Gantry design and FEA analysis

[eci22]

Hi all,
So a thread of mine asking about advice on different X axis rail configurations (http://www.mycncuk.com/threads/13497...arings-designs) kind of deviated into a discussion about the suitability of the material chosen which is 50x50x3mm mild box steel, I didn't mind as all advice is welcome, but I wanted to see some data to backup what I was being told, which is the main point of this thread so I did some FEA analysis:

Goal for the machine
mill 6082T6 Aluminium at 1 to 3mm DOC with an accuracy of between 0.1 to 0.3mm

Dimensions:


600x350mm not a huge gantry by any means

Fixed Ganry Designs- 50x50x3mm mild box steel

A: No bracing used more as a baseline for comparison against other designs


B: Vertical bracing


C: Diagonal bracing


All FEA analysis' uses 980 Newtons force = 100kg

FEA Analysis Type 1, no Z axis plate


Design A: Max displacement of 0.01 mm under a force of 100Kg


Design B: Max displacement of 0.009 mm under a force of 100Kg


Design C: Max displacement of 0.009 mm under a force of 100Kg

FEA Analysis Type 2, with Z axis plate (200x300x20mm Cast Tool Plate Aluminium)


Design A: Max displacement of 0.09 mm under a force of 100Kg


Design B: Max displacement of 0.07 mm under a force of 100Kg


Design C: Max displacement of 0.08 mm under a force of 100Kg

Questions

1.Which is a more realistic FEA setup, Type 1 or Type 2 or something different (and why) ?

2. Is 100kg force a good ballpark figure to use given the cutting parameters of my machine ? This number was a pure guestimate on my part, what is the correct way to calculate?

3.The displacement figures seem to suggest the material (50x50x3) is suited to the task- 0.09 to 0.07mm displacement under 100kg seems perfectly acceptable to me unless I've missed something ?

4. What else have I missed ?

All help appreciated

EDIT:
Voicecoil pointed out incorrect decimal places in second set of results, thank you!

[Voicecoil]

Setup 2 is much more realistic since you want to design for decent performance when the cutter is hanging down a fair way below the gantry, 'coz that's where it will often be used. Having an equal horizontal force on each beam really isn't going to happen as that would mean the workpiece being considerably higher than the bottom of the gantry. 1000N cutting force is maybe a bit much unless you're using big cutters, I've heard figures of 200N tops bandied about before for typical machines such as people on this forum build though I haven't seen the sums behind that. I did find this reference a little while back though:

https://www.ctemag.com/news/articles...e-when-milling

Putting some numbers into the formula for a 1.5mm DOC on a 3 flute cutter at 0.1mm feed per tooth I get a tangential force around 90N for the best 6000 series ali.

It would also be interesting to do an analysis with a plate fixed on the back of your 2 bits of box section as that will make kind of a super box with the Z plate.

PS looking at your pics again, there might be a decimal point adrift in the text for the second set of results.....

[routercnc]

Agree with Voicecoil.
Analysis 2 is closer to worst case as this puts a twisting moment on the gantry as the force is applied at some distance away from the structure and will usually cause the biggest deflection.

I wrote a spreadsheet a long time ago just to play with the numbers and I looked at 3 load conditions.
Vertical load at the centre of the gantry due to the mass of the Y and Z axis and estimate the sag.
Lateral load applied at the tool tip as this will want to turn the gantry into a parallelogram- one reason why raised bed sides is stiffer than tall gantries.
Foreaft load at the tool tip to twist the gantry. This usually causes the most deflection and you need to make the gantry have a shape with material around the outside not 2 isolated beams. So yes plate them together is an option.

I used 80N load for cutting aluminium.

Remember this is all to see relative performance and get a feel for what aspects are important as it will assume perfect joints and you would need to model the whole machine and the cutter to get close to the actual deflection and even this is the steady cutting force not the deflection caused by vibration which will add some more.

The stiffest gantries in terms of numbers are raised bed sides with a large box section as this gives good stiffness for all load cases. But practical considerations mean other options are good including the famous L shape gantry with 2 good sized rectangles joined in an L shape.
In the end you want a single shape with as much material as possible away from the central axis it is trying to twist or bend about (the neutral axis). Once you have the largest outline you then up the wall thickness for many reasons including getting the load into the section from discretely mounted components. Depending on the design the very large sections may need baffles or subdivisions.

It’s fun to look at the numbers and get a feel for it but also look at successful machines to see what has worked before and bare in mind the practicalities of building it and having adjustment capability.

[Kitwn]

I know you are designing on the basis of 50 x 50 material but rather than the complexity of the braces in the designs above have you considered two pieces of 100 x 50 welded together to give a flat face 200 high? Your overall height looks to be about that anyway. I'm really asking because that's what I've built and I'd love to see the deflection calculations.

[eci22]

I know you are designing on the basis of 50 x 50 material but rather than the complexity of the braces in the designs above have you considered two pieces of 100 x 50 welded together to give a flat face 200 high? Your overall height looks to be about that anyway. I'm really asking because that's what I've built and I'd love to see the deflection calculations.

Hi Kitwin, do you mean like this ?


This seems like a very stout design and is better than the bracing I used. I have used it to generate some numbers below- hope they are of interest. But the analysis suggests the biggest component for deflection is the material of the Z plate, it seems to contribute the most. If you are interested let me know your exact materials ,including Z plate and I would be happy to run the numbers for you

I've changed all model calculations to use 100 Newtons of force. Also the Z plate is now 200x300x12mm Aluminium



My main question is where did you perform the welds for the two pieces of 50x100?, A seam weld covering the entire length would lead to significant warp id imagine and tack welds wouldn't hold up, bolts would work I suppose. How did you make yours ?

Agree with Voicecoil.
Analysis 2 is closer to worst case as this puts a twisting moment on the gantry as the force is applied at some distance away from the structure and will usually cause the biggest deflection.

Hi routercnc, can I just say the videos on your CNC build is really inspiring. I learnt so many subtle things the info is worth its weight in gold to me. It's something I come back to time and time again. Thank you for putting it out there !

I wrote a spreadsheet a long time ago just to play with the numbers and I looked at 3 load conditions.
Vertical load at the centre of the gantry due to the mass of the Y and Z axis and estimate the sag.

(All simulation diagrams use 100 newton force)

Vertical Load like this ?


Presumably the only force is gravity and the weight of your cutting tool, which I haven't included.

Lateral load applied at the tool tip as this will want to turn the gantry into a parallelogram- one reason why raised bed sides is stiffer than tall gantries.

lateral load


correct ?

Foreaft load at the tool tip to twist the gantry. This usually causes the most deflection and you need to make the gantry have a shape with material around the outside not 2 isolated beams. So yes plate them together is an option.

Is that the same as moment force around the Y axis of the Z plate ?

Remember this is all to see relative performance and get a feel for what aspects are important as it will assume perfect joints and you would need to model the whole machine and the cutter to get close to the actual deflection and even this is the steady cutting force not the deflection caused by vibration which will add some more.

Yes definitely, I just find this really interesting to do. It's a good way of comparing different designs. I'll use this for guidance only and for learning FEA which is something I have not done before. I also appreciate not having the Y axis, the feet, basically the rest of the machine modeled will skew the results somewhat

The stiffest gantries in terms of numbers are raised bed sides with a large box section as this gives good stiffness for all load cases. But practical considerations mean other options are good including the famous L shape gantry with 2 good sized rectangles joined in an L shape.

Would you mind directing me to a picture of this gantry design ?

Setup 2 is much more realistic since you want to design for decent performance when the cutter is hanging down a fair way below the gantry, 'coz that's where it will often be used. Having an equal horizontal force on each beam really isn't going to happen as that would mean the workpiece being considerably higher than the bottom of the gantry. 1000N cutting force is maybe a bit much unless you're using big cutters, I've heard figures of 200N tops bandied about before for typical machines such as people on this forum build though I haven't seen the sums behind that. I did find this reference a little while back though:

https://www.ctemag.com/news/articles...e-when-milling

Putting some numbers into the formula for a 1.5mm DOC on a 3 flute cutter at 0.1mm feed per tooth I get a tangential force around 90N for the best 6000 series ali.

It would also be interesting to do an analysis with a plate fixed on the back of your 2 bits of box section as that will make kind of a super box with the Z plate.

PS looking at your pics again, there might be a decimal point adrift in the text for the second set of results.....

Thanks for the link Voicecoil, much appreciated. I updated the the force to 100 newtons in my above simulations, I also made my Z plate thinner as I realised 20mm thick tool plate is out of my budget. If I have done the simulations correctly then the numbers still look promising. I will look to add the fixed plate at the back tomorrow. Thank you very much for your input

[Kitwn]

Hi Kitwin, do you mean like this ?


My main question is where did you perform the welds for the two pieces of 50x100?, A seam weld covering the entire length would lead to significant warp id imagine and tack welds wouldn't hold up, bolts would work I suppose. How did you make yours ?

That's about it. just two pieces of 50 x 100 welded together to give 200 x 50. The whole is then welded to the gantry uprights.

Bear in mind that this gantry was the first time I ever tried welding, I bought a cheap stick welder specifically for this job. To minimise the warping I clamped the pieces together and used a series of short welds alternating between the front and back seams. I use a welding technique I've called "Bird Poo" since that's what the result most resembles. Copious use of an angle grinder, gobs of car body filler and a layer of paint make it look much better than it is. The front surface was flattened (not very well) using epoxy.

[Voicecoil]

I also made my Z plate thinner as I realised 20mm thick tool plate is out of my budget. If I have done the simulations correctly then the numbers still look promising. I will look to add the fixed plate at the back tomorrow. Thank you very much for your input

Tip: if you can add some bits of bar to stiffen your Z-plate (i.e. turn it into a channel section) you will do better cost for cost than a flat plate. For example a 10mm plate 180mm wide with some 30 x 15 bar fixed down the edges is about 2.5x as stiff front to back as a piece of 20mm plate 180mm wide - go simulate it if you want to. I mention this because you generally end up with some space between the front and back z plates due to having to accommodate the carriages, ballscrew etc., so why not put something useful in there. The front (moving part) of the z-axis maybe isn't such an issue as the z rails will stiffen that.

PS If you want 0.1mm accuracy, you will likely need to design for static deflection figures rather better than that - remember that cutting metal produces a lot of vibration which can mess things up.

PPS what FEA package are you using? looks good.

[routercnc]

Glad you found the CNC videos useful. It was a good way to pass on the ideas I had seen, and add some of my own thoughts.

In the analysis:
Yes, vertical direction forces are mostly due to gravity but they will be much higher than 100 N as this only represents a Y and Z assembly of about 10 kg. More like 25-50 kg depending on the design, possibly more. This is to see how much the gantry will sag if you are surfacing a plate as in the extreme you would cut a dished shape. There is also a pull down force when using spiral fluted cutters, and there will be forces when drilling or plunging.

The lateral direction analysis is correct for the load direction but because of the grounded sides in your simple analysis it won't mean much on the results you have there.

The fore/aft analysis is in the wrong direction - it would be in the 'Z' direction using the coordinate system you have in the top right corner and would cause the part of the Z axis plate which is hanging down to all bend forward or rearward, and cause the gantry to twist about the 'X' axis as per your coordinates in the picture. This is usually the worst case of all the load conditions.

There are lots of square and rectangular gantries out there but the L shapes gantries were 'invented' by JazzCNC:

[Boyan Silyavski]

Combine both and that's what you will have if you do not design properly the machine.

If you design your Z properly , use proper bearings and mount your spindle correctly, variant 2 will be non existent, so variant 1 is the real deal.
As if you clamp your spindl properly its body will strengthen the Z and only a couple of braces will make the Z equivalent to like a solid chiung of 100x100mm metal


Here is some design wisdom to you: it does not matter what profile you use. A well designed machine will have such design as to simulate at least 10cm wide x 3cm thick steel plate against all cutting directions. Against the 3cm no the 10cm. Or the equivalent. in whatever material/s you do it.

So go and make it 50x50mm but remember what i said if you want your machine to cut vibration free aluminum or even steel.

Check my build at page 7 for the gantry and page 16 and 17 for the Z, to grasp the idea of how serios a gantry and a Z have to be to machine fully extended at 200mm.

Its not only my machine i am bragging about. There at least a couple machines on forum that are seriously heavy duty and one way or another they are build like that.

[eci22]

Tip: if you can add some bits of bar to stiffen your Z-plate (i.e. turn it into a channel section) you will do better cost for cost than a flat plate. For example a 10mm plate 180mm wide with some 30 x 15 bar fixed down the edges is about 2.5x as stiff front to back as a piece of 20mm plate 180mm wide - go simulate it if you want to. I mention this because you generally end up with some space between the front and back z plates due to having to accommodate the carriages, ballscrew etc., so why not put something useful in there. The front (moving part) of the z-axis maybe isn't such an issue as the z rails will stiffen that.

Do you mean like this ?

PS If you want 0.1mm accuracy, you will likely need to design for static deflection figures rather better than that - remember that cutting metal produces a lot of vibration which can mess things up.
PPS what FEA package are you using? looks good.

The FEA software is Fusion 360, it is really nice once you get used to it. What kind of ballpark figures should I be looking at for in the deflection analysis ? At the moment I'm not actually taking figures as real world numbers, but more to compare the deltas between different designs.

Yes, vertical direction forces are mostly due to gravity but they will be much higher than 100 N as this only represents a Y and Z assembly of about 10 kg. More like 25-50 kg depending on the design, possibly more. This is to see how much the gantry will sag if you are surfacing a plate as in the extreme you would cut a dished shape. There is also a pull down force when using spiral fluted cutters, and there will be forces when drilling or plunging.

Great I will, add the additional forces for future analysis

The fore/aft analysis is in the wrong direction - it would be in the 'Z' direction using the coordinate system you have in the top right corner and would cause the part of the Z axis plate which is hanging down to all bend forward or rearward, and cause the gantry to twist about the 'X' axis as per your coordinates in the picture. This is usually the worst case of all the load conditions.

So rotating around the X axis would would be the following force, correct ?

Bear in mind that this gantry was the first time I ever tried welding, I bought a cheap stick welder specifically for this job. To minimise the warping I clamped the pieces together and used a series of short welds alternating between the front and back seams. I use a welding technique I've called "Bird Poo" since that's what the result most resembles. Copious use of an angle grinder, gobs of car body filler and a layer of paint make it look much better than it is. The front surface was flattened (not very well) using epoxy.

Yes I'm quite familiar with the bird poo welding technique : ). When you were welding, did you let the weld cool before removing the clamps and turn the piece around to clamp the other side or did you weld one side un-clamped, turn it over clamp it down and then weld the other side ? It you clamped down the first side then welded and turned over to weld the second side the clamps wouldn't have much effect on the first side at least ?- I'd be really interested to hear your workflow as I've alredy welded my Y axis and I am trying to improve my amount of warp in the rest of the build ( I'm using gaseless MIG, a very very basic machine), I've seen a bunch of you tube videos but haven't dialled in my sequencing yet.

Combine both and that's what you will have if you do not design properly the machine.

If you design your Z properly , use proper bearings and mount your spindle correctly, variant 2 will be non existent, so variant 1 is the real deal.
As if you clamp your spindl properly its body will strengthen the Z and only a couple of braces will make the Z equivalent to like a solid chiung of 100x100mm metal


Here is some design wisdom to you: it does not matter what profile you use. A well designed machine will have such design as to simulate at least 10cm wide x 3cm thick steel plate against all cutting directions. Against the 3cm no the 10cm. Or the equivalent. in whatever material/s you do it.

So go and make it 50x50mm but remember what i said if you want your machine to cut vibration free aluminum or even steel.

Check my build at page 7 for the gantry and page 16 and 17 for the Z, to grasp the idea of how serios a gantry and a Z have to be to machine fully extended at 200mm.

Its not only my machine i am bragging about. There at least a couple machines on forum that are seriously heavy duty and one way or another they are build like that.

Hi Boyan, thanks for your input- do you mean your build log from project 1 in your signature ? If so I just want to point out one thing from the first page of that build log:

2. Money is not an issue for the frame or the length of the supported rails, so i am not going to go cheap to save 10cm of rail or steel profile.

Unfortunately this is not the situation I am in, so I am trying to generate as much data and perform as much analysis on my design so I have enough information to make informed decisions about my build. Do you have images of your final build, it would be great to see an example of the Z axis you are describing. Thanks