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03-07-2010 #1
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
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13-07-2010 #2
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 . . .Last edited by routercnc; 15-07-2010 at 09:43 PM. Reason: updated spreadsheet 15/07/10
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13-07-2010 #3
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...
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13-07-2010 #4
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
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14-07-2010 #5I'm surprised how poor I-Beam is in 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
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?
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.
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15-07-2010 #6
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.Last edited by routercnc; 15-07-2010 at 10:08 PM. Reason: more info
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02-10-2010 #7
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)Last edited by williamturner1; 02-10-2010 at 03:25 PM.
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04-10-2010 #8
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.
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23-05-2018 #9
Thanks for sharing your info. Here is a great paper on torsion of beams. The clear winner is closed shapes, tubes, of all shapes: circular, rectangular. https://www.slideshare.net/edwinrami...-torsion-guide
I'm in the process of beefing up my aluminum extrusion CNC to be a dual-purpose wood/metal machine and have so much to learn. This is a great forum! If any of you would care to view this video and lend some advice, I'd sure appreciate it.
https://youtu.be/2QTZa2Ge9A0
Cheers,
Tyler
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23-05-2018 #10
Hi Tyler
Welcome to the forum. You may find the picture build menu interesting
http://www.mycncuk.com/threads/10066...s-picture-menu
Note the suggested rules of no replies just to keep that thread clean, but see if there is something there. The posters are regulars here so start a new thread with questions for more info on any of the machines.
Thanks
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