Timing belt backlash for multi-stage gear reduction?

[jsheerin]

I'm thinking about making a C/A head for my next router (rotates the router about the Z and X axes to give 5 axis movement). It needs a large gear reduction between the servo and the head - something around 64:1. Going with timing belts and pulleys commonly available from SDP/si, it looks like that would require 3 sets of pulleys. I've been reading a bit, and all I can find is that the GT2 belts are the lowest backlash commonly available. However actual backlash is never really specified... Does anyone know or have a feel for how this would work out? Would backlash add up to unacceptable levels with this many reduction stages?

In comparison, I've been looking at the Thompson Micron Ultra True gear drives and they typically spec backlash in the 10 arc second range, I believe (although that's just from memory). When I was doing the calculations, I think that translated to a 0.015" movement (or lack of movement) of the tool tip on a long tool which didn't sound particularly great to me.

[JLSD]

Hi,
Just a thought, if you're basically tilting the cutter axis, What total angle do you need? Up to around 90 deg. total movement, a ballscrew/lever mechanism could be one answer. I know the output's not linear, but that could be fiddled in software, or by simple calcs if you're moving to preset positions. If you need continuous movement, it really needs a math function input to the controller, but that only needs someone smarter than me! (not hard!) It ought to be way stiffer than any rubber trick, especially 3-stage!
Regards,
John.

[jsheerin]

Thanks for the idea. It is interesting... It seems like it would be a tough way to go for continuous motion using non-custom software which is an eventual goal.

I'm looking to match (or better) the basic capabilities of an HSD head as seen on this machine:
http://www.cncmotion.com/titancanada.htm
Head specs are here:
http://www.hsd-hitec.com/eng/cont/2_assi.asp
Basically the C turns +/- 210 degrees and the A turns +/- 120 degrees.

To start with I'll only be positioning the head and then cutting, but eventually, hopefully after the machine has made some money, I'll be looking to upgrade my cam software to be able to do continuous 5 axis motion.

[stangtjk]

With that high of a gear ratio it might be better to go with an anti backlash worm gear assembly rather than a series of belts and pulleys.

[jsheerin]

Yes, harmonic drives are used in the HSD heads. Is that what you mean by anti-backlash worm gears, or is there another technique there to reduce backlash?

Overall, the goal is to reduce cost. So far almost the entire project is an ebay or industrial auction special. That is why I am thinking about the belt drives. If it turns out to not be practical, then I will have to hunt for some surplus gear drives.

[jsheerin]

Or do you mean two worm gears on opposite sides of an output gear with one driven to remove backlash? Like in US patent 7552661?

Would it be possible to use a separate servo motor with a drive running in torque mode to constantly apply a specified torque to remove the backlash on one of the worms? This seems like it would be possible, but I don't know enough about the electronics side of things to know if this would be practical... So this motor would always apply a constant torque, but the sign of the torque would change depending on which direction the primary motor was moving. Anyone know if this is possible? I'm running out of movement axes if I stick with Mach for a controller, so I'd probably have to be able to do this by using the direction pin for the rotation axis - when the direction pin changes, the direction of the torque would change.

[stangtjk]

I was referring to something like this. I'm not sure how much backlash is actually present with something like this, its basically just 2 gears face to face with a spring loaded between them to remove backlash. It was just a thought don't know much about it.

[jsheerin]

Okay, that's a better (or at least simpler) idea than mine - passive instead of active. So that's basically the same as a rack and pinion split pinion, but the worm has the advantage of preventing back driving, right?

So the question then would become if I could find a reasonably priced commercially available model or if I'd have to make my own up-sized version (which might not be too hard). I sent an email to SDP asking if they had any torque ratings for the parts they sell. The anti-backlash gear is only ~$50, so that would be pretty reasonable. If it won't support the torque I want, then I could do my own with cast iron and steel parts from Mcmaster-Carr for around $270 plus springs and machining. It seems like the biggest problem here might be getting springs in there that would be stiff enough to resist any torque trying to move the head within its backlash. I suppose that would be the advantage of the active version...

[jsheerin]

I suppose another way to get around having to have springs inside the gear (and a split gear) would be to have a second worm gear (as in the active version) but couple it to the driven worm and then spring load it against the gear to take out the backlash.

Another concern I had was efficiency of this type of setup. Looking here:
http://www.roymech.co.uk/Useful_Tabl...fficiency.html
and here:
http://www.engineershandbook.com/Tab...efficients.htm
it appears I could get 70% efficiency with greased steel and cast iron before applying any loads to remove backlash.

[Al_The_Man]

I have traditionally picked planetary gear box on ebay, Bayside is one nice make, lately the prices have been getting a bit steep, I found it sometimes cheaper to buy when a motor was attached for some reason.
Planetary you can get up to 100:1.
Al.

[wildwestpat]

Hi

The main consideration I suspect will be ridgidity and the forces inposed by the cutting action with an alowance for the odd dig in! The use of spring loaded half worm wheels will give you an elasticity in the axis drive. In designing radar aerial mounts I have used tightly meshed worm / wheel centers with the tooth form such that the worm can not bottom on the gear tooth root diameter. This is a common arrangement and is very effective as the adjustment mechanism is easily arranged. The worm and the gear should be made of compatible materials - stanless steel and brass for example with a good lubricant as the tooth pressures are higher than for a normal mesh. The rotation speeds for this sort of mechnism would be low so the lubrication problems should be minimal.

Hope this helps regards Pat

PS Tigter meshing also works with spur gearing but you would not get the back drive protection again there is an increase in friction losses which will limit the maximum speed.

[jsheerin]

I finally got back in front of my computer (well, the one with all my design info on it...). The HSD head has backlash at the end of a 15.7" long tool (or at least the tool tip is that far from the center of rotation) of 0.0016" with a torque of 118N*m applied if I'm reading their spec correctly. If I use a 100:1 planetary gear head reduction, those typically have around 0.5 arc minutes of backlash (Thompson Ultra-true) which would give about 0.0023" of backlash at the same distance. So that could be a possibility.

Looking at the stiffness of the head, HSD specs a stiffness of about 4e-5 in/N. This is actually for a load applied perpendicular to the tool bit when the bit is pointed straight down, but I wanted to compare that to the rotational stiffness of what I'm designing. So I looked at the Ultra true planetary drives again. I'd need a size 18 head for a 100:1 ratio. This would give me a rotational stiffness of 1.1e-6. For the continuous cutting force I'll have available (with the head at full acceleration), that would give me a deflection of 0.0014" at the tool tip. At the peak cutting force, I'd get 0.0055" of deflection. Those seem pretty reasonable. Then again, a size 18 gear box weighs 45 pounds, so it better be pretty stiff... Somehow I doubt I'll find one of those cheaply.

HSD also specs positioning accuracy at 0.004" at the tool tip. This is still something I would need to figure out. However, after reading here:
http://nsa.kpu-m.ac.jp/gijutu/kousak...qnotes.htm#wga
it looks like if I went with the worm gear approach, going with a larger gear would reduce positioning errors due to errors in the worm gear hobbing. Also, this probably points out that it could be a good idea to follow HSD's lead and have an encoder directly on the head itself instead of depending on the encoder on the servo motor.

So from the above, it looks like a planetary head could work fine, but the penalties would probably be cost and weight. A worm gear drive is looking better.

Btw, I know I'm mixing units horribly, but I find it easier to work in metric units for everything but positioning and speed. I still find it easiest to judge those results in English units.