Notes on Machining Techniques for Worm Drives

The requirement to make an accurate worm and worm-wheel pair arose through my efforts to construct an equatorial mount for an astronomical telescope. However, the technique of machining a worm drive (and in particular, the gear hobbing process) may perhaps be of wider interest so I've included it here under the 'Machining Projects' pages.

An astronomical telescope drive needs a high-ratio geared drive to accurately follow the stars as they apparently move slowly across the sky. Further, this drive needs to be of exceptional accuracy if astrophotography is to be undertaken with a minimum of drive correcting. A Periodic Error of less than 5 arc-seconds (i.e., an angular pointing error of +/- 2.5 arc-seconds) is a desirable target for such a telescope drive system. For a little more detail on the impact of machining errors on drive accuracy follow this link. It is debatable whether the effort expended to machine an almost-perfect tracking mechanical drive is worth the trouble, it may on balance be more economical to use a lower precision drive and incorporate an electronic 'drive corrector' (PEC) to compensate for any tracking defects within the gear system. Nevertheless, the technique described below *should* result in at least a usable drive - though it's exact performance will depend mainly on the accuracy and skill with which you can machine the components, and only partly on the use of techniques described below.

I will start by describing the machining of a simple 6" (nominal diameter) worm-wheel gear and it's matching worm. Two such gears are used on an astronomical telescope, the two axes are called Right-Ascension (or Polar axis) and Declination, and only the former needs to be of the highest quality unless the mount is to be computerised for all-sky pointing. Whilst this size of worm-wheel will give reasonable tracking accuracy it's diameter is somewhat less than that required for a top-class mount (we are talking about the $5000 price bracket here). However, the problems of machining worm-wheels above 6" diameter (say, a more respectable 12") may dissuade many people attempting the job in the first place - especially in a modest home workshop. I will therefore give additional notes on any modifications to the machining setup necessary to improve success with larger sizes. It's interesting that even fairly expensive mounts (G11 or LX200 computerised fork mount) don't use RA gears much different from the prototype 6" gear described here. Larger gears (to 12" and larger) fetch 'astronomical' prices on their own!

The main thing to remember about this type of job is that all the machined components need to be *concentric and parallel*, as any eccentricities, excessive clearances or run-outs will quickly destroy any hoped-for accuracy in the drive system. That target accuracy of 5 arc-seconds mentioned above places very stringent requirements indeed on the acceptable run-out and other tollerances in the drive's components (which ideally, are essentially zero) and the methods described are therefore designed to minimise this. For this reason, whilst there may often appear to be easier and quicker ways of doing the job stick to the rule of machining each component complete without removing it from the machine.

Machining Strategy

Wherever possible we will be making our own cutting tools. Whilst commercial gear-hobbing cutters can be purchased they are very expensive, but there are other important reasons for going with home-brew tooling. By using the same machining setup and threading tool to make both the worm and the gear cutter at once we are assured of an exact match - something that cannot be said for using commercial cutters.

Most machining on any given component (for example, an inner bore, outer diameter, and a bearing surface) will be machined together without removing the component from the chuck. To do so would make it very difficult to re-mount on the machine with the accuracy required, and thus completing all operations at once gives the best chance of producing concentric and parallel surfaces. Those with modest machinery will benefit most from this, and there is no reason why very accurate gears cannot be produced with lathes not of toolroom quality. The prototype worm-wheel I describe will be machined from plate aluminium alloy; this has ample mechanical strength for the job as the torque involved (and hence tooth-pressures) are relatively low. The worm itself will be machined from carbon steel, and this combination will last a life-time *provided* it's kept well lubricated and protected from the ingress of grit. Many commercial drives are made from alloy, though perhaps a better combination would be gun-metal (bronze) for the worm-wheel, together with hardened stainless-steel for the worm. Bronze has the desriable characteristic of 'work-hardening' under these exact working conditions, however this very same property makes it difficult to 'hob' without using commercial cutting tools. The home-made cutter described here wouldn't make much impression without adding clearances to the cutting teeth (possible, but difficult without a tool & cutter grinding machine).

For the best and most precise match between worm and worm-gear both the cutting tool and the worm itself will be machined together in the lathe, from the same bar of metal at one setup, and using the same single-point threading tool. One of the worms produced will be the final worm used in the drive, while the other will be converted into our hobbing (cutting) tool.

So far I haven't mentioned details of how the number of gear teeth are derived, nor the exact gear blank diameter or pitch (TPI) of the worm. It stands to reason that the worm pitch needs to exactly match (or very nearly so) the gaps between the teeth on periphery of the worm gear. Indeed, the hobbing process entirely depends on these two components matching, for if they do not then the gear blank will not 'self-index' as the cutter is rotated against it. Luckily, guesswork is not required and there are formulae that will provide these dimensions for us. If you take the trouble to look at the Excel 5 Spreadsheet I made up for my dividing head (available under the 'Experimental' section or by using this link here) you will see within it details for calculation of 20 deg involute worms, the matched dimensions for various DP gears or worm pitches. The exact dimensions (taken from the above spreadsheet) for my prototype gear pair are:

The hobbing cutter actually reduces the diameter of the blank relative to the finished height of the tooth-tip on the gear wheel (this wouldn't happen of course if the gear were simply straight- or hellical-cut), so the the depth of cut (38 thou) needs to be added to the blank's diameter (final size of 6.404 inches). Note that the worm pitch is not exactly 18 tpi, but this is what I will be using. The error of 0.001 tpi is not significant and will be evened out by the gear forming process (I hope).

Using the above criteria it's now possible to grind up the necessary threading tool to cut the worm. Use a piece of 1/4" or 5/16" square high-speed steel, and allow extra side-clearance on the left-hand side of the cutter tip to allow for the worm's pitch-angle. Put the best finish you can on the cutting tool using a slip stone as the finish on the worm teeth will mirror the finish on the tool. This tool is fairly delicate (being only 13 thou wide at the tip) and care must be taken when using it that only small cuts are taken otherwise it can easily snap off.

The worm thread cutting tool.

The first job will be to cut the worm-wheel blank from a flat piece of 1/2" thick alloy plate. Some method of indexing the gear with rough (i.e., in this case I mean rough = not gear-tooth-shaped) machined cuts dividing the blank into the required number of teeth will be necessary, a procedure known as 'gashing'. In the prototype gear 360 cuts need to be made using either a dividing head or a rotary table to provide the indexing. Whilst the final accuracy will not be entirely dependent upon the precision of this indexing it must still be fairly close-tolerance, the better job you make here the less work the cutter has to do. A free-turning bearing support, a sort of turntable, will also be required on which to mount the gear blank, and it's critical that this does not flex and is able rotate the blank concentric to it's bore. This bearing support will be mounted on the rear of the lathe cross-slide with the hobbing cutter mounted between centers.

Next, the two worms will be machined and one will be made into a cutter. Finally, the cutter will be used to machine the worm gear.

Machining Methods

The Gear-Wheel Blank:

Cut your alloy blank out using whatever method you like - I used a bandsaw to knock the corners off and finish turned it (oversize) in the lathe. My RA and DEC axles are 1" diameter (exactly) so I needed to put a bronze bearing in the center having a 1.0005" bore. The best way of doing this would be to make the bronze bushing first (with concentric bore remember!), and then machine the blank so that the bushing is a press-fit in the center. At the same setting, the outside diameter would be finished to size. The only way of doing this at one setup, and it's very important that it be done this way, would be to clamp it to a faceplate using holes drilled through the gear blank. It's otherwise difficult to turn both the outer circumference and also bore the center at the same time. OK, OK., so I cheated, but I know that on my Myford Super 7 the tailstock is setup correctly, so I first bored the center, fitted the bush, and then held the blank against the faceplate (on parallels for clearance) using a rotating center located in the bore. The outer circumference was thus machined to size (and faced off) and I doubt it was more than a couple of 10ths (0.0001") out (any error would show up later when it's checked just prior to hobbing).

Cutting The Worm:

I mounted the length of 3/4" diameter silver-steel in a 4-jaw at one end, and supported by a fixed steady and rotating centre at the other. Take great care when cutting the threads - use plently of cutting oil and very light cuts (final cuts should be no more than 0.001", and the rest around 0.003"). See my notes on thread cutting in the lathe (in the techniques section) because it's important to reduce cutting stresses by using only one side of the tool to do most of the cutting. My own tool-tip snapped off just as the job was finished, but that was due to my hands moving quicker than my brain and stupidly running it into the work instead of away from it! Actually, I was not in the least amused by this because it means I cannot make any more worms to match that particular cutter, I'll have junk it, grind another threading tool up and make a new cutter :(

The two portions of worm thread having been cut on the same piece of 3/4" silver steel (drill-rod). The eagle-eye might notice the tip of the threading tool has snapped off! - luckily I had finished the job anyway.

With the threads formed it's now necessary to produce some cutting teeth on the 'tool' before hardening. This job was done using a slitting saw held in the drill chuck on my vertical mill, with the work held in a 3-jaw lathe chuck mounted on a rotary table. You could just as easily do this with the work mounted on the lathe cross-slide. Note that I set the work at an angle of about 15 degrees to the table to produce 'sort-of helical' saw cuts, the reason being that the tool's cutting teeth were then staggered when presented to the gear blank (more than one cutting tooth engaged at any one time), thus making for a smoother hobbing operation. Additionally, the forward rake of the teeth change throughout the length of the cutter, so by virtue of moving the point of engagement between cutter and gear blank lengthways the cutting action can be adjusted (the more rake - the more aggressive the cutter).

A slitting saw has been used to form the teeth on the hobbing cutter, in this picture the work has been de-burred and cleaned up.
The finished hobbing cutter prior to hardening.

Before hardening the cutting tool (it's left on the bar for that job) make sure the teeth are well formed and have no burrs anywhere. I used a specially ground ultra-thin file for this job - one sold originally for cleaning auto contact-breakers, and thinking about it now I might have been better off making the saw cuts first and threading afterwards - there were a LOT of burrs to remove. A small brass brush on a Dremel-type tool is quite handy for removing small burrs, large ones will have to be stoned or filed off. Anyway, with the cutter cleaned up heat that portion to a cherry red and quench right out in cold water. Polish it up with emery and temper the tool to light straw colour (it needs to quite hard).

Preparing the Gear Blank:

As mentioned, the blank needs to be 'gashed' all around to produce the necessary 360 teeth. The gashes (in my case slitting saw cuts) allow the hobbing cutter to bite and pull the blank around, thus the cuts act as an index for the correct number of teeth. In theory, this job is not necessary because with the correct thread pitch on the hobbing tool combined with the correct diameter of the blank it should produce the correct number of teeth anyway. In practice it doesn't work out (not on my setup anyway).

The gear blank having the 360 index gashes cut with a slitting saw.
The indexed gear blank ready for hobbing.

The bearing support for the gear blank is quite a job in itself and needs care in it's construction, but at least you only have to make it once and thereafter you can turn out as many worm gears as you like. The picture below shows mine, made from an odd-sized pair of new ball-bearings that I happened to have in a drawer. I guess you could use oiled bronze bearings at a pinch, but there will be plenty of pressure on them from the cutter so they must be kept well oiled in use, and the support *must* turn quite freely even when clamped up to prevent flexure - otherwise there is a danger of the cutter ripping the teeth out the blank if it it decides to stop turning for any reason. The only dimension of note is that the midline of the gear blank needs to held at the lathe center-height (naturally), and the whole thing needs to be stiff enough to resist flexure during the cutting process. Of *extreme* importance in this application is that the gear teeth end up exactly concentric with the bore, and to this end the blank needs to turn concentric and (perhaps to a lesser extent) parallel to the lathe spindle axis - use a DTI to check this is so. If you took note of my earlier comments regarding machining all components at one setup to assure concentricity this should not be a problem. One possible way of ensuring concentricity is to make your blank a few thou oversize, and cut the teeth deeper (i.e., to full depth + the amount of oversize). If the plate was eccentric then the cutter should remove that eccentricity (so this might be a good plan anyway - pity I didn't think of it earlier...). If you are going to be hobbing larger diameter gears then it will be necessary (in order to avoid the cutter chattering) to use additional bearing supports at the very edge of the gear blank and placed as close to the cutter as you can get them. Two pairs of 1" bearings mounted above and below on an L-shaped bracket should do the trick, and this arrangement has the added benefit of ensuring that the edge of the blank turns parallel to the lathe spindle axis.

The bearing support for the gear blank during the hobbing process. A pair of bearings are used with the blank trapped between.

Hobbing the Gear:

Well, this is the easy bit I guess. Mount the gashed blank on the 'turntable' support you made and run the edge of it up to the cutter. Start with light engagement between cutter and blank at first, and turn the lathe spindle by hand to make quite sure that the cutter is biting into the index gashes and pulling the blank around. When satisfied, use a low speed and run the blank all the way around a couple of revolutions and inspect the result (use plenty of cutting oil whilst running the cutter). If it still looks OK then increase the speed and increase the pressure of the cutter by moving the blank into it with the cross-slide. Hobbing this way is a fairly slow job (there are no proper clearances on the cutter teeth remember) and it took about an hour to form full-depth teeth on my gear wheel. When satisfied that you have got fully formed teeth, back off the cutter and use the proper worm section to 'lap' then together (well, perhaps more of a cold-forming process actually, or maybe even a polishing process - you could actually use metal polish to speed the process up a bit), half an hour of that with plenty of cutting oil (or polish) will ensure they are an *exact* match (hey - I bet you wondered why both worm and cutter were left together on the same bar?)

So the final result - you have a perfectly matched worm and worm gear. Hopefully the slow forming process will have eliminated the random tooth-tooth errors, and if you have controlled the tollerances well then the periodic error (or systematic gear error) should be minimal too.

This is what it's all about - the hobbing process in action. It will take perhaps an hour with the home-made cutter to fully form the teeth.
That's the DEC worm gear done, now all I need is to make another for the RA axis....


I made a couple of changes to the method when making the second gear: firstly, I tried adding a little top-rake to the cutting teeth on the hob (not all of them, about a half-inch length was enough). I was hoping to improve the cutting action, and that it certainly did! - the cutter only took about a 1/4 the time to produce the same depth of cut. The relief was done by hand using a small grindstone in a Dremel-type tool, and whilst the job didn't look particularly neat it certainly improved things. A couple of points if you do this - start the hobbing using an un-modified part of the cutter, this is safer as it is less likely to mis-index (if that happens you can kiss goodbye to your blank). Secondly, when grinding the relief make sure you leave the full form of the cutting edge intact, only grind up to about 10 thou from this edge.

I also took my own advice and used metal polish (Autosol chrome-cleaner paste) to lap the worm. The reult was a superb finish that is difficult to capture in a photo, but two views are shown in the picture below.
Two views of the lapped RA gear.

Additional pictures below are photomicrographs showing the tooth form of both the gears made so far. Notice in the first image (DEC gear) that the hobbing did not remove all of the index 'gashes' made with the 1" diameter slitting saw. I don't think this will materially affect the accuracy of the gear but it doesn't look very professional. For the second gear (RA) I made the gashes using the corner a 3/4" dovetail cutter, and the smaller/deeper indexes have been completely removed.
The first (DEC) gear teeth, note the remnants of the index gashes are still visible.
The second (RA) gear, index gashing done with a 3/4" dovetail cutter.
So far I have no idea what the tooth-tooth variation is like - which will influence the accuracy of the drive (in combination with the worm itself of course), but the only way I will really find that out is by measuring the tracking Errors when the drive is complete and running.

Addendum: Preliminary test results

The mount was temporarily fixed up with a pair of DC servo motors with feed-back speed control circuits. My 90mm refractor and an illuminated reticle eyepiece (250x) was used to visually assess drive errors. The seeing was not great, but at least it was 'fast' seeing distortion producing fuzzy stars rather than 'slow' seeing which would have resulted in the star wandering around. The drive was set at sidereal rate and a 4th mag star centered in the GA-4 reticle. At first there was visible cyclic error (3-4 seconds) of maybe 10 arcseconds which was disconcerting to say the least. This turned out to be due to a deposit of soft solder in teeth of one of the spur gears which transfers the drive from the motor to the worm. I laboriously dismantled and cleaned this gear then tried again. I'm pleased to say that there was *no* short-period tracking error visible in the reticle eyepiece, although some slight drift in DEC (not correctly polar aligned) and RA (not precisely the right drive rate) was eveident. I only watched the image for 4 minutes instead of 8 minutes, so effectivley I only checked for one half of the worm's rotation. Nevertheless, this result is very encouraging. The only way to really check the drive will be photographically when I have the 12" Newt mounted. Later, I did take some CCD images using an MX5-C with an 80mm camera lens attached, exposures were 3x5 minutes stacked and showed no drift whatsoever, but this is not a definitive test.

(c) Chris Heapy 1998/9.

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