Mounting a timing pulley - Precisely

[harryn]

Hi, I am working on a DIY router / mill which will run from a stepper motor + belt drive system. I know the normal route is a precision ball screw + nut combo, but I would like to attempt this method, after all, it is a hobby, so I can play a bit.

I have identified stepper motors with very little shaft play and reasonable radial load capability with a nominal 1/2 in shaft. This will (hopefully) allow mounting the timing belt pulley directly to the shaft of the stepper motor. Micro stepping will be used to obtain the small precise steps, and special high tolerance belt will be used to help minimize issues there.

The challenge I have is this:
- No matter what I do, there will be at least a small amount of eccentricity in the stepper motor shaft, pulley center hole, and teeth.
- How do I "reduce this to a minimum ?

So far, I am thinking:
- Buy high quality Al toothed pulleys
- Have them lathe bored (I don't have machining tools yet) to 0.005 under size for the shaft and shrink fit them on + set screws
- Use the stepper motor to drive the "assembly and have someone take a "finishing cut" on the pulley teeth to true it up to the last 0.001 or maybe less.

I am pushing a bit on this aspect, as any errors in the eccentricity are amplified X pi in the linear motion, at least the way I am thinking about it.

Any suggestions ?

[Baketech]

This is my favorite method...easy to machine, install and maintain.

http://www.b-loc.com/

[Baketech]

I like keyless hubs for this type of application. Easy to machine, install and maintain.

http://www.b-loc.com/

[Baketech]

I like keyless hubs for this...easy to machine, install and maintain.

http://www.b-loc.com/

[harryn]

Originally Posted by Baketech I like keyless hubs for this...easy to machine, install and maintain. http://www.b-loc.com/

Hi - Thanks for the input. I have seen several keyless hub concepts and they all seem like a better idea than a notched key hub (at least to me). They seem to all be more or less "self centering", at least from the perspective of the hub pilot hole and shaft.

The part that I am still unsure about, is how to get them EXACTLY concentric - in other words - deal with slight imperfections in the shaft, pulley hole location, and teeth machining errors ? Remember, a 0.001 in error in concentricity equates to a 0.003 in error in linear position.

[Geof]

Originally Posted by harryn ....deal with slight imperfections in the shaft, pulley hole location, and teeth machining errors ? Remember, a 0.001 in error in concentricity equates to a 0.003 in error in linear position.

I don't use Mach but have read on here that it has the capability of mapping a feedscrew. Your pulley eccentricity could be mapped the same way surely?

You may put in a lot of effort and find that you still have to map out a 0.001" eccentricity and less overall effort may be involved to assemble things in a simple manner and map out 0.01".

[harryn]

Hi Geof

Thanks for that input - that is a good idea. I guess I will need to figure out how to measure the non-linearity in order to map it in. I am a beginner, so I don't own tooling like this.

I "might" use Mach, but it is not definite. I don't currently own any CAD software, so the conversion of drawings to g code is not so straightforward. If I use g-cam, at least in theory, I can draw my (hobby) parts in sort of as tool paths and this outputs the pulses, at least I think this is how it works.

Your general idea is right though, it is a bit of a bother to get it dead on. OTOH, I have to believe that gears must be mounted pretty accurately in order to work as well as they do.

[Baketech]

Originally Posted by harryn Hi - Thanks for the input. I have seen several keyless hub concepts and they all seem like a better idea than a notched key hub (at least to me). They seem to all be more or less "self centering", at least from the perspective of the hub pilot hole and shaft.

It's anecdotal of course, but I've had these things come it at less than 0.001" runout. They do a very good job at centering things. Probably very close to numbers you get with a shrink fit.... ymmv.

Originally Posted by harryn Remember, a 0.001 in error in concentricity equates to a 0.003 in error in linear position.

Not sure this is correct, how are you arriving at this?

[harryn]

Hi, I assumed that one rotation of the pulley will move the belt length L. If D = Diameter, then L= pi x D.

If the center is offset by distance = d, then the error in the Length (could be as much as) pi x d, or approx. 3.14 x d. I rounded this off to 3 x d.

Now that I think about it more, for each full rotation, this cancels out to zero.

The problem will be that in each 1/2 rotation, you will end up with a position offset of 2 x d ? , so an error in roundness of 0.003 makes an error of 0.006 in position every 1/2 turn - I think.

It has been a long day though, so I might be confusing myself.

[Baketech]

Originally Posted by harryn Hi, I assumed that one rotation of the pulley will move the belt length L. If D = Diameter, then L= pi x D. If the center is offset by distance = d, then the error in the Length (could be as much as) pi x d, or approx. 3.14 x d. I rounded this off to 3 x d. Now that I think about it more, for each full rotation, this cancels out to zero. The problem will be that in each 1/2 rotation, you will end up with a position offset of 2 x d ? , so an error in roundness of 0.003 makes an error of 0.006 in position every 1/2 turn - I think. It has been a long day though, so I might be confusing myself.

I agree that the eccentricity will cause a minor linear error, but I don't think it's nearly that large.

As you have already figured out, the offset does not change the circumference of the pulley...so in other words (Pi x D) is not what you are looking for here.

It is correct though that the eccentricity would cause an error, but I think we can estimate it. For argument's sake let's use a pulley with a 2.0" pitch diameter, and calculate that 1 degree of rotation yields 0.01745" of belt travel from (2.00 x Pi)360
*Ignoring chordal action to make the numbers a bit simpler.

Now imagine a sloppy set-screw connection that has a 0.001" offset. Substitute 2.002" and 1.998" for your instantaneous max and min diameters, and the numbers for 1 degree of rotation look like this:

2.002" = 0.01747"
1.000" = 0.01745"
1.998" = 0.01744"

So the actual belt error is way down in the hundredths...but it gets better, assuming you are driving a ball screw, as this error gets further divided by that ratio too.

So by all means, be mindful of concentricity when you design your parts, but I don't think it's too big of a problem... ymmv

[Geof]

If the pulley is running off center your actual position leads and lags your intended position in a sinusoidal manner. Which is why it should be easy to correct by mapping the motion. It would be possible to build a calibration rig using a digital caliper. Clamp the body of the caliper in a little fixture on the table and have the machine push the slider as it moved.

[harryn]

Thank you for the replies. I probably have been researching this area to death and am becoming a bit anal about it.

Geof, you are right, since the offset is in fact sinusoidal, it should be possible to deal with in software, if I end up using intelligent enough software for everything.

Baketch - Thanks for reminding me of how to add and multiply. It seems I had gotten off track.

It seems like a PITA to map 3 axis on the order of .5 - 1.0 meter with a callipers, but maybe that is what is needed to make it all work. I guess if I reach the point of being super picky, I can always borrow a laser interferrometer and map it that way.

Just for one more round of fun, I went back again to the brecoflex.com web site to see how they spec their timing belt pulleys. This link

http://www.brecoflex.com/?CATID=1&SC...NID=12&PUDE=77

on geometric tolerances poins out a concentricity of 0.05mm which might be tight enough for me to ignore. It also points out a runout error (on the high precision pulleys) of 0.1mm (about 0.003 in), which is in the range I would "ideally" like to achieve on my system, so I can't as easily ignore this. Perhaps to my peril, my DIY system has no gear reduction or ball screw, it is intended to be a direct belt drive from a pulley on the stepper motor, so this area is key to any chance of decent results.

From the Brecoflex catalog b_205 pdf catalog, page 13, pulley LS42 AT10, for a 10mm pitch, high precision belt, 25mm wide, 24 teeth, and effective dia of 76.39mm.

If I assume
- 0.1mm of runout from the pulley spec
- 0.05mm from concentricity error
- 0.1mm from shaft error and mounting error

= 0.25mm potential offset error, or 0.5mm of TIR per 1/2 turn of the stepper motor. If my math is working today, that is about 0.013 inches of error per motor 1/2 rotation - effectively in 4 inches, before I even start with my own system build induced mistakes. Perhaps this is why ball screws are so popular.

I wonder if this kind of error is actually built into quite a number of systems which use timing belts to drive the ball screws, and is just not quite so obvious with all of the gear reductions.