A Cheap Huge Worm Gear

[Stub Mandrel]

2 hours ago, Vroobel said:

Interesting... I just counted, I have 896 teeth. That's surprising, I expected +/- 1, but not 6...

OK, let's count. 896 teeth x exactly 1.5877mm of pitch / Pi = 452.764mm, whilst average diameter of my wheel is 449mm. Where is the difference? 

Is possible, that I have wrong tap, not 3/8" BSW? I chect even this way: 449mm x Pi / 25.4mm x 16 = 888.55, so can't be 896!

Moreover, I've bought 1m of proper threaded rod that is matching perfectly to the grove in my wheel. 

Could you help to solve the problem, please?

It's a problem with free hobbing. The theoretical correct number of teeth is two less than the number that fit into the external circumference - this means a  free-hobbed gear started with zero slip will already be trying to fit in two extra teeth. You can partly compensate for this by starting with a decent cut straight away, but this is hard to achieve for a worm, although not so hard for a spur gear where you can move an angled hob across the blank.

On top of this, unless the wheel is driven by a gear train, you are relying on friction to give the initial drive. That's a big wheel to turn with a lot of inertia so you can expect a degree of slip. Once the hob (tap) has started to cut it will tend to follow the pattern already cut. If your wheel slipped enough to allow six extra teeth, they will have become self-perpetuating.

As for the good fit, let's take 896/890 = 1.006 or a pitch error of 0.6%.

BSW  is 16 tpi =  1.59mm pitch (near enough) 1.59 x 0.006 = 0.01mm, ten microns and less than half a thousandth of an inch.

That's way less than the amount of play/backlash necessary for the gear to operate so the extra teeth will have no measurable impact on the functioning of the gear.

Just use the true count when calculating your stepper drive rate and be happy ?

I would very much doubt that anyone free hobbing a big worm wheel could get the exact tooth count by anything other than chance.

[Vroobel]

31 minutes ago, Stub Mandrel said:

It's a problem with free hobbing. The theoretical correct number of teeth is two less than the number that fit into the external circumference - this means a  free-hobbed gear started with zero slip will already be trying to fit in two extra teeth. You can partly compensate for this by starting with a decent cut straight away, but this is hard to achieve for a worm, although not so hard for a spur gear where you can move an angled hob across the blank.

On top of this, unless the wheel is driven by a gear train, you are relying on friction to give the initial drive. That's a big wheel to turn with a lot of inertia so you can expect a degree of slip. Once the hob (tap) has started to cut it will tend to follow the pattern already cut. If your wheel slipped enough to allow six extra teeth, they will have become self-perpetuating.

As for the good fit, let's take 896/890 = 1.006 or a pitch error of 0.6%.

BSW  is 16 tpi =  1.59mm pitch (near enough) 1.59 x 0.006 = 0.01mm, ten microns and less than half a thousandth of an inch.

That's way less than the amount of play/backlash necessary for the gear to operate so the extra teeth will have no measurable impact on the functioning of the gear.

Just use the true count when calculating your stepper drive rate and be happy ?

I would very much doubt that anyone free hobbing a big worm wheel could get the exact tooth count by anything other than chance.

Thank you for excellent explanation. What do you think about the next wheel? Is possible, that the set will give same or similar result next time? I thought I can prepare little bit smaller wheel, 447mm of diameter instead of 450 (including the 5mm alu bar) that should give result of 888-890 teeth, but I'm not sure now. Perhaps that will give 884 teeth instead 890... 

I think I can make second wheel exactly 450mm big like the first one and just check. 

[Stub Mandrel]

11 hours ago, Vroobel said:

What do you think about the next wheel?

I think it's rather like knurling. You can come up with any number of formulas, but there is an element of chance involved.

What matters is that you even out irregularities and minimise periodic and other errors. Software will take care of any errors in the actual tooth count.

At a radius of 225mm a pointing error of one arc-minute represents 0.001 mm, that's a couple of wavelengths of light. You might get a micrometer that claims to measure to that level of precision and accuracy, but a worm wheel? Think about the challenges we face when pointing scopes with worm wheels 100mm across or less!

We are so blasé about guiding performance etc. and worry about errors that are the equivalent of putting the football into your own net on a pitch in a Australia from a penalty spot in Norway.

If, and only if, exact number of teeth is important to you do it this way. Hob the gear to about 1/4 depth. Cut out the excess teeth and fit to a reduced blank. Make the joint as perfect as you can, better a small gap and perfect alignment than slightly too far across the joint. Now hob to full depth.

[Vroobel]

It was the voice of reason. I lke it!

What do you mean writing 1/4 of depth? Is it 1/4 of depth of tooth or 1/4 of depth of expected grove? And what are the excess teeth? The ones just hobbed to 1/4 of the depth?

The exact number of teeth is not most important. I want to focus on quality of the final product, its surface, alignment. But why not to try to do it with expected number of teeth?

 

[ringz]

Mel Bartels used to make large diameter worm gears using a plastic/nylon threaded rod pressed into JBWeld epoxy glue around the circumference of a plywood sandwich. He also wrote the software to drive the scope through a parallel printer port of a laptop of the time. it was way ahead if its time.

[Vroobel]

I know the way. One of Polish most experienced astro-constructor and inventor, Leszek Jedrzejewski, made that using steel rod bent into the circle. He used specifically cut worm for that. But I wasn't interested in this solution, even looking easier than hobbling. 

[Stub Mandrel]

I think some very high quality systems do away with teeth altogether and run a hardened spindle against a large diameter and very accurate disc.

[Peter Drew]

32 minutes ago, Stub Mandrel said:

I think some very high quality systems do away with teeth altogether and run a hardened spindle against a large diameter and very accurate disc.

I use a similar system to drive my 8.5" refractor.   ?

[Vroobel]

40 minutes ago, Stub Mandrel said:

I think some very high quality systems do away with teeth altogether and run a hardened spindle against a large diameter and very accurate disc.

It's quite possible.

We were in Jodrell Bank last weekend, I couldn't find any teeth there in the radiotelescope, but I found a kind of bar with plenty of holes on side of one skid. That can be another way of indicating the actual position. 

[JamesF]

1 hour ago, Stub Mandrel said:

I think some very high quality systems do away with teeth altogether and run a hardened spindle against a large diameter and very accurate disc.

The Mesu 200 does this, I think.

James

[Vroobel]

Ok, but how to avoid a slip? 

[fwm891]

18 hours ago, Vroobel said:

It's hard to dispute with mats. The circumstance is 1414mm, that gives 450.09mm of average diameter and should give even 890.71 teeth. So why gives 896 teeth? ?

Temperature!. The band will have heated during the cutting ops and expanded giving physically more material for teeth to be formed in. Once cutting ops are finished the band will contract to approx. its original size. However, your also putting a thin band under pressure when cutting the teeth I would expect it to undergo some compression and reshaping.

[Vroobel]

Thanks for interesting note, but the alu bar wasn't warm when I started the hobbling. Yest, it is really worm during the cutting, but later, when the tap goes into the bar in depth of quarter of its diameter. The first few most important passes don't cause the warming able to extend the bar of the 10mm.

[Stub Mandrel]

19 minutes ago, Vroobel said:

Ok, but how to avoid a slip? 

I expect it's a combination of sufficient pressure and accurate balance.

[hdutton]

22 hours ago, fwm891 said:

Temperature!. The band will have heated during the cutting ops and expanded giving physically more material for teeth to be formed in. Once cutting ops are finished the band will contract to approx. its original size. However, your also putting a thin band under pressure when cutting the teeth I would expect it to undergo some compression and reshaping. 

Aluminum's CTE is about 13 x 10^-6 m/m deg C.

About 1.4m of circumference means 0.02mm length gain per deg.C   Since each tooth is a bit over 1mm the proposed about 7mm gain in length would require heating by 350 deg. C.

I really have no idea how this would work but guessing you mean mostly local heating of the band by the tap?  Still seems unlikely that he'd reach anything remotely close to ambient+350C.

 

[Stub Mandrel]

The band is unlikely to expand much, it will have cooled back down by the time it comes around again.

The hob will get a bit warmer, which will have an effect in the opposite direction, but so small as to be negligible.

[Peter Drew]

Experimenting with blank diameters can get you nearer to the required number of teeth. Using the same method, same tap and SAME material can usually reproduce the result. Harder or softer materials seem to react differently.   ?

[Vroobel]

I think so, the temperature couldn't cause the appearing of extra 6 teeth = 10mm.

I cut out next wheel last Saturday and I'd like to make exactly same size of wheel. I don't have expensive 600mm caliper, so I expect +/- 1 tooth. As I wrote, a few extra teeth don't mater for me if I get really different number of teeth, but that will mean something else involves there. 

[Chriske]

In the past we did use hose clamps, like this one. We bought these things by the meter so we could cut the required length. Each package contained 20 meter of the stuff + 20 worms. These worms were very easy to attach.
If you only need to track for observing it's more then adequate.

[Vroobel]

Thanks for the advise, but I think it's not accurate enough for my GoTo project supported by Raspberry Pi. Moreover, how to rotate the mount around more than 360 degrees? 

[Gina]

Do you need to.  AFAIK most if not all mounts can't turn more than 360 degrees or less.

[Vroobel]

Do you mean equatorial mounts, Gina? I have the Dob, so I dont have a problem with the tube looking down, if I good understood.

[Chriske]

5 hours ago, Vroobel said:

Thanks for the advise, but I think it's not accurate enough for my GoTo project supported by Raspberry Pi. Moreover, how to rotate the mount around more than 360 degrees? 

rotate the mount 360° around we never do, and most of us don't do that. That is a calculated disadvantage we can live with.
And indeed it's not meant to be used to do some accurate work.
For more accurate work we had another solution. But I can't post it here because it would be off topic and most of all I do not want to hijack this thread.

[Stub Mandrel]

6 hours ago, Vroobel said:

Thanks for the advise, but I think it's not accurate enough for my GoTo project supported by Raspberry Pi. Moreover, how to rotate the mount around more than 360 degrees? 

You might be surprised how accurate they are, not because they have to be but just as a consequence of the manufacturing process.

[Vroobel]

My friend ask me months ago if I could use this solution, but I couldn't imagine it at work with 450mm wheel, so didn't undertake the idea. Should I regret?