Rigidity and random questions

# Thread: Rigidity and random questions

1. ## Rigidity and random questions

Hi,
I'm trying to figure out a rigid 2.5-3m (100-120") base for a gantry router.
The gantry will slide on a preloaded ball bearing groups on square steel pipes about 100-150mm (4-6"), 5-8mm (~1/4") thick.

Calculated deflections seems horrific, like 0.5mm for 200kgf, but 200 is a blind guess as I actually have no idea what the real-life cutting forces usually are. I've tried some calculators etc. but I guess tangential cutting force isn't the only one, plus there are vibrations, entering the material etc.?
For a 3kW spindle - could 2.5m(100") unsupported "rails" be viable at all? Or is it better to go with something thinner with support points?
Could it be real and what should I consider to be able to cut mild steel with 4mm (5/32") cutter 0.5mm (0.02") deep, 0.35m/min (14ipm) and error ~0.05mm (0.002") for every 50mm(2") of travel?

Another idea - did anyone ever tried to pour a concrete base?
The further I look the more economical it seems to do so - weld two "rails" on steel reinforcements, then pour two slabs of concrete around the length of each one (I want to have the table between rails partially removable to be able to put larger things in).

I know this all sounds quite random - guess in reality I'll settle for whatever works

2. For a 3kW spindle - could 2.5m(100") unsupported "rails" be viable at all?
Sounds like you're talking about regularbearings (skate bearings?) rolling on the tubes? And you want to cut steel? I'd say no, not viable. Not the unsupported rails, and not the 3Kw spindle.

I know of one machine here with a concrete base, but I don't think it's been finished yet.

3. Thanks for reply!
Yes, bearings are regular deep groove ball, but not skate ones (6301 - 12x37x12). They're capable of higher loads and I'm planning to use them in groups of 4 to 8 per contact point, which should total in over 3000kgf per contact point (2 contact points per rail, per side). Could that be enough or the problem is elsewhere?
Could you please give a suggestion on what type of spindle could cut steel with 4mm bit?

Originally Posted by ger21
Sounds like you're talking about regularbearings (skate bearings?) rolling on the tubes? And you want to cut steel? I'd say no, not viable. Not the unsupported rails, and not the 3Kw spindle.

I know of one machine here with a concrete base, but I don't think it's been finished yet.

4. The whole thing needs to be really stiff to cut steel. If the deflection at the tip of the cutter (cutter plus whatever it is attached to) is more than the thickness of the chip, (feed per tooth) then it is guaranteed to chatter, and not cut well. This is why milling machines are HEAVY

5. Thanks.
Well, there will be no alminum parts
I'm rather afraid if going with concrete option it will be too heavy to move ever after..
Could what you say about deflection/chip mean that going with small diameter bits is not a solution?

Originally Posted by neilw20
The whole thing needs to be really stiff to cut steel. If the deflection at the tip of the cutter (cutter plus whatever it is attached to) is more than the thickness of the chip, (feed per tooth) then it is guaranteed to chatter, and not cut well. This is why milling machines are HEAVY

6. The larger the bit, the larger the load, the larger the deflection.
Many router shafts are just not stiff enough, in themselves.
If you can do anything with steel, you will be limited to quite small cutters.
Drilling usually is fine.

7. Good questions and replies above. For milling steel, cutting forces can range from 200 to 4000 N (20 to 400 kg). Your cutter dia, feed, and DoC are modest, so more towards 200N. Here are a few papers that map a range conditions (note their RPMs are lower than routers usually use, so forces higher):
http://www.me.mtu.edu/~jwsuther/Publ.../220_PA002.pdf
http://www.iaeng.org/publication/IME...p1751-1756.pdf
Yes, in addition to the tangential component of the cutting force, there is also a radial component (directed towards the center of the cutter), and usually also a Z component. Z can be either up or down depending on end vs side milling, depth of cut, and helix angle.

And yes, those cutting forces, made worse by each flute entering and exiting the material, can and do incite vibrations in the machine, aka chatter, as neilw20 described. Vibration amplitude is minimized by very high machine stiffness and damping--those are the main goals of every CNC machine designer. Stiffness is also important for accuracy, of course. The basic stiffness equation is:
(Cutting Force) = (Stiffness of the Machine at the Cutter) * (Deflection of the Machine at the Cutter)
Or, Deflection = Force / Stiffness (x = F/k)
Weight or mass helps minimize dynamic accelerations (the equation is F = m*a, or a = F/m), which reduces the consequences of the flutes entering and exiting the material. But depending where it is placed, weight can lower the frequency of vibration, which is generally not good for chatter. And, weight does not help accuracy nearly as much as stiffness does. Designing for high stiffness will need a lot of metal, so the machine will be heavy, but weight isn't the primary goal.

For milling steel with heavy cuts, the stiffness-at-the-cutter needs to be at least 50,000 lb/in. Your cuts aren't at all heavy, so perhaps 20,000 lb/in, but that is just a guess. 20,000 is still challenging, but it's doable if engineered right. See my posts in this thread for a lot more info (yes, lots to learn):
http://www.cnczone.com/forums/diy_cn...ml#post1408004

The long axis of a moving-gantry router is much easier to make stiff than the gantry and Z axes, so that's in your favor for using a ball bearing carriage. The flex will come from 3 places:
1. Deformation of the 6301 ball bearings. 6301 is a smart choice for stiffness as the thick outer race and big balls both help. In another post I measured the stiffness of 608, 6000, and 6200 bearings:
http://www.cnczone.com/forums/linear...ml#post1411350
I'd guess a single 6301 would be in the ballpark of 300k lb/in, maybe more. Using them in groups of 4 won't give 4x the stiffness since contact points will be a little uneven. Conservatively, say 2x, for 600k lb/in. That's plenty for an X axis bearing, even cutting steel. (The Y and Z axes should use profile rail, though.)

2. Local deformation of the tube/rail walls. Round pipe is not a very stiff choice, since the bearings push perpendicular to the wall and there's nothing behind it to support that load. But square or rectangular tube would be very stiff if the bearings rolled near the tube's 4 corners. A500 steel tube is remarkably straight, in my experience. Still, the combo of stiff bearings and a stiff tube may result in the carriages binding along the travel, since the tube width will vary. So, two options:
- Use a (more precise) cold-rolled solid-steel rail, like 3/4" x 4", and mount that to the long tubes. But that will be very stiff, so if the width or thickness is slightly off, it may also bind.
- Roll the 6301s somewhat inboard of the tube corners, where the tube is still stiff enough, but flexible enough to accommodate variations in width.
I'd make some prototypes to test what works.

3. Global bending of the long tube. This can be calculated, as it sounds like you've done already. Yes, at 3m long, even a big tube will need a support mid-way. I would use A500 rectangular tube for the main longitudinal members, I'm guessing around 3" x 6" x 1/4" for a 3m steel cutting machine. I think the best mid-way support is via bolt-on triangulation (like a truss bridge), e.g., see the pic at the end of this post: http://www.cnczone.com/forums/diy_cn...ml#post1407372
Triangulation is extremely stiff and strong, far more than the usual vertical posts that most machines use. That's why bridges and other structures use triangles. Bolting to that long tube avoids welding distortion. Triangulation is stiff enough that you only need 4 feet for the machine--that keeps leveling and keeping it level simpler.

8. Originally Posted by dmalicky
Good questions and replies above.
Thanks a lot for a well written and thorough reply!
Very interesting material and straight to the point. Something to study for some time

A note on contact points:

The right end is fixed to gantry via round stock pin (rotating), left end is tensioned with a bolt downwards. Three joints in the middle are bolted top ones and a rotating pin to hold on both sides the plate with 4 bearings.
I'm hoping this would even the load on all bearings and allow some flex for uneven width via spring action of the leverage. (0.75mm/metric ton)

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