Worm Drive Wheel Blank

[Alan CharlestonParticipant @alancharleston78882]

Hi,

I want to make a worm drive wheel by hobbing a blank with a tap. The worm will be a 2mm pitch trapezoidal screw (8mm diameter).

My question is:

Should the outside diameter of the wheel blank times pi be divisible by an integral of the thread pitch?

Regards,

Alan C.

[DC31kParticipant @dc31k]

No.

The _pitch_ circumference of the worm wheel will be the tap pitch times the specific number of teeth you want (a random integral multiple of the thread pitch could give you a 37t wheel).

The blank has to have a larger circumference (and hence diameter) than that number so you can remove material to cut the tooth spaces. What its actual diameter is compared to the calculated pitch diameter depends on how deep you want to cut the teeth.

Draw a 2D side elevation of the finished setup such that the pitch line of the trapezoidal thread aligns with the pitch circle of the wheel.

[John HaineParticipant @johnhaine32865]

Are you intending to “free hob” the wheel?

[John HinkleyParticipant @johnhinkley26699]

Do you use a CAD program?  Not my go-to one, but I occasionally use Fusion 360 for those jobs that Alibre Atom doesn’t do.  Gear design is one such.  You can download and install an add-on to Fusion called “GF Gear Generator” to do the donkey work for you.. For example, I just knocked this up using random values:

From there, you can save the file for manipulation in your CAD program of choice.

John

 

[John Hinkley]

On John Hinkley Said:

You can download and install an add-on to Fusion called “GF Gear Generator” to do the donkey work for you..

Is the add-on sufficiently asinine to draw the 2mm circular pitch 15 degree pressure angle item that the OP wants?

It would be useful to know if it can cater for ‘non-standard’ gear parameters.

And given that the trapezoidal thread will be used as a hob (where the thread depth is pitch/2), the ability to use/model a non-standard dedendum would be useful.

[John HaineParticipant @johnhaine32865]

It’s not improbable given the limited information from the OP that the intention is to free hob it, in which case trying to design it in cad is probably not very helpful.

[John Haine]

On John Haine Said:

…in which case trying to design it in cad is probably not very helpful.

Being able to 3D model it would enable it to be 3D printed should the free-hobbing not go so well.

It would also allow a home-printed item to be verified for fit and function before sending the 3D model off to a commercial printing service (e.g. JLCPCB) who have machines and materials that would give some strength and longevity to the item.

[Pete RimmerParticipant @peterimmer30576]

2mm pitch is 39.86DP so just buy or make a 40DP worm wheel.

OR

Cut a 40DP gear from brass or delrin at your desired OD/tooth count and then use some hardened TR8x2 screw rod with gashes and relief hand ground into it to free hob the throat. It will be better than trying to free-hob a wheel with a pointy-tooth tap then run it with a trapezoidal form screw they are not nearly the same shape.

[Anonymous]

Cutting a worm wheel from a blank using a tap as a hob works well (a spiral flute tap is advantageous as there is always one section of the tap cutting):

But it is a bit of a crap shoot as to the number of teeth on the worm wheel and the consequent centre to centre distance.

If a specific number of teeth and/or a specific centre to centre distance is needed then it is better to start with a formed blank:

Gash the wheel with the correct number of “teeth”:

And lastly free hob the final involute tooth form (the hob shown is home made):

Andrew

[Nigel Graham 2Participant @nigelgraham2]

Andrew –

I take it you need align the axis of the blank along the table at the helix angle?

…

Alan –

You may find it helpful if you’ve not already done so, to buy a book on gears and gear-cutting.

Mine is indeed by that title: it is Ivan Law’s Gears And Gear Cutting; No.17 in the Special Interest Model Books’ “Workshop Practice Series”. Stockist? Try TEE Publishing as first choice.

This demystifies gears and their geometry, and devotes a chapter to worm-gear.

I have not yet tried gear-cutting but free-hobbing does seem to risk inaccurate teeth profiles or ending up with a fractional tooth under or over the intended number. (Though I doubt you or I would be the first to find that!)

Andrew’s approach, by removing most of the material first, would greatly reduce that risk. He is also using a very rigid machine and accessories, particularly suited to gear-cutting.

.

Trapezoidal teeth?

All the references I have seen specify involute-form teeth so a rack or worm (or hob) has straight tooth sides whose angle reflects the pressure-angle. So I looked into this…

Law’s book therefore states 29º included-angle for the hob and worm, of pressure-angle 14.5º. This is of Acme form although a worm thread is deeper.

(By the same rule, 40º for a PA of 20º, more common now for gears generally.)

Trapezoidal threads’ 30º included angle is so close to Acme that for practical purposes I don’t suppose it matters provided the worm and wheel agree with each other. They might not work too well, or last long, if you try to mate either component with a commercially-made item likely to be of different geometry.

In any case a duo made as in Andrew’s first example, with a tap, may not be quite to the book but still works if transmitting only low effort at low speeds.  The point to watch there is that there is no play on the worm-wheel’s spindle, axially as well as radially, but it rotates smoothly throughout the full revolution. Any drag or wobble there is likely to lead to very por or even scrap results.

.

A final thought…..

In theory you can rotate a spur-gear by worm, not as a serious drive but for, e.g., some sort of fine adjustment mechanism. It’s not ideal and the two shafts cannot be perpendicular to each other, but it may be useful in rare, odd applications.

 

[Alan CharlestonParticipant @alancharleston78882]

Hi All,

Thanks for the replies. This is a lot more complicated than I thought. After watching a few you-Tube videos I thought it was just a case of feeding a wheel blank mounted on a shaft into a rotating tap on a lathe. Clearly this is not the case.

I’ve got Ivan Laws book but after wasting a week trying to cut a 3:1 bevel gear set with bevel angles of 45degrees because he doesn’t mention that it’s only 45 degrees for a 1:1 set, I’m not keen to trust it again.

I’m not all that fussed about the number of teeth I end up with. I have a cheap old reflecting telescope I bought from a supermarket about 30 years ago. The optics are surprisingly good since I replaced the cheap plastic eyepiece lens with an eyepiece from an old pair of binoculars. The main problem is that the mounting wobbles around and it’s difficult to even find the moon so I want to have a way of slowly and steadily adjusting the azimuth angle which would stay put when adjusting the declination of the telescope. I thought a worm screw which is more or less a one way gearbox would be suitable.

I’m using a 2mm pitch trapezoidal screw because a few years ago I got a couple of 150mm lengths of 8mm threaded rod and a tap to convert the topslide on my old Boxford lathe from imperial to metric and I still have one of the rods left.

I think I may give my original idea a go and see if I can achieve what I need – i.e. a means of slowly rotating my telescope.

Regards,

Alan C.

[Nigel Graham 2Participant @nigelgraham2]

For an application such as that, the number of teeth is not critical but you still need make the blank the correct diameter and set the correct depth, to ensure you cut complete teeth and the two parts work together as they should.

Although yours is for adjusting a telescope’s aim, not for transmitting continuous power, you still want the worm and wheel to operate as smoothly as possible.

I’d still trust Ivan Law’s book. To answer you I read the chapter on bevel gears to see where he apparently specifies 45º angles for all bevel gears.

He doesn’t.

I’m afraid I think you have mis-read it.

Although starting with the simplest case, two identical bevel wheels on shafts at a right-angle where the teeth do lie on 45º triangles, he shows the general geometry of the gears from which the angles are derived.

Not specific angles for any given ratio and angle between the shafts, because they are calculated for the particular application.

You can find other text-books on gear-design but the nearer they approach the trade level which Law’s book summarises, the more complicated and mathematical they become.

[Alan Charleston]

On Alan Charleston Said:

…after wasting a week trying to cut a 3:1 bevel gear set with bevel angles of 45 degrees because he doesn’t mention that it’s only 45 degrees for a 1:1 set, I’m not keen to trust it again.

I feel I need to respond to this slur on Ivan’s work. Yes, there are a couple of known errors in the book, that are reasonably widely publicised, but the above is not one of them.

It is quite clear if you study the diagrams that bevel gears have two pitch cones whose vertices touch at a common point and whose angle is determined by the gear ratio of the gear pair. Hence, the lack of trust is in the reader not wishing to invest the intellectual effort rather than in the material on the printed page.

Please study Fig. 36, 37, 38, 39 and 45 in his book and then reconsider your claim.

As above (Nigel’s suggestion), given the low load, low speed and low duty cycle of the application, use a standard spur gear (Pete Rimmer has already told you the spec. of a standard gear that will work adequately with your trapezoidal rod) with a skewed worm to construct the drive. This is how GHT’s Myford headstock dividing attachment works. I have never heard any doubts expressed about the trustworthiness of his work.

[John HaineParticipant @johnhaine32865]

Alan, do you have a rotary table?

[Nicholas FarrParticipant @nicholasfarr14254]

Hi, I have Ivan Law’s book, but I also have A. W. Marshall’s Gear Wheels simply explained, which is available from Tee Publishing.

https://www.teepublishing.co.uk/books/gears/

They also have two other books about gears, one other one by A. W. Marshall, and one by W. O. Davis, which is for small mechanisms.

Regards Nick.

[Les RileyParticipant @lesriley75593]

To add to Andrew Johnston’s post above, I used this exact method to make the steering worm wheel for my 4″ McLaren traction engine. The home-made hob was made when making the worm. I made an extra long section of worm and used some for the actual worm and the rest was gashed and case hardened to make the hob.

I too used Ivan Law’s book. I used it to make all the gear train and the diff. bevels.

The example referred to is unfortunate as although correct, it is somewhat confusing in the choice of values and you need to go through it a few times to get it clear in your head!

 

Les

[Michael GilliganParticipant @michaelgilligan61133]

“Gears for Small Mechanisms” as mentioned by Nick, is an excellent reference work … but it is not a Cook-Book.

Highly recommended if you want the underlying facts … less useful if you want an easy recipe.

MichaelG.

[Nigel Graham 2]

On Nigel Graham 2 Said:

Andrew –

I take it you need align the axis of the blank along the table at the helix angle?

Correct, when gashing the table is set over at the helix angle. When hobbing the table is straight, as the helix is set within the hob. Setting over the table is simple as my horizontal mill is universal, ie, the table swivels and not the common, but incorrect, meaning of having vertical and horizontal milling capability. The same as Les the big worm/wheel set is for the steering gear on my traction engines:

To the OP: It is of course perfectly possible to free hob a worm wheel using a tap. Don’t get too hung up on the OD of the blank. The trick is to feed fairly aggressively towards full depth so the tap cuts only one pattern of teeth. I’d be concerned that the tap mentioned is quite coarse with a small core diameter, so will be weak in bending. It will need the outer end supporting. For the specified application I’d use a standard V-thread. In the application I showed the thread is 7/16″ UNC and is used on the governors for my traction engines:

I have the book by Ivan Law; it is good on some basics and spur gears. But, in my view, is a bit weak on theory for gears other than spur. It is unfortunate that the bevel gear example chosen were mitre gears, as they are a special case.

My go to book for gear design is “Gear Design Simplified” by Jones and Ryffel. It deals with the theory and design of gears in a clear way, but not the manufacture. While there are standards for worm/wheel sets they are not as universal as for spur gears. So the design of worm/wheel sets is a bit of a wild west, and is up to the maker to choose appropriate parameters.

Andrew

[Nigel Graham 2Participant @nigelgraham2]

Thankyou Andrew!

.

Nick –

I have both Gear Wheels Simply Explained and its sequel, Gear Wheels and Gear Cutting, by A.W. Marshall. Unfortunately they do not really help you make the things unless you already have some of the knowledge these books are meant to impart!

I fear though neither would have helped Alan, and as in Ivan Law’s book, Marshall used 1:1 bevel-gears as his basic example, which would appear to have been the source of confusion.

More, Ivan Law answers the problem of the basic nature of bevel-wheel teeth – that they taper so are not at all easy to make – by describing how to cut “parallel-depth” gears.

However, the OP wishes to make a worm-wheel to fit a worm made, if I understand him correctly, from some left-over trapezoidal-thread material. And for adjusting a telescope’s aim, not to transmit continuous power. In which case Law’s Gears & Gear Cutting, and Marshall’s second book Gear Wheels & Gear Cutting, might be of about equal value. Law’s is perhaps the clearer to follow, but Marshall goes into greater depth.

Given the simplicity of the original specification, Pete Rimmer’s suggestion of making a brass or ‘Delrin’ (or I’d add, aluminium) 40DP spur wheel and profiling it using a hob made from the worm material is as good as any, but do we we need worry about the cumulative error?

39.86 / 40 = 0.99, but of what? These are very fine thread and teeth. The error may be small enough for the hobbing to remove, or it might go the other way and erode the teeth by a sort of progressive function whose overall effect would be a very loose fit. Since we’re trying to align an astronomical telescope we want it made as best we can. All the more so if the aim is at some point to add a tracking drive to the instrument.

As DC31k points out, using that spur wheel as it is and mounting the worm at the appropriate angle may well be the simplest solution but I think it would be best used over only a short arc of fine adjustment, and be very unlikely to work as part of an azimuth drive. One way round this, unless the telescope is on a tripod you pick up and turn as a whole to close alignment anyway, is to run the worm shaft through an eccentric bush arranged so you can put it out of engagement for the approximate aim. This similar to the disengaging action on a rotary-table.

 

‘

My particular application is for a worm not wheel as that’s already there – the worm is missing along with the rest of the table drive mechanism on a small Denbigh horizontal mill ancient enough for 14.5º PA to be a safe bet. If I make the worm in brass it’s less likely to ruin the bronze wheel if it’s not quite right, and if all else fails I’ll just have to fit a commercial pair!

I’ve also the question of what to use for my steam-wagon steering-gear. It is enclosed in a box bolted to the floor, so not easy to determine the original though the box’s shape and proportions do suggest worm and quadrant.

That Denbigh is plain horizontal, no universality, so traversing a worm-wheel blank at its helix-angle to gash it would not be possible. In fact the only way I could do it with my equipment, is on the vertical mill (a Myford VMC), with the dividing-head set inclined to the horizontal by that angle. It would have no tailstock support though.

.

DC31k – That language was a bit harsh. By all means point out how someone has not quite understood a reference-book, but please don’t call him lazy. Especially when obviously he is not.

 

[Alan CharlestonParticipant @alancharleston78882]

Hi All,

Thanks again for all your replies. I have found a small worm drive gearbox at the back of a cupboard in my shed which I think will do the job nicely so I don’t need to make my own worm drive.

Without wishing to get into an argument about the merits or otherwise of Ivan Law’s book, I would just point out I spent over a week on and off trying to figure out what I was doing wrong until I came across “Bob’s Better Bevels” in the Model Engineer magazine and I found my mistake within 5 minutes.

Andrew – I would like at some stage to have another go at free hobbing a worm wheel and I found your comment about not worrying too much about the OD of the blank but aggressively moving towards the final depth.

I have 2 questions which are:

What should the final depth be?

Should the blank have a flat face or should it contain an arc with a diameter equal to the tapping drill size of the tap?

Regards,

Alan C.

[Nigel Graham 2]

On Nigel Graham 2 Said:

That Denbigh is plain horizontal, no universality, so traversing a worm-wheel blank at its helix-angle to gash it would not be possible….

The angle for gashing is not especially critical. Just set the dividing head on the Denbigh table at the appropriate angle, without using the T-slots. If necessary remove the alignment blocks on the bottom of the dividing head and tailstock. Getting the cutter centred over the blank so that material is removed symmetrically is more important than the precise angle.

Andrew

[Alan Charleston]

On Alan Charleston Said:

I have 2 questions which are:

What should the final depth be?

Should the blank have a flat face or should it contain an arc with a diameter equal to the tapping drill size of the tap?

I’ll answer the questions in reverse order.

Question 2: If using a commercial tap to cut the worm wheel then it is not necessary to form an arc on the periphery of the worm wheel first. A tap will cut on both root and crest whereas a (home made) hob will likely not cut at the root. So a tap will naturally form the arc. In theory the arc should be designed to clear the core diameter of the worm. But in this application it is not necessary. For the tap free hobbed worm wheel shown above I started wtih a plain cylinder and let the tap cut as needed. For the worm wheel formed with a home made hob I preformed the arc to add clearance. This wasn’t a precision job; done with files in the lathe and checked against a marked out and filed template, as seen in my first post in this thread.

Question 1: As a minimum the depth needs to be at least the depth of the thread on the tap. Beyond that it is really up to the machinist although it will depend, to an extent, on the width of the worm wheel. On my examples above I cut the worm wheel made with the tap sufficiently deep that I had the full thread form on the outer edges. The centre to centre distance on the governor casting was machined from the worm/wheel combination to suit. For the steering gear set I machined to a specific depth, determined by calculation, as the centre to centre distance was set during the design process. On the steering gear worm wheel note that the full depth of the teeth does not extend to the edges, there are small flats at the edge. This is common on commercial worm wheels as the sharp edges are delicate and don’t add much, if anything, to the power transmission capability.

Andrew

[Alan CharlestonParticipant @alancharleston78882]

Thanks Andrew. Much appreciated.

Regards,

Alan C.

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