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routercnc
03-07-2010, 12:59 PM
Attached are my thoughts on CNC design, looking at forces, moments, inertias etc.

Would be interested in thoughts on these ideas, and whether I'm missing anything in these considerations. Some interesting conclusions I think . . .

There is alot to digest here, and some maths, so watch out !

Thanks

routercnc
13-07-2010, 10:13 PM
Ok, so maybe that was too much of a mind dump!

In summary, for the machine being considered:
There seems to be some benefits to the lean back style of gantry where the C of G ends up in the centre of the side rail bearings. This reduces the bearing moment and reduces the risk of binding.
There is a formula for the ideal Z location for the X axis ballscrew which drives the gantry, which ends up being near the Z location of the tool
During constant velocity cutting the ballscrew forces are dominated by the cutting forces
During acceleration, the inertia of the gantry is only a small part of the total force, which is again dominated by the cutting forces
With well chosen geometry (ballscrew/rail/tool), the side rail bearing moment is small, meaning the bearings can be placed close together give more overall gantry movement along the X axis.


Finally, as mentioned in another thread, here is a further update to a spreadsheet calculating deflections and twisting of a gantry. Now added a further calculation for the gantry bending when cutting in the Y direction. So the gantry vertical deflection due to spindle weight, twisting due to cutting in X, and bending/lozenging due to cutting in Y direction can now all be approximated. This gives a rough minimum tool deflection. Comments and errors gratefully received . . .

irving2008
13-07-2010, 10:29 PM
good stuff...

haven't checked through all the math :whistling: but looks good. I'm surprised how poor I-Beam is in torsion, but its clear box section is the way to go... I would expect C-section to perform equally poorly..

I did the calcs once before in a similar way for box section for side supports to gantry instead of plate, you might want to add that option. Also there, I- & C-section might make sense as there is little torsion...

FatFreddie
14-07-2010, 12:04 AM
good stuff...

haven't checked through all the math :whistling: but looks good. I'm surprised how poor I-Beam is in torsion, but its clear box section is the way to go... I would expect C-section to perform equally poorly..

I did the calcs once before in a similar way for box section for side supports to gantry instead of plate, you might want to add that option. Also there, I- & C-section might make sense as there is little torsion...

As I'm sure you know, for the best stiffness to weight ratio in both bending and torsion you basically want to move the material as far away as possible from the neutral bending axis (and have a closed section for torsion), which means ideally a round tube but box section is pretty good and much easier to work with. If you look at bicycle frames where they care a lot about both stiffness and weight the tube forms are generally close to circular, elliptical or a rounded off box

I like the idea of an option for using box on the side supports - it always looks like the weak point on a lot of gantry designs and it would be nice to be able to quantify that.

I'm also interested in the idea of placing bearings close together - I have been designing to get them as far apart as possible working on the principle that it's not expensive to make the axes a little bit longer and it will reduce the effect of any flex in the bearings. It will also let me put the leadscrews in a convenient position rather than the best place to minimise the forces on the bearings - any comments?

Good thread.

Mark

Ross77
14-07-2010, 01:40 AM
I'm surprised how poor I-Beam is in torsion,


In use I beams need to be laterally restrained other wise they will fail way before the design loading has been reached because of Lateral torsional bucking (LTB) and is were the the beam literally rotates under load (due to poor tosion capabilities) and the advantage of the I beams strength (Parallel axis theory) is lost. Of course I'm talking buildings with mega loading, but might apply to to cnc if the I beam is small enough.


As I'm sure you know, for the best stiffness to weight ratio in both bending and torsion you basically want to move the material as far away as possible from the neutral bending axis (and have a closed section for torsion), which means ideally a round tube

Another advantage is that you can reduce the wall thickness and go up in diameter to achieve a strength gain but no increase in weight.


I'm also interested in the idea of placing bearings close together - I have been designing to get them as far apart as possible working on the principle that it's not expensive to make the axes a little bit longer and it will reduce the effect of any flex in the bearings. It will also let me put the leadscrews in a convenient position rather than the best place to minimize the forces on the bearings - any comments?

Not sure its a good idea to just 'want' to put the bearings close together. you need to look at the whole system as one change can affect over aspects and cause all sorts of problems. More info needed :smile:

Of course if you are talking linear bearings then you just need to design within there spec and they are much more tolerant of mis alignment and binding than others. IMO Leadscrews/Ballscrews really need to be in the best position tho.

routercnc
15-07-2010, 10:59 PM
By popular demand I've updated the spreadsheet to include a range of sections for the gantry sides in bending.

I've also added the 'channel' section to the torsion page. I referred to this as C section before, which is not quite correct, since C section is channel with small return flanges on the short pieces (like serifs).

Anyway, see post#2 above for the updates.

As expected the channel is similar to the I beam for torsion (i.e poor), but redeems itself in the bending load case. Overall though, closed sections are good all round choices. The flat plate option for the sides of the gantry looks less good that the other sections, but to get the advantages of the other sections you do need to get the load into them. The easy method of bolting through the flat outer surface is likely to distort the section locally before the rest of it gives you the benefit. A flat plate is likely to be fine for many applications, but if you can get a good connection to a sectioned part then it will be better.

If you can afford the profile and carraige style on the X axis, the moment reaction these provide during Y cutting gives great benefits vs open bearings on supported rails (which rotate!), although they do have a max moment (check the bearing spec).

Enjoy . . .

Ah, another thing. The X axis bearing close together bit. I was surprised at this myself but the maths points to it if:
You are machining thin 2D type parts whereby the tool is in about the same Z location during cutting, and you stick to the equation about relative position of parts (if you are machining deeper parts, then the tool is at different heights, moments creep in, and the geometry is no longer ideal, and you might want to not put the bearings so close)

You are using modest acceleration rates - probably hobby rates would be OK. At very high production type rates the gantry inertia would start to have an effect and again you might not want them so close due to the moment.

My next machine, or future mod to this one, will put them closer together, but I know why I'm doing it and what I want to achieve. You'll have to decide if it works for your application. If you're not sure, go with Ross and space them out a bit.

Ross77
16-07-2010, 02:00 AM
Ah, another thing. The X axis bearing close together bit. I was surprised at this myself but the maths points to it if:



Tell me more, I need to Know :smile:



My next machine, or future mod to this one, will put them closer together, but I know why I'm doing it and what I want to achieve. You'll have to decide if it works for your application. If you're not sure, go with Ross and space them out a bit.


thats the problem, that people look a designs and say "well he's done it like that and it worked" withouth understanding why.....still engineers tend to be belt and braces, think off a no. and double it (or is that the hourly rate?):whistling:

routercnc
16-07-2010, 08:47 AM
OK, bit more about the close spacing of the X axis bearings.

If you run through the 'force_and_moments4' spreadsheet (post#1), you'll see the maths to support it. But there are design conditions:

1. You need to put the C of G of the gantry in the middle of the X axis bearings, i.e. a lean back style of gantry. This removes the moment on the bearings due to an offset C of G.

2. You need to arrange for the ballscrews (or whatever) to be placed at a set distance away in Z away from the side bearings, relative to the distance in Z to the tool from the side bearings. See formula at the bottom of tab3. This ends up being at a similar height to the tool, the slight difference being due to taking account of the friction in the bearings. In practice this would probably mean dual X axis ballscrews so you can run one down each side of the gantry. A single centre drive would get in the way of the cutter!
With this arrangement, at a fixed cutting height, there is no moment on the bearings during cutting.

3. You need to tend to cut at a similar height, i.e. thin materials. Once you cut at other heights, e.g. 3D, then the cutter is not always at the same distance from the bearing in Z, but the ballscrew is. This then starts to add a moment. You could get around this by raising and lowering the workpiece, which I have seen done, but adds complication.

4. You need to use modest accelerations, and modest gantry weights. In my example I used a 20kg gantry, and up to 2000mm/min2 acceleration. The gantry inertia was very small, and hardly added any moment. The main factors were the cutting force moment and the ballscrew force moment which basically cancelled to leave no moment.


With these conditions met, and no resulting moment, you are then left with the X axis bearings only supporting the weight of the gantry. They can then be close together or far apart and react the same load, so you can choose to mount them close together to gain travel. The danger of racking (made worse with closer bearings) is gone because you almost certainly need to drive the gantry with twin ballscrews to meet condition 2.

Hope this helps . . .

Ross77
16-07-2010, 01:26 PM
Thanks for clarifying that, I understand the logic but I would say that it would be a very limited machine tho. Light weight , slow and the added expense of two ballscrews.

The cost for getting slightly longer rails is minimal compared to what you would need to do to counter the close beraings, also bear in mind that plain friction bearings require a 2:1 ratio anyway so they dont bind :smile:


The more I use my lathe im still amazed how even large chunks of steel can flex.
Just my 2 pennth again :naughty:

williamturner1
02-10-2010, 04:13 PM
By popular demand I've updated the spreadsheet to include a range of sections for the gantry sides in bending.

As expected the channel is similar to the I beam for torsion (i.e poor), but redeems itself in the bending load case.

Great work! Thanks for sharing.

I really am surprised at the figures for IBeam. With industrial stock ... eg 100mm Width / 200mm Height / 10mm thickness upper + lower plates, 7mm thickness of upright.
Comparing it to 12mm thick Plate, 200mm height
and RHS 120 x 80 x 3

Ive placed 120x80x3 2m length between two RSJs and stood on its middle and bounced, observing its considerable flex.
I've done the same with a 2.2m RSJ (100x200x10) and done my best tigger impression but observed little if any movement.

but the spreadsheet indicates the opposite should be observed:
DEFLECTION: 31micros vs 2micros (RSJ vs RHS)
TORSIONAL STIFFNESS: 28,000 vs 1,800,000 (RSJ vs RHS)

Colin Barron
03-10-2010, 09:27 PM
Maybe this extra stiffness of the box section is why the likes of axyz and chinese makers use this design for the y axis?
Do they use aluminium or mild steel box section. I bet its steel, stronger and easy to weld plates onto it as well as better stiffness?
what is the main reason diy builders use aluminium, softer so easier to machine, lightness or does not rust?
Any ideas?
I am not American!

routercnc
04-10-2010, 02:04 PM
Hi williamturner1

You might be reading off the wrong rows.

I've compared the 2 shape:
'I beam' width 100mm, depth 200mm, flange 10mm, web 7mm
RHS width 120mm, depth 80mm, wall 3mm

Assuming length 2000mm, and your weight 60kg, and vertical Z deflections are:
I beam 23 microns
RHS 393 microns

Which tallies with your jumping experiment, showing the vertical stiffness difference, where the I beam is much stiffer.

Unless you had a lever arm to jump on (which was very stiff), then you would not be comparing the torsional performance which I would expect to be worse for the I beam.