# Make A Worm Gear



## rdean

Did you know you could make a worm gear if you had the old shaft?  Well me either until I saw a post by another member on here a few weeks back (can't find it now) briefly showing how he cut four slots in a threaded shaft and mounted it in the lathe.  He then mounted a piece of round stock on the tool post and proceeded to cut the threads into it. 
Well I have to try this so I got a piece of 3/8" x 16  threaded rod and cut four 1/8" slots about 3" long 90 degrees apart and mounted it in the lathe with a  live center for support.  I had a 1/2" thick by 3" round aluminum slug so mounted that on the tool post.  I started the lathe and moved the round closer until it started to turn and to my joy it started cutting into the slug.  This is what it looks like after 30 min of cutting.






So if it works that good in aluminum how does it work in nylon and what about a larger size.  I had some 5/8" x 6 acme rod  and some 9" diameter nylon rounds to try again.  I cut off a 8" piece of the threaded rod and cut 4 slots in it  but this time I used a 1/2" end mill offset from the center of the shaft 0.250.  That way the end mill would just cut to the middle of the threaded rod and hopefully have a more aggressive cut.












Never too old to learn something new!
Thanks for looking 
Ray


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## RJSakowski

Ray, an interesting idea.  How did you decide on your gear diameter so the teeth would come out right when you made a full circle?  Also how did you compensate for the reduction in diameter as the "cutter" went deeper into the work?


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## ch2co

Being a newbie on lathe work, gear cutting was still fairly far away on my mental learning list, and then you just had to post this.  
I have a need for simple inexpensive worm gear reduction sets for slow motion controls of manual telescope mount
positioning, nothing precision though, and then you just had to turn me into a potential worm gear cutting enthusiast.
I really should stay off of this site, my wife is starting to complain that she so seldom sees me, and were both retired! 

Chuck the grumpy old guy


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## rdean

RJ
I would like to say that after hours of diligent research and measuring using several math equations I decided on the exact diameter and tooth for each gear but that isn't true.  The aluminum one was just trued up on the lathe to be round and not even measured.  I decided on the diameter of the nylon one because my lathe will only turn 9 1/2" .  There is a formula for figuring all this out but since this was just for fun I just started cutting.  The nylon gear has 165 identical teeth as far as I can see but the aluminum gear has three teeth that are cut somewhat narrower so if I plan on using that gear I would cut it down and start over.

ch2co
You have to give it a try really fun
Ray


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## Mark_f

I have seen this done many times on You Tube, but I would like to know how to figure the diameter needed to get a specific ratio. Yes you can make gears this way, but how to get the ratio needed for a project is the biggest problem.
    It is very clever and looks great, now how do you make it useful.


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## jererp

Just looking at this I think it won't be too difficult to get close to a given ratio.  If you take the input in threads per inch times the circumference of the gear blank, I think you will get the input to output ratio.  Example:  14 tpi x 2 inch dia x 3.14 = 88.96 or 89 rev input for 1 rev output.  Pick a given input thread, and ratio, then use algebra to get the necessary diameter, and see if it packages.


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## Andre

I would use a tap instead of the allthread, Would be much faster, and take a third of the time.


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## sgisler

jererp said:


> Just looking at this I think it won't be too difficult to get close to a given ratio.  If you take the input in threads per inch times the circumference of the gear blank, I think you will get the input to output ratio.  Example:  14 tpi x 2 inch dia x 3.14 = 88.96 or 89 rev input for 1 rev output.  Pick a given input thread, and ratio, then use algebra to get the necessary diameter, and see if it packages.


It seems very simple from the little I've read (I've got a worm&wheel I'm thinking to replace on feed mechanism of my new old Marvel bandsaw), it seems that the ratio is 'number of teeth on wheel : number of 'teeth' (threads) on worm. ie: 60 tooth wheel, single thread worm = 60:1. 40 tooth wheel, 4 thread worm = 10:1. As I said, I'm early in looking into this so correct me please if I've misinterpreted what I've read. 
The method shown by OP and further discussed is the way I was thinking to do it. The worm I need to replace is single start thread at 6 teeth per inch, simple enough to cut on the lathe and made extra long, used to cut the wheel. The cut edge of the wheel I need to replace is deeply concave. Which really threw me because in all the places I've looked for replacements, I've seen nothing like. But after I thought about it, it would seem the deep profile is a product of the face width of the wheel. Additionally, the number of teeth on the wheel is 65, strange but almost assuredly to make it proprietary. I'm thinking that a 60 tooth wheel will be just fine. 





Stan,
Sent from my iPhone using Tapatalk

Oh yea, haven't a clue about pressure angle and pitch diameters


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## rdean

Andre yes a tap would work much better as it is designed to cut.  But I had this acme screw and no tap. 

Well John got me thinking  that I should make a gear with a predefined number of teeth or gear ratio to see how it works out.  I cut out a blank today but ran out of time to turn the exact diameter.  Maybe Tuesday I will have time to try it out.

Ray


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## aeroHAWK

Another trick is, to gash shallow grooves using a dividing head on a mill and a woodruf key cutter or dovetail cutter. These grooves are used to "start" the teeth so that they will aid in dividing the blank into the proper number of teeth.

If a mill and dividing head are not available, you can "go for it" as the OP did in his first post. You do run the risk of getting inconsistent teeth or something similar to making a knurl that has a double start....


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## tomh

try this link for information on making a worm wheel. 
https://books.google.com/books?id=aCcDAAAAMBAJ  (page 209-210)


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## tomh

Well I don't know what I'm doing,  but there is a article in the 1948  popular science  about making worm wheels in detail giving the formula for figuring  the proper  wheel sizes .


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## T Bredehoft

This has reminded me that I have a 5/8 10 LH tap that I made decades ago.  If I could get a salvaged cross feed screw from somewhere I could make a worm gear set rather easily.


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## rdean

I had no idea when I started this thread just what I was getting into.

This is my setup.



Without doing any research I just assumed that at 6 threads per inch and wanting 72 threads on the gear I would divide 72 by 6 to get the circumference of the gear.  Multiply the circumference by 3.14 to get the diameter of the gear.  This is what I got.




It looked great with well formed teeth all the same size and evenly spaced.  I was patting myself on the back when I decided I had better count the teeth just to make sure there were 72 of them.  After numerous counts I found there were only 69 teeth. 
What happened to the other three?  Do I need to increase the diameter of the blank by three teeth and start over with that?
Finally I decided I should probably check out some of the videos and sites suggested earlier in the thread.  Each place I went for information seemed to explain it differently or didn't give a clear cut answer.  I came back here and did a search for worm gear on the forum.  This thread from January of 2015 (http://www.hobby-machinist.com/threads/worm-gear-diameter.31182/ )was very enlightening and the formulas were  mostly  understandable.  (No where have a found an answer to why you have to add 2 to the number of teeth)

I think Mark Stephen said it best:  " I am beginning to suspect the need to sacrifice small furry animals while standing on my head reciting incantations to pull of this bit of black magic. :lmao: There seems to be very little hard math behind it. "  I will gash the teeth first.

Inr 729 Richard offered in this same thread a calculator for free.  Well let me tell you it is great and thank you Richard very much.  The calculator covers many different subjects and I will recommend it to all.

Later
Ray

Well I haven't given up and will be trying again soon


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## RJSakowski

rdean said:


> I had no idea when I started this thread just what I was getting into.
> 
> This is my setup.
> 
> View attachment 106740
> 
> Without doing any research I just assumed that at 6 threads per inch and wanting 72 threads on the gear I would divide 72 by 6 to get the circumference of the gear.  Multiply the circumference by 3.14 to get the diameter of the gear.  This is what I got.
> 
> View attachment 106743
> 
> 
> It looked great with well formed teeth all the same size and evenly spaced.  I was patting myself on the back when I decided I had better count the teeth just to make sure there were 72 of them.  After numerous counts I found there were only 69 teeth.
> What happened to the other three?  Do I need to increase the diameter of the blank by three teeth and start over with that?
> Finally I decided I should probably check out some of the videos and sites suggested earlier in the thread.  Each place I went for information seemed to explain it differently or didn't give a clear cut answer.  I came back here and did a search for worm gear on the forum.  This thread from January of 2015 (http://www.hobby-machinist.com/threads/worm-gear-diameter.31182/ )was very enlightening and the formulas were  mostly  understandable.  (No where have a found an answer to why you have to add 2 to the number of teeth)
> 
> I think Mark Stephen said it best:  " I am beginning to suspect the need to sacrifice small furry animals while standing on my head reciting incantations to pull of this bit of black magic. :lmao: There seems to be very little hard math behind it. "  I will gash the teeth first.
> 
> Inr 729 Richard offered in this same thread a calculator for free.  Well let me tell you it is great and thank you Richard very much.  The calculator covers many different subjects and I will recommend it to all.
> 
> Later
> Ray
> 
> Well I haven't given up and will be trying again soon


It goes back to the question that I asked in post #2


RJSakowski said:


> .......Also how did you compensate for the reduction in diameter as the "cutter" went deeper into the work?


As you cut deeper the pitch diameter decreases.  The diametral pitch remains the same (it's determined by your cutter) so the number of teeth has to decrease.  Now, your cutter is driving the gear so you are probably starting with 72 teeth.  The mystery to me is how you morph from 72  to 69 teeth without having some malformed teeth.

The pitch diameter of a gear is not the same as the outside diameter. the worm engages the gear teeth approximately midway along the tooth and that is where the pitch diameter is measured.  The two extra teeth are what is needed to correct for using the outside diameter.  Note that correction this is for spur gears.  Your worm gear cuts deeper than a tooth depth which is probably why you need three extra teeth instead of two.

Boston Gear has a rather thorough white paper on gear theory. http://www.bostongear.com/pdf/gear_theory.pdf


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## Mark_f

You guys are getting into my question in the beginning of the post. How to figure the ratio. I ain't no gear expert, in fact I have always avoided them. I am trying to find how to figure the diameter of the worm blank AND the diameter of the worm for a given ratio. My brain smokes and seizes up trying to understand worm gears


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## RJSakowski

Figuring the ratio is fairly easy.  For a single start worm, each turn of the worm advances one tooth on the gear.  The number of teeth on the gear determines your ratio. With in reasonable limits, the diameter of the worm doesn't figure in.  Its kind of like a helical rack and pinon except the rack is wrapped around a shaft.  The pitch diameter of the mating gear is determined by the pitch and the number of teeth.


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## Mark_f

RJSakowski said:


> Figuring the ratio is fairly easy.  For a single start worm, each turn of the worm advances one tooth on the gear.  The number of teeth on the gear determines your ratio. With in reasonable limits, the diameter of the worm doesn't figure in.  Its kind of like a helical rack and pinon except the rack is wrapped around a shaft.  The pitch diameter of the mating gear is determined by the pitch and the number of teeth.



This is kind of like the chicken or egg theory, which came first. Ok...I can see the worm diameter makes no difference. So, do you make a worm gear with the number of teeth needed and then make a worm to match or just pick a TPI and make the gears to match it?


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## RJSakowski

mark_f said:


> This is kind of like the chicken or egg theory, which came first. Ok...I can see the worm diameter makes no difference. So, do you make a worm gear with the number of teeth needed and then make a worm to match or just pick a TPI and make the gears to match it?


I would think you need to make the worm.  It would be cut like a screw thread but with the proper profile. 

Conceivably you could cut the gear to match but the equipment required would be quite complex.  The gear is essentially a helical gear and and has to be rotated in synch with the cutter.  The OP's method of cutting self -rotates the gear to maintain the synch as it is cut.  Here is a You Tube video the does a great job of explaining the process.  The hobbing process at the end is very similar to what the OP is doing. The gashing part is what is missing and why the 72 teeth morphed into 69 for the OP.


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## rdean

More experiments in process.  
I have found three different formulas for computing the diameter of the worm wheel but most of the formulas end up very close to the same result and do add 2 teeth in the formula.  
Richards calculator  not only gives numbers for the wheel but also the screw if you want to make that.  The calculator even gives figures for an envelope worm gear.

Mark I am going to keep going until I find the answer one way or the other.
I would like to find a process that is repeatable without gnashing the blank first.

Ray


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## aeroHAWK

rdean said:


> I would like to find a process that is repeatable without gnashing the blank first.


Let me make this simple... *YOU WON'T*_!_

The "correct" way to make a worm gear is to use a hobber that is made for it. If you don't have the special machinery, you can do what you have already done. However, it will NOT be repeatable. The way to have any chance to make it repeatable is to gash the teeth partially, to give the makeshift hob a guide to work with.

Otherwise it will be hit-or-miss.... (mostly miss - as you have discovered)


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## jererp

rdean said:


> It looked great with well formed teeth all the same size and evenly spaced. I was patting myself on the back when I decided I had better count the teeth just to make sure there were 72 of them. After numerous counts I found there were only 69 teeth.


I think what we are disregarding is the contact area on the worm gear.  What you have cut is much deeper than the depth of one thread on the "worm", and as such the actual pitch diameter of the worm gear is smaller than your calculated size.  That is why the formula in the other thread added 2 teeth, to give you that good contact area.   I think if you stopped at your original calculated depth, you would have 72 teeth, just not much contact area.


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## John Hasler

You could make a gashing tool by making a tool similar to the one you are using but with the correct TPI for the starting diameter.   Start with it and then switch to a tool with the correct TPI for the finishing diameter.  It might also help to cut a groove to match the minor diameter of the worm around the blank.


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## John Hasler

Idea:  
1) Cut a groove in the blank the minor diameter of the worm and as deep as you want the minor diameter of the threads in the gear to be.

2) Make a tool just like the one you are using but two or three times the length.  Then turn a taper on it so that the teeth go from full height somewhere in the middle to just a minor-diameter shaft toward the end.

3) Start with the blank running on the skinny end of the tool and gradually advance it into the tool until you are cutting full depth threads.


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## Mark_f

rdean said:


> More experiments in process.
> I have found three different formulas for computing the diameter of the worm wheel but most of the formulas end up very close to the same result and do add 2 teeth in the formula.
> Richards calculator  not only gives numbers for the wheel but also the screw if you want to make that.  The calculator even gives figures for an envelope worm gear.
> 
> Mark I am going to keep going until I find the answer one way or the other.
> I would like to find a process that is repeatable without gnashing the blank first.
> 
> Ray



I think gashing the blank is an important step unless you are using a dividing head to make a gear.


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## RJSakowski

If you look at the hob in the video at about 5:40 in, it is not that much different than your homemade hob  The primary difference is that the teeth are staggered.  When you use your hob, once every quarter turn, the hob is essentially disengaged from the gear.  Since the gear is being driven by the hob, it can momentarily stop rotating, losing synch.  This is most likely what causes the loss in teeth as the hob cuts deeper into the gear.

+1 John,  I think you have hit the solution.  It should solve the problem of the changing pitch diameter as the tool cuts deeper.  The final remaining element will be to determine the diameter of the groove to make your tooth count correct.  I expect that the spur gear formula Do = Dp +2/P = N/P + 2/P = (N+2)/P where Do is the diameter at the bottom of the groove, Dp is the pitch diameter, , P is the worm pitch, and N is the number of teeth will be very close.

The length of the taper will determine the chip load for each cutter tooth.  If an Acme thread profile is assumed and 10 tpi, the tooth depth would be about .050"  There are four cutter teeth per revolution and if the cutting depth was .0005", you would need 25 threads to cut from zero to full depth. Add a couple of full depth threads at the end and you would need 2.5 to 3" for the cutter.


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## Mark_f

I just watched the video. One day here, I am going to have to try this ( I am back in the darned hospital again right now),but it appears to me, you make the worm first. MAKE TWO! one preferably from say drill rod, the other from steel. The one made from drill rod gets grooves cut in it to make a hob like in the picture. Use it to cut the worm gear and you then have a " set" when you finished. Keep the hob you made , in case you ever want to make another. If you want , harden the hob you made and finish grind the grooves to make it better. Did I miss something?


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## RJSakowski

mark_f said:


> I just watched the video. One day here, I am going to have to try this ( I am back in the darned hospital again right now),but it appears to me, you make the worm first. MAKE TWO! one preferably from say drill rod, the other from steel. The one made from drill rod gets grooves cut in it to make a hob like in the picture. Use it to cut the worm gear and you then have a " set" when you finished. Keep the hob you made , in case you ever want to make another. If you want , harden the hob you made and finish grind the grooves to make it better. Did I miss something?


Mark, you are darn close.  What Aerohawk says is true if you use a conventional hob.  You can't cut the whole tooth in one pass so there would be a change in the number of teeth as you cut deeper ending up with a messed up gear.  This is because the hob is controlling the rotation.  The gashing process in the video does a rough cut under controlled conditions (indexing fixture, depth of cut, angle of cut. This does two things. First, it removes most of the material so you can start close to the final diameter and second, it provides a pre-cut track to guide the hob as the hob rotates the gear.

However what John is proposing will work because you are starting at the finish diameter and cutting deeper and deeper teeth.  Because the diameter isn't changing, the number of teeth doesn't change.  So make a hob as John is proposing.  As you state, make two worms ( or make one long one and cut in half).  Taper the end of one cut the grooves to make the hob, and harden if you wish.  The attached file is my conception of the hob.  It is a 3D PDF so you should be able to rotate it and zoom in for close up detail.


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## rdean

I have success and failure.
Here are three worm rings that have 72 teeth each.   The outside two are 0.125 deep and the center is 0.180 deep with a diameter of 3.929.




I made three cuts to insure the process is repeatable and the deeper you go the tooth count stays the same but the teeth get narrower until they are cut out entirely.

The failure part is that "aerohawk" was right.  I could not make a gear with a predefined number of teeth with out gnashing the blank first.  One trail for 120 teeth came out 118, 122,and 119 all cut at the same outside diameter.  
I used my rotary table to cut 72 slots about 0.025 deep to mark the teeth.  I could not make the tooth count change even though I really drove the cutter into the blank easy or rough the tooth count stayed the same.
I think the most important part of making a worm wheel is cutting the tooth locations.  The diameter of the blank can be a little small or a little large but you still get the same number of teeth.

Thanks for looking
Ray


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## Mark_f

rdean said:


> I have success and failure.
> Here are three worm rings that have 72 teeth each.   The outside two are 0.125 deep and the center is 0.180 deep with a diameter of 3.929.
> 
> View attachment 106841
> 
> 
> I made three cuts to insure the process is repeatable and the deeper you go the tooth count stays the same but the teeth get narrower until they are cut out entirely.
> 
> The failure part is that "aerohawk" was right.  I could not make a gear with a predefined number of teeth with out gnashing the blank first.  One trail for 120 teeth came out 118, 122,and 119 all cut at the same outside diameter.
> I used my rotary table to cut 72 slots about 0.025 deep to mark the teeth.  I could not make the tooth count change even though I really drove the cutter into the blank easy or rough the tooth count stayed the same.
> I think the most important part of making a worm wheel is cutting the tooth locations.  The diameter of the blank can be a little small or a little large but you still get the same number of teeth.
> 
> Thanks for looking
> Ray



My thoughts are to make the cuts on the job at an angle and then the job will be engaged at all times. It would be similar to having the teeth staggered


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## aeroHAWK

rdean said:


> I used my rotary table to cut 72 slots about 0.025 deep to mark the teeth.


The thing that is great, is that you demonstrate that it doesn't take much to do the trick.  The video shows the gashing cuts the teeth almost completely (and using an involute cutter). Whereas you cut only .o25 deep.

What did you use to cut the slots?


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## rdean

I used a long 1/8" ball end mill to cut all the way across the blank so I could cut 3 gears.  The slots were not all evenly spaced as the end mill liked to veer off on some.




I think the slots would only have to be about 1/4" long in the center of the cut just to start the teeth.

Cheers
Ray


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## Mark_f

When making spur gears, you can line up the blanks and cut several at once, but I would think worm gears have to be cut one at a time.


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## RJSakowski

rdean said:


> I used a long 1/8" ball end mill to cut all the way across the blank so I could cut 3 gears. The slots were not all evenly spaced as the end mill liked to veer off on some.


 Ray,
Did you angle the table to account for the pitch of the worm or just cut straight across?


mark_f said:


> When making spur gears, you can line up the blanks and cut several at once, but I would think worm gears have to be cut one at a time.


Mark, 
You could cut a whole bunch much like threading a lead shaft and cut it into sections.
BTW, I hope you are feeling better soon!

Bob


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## Mark_f

RJSakowski said:


> Ray,
> Did you angle the table to account for the pitch of the worm or just cut straight across?
> 
> Mark,
> You could cut a whole bunch much like threading a lead shaft and cut it into sections.
> BTW, I hope you are feeling better soon!
> 
> Bob



Thank you, I am doing better. 
I having a hard time wrapping my head around that idea because I thought there's a concave groove in each gear.


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## RJSakowski

From the video that I posted they didcut a concave groove but they also cut much deeper than Ray, ending up with a nearly finished tooth.  It looks like Ray is just providing a shallow track to get the process started.


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## rdean

Me too "Get well soon Mark"

I just cut straight across the face to make 72 slots for the teeth of the hob to catch on.  They weren't evenly spaced either because of the long, small end mill wanted to move around some but I didn't notice it until they were all cut.
After cutting the worms I came back and cut out the slots that were left between and on the outsides to make it easier see each worm cut.

Ray


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## rdean

I did learn a couple of useful things making these.

I cut these threads very deep probably past the center of the hob and the tooth count did not change.  The teeth got thinner until they were destroyed.  Not sure what would have happened if I had went further.




I did find many different formulas for finding the diameter of the wheel and some were very involved and most confusing.

Here is the one I like the best.

How many teeth do you want?                                     72
Now add 2  ---                                                            72+2=74
How many teeth per inch on the hob?                           6
Divide teeth +2 (74)  by hob teeth per inch (6) =     12.33333  (this is the circumference)
Divide the circumference by 3.14 =                          3.928  (this is the diameter to start with)

The only thing you have to remember is to add 2.  What could be easier?

Have a nice day
Ray


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## rdean

Now to make something useful from the gear.
I noticed the last time I mounted the vise on the manual mill that my back let me know that I shouldn't do that anymore.
I took the gear that I had made with three sets of teeth and cut two of the sets down to make a flat area.  I then mounted them on a piece of 1/4" plate like this.



And that was attached to this.




Which made this.









Have a nice day
Ray


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## aeroHAWK

Looking good Ray! 

Next, you'll get tired of turning the crank and find a motor...


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## RJSakowski

Ray, It looks like a good use for your worm gear.  A nicely done project overall.

I would caution you about putting some sort of safety lock or brake on your lift, if you haven't already done so, if you are going to be lifting heavy weights like that to prevent the possibility of serious damage or injury,  Should one of the Nylon teeth fail, you could get a chain reaction of tooth failures.

Bob


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## MarkM

Something to consider with the worm.  The helix angle changes with the diameter.  When you nash your worm gear account for the helix angle of the hobb.


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## markba633csi

I agree with RJ, I would be cautious about lifting heavy weights with nylon gears, keep your feet clear at the very least, and fingers too


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