Gantry mill

[Zach_G]

Thank you for posting the note about Mori Seiki's ridgidity design goals. I felt so enlightened I had to run my own designs through solidworks' FEA and found out they were woefully flexible from relying on intuition as to what's stiff rather than anything quantitative. Over the past week I've been redesigning to hit 220klb/in in the X with 4" spindle-table clearance and 80hz. Now I feel confident in proceeding with the build so again thanks and here's what I'm up to. That's 8x8x3/8 steel tube and a minimill spindle for reference, heck of alot smaller than your plans! Good luck I'll be watching

[jsheerin]

Nice work. Note that your linear bearings, ball screws and spindle will have some non-infinite stiffness of their own, so if you have your bearings fixed in your model and you get 220klbf/in, then your actual machine will have a lower stiffness when you have the bearings and ballscrews deflecting. It's still probably a good target to shoot for though.

[jsheerin]

Making progress... I added forward diagonal braces as well as boxing in the horizontal beam that connects the gantry legs to the X axis, and I cleaned up some miscellaneous stuff. I'm now into a workable area of stiffness - X is 290k lbf/in and Z is 430k lbf/in. The first resonance is at 46Hz. The highest area of stress for both is at the corner of the vise jaw that I'm constraining. When I drop the max stress level to see what else is getting stressed, the horizontal beams are still getting lit up along with various other beams. I'm thinking I might be able start removing some beams from the rear corner, but first I'm going to do a complete model so I can apply a load in the Y direction and see how that does. I'm also going to see if I can figure out how to specify the stiffness of my bearings in the model so that's taken into account as well. Mode shape, deflection and stress plots are below.

Now I get to go shovel snow - 6" in the last 4 hours or so and a snow plow truck just got stuck outside my house...

[jsheerin]

I did some more modeling today - I mirrored my geometry and edited my script that I use to set up and run these models to apply all the contact properties to the new bearings which worked out really well. Then I started playing with options in the contact settings that effect the stiffness of the bearings. I did figure out how to change the stiffness in the model, but I can't figure out how to make it what I want it to be. I made a little test model to play with and it was giving me weird results. So more research is required there... I also tried to find what the stiffness values for THK bearings are as part of that, and they are not published as far as I can tell. At least I couldn't find them in their catalog. That seems dumb, to put it mildly. They have a little section about what rigidity (stiffness) is - basically the formula K=F/x - but they don't give you any info about what K is for the various models. They do talk about preload and how deflection under load changes with preload (for some mystery bearing - they don't tell you which model it is). And they do tell you that you get less deflection for the same load with the higher preloads. So it sounds like what I want are the medium (C0) preloaded bearings. I have a big box of THK bearings that were essentially free, and I have some rails which I may or may not use for this, but from reading the catalog they typically only build preloaded bearings as a set with the rails, so mine are probably normal preload (very slight to none). They do give you a table of what the preloads are for the various bearings in the catalog. I also found in Slocum's Precision Machine Design a table of stiffness values for various THK HSR bearings (which are what I have) which he says was supplied by THK (which just annoys me more - why don't they put it in the catalog?), but they're only for medium preload, probably not what I have, and so I'm not sure how useful that is at the moment (well, it's not useful at all if I can't figure out how to get my model to work with a specified stiffness for the bearings...). The THK catalog did point out that no preload to medium preload had a stiffness increase of something like 4.5x, so I took that along with Slocum's data as a starting point when I was playing with the bearing stiffness in my model.

So if anyone knows anything about this, by all means, chime in. And maybe of more interest, can I measure the preload of my bearings on my rails, then measure the ball diameter in my bearings, and then swap in larger balls to get a desired preload?

Anyway, the results of my having a complete model to play with - I can simulate a load in the Y direction. The stiffness was 125k lbf/in, so this is the most flexible direction at the moment. Max stress is around the lower Z axis bearing. So I'll try beefing that up along with continuing the bottom horizontal beam all the way under the X axis.

[rowbare]

Given the data from the catalog, and the stiffnesses from the table in Slocum's book, can you calculate the k value? From what you have described, I would expect the k value to vary a bit according to preload but the upper bound will be somewhat less than that of the rail alone.

bob

[jsheerin]

Not as far as I can tell. K is stiffness. So it's given in Slocum's book for some bearings, but what I'm unclear on is the way to find it for any bearing.

The question is how much less than the stiffness of the rail is it - the rail is somewhat accounted for in my model already (it's just a square). The tricky part is the internal structure of the bearing block and the balls, and how all that deforms under load. It's complicated enough that I wouldn't bother to try modeling it - that's why I expected THK to have published numbers for it.

[jsheerin]

.

[jsheerin]

I am building the machine from surplus (used) parts. Because of this I can't know for sure that I can buy a certain part at any time like I could if I was buying new parts. So before I can design my machine, I need a lot of the parts so I know how big they are, how much they weigh, what their performance is, etc. (spindle, ball screws, servo motors, spindle motor). Then I can design the machine structure to put the parts on.

You're right that every machine will flex under load and every design will have a weak point. The question is how much will they flex, and will that weak point be a problem when you're using the machine. A little flex is not a problem. A lot of flex is. I have a goal for how stiff the machine needs to be. When my design work shows that the machine reaches that goal (and doesn't have a bunch of unneeded steel in it), then I am done designing and can start building. If I randomly decide that I like the design as it is and build now, it won't perform as well as I would like and I will have wasted money on materials and time building it. I know lots of other people here just start building their machine without doing anything more than sketching out a design, if even that. I don't think that's the best way to go, but I keep that opinion to myself when I post in their threads and just offer suggestions based on my experience (if I have any) to try to help them out with any problems they're having. I would ask that you do the same if you choose to post in my thread. If your only suggestion is to start building before I'm done designing, then please don't post in my thread.

[jsheerin]

I think I figured out how the fkn contact stiffness parameter in ansys works. This is the parameter I'm trying to use to include the stiffness of the bearings in my fea model. By default fkn=1. This means that when the surfaces you're looking at contact each other, the stiffness of the contact region is just the stiffness of the parts multiplied by 1. I think (...) this stiffness would be what you'd calculate by figuring out the pressure between the two surfaces, dividing by the material's modulus of elasticity to get the strain, multiplying that by the thickness of the parts to get deflection, and then dividing the applied load by the deflection to get stiffness. So if you set fkn=0.1, then the stiffness between the two parts in contact would be 1/10 that value, etc. On the other hand, if you set fkn to be a negative number, Ansys interprets that as being an absolute value of stiffness instead of just a scaling value. This is what I'm trying to use to input the stiffness of a bearing I pick. I tried inputting the stiffness value directly in units of N/m (since I'm working in SI units), but that didn't work - the stiffness was way too low and the machine deformed all over the place, but almost all at the bearing locations. So after some more research and testing in Ansys, it looks like the fkn value is actually in units of N/m per m^2 (which I only found referred to in one tiny place in the manual or maybe even on the net - seems like that should be in big bold lettering...), so it's stiffness per unit area. This does make sense though, as otherwise Ansys would have to figure out the area you're applying the stiffness over and then figure out the actual stiffness for each element on the surface itself (the springs would be in parallel and thus the stiffnesses would add). So I need to know the surface area of each surface of the bearing (sides and top - the stiffness is the same in both directions on the HSR's, but the side and top areas are different in my model while the actual bearing area in the bearings are the same), and then I need to divide the stiffness of the bearing by the area of the bearing surface to get the appropriate fkn value. So instead of my initial estimate of 1.44e8 N/m for a no-preload HSR25 bearing, the value I need to input for fkn for the top surface of the bearing is 7.44e10 (N/m/m^2) as my surface area is 1.935e-3 m^2. Doing this on a test model, the deflection and stiffness turned out right, and the stiffness of just the material did combine in parallel with the stiffness of the bearing I specified within about 2% of theory for several cases. The obligatory screen shot of the quick test model I used to test this is below. The smaller block is a very simple bearing that is riding on top of the longer rail. Under a load of 100N vertically pulling up on the block, it moves up 0.714e-6 meters for a total stiffness of 1.40e8 N/m.

[jsheerin]

I did some more modeling today with the stiffness of the bearings included. One other detail I figured out is that you have to cut the stiffness in half for the sides of the bearings, since you have two sides and their stiffness is in parallel. So my complete machine stiffness ended up being:
X: 94k lbf/in
Y: 63k lbf/in
Z: 267k lbf/in
This is with my estimate of no preload THK HSR25 bearings (and my estimate does come close to what equivalent size NSK bearings with their lightest preload have for a K value). So I have a pretty good drilling machine design at the moment, but not as good at milling. I did some quick estimations of how much stiffer just the frame would have to get using my current bearings to hit Mori Seiki's lower limit of 228k lbf/in, and they won't do it. With no preload I'd probably need long HSR35's or HSR45's to get there even theoretically but practically much bigger bearings like HSR85's. However if I can preload the bearings up to a medium (C0) level, then I could get by with my HSR25's and just have to increase the frame stiffness about 1.3x in X and 3x in Y (Z would be fine).

If I shoot for Mori's higher performance level, I couldn't use non-preloaded bearings of any size that THK makes (at least up to HSR85 which are massive), but I could get by with HSR65 medium preload bearings if I also stiffened the frame around 4x in X, 9x in Y, and 2x in Z. So I don't think that's going to happen - HSR65 bearings are out of my price range, while I already have a box of HSR25 and HSR35's, and I don't think my garage slab can support enough steel to make the frame as stiff as would be required, and plus if I can't find a source for extremely cheap steel, the amount of steel required would be well out of my budget.

So this helps define my goal better - I'll shoot for 228k lbf/in, I'll have to figure out how to preload my bearings or buy preloaded bearing and rail combo's, and if the HSR 25 bearings look okay for load/life calc's I'll use those (I need to redo those with new weights from my current frame design). Otherwise I'll shoot to use HSR35 bearings.

[jsheerin]

If I understand THK's explanation in their catalog correctly, I think to preload the bearings I'd need to increase the ball diameter between 0.00014" to 0.00040" for the HSR25's to go from no preload to medium preload assuming the rails I have are not worn. In reality the rails probably are worn a bit and I'll need to try to measure the radial clearance of the bearings on their own rails. For HSR35's, the range would be 0.00020" to 0.00054".

How I came to these numbers: For the HSR25's THK specifies normal radial clearance as -6 to +3 um and medium clearance as -26 to -16 um. So I could potentially need to remove 10 to 29um of clearance. This would be 0.000394" to 0.001142". The ball contact points are on a 45 degree angle to the radial direction (vertical through the bearing / rail), so that would mean that an increase in the ball diameter would give a vertical height increase of diameter difference * sin(45deg) = 0.707*diameter difference. But if you increase the ball diameter, the balls are above and below the ridge on the rail (and on opposite sides of the rail), so the difference in preload will be twice this, so divide by 2. That gives the numbers above.

[ebrewste]

At least I couldn't find them in their catalog.

That's a bummer. I distinctly remember the stiffness data being in the THK catalog 15ish years ago. They did a good job of that data back then. I wish I still had that around to help you out.

[ad_bfl]

Just want to make sure I understand the Mori reference number/benchmark.

220,000lbs per inch displacement at the tool tip - correct?

[jsheerin]

Yeah, they must have the data - they reference stiffness values in the catalog, but don't give a big table with actual numbers (unless I'm just missing it...). I assume that I can get the numbers if I contacted THK (along with asking about preloading), so I'm working on sending a request for information (have to register on their site, etc...).

I'm taking the Mori number to be 1" displacement for 228,000 lbf at the spindle nose now instead of the tool tip (as the tool was the most flexible part of the model even being 1" in diameter and it was suggested to me that I was overly handicapping myself which I agree with). So the tool will do what it will, but the frame will still support the tool holder.

[ad_bfl]

wow, I am WAY overbuilt (structurally, not including the linear bearings).

How does that compare to the value Slocum used in his thesis?

If I remember, he had a reference he was using for his design of the tool grinder. Tonight I will see if I can dig that out.

Thanks
Al

[ebrewste]

I don't know if this is of any help, but here is the data for the Thomson lm guide line.

http://www.thomsonlinear.com/website...uides_cten.pdf

Page 107 shows the stiffness curve for their 25 size lm guide.

[jsheerin]

You may not be overbuilt though - the linear bearings can have a really large effect on the overall stiffness since they are essentially springs between all the pieces of the machine. For example, if all your frame components were infinitely stiff, then the stiffness of the entire machine would be the combined stiffness of the linear bearings. But since your frame isn't infinitely stiff, the total stiffness will be less than the stiffness of just the bearings. That's why I spent so much time figuring out how to include them in my model (which I'll now directly transfer over to reworking my cnc router, which will get built before anything on this project does...).

I'd be interested in Slocum's value if you can find it. I've been reading his book but haven't read that section (I seem to remember he has a section on design of a grinder).

[Zach_G]

"When designing a machine tool for a certain performance/accuracy, one of the most important criteria is the effective stiffness of the tool/work piece interface. This value describes the magnitude of the force [N] required to push the tool away from the work piece by a unit length [μm]. In general, values between 10 and 25 N/μm are considered to be adequate for machine tools. For the STG, the structural loop stiffness was targeted to be on the order of 50 N/μm, making this machine well suited for accurate machining."
pg. 26

That comes out to 57.1-143 klbf/in, or 286 klbf/in for the grinder design.

[jsheerin]

Thanks - it looks like those are about in the same range as the THK blocks. I found a place to submit a question on THK's website, so I'll see if I get a reply.

[jsheerin]

Thanks for the additional numbers Zach. Zach's quote is from Bamberg, which he previously linked I think, but here it is again:
http://www.mech.utah.edu/~bamberg/re...e%20Design.pdf

So my 228k lbf/in goal is probably a bit on the overkill side (I wonder how Mori gets to 686k - maybe that's without linearing bearings?), but overkill is fine and I'll see if it's possible to get there. Additionally I'm still not considering the compliance of the spindle bearings, ball nuts, and ball screw thrust bearings, so my real world number will be a bit lower than what I predict in FEA unless I measure those stiffness values and include them. I've got an idea how to measure this on my ballscrews, but I'd probably need to get a more accurate dial test indicator first. I might play around with it with my current dti and see what I can see.