[dmalicky]

I'm looking for data on the stiffnesses of the different rail/bearing options: V-rail/V-roller, CNCRP-style flat bar/carriage/skate wheels, supported round rail, and profile/square rail. I'm guessing that's the general order of stiffness.

So far, I've only found good info on profile/square rail:
Slocum's book: Precision Machine Design - Alexander H. Slocum - Google Books
NSK LY15 light preload: 137 N/micron (780k lb/in)
NSK LY20 medium preload: 196 N/micron (1120k lb/in)
THK HSR 20TA medium preload: 490 N/micron (2800k lb/in)

Hiwin AG rail on page 43: http://www.automation4less.com/pdfs/hiwinaglg.pdf
AG15S Z0 (very light preload): 10 kgf/micron, 98 N/micron (560k lb/in)
AG20C Z1 (light preload): 24 kgf/micron, 235 N/micron (1340k lb/in)

For supported round rail data, there is this youtube video from Thomson: https://www.youtube.com/watch?v=rq4Pis6Zhf4
The vertical stiffness of that profile rail is 800k lb/in, and the supported round is 210k lb/in.
Thomson has a plot of their heavy duty XR bearing stiffness (again, vertical push), but I've not seen anything else on supported round.

I imagine supported round is more flexible in the lateral direction as the trapezoid base bends? And also the vertical tension direction (pulloff), as the open bearing opens up slightly?

Has anyone measured the stiffnesses of V-roller/V-rail or CNCRP/flat bar/skate wheel designs? I'm mostly interested in the latter, for cost reasons, of course.

Or from the experience side, has anyone built a very stiff machine using flat bar/skate bearings and/or supported round rail?

Thanks for any leads,
David

[harryn]

There is quite a bit of published data on commercial rails, such as hiwin / nook / TSK, although it isn't always so easy to go through.

In addition to the load capability, the torque resistance is a big part of the actual results. For instance, a 15mm might have enough static load, but lack in torque resistance in some directions. Preload also is a factor.

If you go large enough, sometimes it is enough to just have one of those rails rather than trying to align two of them. Their precision and preload are very handy when they are aligned, but kind of demanding for home builders.

The rail mfgs suggest that if a rail is not stiff enough, just add another carriage (more bearing surface) to double the capacity and they seem concerned about overloading the rail itself.

I think the next best setup to consider are the IVT rails from pacific bearings. I think it is pbc.com.

They are based on a V bearing setup and publish load and torque ratings. There are a couple of different models and I have a little info on one model in my build log. I am attempting to use one rail in that router build for easy alignment.

Round supported rails are probably next on the list, and yes that trapezodal base is narrower than the main rail, but pretty quickly I found that most rails have tapers somewhere.

The cncrp are probably next on the list. I have a few of those and they are fine for small hobby builds, but I have not looked for any actual rating data.

It is useful to look at how they mount to get an idea of the expected stiffness. They are essentially a 1/4 inch (6mm) semi-supported steel rail with no crown, so you can compare this to even a small hiwin of 15mm with dual crowns and dual bearing sets. At best, it is 6/15 th (40%) of a small hiwin.

Even with these limitations, people do successfully build hobby quality routers with them all of the time.

[dmalicky]

Thanks for the info. I'm actually just looking for stiffness data (lb per inch), which seems harder to find... the load and torque ratings (lb, in-lb) are plenty for my needs.

I hadn't seen the IVT system, thanks. Yes, the profile rail is 2nd to none. It would be interesting to know how much of the stiffness is due to rail/rod/bar/base/carriage flex, and how much the balls compressing against the races (Hertzian contact). I'm guessing the CNCRP skate wheels are very roughly 2/3 the stiffness of supported round in the best case directions, as the rolling bearing adds another contact interface to the 2 on each side of the balls. But supported round might be worse in the trapezoid bending and pull-off directions.

I could do an FEA model, but I'm not sure I have enough data to make a good one. Sounds like I'll need to buy some parts and test them, unless anyone else has done that.

[harryn]

Interestingly, both the V rails and the profile rail use similar concepts. The shape of the contact area is actually pretty similar, the ball bearing designs just have many more contact points to spread out the load. You can exactly see this in the vendor ratings, if one carriage is not enough, add another and it doubles the rating. Similarly, V bearings are rated "per bearing".

Profile rail itself is actually surprisingly flexible and depends 100% on how it is mounted. The same is true of the V rail.

IMHO, the biggest challenge is not finding a rail and frame combination that are stiff enough, it is aligning two of them to each other so that they don't wear each other out during use. In a professional, high volume shop this is designed in, but at home, it is a critical point.

My suggestion is to try hard to use a single large rail and block rather than two rails in parallel, when practical. If you need more capacity, add another block rather than another rail. This isn't always possible.

I have some of the skate bearing setups and they work, but the value of having a ground, hardened rail becomes obvious pretty fast.

[louieatienza]

Interestingly, both the V rails and the profile rail use similar concepts. The shape of the contact area is actually pretty similar, the ball bearing designs just have many more contact points to spread out the load. You can exactly see this in the vendor ratings, if one carriage is not enough, add another and it doubles the rating. Similarly, V bearings are rated "per bearing".

Profile rail itself is actually surprisingly flexible and depends 100% on how it is mounted. The same is true of the V rail.

IMHO, the biggest challenge is not finding a rail and frame combination that are stiff enough, it is aligning two of them to each other so that they don't wear each other out during use. In a professional, high volume shop this is designed in, but at home, it is a critical point.

My suggestion is to try hard to use a single large rail and block rather than two rails in parallel, when practical. If you need more capacity, add another block rather than another rail. This isn't always possible.

I have some of the skate bearing setups and they work, but the value of having a ground, hardened rail becomes obvious pretty fast.

It's pretty trivial to line up the second (slave) profile rail - you simply reference it off the master rail. One way would be, for example in a gantry, once the master rail is installed, use the carriage plate with the bearing blocks installed to "locate" the slave rail. Another way is to have lips or grooves machined for the rail as a datum edge. There are documents in the THK site that review all possible mounting options.

It may not be a good idea to use a single rail/block since that can potentially put a very high moment on the block. This also might not be a good thing for rails designed for horizontal use only. It's probably also more practical (and less expensive) to use a smaller rail with two blocks than a larger rail with one extended length block.

[ger21]

IMHO, the biggest challenge is not finding a rail and frame combination that are stiff enough, it is aligning two of them to each other so that they don't wear each other out during use. In a professional, high volume shop this is designed in, but at home, it is a critical point.

I'm with Louie here. When talking about profile rails, adding a second and aligning it to the first is a pretty simple process.
Using the first rail and a temporary carriage, it's basically a matter of sliding the carriage along the first rail, bolting the second rail as you go.

Using a single rail on a gantry, can lead to extremely high moments. If not mounted to a steel frame, I think the mounting of the rail would possible fail.

[dmalicky]

An update--I've been working on measuring the stiffness of various linear bearing & rail options. So far I've built a fixture and tested some vee bearings and various deep-groove ball bearings.

RM2 Vee Bearings
I bought 1 RM2 from VXB and 6 from ebay (ABIsupply2012). All have a fair bit of lateral (angular) slop. Installing a 4" rod in the bore, the slop measures an average of 0.010" at 4" for the 7. At a radius of 0.5" (middle of the Vee), that reduces to 0.0012" lateral slop. At the cutter (using http://www.cnczone.com/forums/diy_cn...ml#post1408004), that works out to about 0.003" slop for AB=BC. For RM2s on both Y and Z, that would be 0.006" slop at the cutter.

RM2s are a double row angular-contact bearing (http://www.vxb.com/ball-bearings-images/kiit8351-1.jpg) with a vee outer race. As many of you know, those type of bearings cannot be made without some slop.

So then I tried some ~0.0002" oversize pins (McMaster 98372A437) to expand the inner race -- that removed the slop in 5 of the 7. With the 2" long pin installed, I crudely measured the lateral stiffness using a vise, fish scale, and caliper. (Since I'm pulling and measuring at ~1.6", the physics require multiplying the stiffness by (1.6/0.5)^2 to get the stiffness at the Vee.) That worked out to roughly 50,000 lb/in -- pretty flexy, barely enough for wood. The radial stiffness is much higher, of course, but vee bearings depend on the lateral, too, and the weakest mode will dominate.

Fixture
Next I built this fixture to measure the radial stiffness of deep-groove ball bearings riding on a flat steel surface (like CRS rails, but not flexible like 1/4" CRS).
Attachment 217444

Load is applied by the threaded rod/nut, through the load cell, through the wooden load carriage (which goes around the dial indicator), through the 7/8" steel plate, to the top of the bearing.

The bearing is clamped tightly between double-shear steel supports (a load is applied to align the supports to the base, then the axial bolt is tightened). The steel supports are machined and ~polished so their bottom surfaces are parallel to the ~polished base. (I originally also clamped the supports to the base, but it made almost no difference in the results.)

The 0.0001" resolution dial indicator sits on a raised platform independent from the vertical guides and the wooden carriage (so they don't affect the measurements). The platform sits on 4 threaded rods into the base, placed symmetrically around the indicator so any bending/angular deformations in the base get cancelled out. The indicator's spindle goes through a hole in the wood to touch the 7/8" steel plate, directly above the bearing: as direct a measurement as possible.

To test the stiffness of the fixture, I placed one of the steel support blocks (w/o bearing) in the crunch zone, applied a tare load of 10 lbs to take out the slop (zero'd the indicator there), then applied a load of up to 400 lbs. At 400 lbs, the indicator read between 0.0003" and 0.0005", for a fixture stiffness of ~1 million lbs/in. That means I can probably reliably measure bearings up to ~300,000 lbs/in stiffness (before corrections for fixture flex become a major source of error). I may get some thicker steel for a new base, to increase stiffness.

Bearings and Testing
Next I looked at common bearing dimensions and prices to pick candidates. The 6200 looked promising as it's heavier duty than the 608 skate bearing -- bigger balls and its races are much thicker. 1621 also looks stiff but it's pretty large. The 6000 is in between the 608 and 6200, as a control. I had a 1/2" needle on hand, so included that (and have some smaller ebay needle bearings on order). The support blocks for the 6200 and 6000 were made first; I learned they didn't need to be so complex after testing them, so the others are simpler.
Attachment 217446

The RM2 test is more complex. I clamp the bearing to a 3/4" vertical rod, then push on the dowel between 0.63" and 1.0" away from the center of the bearing. I correct the deflections for the rod bending, as well as the extra leverage (the vee groove only has 0.5" leverage)--that requires taking the square of the leverage ratios. Once corrected, the data for the different lever arms agreed with each other within about 10%.

The test protocol is to apply a ~200 lb load to 'seat' all the mounting surfaces (100 lb for RM2), then apply a 10 lb tare load and zero the indicator. Then apply 30, 60, 100, 150, 200, and 300 lb loads and record deflections. Repeat test by rotating the outer race a bit. Usually, repeat test by replacing the bearing.

Results
For data analysis, first I back out the fixture flex from the deflection numbers (small correction). Also backout the 10 lb tare load for net loads. Plot the data (y-axis is in thousandths of an inch):
Attachment 217448

The order is as expected. The RM2 Vee is softest (lateral direction), followed by 608, then 6000, then 6200, then the needle. I'd hoped the needle would be even stiffer, but these low cost ones have thin stamped steel outer races. Only the 6200 and needle show stiffening with load; the others are pretty linear. The RM2 Vee plots are probably optimistic, as it was more difficult to tare reliably and get the slop out. I also included the Thomson youtube data for reference, although that also includes the rail deflection.

The position of the outer ring does matter a bit: if a ball is directly in line with the load, deflection is less by about 0.0003" for the 6200 and up to 0.001" for the 608. The 6200's thicker race evidently does help, and so it's likely to roll smoother under heavy loads.

Stiffness can be calc'd "locally" (the slope of the deflection curve) or "gross" (just load/deflection). Here is the latter:
Attachment 217450

- The RM2 stiffness agrees well with the crude measurement I did earlier (50k lb/in).
- The 608 is respectable at 140k lb/in -- that's on target for a total (aggregate) stiffness-at-the-cutter of about 2800 lb/in.
- The 6000 is in between the 608 and 6200, as expected. Evidently, the thinner races of the 6000 hurt more than the bigger balls help.
- The 6200 is around 200k-230k lb/in at (I think) typical loads--an upgrade from the 608, but its larger size also has disadvantages (e.g., the rail will flex more, because it needs to be cantilevered more than 1/2" for the 6200+bolt to fit.)
- A needle is looking good for the center bearing in a CNCRP style carriage.


Next, I'll be simulating (FEA) CRS rail deflection, and deflection testing the SBR20 and TBR20.

[dmalicky]

In short: SBR20 is pretty good in compression and pretty bad in tension.

This test is more complex, because there are 5 interfaces that might flex in the system:
1) 7/8" Steel Loading Surface to top of SBR20 Block: Probably small, if any.
2) SBR20 Block to LM20UU Bearing Shell: Probably small, if any.
3) LM20UU Bearing Shell to 20mm Rail: Probably most of the flex.
4) 20mm Rail to SBR20 Rail Extrusion support: SBR20 has a bolt every 150mm (6"). I varied the location of this bolt relative to the SBR20 Block between 0" and 3". In tension, 0" should be stiffest; 3" should be most flexible. I checked/tightened these allen bolts before testing.
5) Rail Extrusion to Steel Base: SBR20 also has bolt holes every 150mm (6"), although more could easily be drilled. I varied the clamping distance between 1" and 3". In tension, 0-1" should be stiffest; 3" should be most flexible. Clamped with 4 Kant-Twist clamps, very tight.

Fixture setup
Attachment 217778


Since machines often use SBR20 to take both tension and compression, I tested both directions. The 10 lb tare load doesn't work for that, so I found the resting zero location by cycling between tension and compression and observing where it returned. This resting zero was within 0.0002", often better. Still, 0.0002" is quite a bit for loads of 30 or even 60 lbs, so those data are pretty noisy.

Results
Below are the load vs deflection plots. Dotted lines are tension. Solid, compression. The same color line is used for the same setup.
Attachment 217780

Notes to understand the plots:
- "Loose" and "Tight" refer to the set screw on the side of the bearing block. As it is tightened, the friction goes up and the noise of rolling rises in pitch. If too tight, the rolling becomes rough -- I set it just under that for "tight". (That will likely shorten the ball life, though.)
- "RB@3" means the Rail Bolt is 3" away from the bearing block -- the most flexible case for tension. RB@0 should be the stiffest for tension, and it is (dotted orange line).
- "EC@3" means the Extrusion Clamps are 3" away from the center of the bearing block -- also most flexible for tension. EC@1 puts the clamps as close as they can get to the center of the block (1").

Below are the stiffness (load/deflection) plots. I omitted the 30 lb points because errors are amplified for a ratio of small deflections and loads. The 60 lb points are suspect, too.


So, to help interpret the plots:
- Blue vs everything else compares a loose set screw to a tight one. Very flexy in tension, as expected. Curiously, it is stiffest in compression at high loads.
- Green vs Red compares the extrusion clamps far away (Red) vs close (Green). No clear trends that make logical sense. Possibly, the Red curves had an inaccurate zero position, which would shift both curves.
- Red vs Orange compares the Rail Bolt far away (Red) vs right under the bearing (Orange). Orange is stiffer than everything else in tension, as expected.
- Black is the average of all 4 cases.

Conclusions
- In compression, SBR20 is reasonably stiff, averaging around 200k lb/in for each block. The plots are very consistent with the youtube video of Thomson's round rail.
- In tension, SBR20 is very flexy, averaging around 60k lb/in for each block. This is probably caused by poor ball track placements (see jpg link in first post), as well as the bearing housing opening up under tension. SBR25's ($) ball tracks appear to be oriented better for tension.
- For light tension loads, the sparse 150mm spacing of the rail bolts appears to be a weak spot (the dotted orange curve has pretty good stiffness up to about 100 lb tension). If it would hold, it might help to epoxy the rail to the extrusion along its whole length. (I imagine grinding through the case and tapping more holes would kink the rail?) Import TBR20 rail has the same 150mm spacing. Thomson and other companies ($$) offer 100mm spacing.
- The extrusion clamp spacing doesn't seem to be very important; 150mm bolt spacing is probably adequate.
- Lateral stiffness is unknown, but it should be in-between tension and compression. Rail flex is a main concern, and the sparse 150mm spacing of the rail bolts will likely be a similar problem. At least there are ball-tracks in the right places, though.


I've also tested some TBR blocks but so far they are worse than SBR for both tension and compression. I don't know if I got bad parts or if this is a design issue. I've tried some experiments to sort it out, but so far, the cause is unclear.

[nekidfrog]

I really wish I would have found this info on the RM2 bearings before I decided to use them for my linear rails.

[mactec54]

dmalicky

It's good to see that you have done this testing, that gives a good indication, of what the hobby builder can expect to get from what they are using for rails, most that are using the round linear rails have been mounting them incorrectly ( under tension ) if they are used in compression as you have found out, they will do a reasonable job for small machines

There is no substitute for the real thing, but where cost is an issue, the hobby builder does not have a choice, but to use what they can afford

[dmalicky]

nekidfrog, Yeah, I liked the simplicity of RM2, too, until I saw the data. If you've not bought or built anything, it's just part of the long learning curve towards making a stiff machine. And if you have, it's still better to know now than after your first cut! If going for stiff, also see these posts/threads:
http://www.cnczone.com/forums/diy-cn...ml#post1430502
http://www.cnczone.com/forums/diy-cn...ml#post1439222
http://www.cnczone.com/forums/diy-cn...ml#post1426678
http://www.cnczone.com/forums/diy-cn...ml#post1408740 (and page 2 of that thread)

mactec54, Thanks for the feedback. I find it's an interesting challenge to achieve reasonably high stiffness at low cost. The 3rd link above analyzes the bearings in context, for a variety of cutting conditions. For longitudinal forces at the cutter, this post has a calculator to compare orientations: http://www.cnczone.com/forums/diy-cn...ml#post1435822
The short answer is that vertical-opposed is up to 2x as stiff the usual horizontal orientation.

[nekidfrog]

Sadly I had already built and learned my lesson the hard way. So now saving up for new rails.

[dmalicky]

Until then, somewhere I read that the V-rollers can be improved (somewhat) by putting additional 3/8" ball bearings on each side of the RM2. I think it was a Mechmate user, but I can't find the link.
Also the slop can be reduced to ~zero by press-fitting in a 0.0002" oversize dowel pin. McMaster has low-strength dowels that can be threaded on both ends, to turn them into a 'bolt'. McMaster-Carr
Neither are great solutions, but should help.