cnc machine stiffness calculator

For those interested, I thought I'd post my updated stiffness calculation spreadsheet in a new post. This spreadsheet is intended for a typical moving gantry cnc routing machine, and may help with the design of the basic structure. X axis is the long axis which the gantry jogs along. Y axis is spanned by the gantry, and Z axis is up and down.

General process is:
step1. Select 'gantry top' tab and study diagram
step2. Enter required load, material and other data
step3. For your chosen section(s), enter geometry (e.g. RHS, tube)
step4. The deflection calculations are then shown below
step5. You can then select one of these sections to be used in the tool deflection graph

Repeat the above for 'gantry sides' tab

Finally, in the 'tool error' tab, enter the required accuracy and the section results selected in step 5 from the previous tabs are shown as an ellipse for the X and Y deflections. Z direction is just a bar graph. You may wish to add a safety factor to the required accuracy figures to account for parts of the machine not modelled.



New features in version 7 are:

• Stiffness approximations of commercial ali profiles (e.g. Hepco)*
• I value calculations for arbitrary shapes, not just RHS, round etc. This is a standalone calc and gives vertical bending deflection only.
• Gantry top bending in the X direction (previously ignored)
• Visual tool deflection error graph vs requirement

Usual disclaimers apply.

* method used is to create an RHS section with similar properties

Thank you very much :)
So much to learn.

Flash git. :smile:

Looking good mate , now I don't have to do it......:tup:

I see you have covered up the torsion calc bit, is that work in progress?

I like the bit about tool deflection and what is actually required, I have just got there from a spindle design point of view and it would suggest that the best place to look for weakness is the tool itself. Seems daft to design a really rigid machine with crazy fast rapids if you are only using small tools with a slow low powered spindle, theres so much to consider with this CNC game eh :rolleyes:

Any way going off topic, save that for the spindle one....

: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.

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[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.

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That makes me feel better, I thought I was just being lazy using FEA. :whistling: If you just want to calculate the K value and dont want full blown FEA then I tried this software and seemed very good. About £40 for a licence, if you go for it.

or this is free working demo, cant save or print (think you can screen capture tho) aproximate k value but very quick for calculating composite beams.

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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.

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sure paste it in, the spindle design bit has lead me to start at the cuuting tool so Im working on the feeds and speeds and required forces at the mo. so that should help as well.

I just want to say "thanks" to routercnc for this very useful design tool. It has quickly helped me to make some choices on the gantry design. I was surprised at the efficiency of box sections over simple plate, which most aluminum deisgn home routers / millers use. I had trouble with commercial extrustion section, but found the formulae in the "item" (Bosch - Rexroth) catalogue for deflection and torsion. There is also a free useful program "Tech Toolkit" produced
http://www.8020.net/Design-Tools-26.asp by the American outfit 80/20 which calculates the deflection for their profiles and you can define your own sections in it if you know the material and moments of inertia. Overall well done and so useful!. Measure twice cut once eh!!!!

can some one do a quick video and post it, phew, too much to take in and i am having headache trying to work out haw to fill in

help please

What a awesome calculator. Thanks a lot !

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.

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Originally Posted by 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.

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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.

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.

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Originally Posted by 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.

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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:


Attachment 26487
Attachment 26488

Attachment 26489

Attachment 26490

Hope this helps.

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Originally Posted by routercnc

New features in version 7 are:

• Stiffness approximations of commercial ali profiles (e.g. Hepco)*
• I value calculations for arbitrary shapes, not just RHS, round etc. This is a standalone calc and gives vertical bending deflection only.
• Gantry top bending in the X direction (previously ignored)
• Visual tool deflection error graph vs requirement

Usual disclaimers apply.

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Hi routercnc,

the stiffness calculator looks incomplete. Is it still cooking on the back burner, or did you abandon it completely, lost interest? If so, it'd be sad because it's hard to explain how important I feel this tool is.

Regards,
DN

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Originally Posted by dn7

Hi routercnc,

the stiffness calculator looks incomplete. Is it still cooking on the back burner, or did you abandon it completely, lost interest? If so, it'd be sad because it's hard to explain how important I feel this tool is.

Regards,
DN

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I wrote this along time ago when I was designing my first machine to explore the importance of design choices. It got to a point where it worked well enough and would allow most users to gain some design principles for their own machine. I stopped there and have no plans to go further. For the next level of analysis with more complex shapes you need to step up to FEA but this works in a different way and needs commercially coded software to run. My advice would be to have a play and come away with some principles, such as material needs to be far away from the neutral axis to resist bending and torsion. But in the end the design still needs to be practical and buildable.