belt drive design and other questions

[born2bewilder]

Hi, I've been dropping dollars at a local surplus store, buying things that I thought would further my CNC router project. It's currently at the 'napkin' stage of design progress, and I would appreciate some input on some design choices I've been mulling over. This is my first build from scratch; I've been aiming for a wood or light metal router/mill with a work envelope in the 48x48x18 inch neighborhood.

I recently picked up a pair of Gates Carbon GT belts for a song, 8mm pitch, 36mm width, and have been wondering how best these might be used as an actuator for the x axis. Some ideas I'm considering:

1) Central belt between two sprockets, with a belt mated plate attaching belt to the gantry along it's line of travel, probably under the gantry on the bottom of the machine.

2) Two belts between two sprockets each with belt fixed to gantry along both sides. I don't have paired drive motors, so it would be one motor attached to a shaft that spans the width of the machine, one sprocket driven per belt.

3) Cut the belt and use a two backside idle rollers and one driven sprocket, motor mounted to the gantry. Belt mating plates machined to fix both ends, 5+ teeth.

As for context of the build: X axis gantry runs on 2" round linear bearings. Motor is a somewhat underdriven large servo, expected to provide ~1000 oz-in continuous and ~2000 oz-in momentary peak. Gantry weight expected to be in the neighborhood of 200 lbs.

Some questions that occur:

Is it a problem to move a gantry with a single belt? Does it matter a great deal if the belt is not centered near the gantry center of mass?
In the extreme case, what about a gantry attached to a side mounted belt on one side only (assuming a 48-inch-ish wide gantry)? Would the skew forces induced by this loading present a problem?

Are there particular advantages or disadvantages to using the 'cut and laid flat belts' with backside rollers? An obvious ones is reduction of belt slop without a free-hanging, moving belt. At what length does that become a big issue?
Another thing I'm curious about, does using backside rollers increase wear rate on the belts?
Also, my servo motor weighs about 70 lbs. Would mounting this on the gantry be adding too much unnecessary mass?

Any thoughts on the ideal size of driving sprocket? I saw some ebay deals for a 4 inch diameter. It seems to me this would be way too little torque to properly accelerate a fairly heavy gantry. Can anyone confirm my suspicions?
Two inch diameter sprockets seem close to ideal, but is also the minimum size recommended for this type of belt. Would a small diameter sprocket contribute unduly to wear on the belt?


So, right now I'm just throwing out ideas and seeing what sticks. I'm currently leaning toward a single below-gantry belt, directly drivin if I can use a 2" sprocket, or maybe 5:1 belt reduced using a larger sprocket?
All comments are appreciated.

-b2b

[PaulRowntree]

Ok, here are my thoughts, for the $0.02.

1) The Z envelop of 18" is very, very tall, and is probably not going to be very stiff usinghome construction. Most folks have ~6" on large machines. Some software packages such as Vectric's Aspire and Cut3D can slice a job to make use of thinner pieces.
2) an 8mm pitch seems to be long; I've seen T5 and XL being used, at ~5mm
3) Unless the gantry is super stiff, pulling it by one side will cause it to rack. Some folks add a steel cable 'sliding know' to keep the gantry advancing straight, but on bigger machines most just add dual X drives.
4) Every pound of weight must be moved and accelerated. At 70 pounds, accelerating this at reasonable rates will take much more of your motor strength than the cutting forces.
Cheers!

[born2bewilder]

Thanks for the input.

The 18 inch measure was because I have thoughts to upgrade to 4, 5, or 6 axes at some point in the future. Plus I have two supported 1/2" round rails that're 24" long.
What would be the largest factor precluding such a design? Is it the stiffness of the bearings supporting the z axis slide, or is it the stiffness of the gantry itself that is the greater limitation?
With 24 inch rails, how long should the slide block be to resist lateral forces? I only have 1 double bearing per each rail right now, I'm thinking a second set of bearing blocks would be needed. Or perhaps an additional set of rails as well.
I've been thinking about making a 'box' structure for the gantry length, a try for maximal stiffness with cheap materials. Maybe start with mdf, upgrade to aluminum plate or extrusions later....

What does pitch effect? Besides limiting sprocket size, I know of nothing.

If I had the full 2500 oz-in of that 70 lb motor I wouldn't worry as much, but since I don't think I'll have that available for a while, I think I will try to minimize my gantry mass and keep the motor on the frame...

[PaulRowntree]

Going to multiple axes on the gantry is such a big step forward that most people learn the ropes on a 3 axis tool that they can build well. There are a few 5-6 axis machines on this site, but they are generally VERY big, very solid, and usually out of steel. So I would start with a reduced Z that does what you want and keeps/makes you happy, then go big at a later stage.

I will leave the stiffness question to the experts. ger21 has suggested that you assume 5-20 lbs of cutter forces for a wood cutter, so you want to maintain your target accuracy subject to these loads. The linear bearing specs can guide you on this. I have skate-based linear X & Y rails that work well enough, but pro-grade (if big enough) would be better. Time permitting I am moving to V-groove bearings on Y then X.

As you say, longer pitch means larger diameters, and therefore lower resolution unless you have a reduction stage involved. Don't count on microstepping to increase the resolution, especially under load. Maybe the difference between 5 and 8 mm isn't as big a deal as I let on.

Cheers!

[Bear5k]

Thanks for the input.

The 18 inch measure was because I have thoughts to upgrade to 4, 5, or 6 axes at some point in the future. Plus I have two supported 1/2" round rails that're 24" long.
What would be the largest factor precluding such a design? Is it the stiffness of the bearings supporting the z axis slide, or is it the stiffness of the gantry itself that is the greater limitation?
With 24 inch rails, how long should the slide block be to resist lateral forces? I only have 1 double bearing per each rail right now, I'm thinking a second set of bearing blocks would be needed. Or perhaps an additional set of rails as well.
I've been thinking about making a 'box' structure for the gantry length, a try for maximal stiffness with cheap materials. Maybe start with mdf, upgrade to aluminum plate or extrusions later....

What does pitch effect? Besides limiting sprocket size, I know of nothing.

If I had the full 2500 oz-in of that 70 lb motor I wouldn't worry as much, but since I don't think I'll have that available for a while, I think I will try to minimize my gantry mass and keep the motor on the frame...

To get the greatest precision and load-bearing capacity, you will want to go with two slides/bearings per rail with a bit of distance between them. That will eat-up the 24" rails pretty quickly. Also, whether or not they are supported rails also makes a big difference. If these are "naked" rails (unsupported; affixed only on the ends), then you will definitely want to consider cutting loads very carefully. With supported rails, this isn't really an issue. What is an issue is Z-axis design.

There are two types of Z-axis to consider (roughly). One where the tool is affixed to the Z-axis table and one where the Z-axis table attaches to the Y-axis (aka a "dipping style" Z-axis). For a standard design where the tool attaches to the table, you will quickly run into problems once you get much beyond 5" - 6" of travel. The reason being that your Z-axis frame has to be at least as long as your table + travel. If your maximum Z-axis cutting range of motion is only an inch or two, then standard cutting bits are fine. If you want to be able to machine a full 6" range of motion, then your bit must be at least 6" long. That's a lot of horizontal stress for most bits (and before dealing with accentuated run-out).

A way around this is with a "dipping" Z-axis where the tool is attached to the frame of the Z-axis and the table is what connects to the Y-axis. The upside of this is that you now have the ability to more effectively move the axis out of the way as your gantry moves over the work piece. The downside is that this is a weaker axis overall, so you have to add structure to it (larger rails, ticker support members, etc.) to have similar strength to the "standard" Z-axis.

Finally, pitch affects pulley size, and pulley size affects gearing. With most servo motors, you will want to gear-down the motor when using a pulley drive (imagine 5,000 - 6,000 rpm moving 3 - 4" per rev!).

[born2bewilder]

I was thinking of DIY'ing a rotary table somewhere inside the tool envelope. But yeah, that's a future plan... just trying to keep my options open. 3 axis is all I will have for the near future, so I'd best make sure I do that well, at least.


So, as I understand it, you are describing two options: one with rails fixed to the y gantry slide, with sliding bearings blocks; and one with blocks fixed on the y gantry slide, rails that slide attached to the tool platform.

If that's right, then yes I was envisioning the 'dipping' z with moving rails.

Why would one arrangement be any better than the other? It seems that if the distance between bearing blocks were equivalent, than forces on the bearings would be the same?

Or perhaps not. I suppose that if the z gantry sliding rail thing was at full extension (as low as it can go) then the tool head would be a farther distance from the bearings themselves. So the lever-arm advantage would increase reflected cutting forces... I think i get it....

I originally thought that I could use one 'twin' bearing block per rail, only. Once I had them in my hands and saw how short they are, that plan seemed impractical. I've ordered a set of additional blocks. I'm figuring 10-12" total length on the bearing block mounting plate, affixed to the y gantry slide, and 'dipping' z rails. 12-14" total z travel. 8-10" center to center rail separation. Intuitively I'd think that would be good enough for reasonable stiffness, assuming the structure itself is sufficiently stiff..


Regarding other matters, for some reason I'd only considered a belt drive x-axis. I see now a belt drive y-axis makes a lot more sense... faster accelerations from reduced mass. I'm considering a 3:1 belt reduction from motor to drive sprocket, which would be a 3" diameter drive.

Assuming 62 lb-in torque, 2000 rpm from my motor:

that would be 62 lb-in * 3 = 186 lb-in/1.5" radius = 130 lb force linear. y-slide and z-axis, maybe 50 lbs. all together? That would be >2g acceleration, wouldn't it?

2000 rpm / 3 = 666 rpm * 3" * pi = 6276 ipm max rapids. That sounds nicely quick to me.

3600 ppr encoder * 3 = 10800 ppr / (3" * pi) = 1145 pulses per linear inch. = .00087" resolution (??)

I've heard that encoder resolution should be something like 5-10x the performance you want. Does that mean I shouldn't expect better that .004-.008" accuracy or repeatability with this setup? Anyone care to check assumptions on my math here?

One additional question: Is is possible to use a timing belt in a vertical orientation? As in, the sprocket axes are vertical, with the belt 'laid flat' like a snake on the floor. I am guessing that may lead to excessive wear on the belt edges or sprocket flanges, but I haven't read anything about that specifically, that I can recall.

[Bear5k]

I think you've got it enough to start asking the right questions.

For the belt, depending upon the distance between the sprockets, belt orientation may not matter. That being said, you'd want to be real clear about what you are wanting to do with the belt. In many cases, you will find it easier/cheaper, especially for a first build, to go with a rack and pinion set-up rather than a long belt (which tend to stretch over time, among other things). If you are talking about a short belt just for mechanical advantage, then we are back to orientation doesn't matter.

For long belt drives, read this thread:
http://www.cnczone.com/forums/linear...e_ever_if.html

There are some great ideas in there.

[born2bewilder]

For the belt, depending upon the distance between the sprockets, belt orientation may not matter. That being said, you'd want to be real clear about what you are wanting to do with the belt. In many cases, you will find it easier/cheaper, especially for a first build, to go with a rack and pinion set-up rather than a long belt (which tend to stretch over time, among other things). If you are talking about a short belt just for mechanical advantage, then we are back to orientation doesn't matter.

For long belt drives, read this thread: <URL>

The 36mm wide Carbon GT belts I found are rated to carry around 100 HP at higher RPMs. I figure no matter how you cut it that equates to less force than my motors could conceivably exert on them.
The brochures make claims of having very little stretch as well, after some length of a break-in period. For these reasons I thought they may be quite appropriate for this application.

Ah, here's something I just ran into:

Low stretch linear motion belts including PolyChain are well-suited for positioning applications. Belt elongation under load within the range of half a millimeter per meter of belt length (0.05 percent) is easily achieved. A 37 mm standard belt width is rated to a minimum breaking tension of over 42,000 N.

So, reading similar stuff convinced me to consider this whole belt drive thing in the first place. Of course even with the belts for scratch, it looks as if getting the rest of the parts might be expensive...

I'm thinking of using them with two same size sprockets, run along the y axis gantry beam. Total span might approach 70". I thought that that span might be excessive for having the sprockets oriented with their axes vertical, but I'm second guessing my first thoughts. The total weight of the belts is only just over a pound, and since there will likely be several hundred lbs of tension on the belt, mass would be a negligible component of the bigger equation, I'm guessing. Shaft alignment is probably far more important.

So, if anyone has any experience with belt drives, I'm now considering other factors that might limit the span. Particularly, whether belt 'whip' or 'flap' or whatever from running at high speeds would be an issue.

Also, how much tension would be necessary? Is their any design rule of thumb for that when the application is linear motion? I didn't find much of use in the Gates literature...

[ger21]

While belts don't stretch much, they can flex quite a bit. If you actually achieve the numbers you're talking about, when you move from one position to another and stop, it's going to "bounce" back and forth a little.

[Bear5k]

The 36mm wide Carbon GT belts I found are rated to carry around 100 HP at higher RPMs. I figure no matter how you cut it that equates to less force than my motors could conceivably exert on them.

Don't get too hung up on a power rating. Power is work over time, or for circular motion, torque * rev/sec * 2Pi. What you want to focus on is the torque rating. Also, you don't want to look at the breaking strength other than to verify that it is a Really Big Number compared to anything you will be doing. For precision work, you want to focus on elasticity: how much will the belt stretch under load.

The brochures make claims of having very little stretch as well, after some length of a break-in period. For these reasons I thought they may be quite appropriate for this application.

There is a huge dependency on the implementation here. A long, unsupported belt will be virtually impossible to fully pre-tension, which means that it will introduce a fair bit of backlash and also possibly have issues with settling times (a "bungee" effect). What is brilliant about the Bell-Everman solution is the elegance of the pre-tensioning and how little of the belt is under tension at any one point.

Does any of this matter? It really depends upon how accurate you want your machine to be. If you plan on doing a large number of straight cuts/grooves in wood for rough cabinet work, and you need to do such cuts quickly over large sheet stock, a belt drive is very economical because the error is well within the tolerance of the cutting. If you are planning on doing fine relief work or lithophane engraving, then you will need to consider the design and the build very carefully to make sure you get the belt appropriately tensioned and can maintain that over time.

Ah, here's something I just ran into:

So, reading similar stuff convinced me to consider this whole belt drive thing in the first place. Of course even with the belts for scratch, it looks as if getting the rest of the parts might be expensive...

I'm thinking of using them with two same size sprockets, run along the y axis gantry beam. Total span might approach 70". I thought that that span might be excessive for having the sprockets oriented with their axes vertical, but I'm second guessing my first thoughts. The total weight of the belts is only just over a pound, and since there will likely be several hundred lbs of tension on the belt, mass would be a negligible component of the bigger equation, I'm guessing. Shaft alignment is probably far more important.

So, if anyone has any experience with belt drives, I'm now considering other factors that might limit the span. Particularly, whether belt 'whip' or 'flap' or whatever from running at high speeds would be an issue.

You will want to account for that with such a long span. Check out a few of the designs that have been built and you will get some ideas of how to bring it together.

Also, how much tension would be necessary? Is their any design rule of thumb for that when the application is linear motion? I didn't find much of use in the Gates literature...

I'll leave this to others who have built such things. I looked at both belt and R&P designs a while ago before settling on good, old screw-drive. I am seriously tempted by the Bell-Everman design, but I won't play with that for a while.

[terminator]

HI

I AM TRYING TO BUILD A 4TH AXES FOR MY DECKEL MILL. THE QUESTIONS ARE MANY BUT CAN ANY ONE HELP?
I HAVE A STOBER AC SERVO MOTOR AND TREE PHASE AC SERVO DRIVE.
THE SERVO MOTOR RATED 7000 RPM MAX.
I WAS HOPING TO USE A TIMING BELT SETUP LIKE THE CAMBELT OF A CAR.
SHORT BELT 30MM WIDE AND REDUCTION BELT PULLYS.
NO WORM GEAR. TIMING BELT BIG PULLY MOUNTED ON BEARING SHAFT BEHIND CHUCK.
THE SERVO MOTOR HAS A 24V DC BRAKE INTERNALLY.
THE ACCURACY OF MY MILL IS 0.02 MM AND I WOULD LIKE TO COME CLOSE TO THAT.
IS IT EVEN WORTH TRYING OR DOES THOSE BELTS STREACH TO MUCH? OTHER DISADVANTAGES OF USING BELTS HERE?
I HAVE A SOLENOID BRAKE THAT I CAN FIT ON THE MAIN SHAFT ASWELL.
IS THERE ANY COMERCIAL CNC ROTARY TABLES WITH THIS SORT OF SETUP?

IF I SETUP THE 2 PULLYS AND BELT AND PUT ENOUGH TENSION THE SYSTEM FEELS VERY RIGET TO ME.

REGARDS
MACGUIVER
SA

[harryn]

The main challenge of using a belt in a cnc application is elongation stretch, either under the average load, or under peak loads. The secondary challenges are linearity of the teeth, and how much backlash is in the "belt to pulley" interface.

When used in power transmission applications, the main challenge is actually not elongation, but tooth strength. You can get a sense of this situation by thinking about how your engine actually uses this belt. At least in the cars I have seen, there is an angle sensor which clicks off each rotation to reset the zero point, and that is not even dealing with backlash, just slop.

I have been studying belt reduction and drive methods for a while now, and I don't consider myself and expert, but perhaps I have avoided 50% of the possible issues by reading a lot.
- A good belt to consider if AT5 with at least a 50mm wide belt.
- I strongly urge you to consider steel reinforced belts, not the carbon or kevlar ones, because they elongate less
- Most belt setups are limited to 3:1 reduction due to pulley availability, but with AT5, you can get ratios up to 5:1 sometimes in one step.
- There are a number of firms that make belts, pulleys, etc. Brecoflex has an excellent web site and tons of info on the subject, so at least consider to read everything they have posted.

I am honestly not sure if you can hit your goal or not with belt reduction, but I can also tell you that the specs on a lot of speed reduction methods, even from first class suppliers will also struggle to hit it. It is entirely possible that you will need to map your rotary setup in software to meet that goal, regardless of method used.

Imagine if the center of a drive pulley or gear is off by even 0.01 mm concentricity with the gear teeth. Even if everything else is perfect, your error is already (Pi) x ( 0.01 mm) = 0.0314 mm.