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Both Beacon Hill worms in their profiled 'housings' are shown
alongside with the 34t timing pulleys fitted. Note how the worm
size and pitch have to match their own particular wormwheel. The 11" wheel
worm is in the foreground with the 8" wheel worm behind.The number of teeth [287] remains constant. While the circumference of the wormwheel sets the tooth [or screw] pitch. Or rather vice versa. The desired number of teeth x the pitch sets the circumference and thence the diameter of the wormwheel. Only specific wheel diameters/circumferences will produce teeth of a useful pitch which can be actually be cut as a "screw thread" for the matching worm. So it is better to start with the pitch of the worm and design the wheel to match the required number of teeth. 360 teeth is a popular number but makes for very fine teeth in smaller wheel diameters.
Beacon Hill uses 287 teeth. Why? Because 1436/287 = 5. 1436 = the number of minutes in 23 hours and 56 minutes [and 4 seconds.] Which is the sidereal [star] day which is slightly shorter than the average solar day.
A normal [single start] worm and wheel reduce the rotational speed of the worm by the number of teeth on the wormwheel. 287:1 allows a 5 rpm synchronous motor to accurately follow the stars. The 287 teeth are also much more robustly sized, than 360, in any likely amateur instrument sizes. [6-12" diameters are popular]
A poorly constructed or badly adjusted mounting will allow a finely pitched worm to drag sideways over the relatively tiny, wormwheel teeth. You may well imagine the damage that might cause! Big teeth need a very much sloppier fit before they will allow the worm to escape from the wheel teeth. They are also far more forgiving of fit between the worm and the wheel teeth. There is no loss of accuracy nor grave disadvantage in having a "higher gear ratio" than 360:1. So 287 teeth is actually a good choice from a number of standpoints.
A worm is rather like a section of screw thread whose diameter must also match its wormwheel. A completely random choice of [odd] pitch would make the worm all but impossible to produce in a normal screw-cutting lathe. A worm is not a normal [i.e. nuts and bolts] screw thread. Because the tops and bottoms are flattened in the form of an ACME thread. These threads are commonly used for vices, G-cramps [C-clamps] and other very heavily loaded screwed devices. Lathes, mills and other machines use them for driving the slides, tables or tools along very accurately with very little wear.
Only the flanks [sides] of the teeth do the driving and the worm must not bottom in the wheel teeth. If they bottom then that would set the clearance between the flanks of the worm "thread" and the wheel teeth. The space between two components must be adjusted have just enough clearance to avoid any backlash. i.e. Without any free rotary movement of the wormwheel. An absence of backlash can only be achieved with accurately cut wormwheels and worms. The radius of the teeth cut on the circumference of the wheel must not change. On a telescope wormwheel the teeth are in fact short slots with a radius to match the diameter of the worm. Spur gears have "straight cut" teeth which make rather poor wormwheels. There would be very little contact area over very few teeth leading to backlash and rapid wear. The correctly formed wormwheel teeth provide a very snug, intimate fit on the worm over a much greater number of teeth.
In fact one can use a screw cutting tap to 'hob' the teeth on the circumference of the wheel. In the case of the Beacon Hill wheels the large diameter of the matching worm would require a very large diameter tap. Getting enough thread cutting length on the tap to be able to support it properly at both ends adds to the problems with large diameter wormwheels. The cost of such a large tap might run into the hundreds of pounds or dollars. Now add in the cost of a large thick blank of machining quality aluminium. You might as well cut out the "middle man" [yourself] and buy a commercial worm and wormwheel set form one of the respected suppliers.Though a scrap length of [unworn] acme threaded rod could be slotted lengthwise to form the vital cutting faces as seen in the screw cutting tap. Normally the circumference of the wormwheel would be gashed with a small circular saw or fly cutter to form a guide for the tap's thread to form. The wheel blanks has to be firmly mounted and turned one tooth a time as the cutter or saw is wound into the wormwheel to make each tooth. The easiest way for an amateur to divide a wheel is using commercial perforated strip wrapped tightly around a plywood disk. A sturdy plunger is then inserted into each hole in turn to lock the large disk a fixed number of times around the circumference. Roofing reinforcement strip is an example of a perforated strip available in long lengths.. There may be others with smaller spacing of the holes to keep the master dividing plate within reasonable bounds. 287cm / Pi = 91.3xcm diameter. About 3' diameter is not impossible to mount on the same axle as the intended wormwheel.
Trying to plunge a large tap [as shown] straight into the edge of the wheel could become a disaster. With no guarantee that the teeth would even have the correct pitch and the vibration might be awful. Commercially made wormwheels are usually power driven at exactly the correct speed to match the rotation of the special cutter to ensure the pitch is very accurate. The enormous cost of the machine and its range of specialist cutters ensures a very high price unless a huge number of wormwheels are made.
The spacing of the teeth [pitch] known as wheel dividing, must be identical the whole way around the wormwheel. If the pitch of the teeth change [at all] then the worm cannot bed closely against the wheel. Lapping, that is running the worm against its wheel with an abrasive medium, can help. Though it is a slow process and can ruinously damage both wormwheel and worm.
Only the very finest abrasives should be used. [Metal polish?] Beacon Hill advise against such measures except when using plain oil to polish the rubbing surfaces. The danger is that abrasives can lodge in the metal surfaces and continue to cause wear over a very long period. If the wear is considerable then the pitch could change. Or the width of the 'screw' threads on the worm could become thinner. While the gaps in the wheel teeth might broaden. Producing such a sloppy fit [and tooth bottoming] that backlash would rear its ugly head.
However, if lapping is done to perfection the worm eventually becomes a 'diablo' and has contact over a much greater number of teeth in the wormwheel. The huge worms and wormwheels on the great professional telescopes were usually lapped with optical rouge. This ensured uniformity of pitch, low friction and a perfect fit. Though these people were experts at what they were doing.
Chris Lord has an interesting discussion on his lapping technique of the stainless steel worms on the bronze wormwheels. He was trying to improve them when he fitted an AWR system to his truly massive, Calver, antique telescope. Just don't blame me or your wormwheels if you ruin them through ignorance. Having abrasive liquids running about will easily trash any bearings if it gets near them.
Chris Lord's calver stepper piece:
Scroll down to Implementation for his description of lapping his worms to the wormwheels.
But note the very tough materials he was working with, the relatively small worm diameters and very fine teeth! Do not assume that a relatively coarse pitch worm and wheel, like Beacon Hill's brass on aluminium, will respond in a remotely similar fashion! Better limit yourself to "Solvol Autosol" polishing paste if you are sorely tempted to "have a go." But don't say I told you so. I am warning you against even trying unless you have a modicum of mechanical or engineering common sense. You'd have to be absolutely certain the worm was perfectly meshed and absolutely square. Or you might as well throw them away. Get any abrasive in the worm bearings and you can throw those away too. Don't say you haven't been warned if you are daft enough to try this on any other mounting! If you think chucking half a tin of "Brasso" in "the works" of your own mounting will improve it then you aren't remotely qualified enough to try!
Click on any image for an enlargement.
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