worm gear diameter

[MarkStephen]

OK. Thank you very much for your effort Terry! I have a sneaking suspicion that this is more correct than anything I have come up with so far. I looks like the numbers are falling about in the middle of the math versions I was using which was giving me 44 or 36 tooth.

I've been holding off on making another run at this, lacking the desire to ready yet another piece of stock for the scrap bin, but with these new formulas, it's time to give another run at it. I have a little work to do today before I give it a try, so it will be later on this evening at earliest before I can report back.

My end game with this is to make a small rotary arbor to mark dials and cut little gears. The gears don't need to be of great precision and need to do little more than mesh and turn, requiring torque measured in fractions of a single oz/in. I might work the math for a 36 tooth, as that would put the dial for it on base 10, (0-9).

Wish me luck. :rubbinghands:

Mark

 

[Terrywerm]

I am a bit confused here. I assume that 1/2-13 worm translates to 13DP. I used e-machine software and I get different calculated numbers. My assumption is that 13 tpi does not translate to 13 DP, am I right?. Does anyone know how this translates?

View attachment 92828

Caster

EDIT: I referenced Ivan Law "Gears and Gear cutting" and got this formula for OD. OD = (N+2)/DP where N is the number of teeth and DP is the number of teeth per inch. So (36+2)/13 = 2.923. The TPI on the worm/screw is the DP and the OD should be 2.923 as e-machine computes.

Caster, Diametral Pitch (DP) is defined as the number of teeth per inch of pitch diameter. So, if a gear has a Pitch Diameter (PD) of 2", and has 40 teeth, it is said to have a DP of 20. The thread pitch of the worm would equal the Circular Pitch (CP) which is the distance from a given point on one tooth to the same point on an adjacent tooth, measured along the PD, not along the OD. Not only that, the figures you are using are for spur gears, not worm gears.

I must admit that I initially thought that the dimensions for a worm wheel would be very similar to those for a spur gear, but I quickly found that I was mistaken. The sad part is that Ivan Law doesn't go into the calculations for worm wheels in a very good fashion from what I have found. Maybe it is there in the book, but I just need to dig a little deeper.

The latest calculations that I found were from an entirely different source, namely a DVD by Jose Rodriguez called 'Making Gears the Easy Way', available from Little Machine Shop for $43. This DVD has some great information in it, but it is BORING as all hell. It uses four hours to present information that could be presented in one fourth of that, maybe even less. I have not found it possible to sit through even one hour of it without falling asleep, no matter how much coffee I've had or how much sleep I've had the night before. My apologies to Jose, the maker of that video, I am just being brutally honest here. If you want to learn how to make your own gear hobs, and cut them that way, the DVD is worth the money. Just make sure you've got an IV set up with espresso to keep you awake while you take notes.

One last note about using a tap to cut teeth on worm wheels: Best practice is to gash the wheel blank using a form tool and an indexing head. The mandrel that the gear is mounted to must be set at the helix angle of the worm gear so that the gashes are set at the proper angle on the worm wheel. Once the wheel has been gashed, the worm wheel is set up so that it can rotate on its own, and the tap is used to finish the cutting of the teeth of the worm wheel to their final dimensions. Gashing the blank first guarantees correct placement of the teeth prior to cutting them to their final shape.

So, now that you guys have gotten me started down this slippery slope, I suppose I shall have to indulge in some worm gear making of my own!!

 

[mce5802]

Thanks again Terry your going to the trouble to figure this out is above and beyond. Who needs MH just post a question on this forum! Lot of expert help around here. Again, greatly appreciated. I'm going to do a blank in delrin or smthn first and il post a pic of the results hopefully this week. I've gotta wrap up another outside project before I get back to this one ( bills to pay, taxes due, just like everyone else) but I'll let u know as soon as I get back to it

 

[Terrywerm]

No problem, Mike, take your time. I am currently off work, recovering from surgery, so my physical activity is limited. Luckily my ability to research something is not hindered, and, it gets my curiosity going when a problem like this one comes up.

Just don't forget to gash your gear prior to free hobbing it, and all will go well.

 

[benmychree]

Why not just buy a set of stock gears for the project? Boston Gear makes them.

 

[Terrywerm]

Why not just buy a set of stock gears for the project? Boston Gear makes them.

What's the fun in that when we can take ten times as long to make them, while spending twice the money? :rofl:

In reality, both of the members that inquired about this are building their own indexing heads or rotary tables, I forget which, not that it matters. There's no satisfaction like saying you built the whole thing from start to finish, including the worm and worm wheel.

I guess it all depends on what the desired result is: acquiring an indexing head, or building an indexing head. BIG difference. :allgood:

 

[lnr729]

One thing that is overlooked when people make their own hob is that the hob has to have a larger diameter and a longer tooth. The reason for this is that the hob has to cut the clearance at the bottom of the worm wheel teeth (the dedendum is always more than the addendum). A tap does not make that provision nor home made hobs, it is for cutting threads not gear teeth. Without the clearance cut into the teeth of the worm and wheel (both pieces) there is a tendency to bind as the teeth tips foul on the roots of the opposing gear. All is not lost, the work around is to make the worm and the wheel slightly smaller to prevent the binding. This has the effect of reducing the addendum and putting the clearance at the tooth tips rather than at the roots.

When hobbing a worm wheel it is customary to gash the teeth to ensure that the correct number of teeth are cut. With out the gashing you can get lucky and it comes out at 90 teeth but just as easy at 91 teeth. In order to gash you need a dividing head ideally angled upward at very close to the helix angle. Gashing is just roughing in the teeth so the hob (or tap) only has to finish the teeth.

The other problem that is often overlooked is the worm. The teeth need to be thinned a bit to provide some backlash. A gear without backlash is going to bind.

The worm wheel also needs to be crowned. Commercially crowning is done with an over sized hob or by applying a sideways cut (to in essence make a helical gear over a short distance). Crowning is important because with out it if there is no tolerance for angular misalignment. Crowning also makes assembly easier. If you plan on having your worm disengage then crowning is an absolute must. You can fake crowning by making the worm under size and adjusting the shaft center distances to suit.

 

[mce5802]

Why not just buy a set of stock gears for the project? Boston Gear makes them.

Yeah I know. I looked. But I have the machines and it doesn't look too hard to do, after all, like Terry said, that's kinda why we're all in this....we enjoy making the stuff

 

[caster]

I think I finally understand.

a 20 tooth 20 DP gear will have a 1" diameter (pitch circle diameter not outside diameter).
So each tooth width (tooth and space) will equal diameter x Pi / #teeth. 1 x 3.14 / 20 = 0.157



I was under the misunderstanding that a 20 DP tooth width was calculated on the circumference, tooth width would be 1" / DP or 1/20 = 0.05 which is incorrect. Which led to confusing worm TPI as DP. It seems that TPI x Pi would equal DP.

Caster

 

[Terrywerm]

I think I finally understand.

a 20 tooth 20 DP gear will have a 1" diameter (pitch circle diameter not outside diameter).
So each tooth width (tooth and space) will equal diameter x Pi / #teeth. 1 x 3.14 / 20 = 0.157

View attachment 92951

I was under the misunderstanding that a 20 DP tooth width was calculated on the circumference, tooth width would be 1" / DP or 1/20 = 0.05 which is incorrect. Which led to confusing worm TPI as DP. It seems that TPI x Pi would equal DP.

Caster

Sorry, caster. Close, but not quite. The correct formula for Diametral Pitch is DP = PI / CP.

With a worm gear, TPI on the worm is very close to the same as Circular Pitch (CP) on the worm wheel, but not quite equal, due to the helix angle of the 'thread' on the worm. But, it is close enough that for the size of the worm gears that we typically work with, that for all practical purposes, CP will be equal to TPI within a thousandth or less in most cases. From there, the DP can be calculated: DP = PI / CP or, if you prefer, by substitution one could say that DP = PI / TPI of the worm.

Now, the tooth width that you are referring to is known as Circular Pitch (CP) which is usually defined as the distance from a point on one tooth to the same point of an adjacent tooth (usually center to center), measured at the Pitch Diameter (PD). Tooth width (also known as circular thickness) is the actual width of just one tooth by itself measured along and at the Pitch Diameter. The tooth thickness needs to be less than half of the CP to allow for clearance on the back side of the tooth.

This diagram should be helpful, but keep in mind that the DP is not a measurement at all but is a theoretical figure, it cannot be physically measured or laid out on a drawing. Also remember that this diagram is for spur gears, not worm gears, although the nomenclature would be the same. For us to hold meaningful discussions on this subject, we all need to get on the same page regarding the various measurements. I know that they are confusing, but work with them a little while and study them and it will start to fall into place a little better. I had a lot of trouble with them at first also, and my head started swimming when ever the terms started flying about, but in time it all became clear as mud... I think... sort of... well... ah... um... where were we again?? :headscratch: :rofl:



I cannot recommend strongly enough that anyone interested in making their own gears should get a copy of Ivan Law's book, it is a gold mine of information for the home machinist and does a great job of helping to understand how the various measurements relate to each other. It is too complicated a subject to learn it all here in this forum, but we'll give it our best shot!