CNC Router for Hardwoods: Evaluation and Questions - Page 3


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Thread: CNC Router for Hardwoods: Evaluation and Questions

  1. #25
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    Could you guys elaborate a bit. Two separate beams? Perhaps you mean two of my 3060 beams married together? Perhaps a different beam that is just plain bigger?

    thanks for the suggestion



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    I used 2 3030 extrusions connected on ends and a plate connecting it all on the back side.
    http://www.cnczone.com/forums/1313418-post4.html

    You could do the same and just stack 2 of the extrusions I your current design.

    Steve



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    Good discussion and advice in this thread. Here is some input on the Gantry rail (your X axis) mounting height locations.

    Profile rail/bearings are unforgiving for the flatness and parallelism of the mounting surfaces (they lock up). The single front face of 8020 may be flat enough, or could be purchased, machined, or epoxy-leveled to be flat. To have both the top and bottom faces of the 8020 flat and superbly parallel to each other--that is less likely and would take 2 machining operations to correct. So I would mount them to the front (like almost all commercial machines do, probably for the same reason). Yes, front mounting has less vertical spacing between the bearings, and so there will be more flex at the tool from bearing flex. The usual fixes for that are to use two extrusions, as Steve mentioned, or preferably, a single larger extrusion (stiffness goes by size^4, whereas two extrusions are only twice as stiff. Also a single extrusion keeps the surfaces aligned).

    In your case, if only cutting wood, you may be fine with a single 3060 as far as bearing spacing is concerned (as Gerry said, flex of the extrusion itself is another issue). Profile bearings are extremely stiff, so they don't need as much vertical spacing. I've been working on an xls spreadsheet to quantify these decisions -- now updated and attached. (The math is in this post: http://www.cnczone.com/forums/diy_cn...ml#post1404620)

    Assuming you are only cutting wood (no alum or steel), an aggregate stiffness-at-tool of about 5k lb/in would be plenty. That aggregate stiffness accounts for all the flex in roughly 10 components (Spindle, Z car, Z bearings...). To hit that 5k aggregate stiffness, we need each component to have an effective stiffness-at-the-tool of 10x that -- i.e., 50k lb/in. (Think of ten 50k springs in series --> 5k overall.) So, plugging in numbers for front mounting:
    AB=4.5" (for 3060 extrusion)
    BC=11" (my estimate from your pics; it's the distance from the lowest tool tip to the lower rail)
    k = 3.7M lb/in (the combined stiffness of two LG20C Z1 bearings)
    we get a stiffness-at-cutter of 207k lb/in.

    CNC Router for Hardwoods: Evaluation and Questions-screenshot115-jpg

    That is plenty stiff for your needs (and actually on track to cut aluminum, but other parts will probably flex too much). So for wood cutting with profile rail, a relatively short vertical spacing is ok. If using skate bearings, we'd want much more than 4.5" vertical spacing.

    It is helpful to get Z1 preload, as Z0 would have a bit of slop that would result in more slop at the cutter. The effect of bearing slop at the cutter is now also calculated in the updated xls.

    The same math applies to the vertical spacing of the Z bearings--those account for 1 of the other ~10 springs.

    Attached Files Attached Files
    David Malicky


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    Yes, I agree with your conclusion on the profile rails being ok on the spacing, the weak point is still the extrusions and spreading this load reduces the effect.
    Would probably be fine for most wood cutting, so just need to weigh the cost etc on adding a little more rigidity.


    Steve



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    Thanks for the spreadheet dmalicky, I had admired the math in the other post! I was a bit intimidated by it, thanks for taking the time to plug my numbers in. Now I see how to use it! I will take a look at other extrusions or materials to make the x beam out of (I had been referring to this axis as Y- my bad). I like the idea of having more rigidity before I move on to any other parts of the machine. Nice machine Steve, I love the way you tied the 3030 beams together.



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    Not sure if you have looked at 8020's program for calculating deflection of their extrusions. This might help to understand the loads and how much it may deflect.


    Steve



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    thanks steve I will have a look.

    I just glanced at Misumi GFS8-100200 and Bosch 100200. It looks like they both have 100 x 200 mm extrusions. Do I have to get the price straight from them or are there better ways to purchase from them in the US? I am going to need 1580mm which I expect to be pricey.



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    I had been referring to this axis as Y- my bad
    Imo, the gantry beam is the Y axis.

    Gerry

    UCCNC 2017 Screenset
    http://www.thecncwoodworker.com/2017.html

    Mach3 2010 Screenset
    http://www.thecncwoodworker.com/2010.html

    JointCAM - CNC Dovetails & Box Joints
    http://www.g-forcecnc.com/jointcam.html

    (Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)


  9. #33
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    Quote Originally Posted by Sapele View Post
    thanks steve I will have a look.

    I just glanced at Misumi GFS8-100200 and Bosch 100200. It looks like they both have 100 x 200 mm extrusions. Do I have to get the price straight from them or are there better ways to purchase from them in the US? I am going to need 1580mm which I expect to be pricey.
    The Misumi GFS8-100200 is a very heavy duty extrusion; the 8020 stuff doesn't compare to it at all. I bought two lengths a while back, one for a machine I'm building for myself and one for a client. A 920mm length weighs in at 40lbs. The walls are about 6mm thickness I believe. And you can buy them with the faces milled flat if desired. They're not cheap, the above length cost about $200. Misumi and Bosch both list prices. Misumi sells direct from their warehouse here in teh US (I believe they extrude their parts here too). Bosch sells through distributors. Really, I didn't think so at first, but after holding these extrusions in hand, it's kind of ridiculous to consider these things flexing under normal (or even abnormal) conditions!



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    Steve, yes, 2 extrusions spaced apart is a good way to reduce the forces and thus the deflection of the extrusions. If a larger extrusion is available, that would be most efficient for stiffness/weight.

    Sapele, glad it's helpful! On X vs Y, I had read your first post as saying the 3060 gantry beam would be the X axis. There's no agreement in the CNC world on these things (largely depends where the operator will stand), but I'm with Gerry that X is usually the long axis and Y the cross/gantry-beam-car axis.

    The 8020 deflection calculator is a start, but unfortunately much/most of the deflection in a gantry is torsional, which it doesn't do. (EDIT: unless using 2 beams like Steve; with it and the xls, you can find the bending deflection of each beam, then get the cutter deflection.) I've seen so many people use the 3060 that I've been curious how it does, so did a quick FEA.

    The extrusion is 57" long with an 8" wide YZ-car (~rigid), for 49" of gantry-car travel. The tool load of 100 lb is applied 10" below the bottom of the 3060 (diagonally with a small z component).

    Total deflection is 0.0096" for a stiffness-at-the-tool of 10k lb/in. So it would be hard to get an aggregate stiffness of 5k lb/in if one component is already down to 10k -- everything else would have to be very stiff. The deflection plots shows more torsion than bending:

    CNC Router for Hardwoods: Evaluation and Questions-screenshot116-jpg
    CNC Router for Hardwoods: Evaluation and Questions-screenshot118-jpg

    If the Z clearance is reduced to 7", deflection is 0.0071", for a stiffness of 14k lb/in... not much better.

    If also the length is reduced to 38" (30" car travel), deflection is 0.0042", for a stiffness of 24k lb/in. With profile bearings, I could see that machine hitting an aggregate stiffness of 5k lb/in.

    Further reducing the length to 30" (22" car travel): 0.0031", 32k lb/in.

    Most DIY routers are probably around 1000 lb/in (our K2 3925G is, too), so those stiffnesses would certainly be capable of cutting wood and some aluminum. Just not heavy cuts w/o deflection, chatter, etc.

    If there is a cross-section dfx or dwg for one of the 100x200 extrusions, I could try that, too. Roughly, since it's 1.3x the size of the 3060, it should be (1.3)^4 = 2.8x as stiff (assuming a scaled cross section). So for the 57" length and 10" Z, that's 28k lb/in -- pretty good for wood.

    Last edited by dmalicky; 01-02-2014 at 01:06 AM.
    David Malicky


  11. #35
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    Being inconsistent is worse than being wrong! Sorry for the confusion.. Y axis it is.

    This torsional analysis is brilliant. The numbers are confusing to me, but the picture is clear to this non engineer. Thanks so much for this! I was able to get a price and a DXF from Misuni. $477 for the 100200. Its pricey but this seems like an appropriate place to splurge. DWG is attached at the end.

    CNC Router for Hardwoods: Evaluation and Questions-sixorwindow-jpg

    The bigger beam increases the bearing spacing to about 6" which changes the Effective Stiffness of Bearings at cutter to 323 lb/in and the force on the bearings from 244-344 to 183-283. I am not sure how significant these increases are? If I am reading all of this correctly the bigger beam with the wider spacing reduces the twisting force and the bigger beam will resist twisting better than the smaller 3060.

    A question about measuring for the spread sheet:

    When measuring for BC do I measure from the red arrow by the cutter to the red arrow or the blue arrow? Somewhere else?

    CNC Router for Hardwoods: Evaluation and Questions-sixorwindow-1-jpg

    Attached Files Attached Files


  12. #36
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    Good to hear it's helpful, and thanks for the drawing; results below. No problem on X&Y, of course.

    Yeah, I skipped a lot of background on the numbers (not sure what's already clear; you may know much of this already...). The basic idea of Stiffness is
    Force = Stiffness * Deflection
    Solving for stiffness, we get: Stiffness = Force / Deflection
    So if we apply a known Force and calculate or measure the Deflection, we can find Stiffness.
    So, in the prior gantry analysis, when we:
    - apply a 100 lb load at the cutter, and
    - see a deflection-at-the-cutter of 0.0096",
    - then the effective stiffness-at-the-cutter= (100 lb) / (0.0096 in) = 10,400 lb/in = 10k lb/in

    Those deflection and stiffness numbers only account for the twist and bending of the gantry extrusion. In a real CNC, there are about 10 components that contribute to the total (aggregate) deflection-at-the-cutter, and the stiffness-at-the-cutter:
    1. Spindle and Tool
    2. Z Car
    3. Z Car Linear Bearings & Rails: the xls calculates this
    4. Gantry Car
    5. Gantry Car Linear Bearings & Rails: the xls calculates this, too
    6. Gantry Tube: usually hard to calculate without a computer model like above
    7. Gantry Uprights/Risers/Legs
    8. Gantry Feet Bearings & Rails: a strategic design will cause these to have little cutter deflection compared to the other linear bearings.
    9. Long Frame Tubes that support the long rails
    10. The rest of the Frame, Bed, and Spoilboard
    11. Workpiece: hmm, well that's 1 more than 10 components. The spot where the cutter contacts the workpiece is actually the reference point for cutter deflections. An equal and opposite force of 100 lb is applied to the workpiece, and it deflects, too, but since it's not part of the machine I assume it is rigid. So we're back to 10 components.

    A force of 100 lbs at the cutter will cause each of those 10 components to bend/twist/compress/etc, and each of those movements will then cause the cutter to deflect. So each component has a contribution to the *total* deflection-at-the-cutter. We can find that total by adding up all the individual contributions. One way to think about that is to pretend that all the other 9 components are rigid except for the one were looking at. Let's say we did that and found each component caused an identical deflection-at-the-cutter of 0.002".
    So for *each component*, the effective stiffness of that component at-the-cutter is (100 lb) / (0.002 in) = 50,000 lb/in.
    The *total deflection* at-the-cutter is (10 components) * (0.002" for each component) = 0.020".
    The *total (aggregate) stiffness* at-the-cutter is (100 lb) / (0.020 in) = 5,000 lb/in.
    Notice that (50,000 lb/in) / (10 components) also equals 5,000 lb/in. That's why we shoot for 50,000+ lb/in or more for each component.

    In reality, the components will cause different amounts of deflection-at-the-cutter, of course. For a wood cutting machine, profile bearings will result in almost no deflection-at-the-cutter. So, some of the other 10 components can be more flexible than 50,000 lb/in.

    For a target total stiffness-at-cutter, there are some posts in the archives on that. Summarized:
    Typical CNC machining center: 50,000 - 150,000 lb/in http://www.mech.utah.edu/~bamberg/re...e%20Design.pdf
    Efficient steel cutting: 60,000 lb/in http://www.cnczone.com/forums/mechan...tml#post916569
    Efficient aluminum cutting: 20,000+ lb/in (~1/3 of steel, based on modulus)
    Efficient wood cutting: 4,000+ lb/in (~1/5 of aluminum, based on modulus)


    Quote Originally Posted by Sapele View Post
    The bigger beam increases the bearing spacing to about 6" which changes the Effective Stiffness of Bearings at cutter to 323 lb/in and the force on the bearings from 244-344 to 183-283. I am not sure how significant these increases are? If I am reading all of this correctly the bigger beam with the wider spacing reduces the twisting force and the bigger beam will resist twisting better than the smaller 3060.

    A question about measuring for the spread sheet:

    When measuring for BC do I measure from the red arrow by the cutter to the red arrow or the blue arrow? Somewhere else?
    Yes, that's helpful for the bearings to experience less force, and for more stiffness. But for a wood cutting machine, profile bearings are stiff enough either way. You can see from the xls that their "Resultant Elastic Deflection at Cutter" is 0.00031" -- tiny and that's very helpful since they will make up for the gantry tube which is difficult to get stiff enough. Yes, the main benefit of the larger extrusion is that it will twist less than the 3060.

    I was sloppy in my description of BC--sorry. Yes, it is the distance from the tool tip to the blue arrow.

    And here's the GFS8_100200, with 10" of Z clearance and 49" of travel:
    CNC Router for Hardwoods: Evaluation and Questions-gfs8_100200-jpg
    Looking pretty good with 0.004" deflection. It's effective stiffness-at-the-cutter is (100 lb)/(0.004") = 25,000 lb/in. Since your profile bearings are much stiffer than they need to be, it's fine for this component to be 2x more flexible than the goal. In numbers, if we budget 0.002" for each component's deflection-at-the-cutter, the gantry is 0.002" over its budget, but the Z and Y profile bearings are each 0.0017" under their budget. So combined with the profile bearings, this gantry tube is fine.

    David Malicky


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CNC Router for Hardwoods: Evaluation and Questions
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