Worm Gear Discussion

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Subject: Worms and Worm Wheels --part 1 of 5

From: Doc G

The Meade telescope drives are not made with true worm wheels. GASP!! A true worm and worm wheel are a pair of matching elements of which the worm is a spirally cut gear that has the shape of a screw. It crawls along so it is called a worm. The big round gear that mates with the worm is usually called a worm wheel or a worm gear. A proper worm wheel that mates with the worm must be a "hobbed" gear. That is, it is cut with a "hob" that has the exact size and geometry of the worm. This is a complex and expensive process. It results in gear teeth that fit the worm exactly over a considerable surface.

The Meade worm gear is not a hobbed gear. It is sometimes, kindly, called a non-throated worm gear. In fact it is a simple flat spirally cut gear. It does not have a tooth curvature that matches that of the worm at all. There is technically only one point of contact between the worm and the gear. This is unlike the true hobbed worm wheel which has a large contact surface.

The flat spirally cut gear is much easier to make and thus much less expensive. I have not made a survey of what mounts use what kind of gears. Certainly the high quality, high cost mounts use a true worm wheel. (Fully throated teeth)

I have know this for many years now but have been reluctant to make this fact so clear. But with the current discussions about worm, gears, lapping and the like, is needs to be said.

What it means is that some lapping, if it removes material from the wheel, will increase the contact area between the worm and the gear teeth and might very well improve the behavior of the drive. With a properly hobbed and polished worm wheel, lapping should yield almost no improvement. If you want to see the quality of the machining on the gear, take a look at your gear with a 3 or 5 power magnifying glass. It should carry a bright polished looking surface.

I do not want to start a flurry of lapping because it is a delicate process which could do a lot of damage. It is very hard to lap a gear with an existing worm because the gear has softer material than the worm and it is the harder material that generally gets worn down in a grit lapping process. It is just like the pitch laps the glass not the other way around. So do not try it unless you know exactly what you are doing.

So at last the truth about the gears and probably why they have such large run outs, retro motion and so forth has been said. They are not true worm wheels but are flat spiral cut gears.

Worms and worm wheels, as in the Byers drives, in the smallest size which is about 7 1/2 inches cost upwards of $ 600 for the set. The gears alone, for a drive I am making, 12" diameter and 1 " thick with a 2" worm, cost over $1500. So again we have a case where money speaks!


Subject: Worms and Worm Wheels --part 2

From: Doc G

Bill Arnett wrote:
> OK, I can see why the Meade gear is cheaper. And it is clear that a
> "hobbed" gear set could transmit a much larger force. But why does this
> matter for a telescope drive? The amount of force is trivial. Surely,
> there's no danger of the gears deforming under the load of moving the scope.
> So why should we pay big bucks for a better gear?

This is a great question Bill. I could hardly wait for someone to ask.

There is a detailed discussion about the worm wheel action on my web site. Probably more than anyone wants to know. I will state the matter briefly here.

With the flat spiral cut gear, the worm can move laterally in the gear teeth. In fact it will try to bend the gear or try to crawl to one side or the other of the flat gear. There is nothing to restrain it.

With the hobbed gear, the worm fits snugly into the worm wheel teeth. The worm then cannot move the gear laterally. Think about looking at the end of the worm with the worm wheel engaging the worm. The teeth have a curvature which exactly fits the worm. This gives lateral stability to the contact between the worm and the worm wheel.

This contact area is very important to correct and precision operation of the drive. Everything happens at this contact area. With the flat gear sticking and retro motion are possible as the gear flops back and forth. The deeply cut hobbed worm wheel does not allow this action. The worm wheel essentially grips the worm over a large circumference of the worm.

I hope this work description works for you. I should make some diagrams of what is going on. Take my word that worms and hobbed wheels are the only correct way to make a precision drive.


Subject: Worms and Worm Wheels --part 3 Top

From: Doc G

John Ruthroff wrote:
> I would speculate that the more gear-to-gear surfaces there are, the more
> opportunities for *slop* there are in the system. With your LX200 off, gently
> turn the manual declination adjustment knob (with the big declination knob
> locked). If yours is like mine, you can turn it back and forth and gasp at how
> much slop there is in that gearbox! True, those are plastic gears and are
> probably not very well made, but all those surfaces clunking against one
> another don't help matters. I'm not sure how many of those gears are in the
> power train when the motor is being used to move the scope, but I'd think
> better gears in the gearbox would be helpful.

The gear box has a 60 to 1 ratio. There are three gears used to get this ratio. The gears are a combination of metal and plastic (probably Delrin) The metal gears appear to be stamped and the plastic gears are molded. The gear box is as you suggest, very loose. It typically has 10 to 70 arc seconds of slop as referenced to the OTA. This is why there is a Dec backlash.

> At least a worm system has only one
> gear-to-gear surface. I've wondered is the declination drive would benefit
> from a motor that doesn't require as much gearing-down as the current
> arrangement. It probably wouldn't slew as fast, but how fast (except for
> satellite tracking) do we really need the 'scope to be able to move anyway? I
> run my motors on the "3" setting...helps keep the noise down too.

Making the two drives different would require making two different drives. That costs money.

> I think the difficulty of making good gear sets has to do with the precision
> matching that's required. The more precise the matching, the better the
> results, i.e. less *slop*. Of course that takes better equipment, skilled
> operators (if there is still a human in the chain) higher quality materials,
> better quality control and more time...which of course all equals more money.

These ideas are all true. See my comments to Bill's questions below about the accuracies required.

> I've often wondered about some sort of a *belt drive* arrangement where a belt
> of some material would be the contact surface between the worm and the gear.
> Thus, the precision machining would be limited to ensuring that the holes of
> the gear were at exact center and that they were perfectly round, which would
> seem to be an easier (and cheaper) task than having to also cut teeth into
> them. I thing the problem then shifts to how much elasticity the belt material
> has, and how much slop that would introduce. Apparently it must be a lot of
> slop, as it's hard to believe that it's an original idea.

With the development of high precision non stretchable belts, there are some designs that use belts. The Paramount from Bisque is one example. Belts show cogging just like gears. There are some friction drives that use neither belts nor gears. Friction drives are not without problems.

There are actually many different drive schemes described in the literature. The worm/worm wheel has persisted because, at its best, it is strong and accurate. With PEC and autoguiding you can get sub arc second tracking.

Bill Arnet wrote:
> > Next question: why use a worm in the first place if it's so difficult to
> > get it right? A worm is an easy way to get a large reduction but a series
> > or regular gears will do the job, too.
> >
> > Also, GEM manufacturers like to brag about how big their gears are. Why
> > does this matter?
> >
> > Finally, why is it seemingly so hard to make good gears? From a software
> > point of view :-) a gear is just a silly hunk of metal with a funny shape
> > that ought to be easy enough to cut with CNC machine: set it up, pump out a
> > hundred pieces per hour. What am I missing?

There is no easy way to get very large reduction ratios without a worm gear. A typical worm/worm wheel ration is 180 to one or for the better gears 360 to one. Getting 10 to one with regular gears is a lot so you would have to have three stages of reduction and making precision gears to do this would be very difficult and costly.

A Large gear is an advantage in proportion to the size of the gear. The reason is that the worm has a much longer lever arm and thus any imprecision in the worm is reduced with the longer lever are. Think about the precision of the worm to worm wheel accuracy you need. With a 6" wheel , 3" lever arm, the accuracy at the worm to wheel contact has to be about 0.1 microns. Green light has a wavelength of 0.5 microns. So we are talking about cutting and polishing metal parts to the accuracy required for optical parts.

You see the job is not easy. If the wheel is larger, the accuracy at the worm is proportionately greater and the wheel and worm are a bit easier to make. The problems are no easier for ordinary gears, but you have more gears to make and the first mating pair require the same accuracy.

Normal gear cutting is done to a ten thousandth of an inch or so. That is about 2.5 microns. So the gears for astronomical mechanisms are about 50 times poorer than necessary for one arc second pointing. They are about right for one arc minute pointing.

If the main gear in the LX is cut to 0.0001" (good to very good gear) than the wobble would be expected to be about 50 arc seconds. And so it is.

So when you start to put some real numbers in this, you find that great precision is required. That is, mechanical gear precision similar to optical precision. That is why a 10" Byers gear set of research grade only offers 5 arc second precision.

So crank up you CNC machine, but be sure you are getting out optically precise parts. (G)

Very large telescopes do use regular gears. They also have PEC systems that take out the harmonics of the main gear, the harmonics of the second gear, the harmonics of the third gear and so forth.


Subject: Worms and Worm Wheels --part 4 Top

From: Doc G

Bruce Johnston wrote:

> Do you think that a replacement set of R.A. gears for the LX200 would
> significantly help in the periodic error training, and the consistency of the
> periodic error? Naturally, I realize that there are many, many variables,
> and quality of the gears would be a factor I would assume, but what do you think?

I believe that a Byer's quality gear and worm would improve the LX telescope. Even, that is, if it were only a 6" drive.

> Are there 'tweaks' that can be done to the existing R.A. set, as is
> done with the Dec, to make the scope give good periodic error after training,
> or is it hopeless? Can a precision set, made the same size, etc. as the
> LX200, take care of these woes, do you think?

The tweaks for the RA drive are the same as those for the Dec drive. In some ways the RA drive is easier since it only has to move with precision in one direction. Mechanical deviations of 50 arc seconds can be reduced to 5 arc seconds with PEC. A caveat is that the same section of the gear should be used all the time and the PEC should ideally be done over more teeth. (See my post to Bill Arnet about this matter)

I believe that the worm gear and the drive would have to be replaced since the worm is the wrong pitch for a 360 tooth worm wheel. I have seriously thought about trying a project of a new drive mechanism. But my project list it too full right now.
> I'm disappointed in the inconsistency I get after a training
> session. Next night, it's right back to the erratic movements.

That happens because the PEC trains on only one tooth of the wormier.

The LX system does not allow for more sophisticated training. Though it should be realized that if you do successive training on the same star, you are training on several different teeth. The hope is that the PEC makes the scope smooth enough so that the CCD guider takes care of the rest. I have little experience with the SBIG AO unit, but it too has been said to take care of some mechanical problems at higher frequencies.

All of the computer and other add on fixes of course work better if the mechanics are excellent in the first place. But they also are costly.

I have come to believe that you get a lot of telescope for the money with the LX. You also get an elegant design that others are still, ten year later, trying to match. (the GOTO system) But I also believe that you can do a lot better for a lot more money. Mounts from several manufacturers like the Paramount, AP, Losmandy and others make fine equipment for a fine price. I would say that for twice the money you get twice the performance, but for five times the money you probably only get three times the performance. It's the law of diminishing returns.


Subject: Worms and Worm Wheels --part 5 of 5 Top

From: Doc G

Bill Arnett wrote:
> > Very large telescopes do use regular gears. They also have PEC systems
> > that take out the harmonics of the main gear, the harmonics of the
> > second gear, the harmonics of the third gear and so forth.
> So why don't we do it that way, too? Software is cheap.

It is true that we could use software to correct amateur drives more accurately. The professional drives are corrected, not with a simple PEC type system, but they are corrected for all of the sky at the gear level and for all of the sky at the absolute pointing level. The origin of a program that Bisque calls T-point was the effort to make the tracking and pointing of the English Australian telescope perfect.

In contrast, the Meade PEC corrects for only one turn of the worm located on one tooth of the worm gear. Ideally, as with the professional system a full sky PEC would correct for the entire travel of the worm around the worm gear. This would become several hundred points per worm turn and about for half of the teeth in the worm gear. The task of doing the PEC would be large from a practical point. Not difficult for the computer of course. But with all sky training, the scope would have to be permanently aligned and the clutches never released so as to keep synchronization.

Under these conditions one could do a combination of PEC as T-point just as the professionals do.

There is a second deterrent to making PEC work well. That is the tightness and consistence of the worm/wormgear mechanical contact. There is a bit of hysteresis in the mechanics of the less accurate systems. This factor is very hard to program out because it is erratic and non-linear.

I believe that with good, permanent mounting and good maintenance of an LX, it could perform very much better. Several of our mapug members have, I believe, made good use of T-point. I know of no one who has tried to develop a full sky PEC.


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