cnc machine stiffness calculator

[routercnc]

:tup: thanks Ross and ecat.

Torsion - I don't know how to calculate the twisting (torsion) constant K for arbitrary shapes so it is work in progress. There's probably a parallel axis theorem equivalent. But all the regular shapes are done.
[EDIT: Bit of research and it's not possible to calculate the torsion constant for arbitrary shapes since they are not symmetrical and will warp, leading to large errors. Only option is to use FEA (Finite Element Analysis) software. Alternatively choose a regular shape which is closest to your arbitrary shape, and use Engineering judgement over whether your arbitrary shape is likely to be better or worse than this for torsion. Sections with more material distributed around the outside are the best for torsion e.g. sections approaching a tube.


The other work in progress is the router mounting plate tab - lots to do here. At the moment all the Z axis is assumed rigid, including the cutting tool.

The more I add to this sheet, the more I realise how much is missing, but hopefully it's a start.

Ross, I think you can still contribute. You were working on a Z axis weights sheet - that could be useful to tab at the front of this one because at the moment the Z axis weight (or mass!) is a user estimate.

[MX55CNC]

Good afternoon.
Please tell me with the calculations in your table:
Calculating Ixx values for more complex shapes (using parallel axis theorem)

Please give an example.

[routercnc]

Good afternoon.
Please tell me with the calculations in your table:
Calculating Ixx values for more complex shapes (using parallel axis theorem)

Please give an example.

I’m away from the PC so will give a brief explanation. For complex shapes you need to break it down into a series of standard shapes such as rectangles, calculate the Ixx for each shape, then multiply by the area of each shape and the square of its distance from the overall shape neutral axis and sum these values together.

Google parallel axis theorem for examples. I’ll post a better explanation another time.

[Voicecoil]

You may be able to save a bit of time analyzing the components using this:

https://skyciv.com/free-moment-of-inertia-calculator/

It does shapes such as I beam, T beam and angle as well as tubes.

[routercnc]

You may be able to save a bit of time analyzing the components using this:

https://skyciv.com/free-moment-of-inertia-calculator/

It does shapes such as I beam, T beam and angle as well as tubes.

That's quite a handy calculator, so it might be all you need.


But if you want to know what it is doing, there are quite a few steps involved (which is why you are better making a spreadsheet if you want to do lots of them). I've shown a worked example which uses 2 rectangles in a T shape. You can make any shape using more rectangles but need to include more terms in each equation associated with each new rectangle.

The T shape is worked through in 7 steps:









Hope this helps.