusion calculates, but nothing was working. I sanity checked the properties given by Fusion and they were not at all what I expected. Some of the inertia matrices are not even valid, they were symmetric but their eigenvalues are negative.