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mce5802

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#1
Question about making worm gears

I just had a question while we're somewhat on the subject, and as I can't seem to figure out how to start a new thread, I thought I'd ask it here. I'm building an indexer, and I decided to make the worm and worm gear. I ordered a 1 1/8 6 acme tap to cut the gear with. I need to figure the exact diameter of the gear for 90 teeth. I've googled it, I got one formula but it's clear as mud. Now simple math tells me for 90 teeth at 6 tpi I'd need a circumference of 15, diameter of 4.774. But that's PITCH diameter, right? Not the od of the blank? So do I add 2(.3183) or how do I go about getting that dimension? Not trying to hijack a thread here, I apologize in advance for any inconvenience.:nervous:
 

terrywerm

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Re: dividing plates

I just had a question while we're somewhat on the subject, and as I can't seem to figure out how to start a new thread, I thought I'd ask it here. I'm building an indexer, and I decided to make the worm and worm gear. I ordered a 1 1/8 6 acme tap to cut the gear with. I need to figure the exact diameter of the gear for 90 teeth. I've googled it, I got one formula but it's clear as mud. Now simple math tells me for 90 teeth at 6 tpi I'd need a circumference of 15, diameter of 4.774. But that's PITCH diameter, right? Not the od of the blank? So do I add 2(.3183) or how do I go about getting that dimension? Not trying to hijack a thread here, I apologize in advance for any inconvenience.:nervous:

No inconvenience, but we do need to get this split out to it's own thread which I have done for you. To start a new thread, go into the forum where you wish to post, then on the left center of the screen you will see a button marked "+ Post New Thread" Click on that button and type away!!

As for your question, it looks like it will get a bit involved, so we will address it shortly. I have to do a little digging on this one, but I think I have your answer in my head. Just want to make sure before I commit it to a post.
 

mce5802

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I'm working on building an indexer utilizing a worm and gear. I've decided to try and make my own worm and hob a worm gear. I ordered a 1 1/8-6 acme tap to cut the gear. The question I have is how to figure the precise diameter the gear blank. If I use a 90:1 reduction I'd need a circumference of 15", dia. of 4.774 to get those 90 teeth. But thinking about it I'm fairly certain this would be PITCH diameter and the diameter of the blank needs to be larger than this. I've googled it and got a formula but in this formula I need the distance center to center of the worm and wheel and I'm not sure how to get this number. Could use some clarification on the whole formula for that matter. Thanks in advance for any help.
 

RandyM

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#4
Looks like we had two threads going for the same thing. I merged them into one, that is why it looks the way it does.
 

terrywerm

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Re: Question about making worm gears

I need to figure the exact diameter of the gear for 90 teeth. I've googled it, I got one formula but it's clear as mud. Now simple math tells me for 90 teeth at 6 tpi I'd need a circumference of 15, diameter of 4.774. But that's PITCH diameter, right? Not the od of the blank? So do I add 2(.3183) or how do I go about getting that dimension?
Your calculation of 4.7747 is correct and it is the pitch diameter or PD.

We know that the number of teeth (N) is 90 and that the calculations will be in inches

To calculate the outside diameter or OD, we need to first calculate the diametral pitch or DP.

DP = Number of teeth / PD DP = 90/4.7747 = 18.8493

So we now have the DP of 18.8493

OD = (N+2)/DP OD = (90+2)/18.8493 = 4.8808

Look good??
 

terrywerm

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Looks like we had two threads going for the same thing. I merged them into one, that is why it looks the way it does.
The original post was in another thread, and I posted that it should be in a separate thread, then went back and moved the original post to a new thread. The OP must have started a new thread while I was taking those steps. Thanks for merging them, Randy!
 

terrywerm

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I just stumbled on something else, and it has to do with the way in which you plan to make your worm gear and worm wheel. If you plan for your worm gear to be at 90° to the worm wheel, you will need to cut the worm wheel in a helical fashion which changes EVERYTHING and the OD and PD will need to be a bit larger. I am just trying to find out how to calculate that part of it because I don't have it handy or know it off the top of my head. If you plan to set the worm gear at the helix angle so that the teeth on the worm wheel will be at 90° to the wheel, then your worm wheel could be done the same as a spur gear and the dimensions I gave would be correct.

I also found that the oddball DP of 18.8493 will be a bit problematic with the proper calculations for this.

So, how do you plan to do this??

Additionally, you might want to get a great book on making gears: Gears and Gear Cutting by Ivan Law. It includes everything you might want to know about making your own gears in a hobby machine shop. You can find it on Amazon and probably on eBay too. I highly recommend getting a copy of it!
 
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MarkStephen

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Thank you Terry, I am going to give this math a try this evening. I have had a real miss and miss with this, hobbing a worm wheel with a tap. Was shooting for 40 tooth and first try ended up with 44 teeth. Second try after trying some other math, 36 and maybe 1/2 teeth.:dunno:

What you have provided is completely different than anything else I have found on the subject. I'll now be shooting for a 36 tooth with a 1/2" - 13 worm.

If I did your math correct, I get a PD=0.8814 / DP=40.8441 / OD=0.9303.

Here's to hoping this time it works out.

One thing, how far will i want to advance the cutter (tap) into the work? Does 0.047 sound about right? (major diameter - minor diameter) / 2 or for a class 2A thread, (0.4985-0.4041)/2=0.0472

Again, thanks for your input on this.

Mark - (who is learning something new today)
 

terrywerm

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The math is entirely different for worm gears than for spur gears because of the helix angle of the worm gear that is involved, and I haven't had the time to go through all of the information on worm gears and worm wheels, it is quite a bit of reading. I have not studied them in any detail before now because I have not had any projects involving worm gears, and don't envision any in the foreseeable future. That is why I suggested getting the book that I mentioned earlier, as I think you will find it very helpful. Your numbers do appear to be pretty close, however.
 

MarkStephen

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OK, got ya. I must of been typing when you made that post before mine. (happens to me all the time). Found a pdf of the book on line and am looking through it now. Thanks again.

Mark
 

terrywerm

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You are most welcome, Mark. Let us know how it goes, and don't be afraid to share a short version of what you have learned. We could all benefit from it!
 

mce5802

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#12
Thanks Terry! That's what I needed. I'm gonna get that book too. Sorry about the confusion with the new thread. Haven't had a chance to check back til now. I was planning to cut the gear with an acme tap and the gear mounted on a shaft in the compound of the lathe allowing it to turn. The tap should put the helix angle on the blank as it turns if my thinking is correct? Thanks a million. Lot of experienced help on this site, and it's appreciated.
 

terrywerm

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You also are most welcome, Mike. Let us know how it goes. I am going to be sitting down with the book myself in just a bit since you fellas have my curiosity going now with the differences between spur gears and worm gears. Sorry I wasn't able to come up with the just the right numbers right off the bat, but that's how it goes sometimes in the hobby machining world.
 

RandyM

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Very cool thing you are attempting to do. I really hope we get see your experiment.
 

MarkStephen

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Well, I'v at least learned that using a spiral flute tap is far preferable than using a straight flute. It's explained that when free hobbing a worm wheel, the space between the flutes will cause the wheel to stop and skip in its rotation. Makes sense to me and I have seen this happen first hand. That's why i have seen some videos where the operator has turned a concave into the wheel that is the same radius of the tap drill for that tap. Making this radius more than a 90* Arc allows the next cutting edge to enter the work before the last one leaves, provided your using a 4 flute tap.

Something around 135* seems to be working well for me.

Arc.png Arc1.png


Now I still need to find the math that works for this. I can cut the worm teeth but can't hit on the tooth count I'm shooting for. I have found this for inch threads , but it's not working for me -
Code:
Number Of Teeth/TPI*Pi
- for the bottom of the grove. That just doesn't seem right to me, like it's missing something, and from mt results using it so far it would seem that my suspensions are correct. :dunno:

So I'm still looking for some good math on the subject and I'll post back if I stumble into anything useful.

Thanks everyone for your interest in this.

Mark

Arc.png Arc1.png
 

jocat54

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#16
If you go to this link (WM BERG Gear Data) http://www.wmberg.com/tools/ and download the gear data you will get a calculation chart for alot of different gears,including worm gears, you input some data and it does the formula.

It's a pretty neat tool to use. I used it a lot when I was cutting the metric conversion gears for my southbend and they all worked out well

Good luck
John
 

chuckorlando

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I done some reading on this a month or so ago. It seemed to me there was no hard and fast way to do the exact math. It really seemed to me that making the driven was a bit of trial and error.

Now I can tell you what I done... I found the tpi of the worm. Then went to the tap drill chart:nuts: and found a nut from the same tpi that best fit Dia of space I was filling. Then more or less flipped it inside out. The ID of the nut became the OD of the gear.

Two points

I was limited by size so all I cared about was the largest gear in that tpi that could fit in the space.

I learned the hard way that straight flutes stall the work. I have not got the spiral flute yet because it's a 24mm tap and not cheap. So I currently have no idea if my theory is full of idiocy or not ahaha
 

caster

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Thank you Terry, I am going to give this math a try this evening. I have had a real miss and miss with this, hobbing a worm wheel with a tap. Was shooting for 40 tooth and first try ended up with 44 teeth. Second try after trying some other math, 36 and maybe 1/2 teeth.:dunno:

What you have provided is completely different than anything else I have found on the subject. I'll now be shooting for a 36 tooth with a 1/2" - 13 worm.

If I did your math correct, I get a PD=0.8814 / DP=40.8441 / OD=0.9303.

Here's to hoping this time it works out.

One thing, how far will i want to advance the cutter (tap) into the work? Does 0.047 sound about right? (major diameter - minor diameter) / 2 or for a class 2A thread, (0.4985-0.4041)/2=0.0472

Again, thanks for your input on this.

Mark - (who is learning something new today)
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?

13dpgear.JPG

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.

13dpgear.JPG
 
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John Hasler

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Thank you Terry, I am going to give this math a try this evening. I have had a real miss and miss with this, hobbing a worm wheel with a tap. Was shooting for 40 tooth and first try ended up with 44 teeth.
Mark - (who is learning something new today)
40 teeth would be for the pitch diameter. When you start you are operating at the OD which is larger and therefor has room for more teeth. I think you need to somehow cut some initial teeth to guide the hob (IIRC this is called gashing).

Suggestion: start with a tap with a slightly lower TPI such that 40 teeth will fit around the circumference. You might need to start with a slightly oversized blank . Use that tap to cut gashes well below the final OD. Then turn the blank down to final OD and finish with your "correct" tap, which should track the gashes.
 

terrywerm

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#20
Okay, I found a little more information on this, and I also redid all the math a little bit more carefully, first for Mike's 90 tooth gear using a 1 1/8-6 ACME tap, and then for Mark's 40 tooth gear using a 1/2-13 tap. Dimensions are all in inches unless noted otherwise. Here we go!

This method that I found for calculating worm wheels uses a constant in it's formula, and simplifies things quite a bit. There is one formula to calculate the OD of the gear blank, and another formula to calculate the face width of the worm wheel.

Number of teeth (N) of the worm wheel is determined by the desired gear ratio of 90:1. As we all know, with a single start worm, the number of teeth on the worm wheel is equal to the numerator of the gear ratio. In this case, 90.
Depth of tooth (D) needs to be known and we can get that information from Machinery's Handbook based on the tap that is being used to cut the worm wheel. In this case we are using an ACME tap, 1 1/8-6, which is .0933 for the total thread depth. Using the total thread depth should leave some clearance when operating which is a good thing.
Worm tooth Pitch (WP) which is equal to 1 inch divided by 6 TPI or 0.166666666
Face width (F) is calculated by the second formula.
.3183 and 2.38 are constants used in these two formulas.

OD = .3183 x WP x N +(2xD)
F = 2.38 x WP + 0.250

Here goes the math:
OD = .3183 x WP x N +(2xD) = .3183 x 0.166666666 x 90 + (2 x 0.0933) = 4.77449991 + 0.1866 = 4.96109991 rounded off: OD = 4.961"
F = 2.38 x WP + 0.250 = 2.38 x 0.166666666 + 0.250 = 0.646666665 rounded off: 0.647"

Mike needs a gear blank with an OD of 4.961" and a width of 0.647"


Now lets plug in the numbers for Mark's situation. He is using a 1/2-13 tap for cutting his worm wheel, and desires a 40:1 gear ratio.

N = 40
D = .0916 which is derived from .500 - .4084 (major diameter minus minor diameter) By using a class 3A thread dimension, we should have some clearance built in.
WP = 0.076923076 which is derived from 1" divided by 13 threads per inch.

OD = .3183 x WP x N +(2xD) = .3183 x 0.076923076 x 40 + (2 x 0.0916) = 0.9793846 + 0.1832 = 1.1625846 Rounded off: OD = 1.163
F = 2.38 x WP + 0.250 = 2.38 x 0.076923076 + 0.250 = 0.43307692 Rounded off: F = 0.433"

Mark needs a gear blank with an OD of 1.163" and a width of 0.433"

I almost forgot: Depth of cut can be figured very simply: Multiply the OD of the worm (not the worm wheel) by 0.2 and use this as the depth of cut. This will allow proper engagement of the teeth on each other to be able to transmit torque to the worm wheel without stripping any teeth, unless of course you get ham handed and really crank on it!

So there you have what I found. Mike and Mark, how do these numbers relate to the figures you guys were working from?? Let us know, as this is a great learning experience for all of us, me included!
 

MarkStephen

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#21
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

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#22
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

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#23
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

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#24
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.
 

terrywerm

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#26
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

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#27
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

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#28
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

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#29
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

20dpgear.JPG

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

20dpgear.JPG
 
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terrywerm

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#30
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:

wSpurDefinitions.jpg

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!

wSpurDefinitions.jpg
 
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