# The gears in my head don't mesh



## Suzuki4evr (Apr 2, 2020)

I have a question. If I want to make 4 new gears but I only have the number of teeth of each gear, how do I calculate the OD's of the gear blanks if I have none other variables available? Because I am making new gears,I don't have any other variables. The gears are for my lathe and in the picture below it shows the configuration.


If I have the OD,I can work out everything else,but I just can't figure out how to get the blank OD's. I know some are going to give me formulas using the module or DP or other variables ,but remember I do not have any of that. I hope someone can shine a very bright light on this,because I am starting to feel stupid not being able to figure this out.

Thanks guys 
Michael


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## matthewsx (Apr 2, 2020)

This might be an unorthodox approach but how about cutting circles from thin plywood in about the size you think will work and seeing how they fit on the lathe. I'm not any kind of expert but if they fit in the physical space and have the right number of teeth that's all that should matter, right?

Cheers,

John


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## Suzuki4evr (Apr 2, 2020)

John,I don't think it works quite like that. Making gears is actually a precise mathematical process from the little I know. But thanks for the idea. If all else fails........


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## cathead (Apr 2, 2020)

Machinery's Handbook has a wealth of information concerning gears.  There are drawings and formulas
that one can use to get the dimensions you need to make most any gear.


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## Suzuki4evr (Apr 2, 2020)

I did page through it,but still could not get the answer I want seeing that I only have number of teeth.


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## Suzuki4evr (Apr 2, 2020)

I count have missed it somehow.


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## graham-xrf (Apr 2, 2020)

@Suzuki4evr :
Hi Michael
The final dimensions are precision, but the quick-'n -dirty check with a temporary plywood dummy, or bit of plastic can lead you straight to the correct gear, and remove ambiguity, if you only have the number of teeth.

An obvious question is.. does anything survive of the originals? If you can get at them, you can measure the pitch. Even an approximation may be enough to then figure out the rest of the gear - because the possible combinations are limited.

gear guide.pdf has a table of pitch comparisons on P602, various calculation examples, etc.

If you know, or can measure, the distance between the shaft centres, then the number of possible solutions that have the known number of teeth rapidly become fewer.

p-1930-bg_engineering-info-spur-gears has very complete tables and information about gears on P309 and P311.

Unfortunately, the madly comprehensive gear_guide1.pdf is 21.4MB, and so too large to upload to HM.


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## Suzuki4evr (Apr 2, 2020)

Thanks Graham. I do not have originals,but can measure distance between centres of the shafts though.


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## francist (Apr 2, 2020)

I think you will need to determine the pitch of the gears on your lathe first, either module or DP and what that number is, then you’ll be able to use a formula to derive the diameter easily enough.

Trying to match tooth profile of the existing teeth of another gear on your lathe is one way although subject to a lot of error. Or, seek out someone with same lathe who may know what the profile is? If you have a gear tooth profile gauge, this task is exponentially easier!

-frank


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## RJSakowski (Apr 2, 2020)

inch:  O.D. (inches) x diametral pitch = no. of teeth + 2
metric: O.D. (mm) /mod = no. of teeth +2

All the gears that mesh will have the same diametral pitch or modulus.  From an existing gear, counting the teeth and measuring the O.D. will give you the diametral pitch or modulus.  Then you can calculate the I.D.'s of the missing gears from the number of teeth.


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## benmychree (Apr 2, 2020)

First, you need to figure if the gears that you have are diametral pitch ( imperial measurement) or module (metric), then you need to figure out the pitch and whether or not the gears are 14 1/2 degree pressure angle or 20 degree P.A.  If your machine is made offshore it is likely that they are Module system.  The OD of a gear is figured (in the case of D.P.) gears by the formula:  N(number of teeth) +2 divided by D.P. = OD, The formula for Module is similar, but different.  Your biggest challenge will be figuring out the D.P. or Module; for DP there are charts in the handbooks with profiles if the different pitches, Module may be harder to find ---   But, if you were to give the OD of the 66 tooth gear and also the Root diameter of it, the Module could be deduced, otherwise you may look for a set of plastic templates of Module gear teeth and figure it that way, once you find the module, its all simple formulas.


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## MrWhoopee (Apr 3, 2020)

Well isn't this a pretty little puzzle. From the looks of the gear chart, it's an Asian lathe. We will need the center to center dim for the shafts, call them C1 for the upper gear set & C2 for the lower. Assuming Module gears, module will be the same for all gears (of course), call it M. Number of teeth =T. Reference (pitch) diameter (Rdx) = M x T.
Once you have the center to center, you can solve for the module
For the upper set of gears:
Gear 1 = 66 teeth, Rd1=66M
Gear 2 = 55 teeth, Rd2=55M
C1=(Rd1+Rd2)/2
C1=(66M+55M)/2
2(C1)=66M+55M
2(C1)=121M
(2{C1})/121=M

.To calculate the OD,
OD (in mm)=(T+2) x M

Someone please check this, it's late.


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## RJSakowski (Apr 3, 2020)

You don't need to measure center to center.  If you have one gear, measure it's O.D. and count its teeth.  You can calculate module if it's a metric gear or diametral pitch if its an inch gear from those numbers.  The calculated result will come out an nice number, i.e., either 1.00, 1.25, 1.5,etc. for metric gear modulus.  If the number is squirrelly, assume its an inch gear and calculate the diametral pitch.  Diametral pitches are all whole numbers.  If you get something like 15.7, it is a metric gear.  

Typically, the calculations may be off slightly due to the O.D. measurement not being accurate but they will be very close to the ideal.


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## RJSakowski (Apr 3, 2020)

Common diametral pitches: 6, 8, 10, 12, 16, 20, 24, 32, 64
Common modulus values: .4, .5, .75, .8, 1, 1.25, 1.5 2, 2.5, 3

For smaller lathes,  you are most likely to have diametral pitches in the 16 to 32 and moduli in the range of .8 to 1.5


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## rgray (Apr 3, 2020)

The tooth count on that 95 gear might give a pretty good clue as to what can physically fit.
Assuming module gears. Module 1 95 tooth gear is 3.8189 O.D.
The mating 57 tooth module 1 gear is 2.3228 O.D.
So that takes up 6.1417 inches of room. If that's large or small go from there.
I think module 2 is popular on asian equip. that would take up 12.2835 inch


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## DavidR8 (Apr 3, 2020)

What's the make and model of lathe?


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## Reddinr (Apr 3, 2020)

There is a program called Gearotic Motion that solves this problem easily, produces drawings etc.  $120 though.


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## Suzuki4evr (Apr 3, 2020)

MrWhoopee said:


> Well isn't this a pretty little puzzle. From the looks of the gear chart, it's an Asian lathe.


This is a Mashstroy 1.5m btc lathe and it is from Bulgaria. C1=120mm and C2=150mm.


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## Suzuki4evr (Apr 3, 2020)

DavidR8 said:


> What's the make and model of lathe?


I think I have answered your question too.


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## Suzuki4evr (Apr 3, 2020)

I have measured the gears on the lathe and I used it for reference for the change gears I want to make and it looks like the module are M2.0 if I use the information the members gave me. That being said, I can say this is a metric lathe so it makes sense that the gears would be Module and not DP. In the pic below it shows the gear configuration on the lathe as it is now.


Now that I have the module,I will be able to work out the rest. If someone thinks I am missing something, please let me know, but I think I am ons the right course now.


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## RJSakowski (Apr 3, 2020)

Suzuki4evr said:


> I have measured the gears on the lathe and I used it for reference for the change gears I want to make and it looks like the module are M2.0 if I use the information the members gave me. That being said, I can say this is a metric lathe so it makes sense that the gears would be Module and not DP. In the pic below it shows the gear configuration on the lathe as it is now.
> View attachment 319378
> 
> Now that I have the module,I will be able to work out the rest. If someone thinks I am missing something, please let me know, but I think I am ons the right course now.



As benmychree said above, you will need to know the pressure angle. It will be either 14.5º or 20º.  This can be rather tricky.  The best way is to compare the tooth profile to a known P.A.  There are sources online with images which should aid with that.


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## Suzuki4evr (Apr 3, 2020)

Thank you RJ. Will do


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## matthewsx (Apr 3, 2020)

matthewsx said:


> This might be an unorthodox approach but how about cutting circles from thin plywood in about the size you think will work and seeing how they fit on the lathe. I'm not any kind of expert but if they fit in the physical space and have the right number of teeth that's all that should matter, right?
> 
> Cheers,
> 
> John


I understand the challenges of computing the gears


graham-xrf said:


> @Suzuki4evr :
> Hi Michael
> The final dimensions are precision, but the quick-'n -dirty check with a temporary plywood dummy, or bit of plastic can lead you straight to the correct gear, and remove ambiguity, if you only have the number of teeth.
> 
> ...



this is what I meant with a mock up. Of course you need the correct pitch, form, and a bunch of other stuff but if you can figure the physical size that should help. Still not an expert and my machinery’s handbook is 2000 miles away


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## Suzuki4evr (Apr 3, 2020)

matthewsx said:


> my machinery’s handbook is 2000 miles away


How did this happen???????? Ok I understand your mockup idea now.


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## matthewsx (Apr 3, 2020)

Yep, it’s back in Michigan. looks like the experts have arrived


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## Suzuki4evr (Apr 3, 2020)

Thanks anyway for your input.


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## MrWhoopee (Apr 3, 2020)

Suzuki4evr said:


> This is a Mashstroy 1.5m btc lathe and it is from Bulgaria. C1=120mm and C2=150mm.



(120*2)/121=1.983
(150*2)/(57+95)=1.973

So, yes, a 2.0 Mod.


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## graham-xrf (Apr 3, 2020)

Even when it's late, and he's totally knackered - he was not wrong!


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## LEEQ (Apr 4, 2020)

pressure angle should be 20degrees.https://www.hobby-machinist.com/threads/g4003-change-gear-specs.83304/#post-732305 In this thread I discover and do the math to check pressure angle. You can do the same with a gear from the lathe. It should confirm both module and pressure angle. I learned that bit so I didn't buy the wrong module or pressure angle of cutters. I believe your blanks will be teeth + 2 X module. IE... 50+2x2=104mm blank for the 50 tooth gear. I look forward to seeing your figures and your shiny new gears.


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## Suzuki4evr (Apr 4, 2020)

Hallo LEEQ.
Well I a bit far away from actually making the gears,because of two things. One is the lockdown we are in and B,I can't order any tool or cutter online now because our Rand vs Dollar are in the dumpster at the moment. But what I can give you is the results on the OD's of the blanks working on Module 2 with 20dgr PA. Gears blanks are as follows :
N66 (OD=136mm)
N55 (OD=114mm)
N95 (OD=194mm)
N57 (OD=118mm)
In DP it is 12.7
I want to thank everyone helping with this. Next up is material to use,I am thinking 1043 (EN8), and to heat treat or not on the gear teeth,but I am leaning towards yes. I don't know if and when they will lift this lockdown, but as soon as I get to knocking out some gears,I will post it.


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## MrWhoopee (Apr 4, 2020)

Suzuki4evr said:


> In DP it is 12.7



Which, oddly enough is half of 25.4. Why does that number sound so familiar?


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## LEEQ (Apr 4, 2020)

Is that the number of licks to the center of a tootsie pop Mr. Owl?


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## Suzuki4evr (Apr 5, 2020)

MrWhoopee said:


> Which, oddly enough is half of 25.4. Why does that number sound so familiar?


Thank you for all your help MrWhoopee


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## Suzuki4evr (Apr 5, 2020)

LEEQ said:


> Is that the number of licks to the center of a tootsie pop Mr. Owl?


Don't know what this is about, but sounds like an insde joke


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## rgray (Apr 5, 2020)

MrWhoopee said:


> Which, oddly enough is half of 25.4. Why does that number sound so familiar?



Number of millimeters in an inch.


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## Suzuki4evr (Apr 5, 2020)

rgray said:


> Number of millimeters in an inch.


Exactly.


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## LEEQ (Apr 5, 2020)

If ya notice, mod 1 is 25.4 dp. Mod 2 is 12.7 dp. So at least that helps make it easier for the imperial thinkers. Suzuki, the silly reference was from an old candy advertisement. I was just funning.


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## MrWhoopee (Apr 5, 2020)

LEEQ said:


> If ya notice, mod 1 is 25.4 dp. Mod 2 is 12.7 dp. So at least that helps make it easier for the imperial thinkers.



Demonstrating that Module and Diametral Pitch are not really all that different. In fact, the term "Diametral Pitch" more clearly explains the concept and could be applied to either system. I suggest Metric Diametral Pitch (MDP) and Imperial (or Inch) Diametral Pitch (IDP) as replacements for the existing terminology. It has only been through the course of this discussion that I have clearly understood the similarity.


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## RJSakowski (Apr 5, 2020)

A lot of useful information here: https://en.wikipedia.org/wiki/Gear


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## Suzuki4evr (Apr 6, 2020)

LEEQ said:


> If ya notice, mod 1 is 25.4 dp. Mod 2 is 12.7 dp. So at least that helps make it easier for the imperial thinkers. Suzuki, the silly reference was from an old candy advertisement. I was just funning.


I thought it must have been some kind of advertisement.


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## graham-xrf (Apr 6, 2020)

MrWhoopee said:


> Demonstrating that Module and Diametral Pitch are not really all that different. In fact, the term "Diametral Pitch" more clearly explains the concept and could be applied to either system. I suggest Metric Diametral Pitch (MDP) and Imperial (or Inch) Diametral Pitch (IDP) as replacements for the existing terminology. It has only been through the course of this discussion that I have clearly understood the similarity.


OK - that looks useful. MDP and IDP.
As well as MDP meaning "Metric", the "M" in there carries with it the reminder that "that was the one using Module". They are seen as being different only by a conversion constant between Imperial and Metric.

I am not experienced enough with gears at the hands-on level, but I will be reading up on it now. The untangling of this problem has sort of bumped me into a better understanding of it all.


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## Suzuki4evr (Apr 6, 2020)

graham-xrf said:


> OK - that looks useful. MDP and IDP.
> As well as MDP meaning "Metric", the "M" in there carries with it the reminder that "that was the one using Module". They are seen as being different only by a conversion constant between Imperial and Metric.
> 
> I am not experienced enough with gears at the hands-on level, but I will be reading up on it now. The untangling of this problem has sort of bumped me into a better understanding of it all.


I am glad your interest are tweaked. If you have the right tools, it is fun to make gears. I have only made about 4 gears by trial and error for my thread dial indicator and it was fun when you get it right. I still have to finish the post on that now that I think of it. I only needed help with this problem because I only had one variable. BUT Mrwhoopee and other members, I must apologise for something. I noticed today and I don't know why I didn't see it before,but the module of the gears on the lathe is actually stamped on the gears. And should have given me a clue and second variable I needed. See pic below right next to the z=50/80 there it is,M2


So once again sorry for that. But l learned something along the process of making the gears mesh in my head agains.


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## MrWhoopee (Apr 6, 2020)

Suzuki4evr said:


> So once again sorry for that. But l learned something along the process of making the gears mesh in my head agains.



Do not apologize! This was a very entertaining and educational little journey. If you had just told us the module, we would have missed out on a better understanding of gearing. Thank you.


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## Janderso (Apr 6, 2020)

I'm glad you enjoyed it, I ran out of fingers and toes to count


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## Suzuki4evr (Apr 6, 2020)

I do have another question?  When I get to cutting the gears,how would I go about cutting the smaller gear seeing that the two gears are made out of one piece of stock. I mean the cutter would not be able to follow through. And as far as I can teel these are not two pieces pressed into eachother.


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## graham-xrf (Apr 6, 2020)

Milling, broaching, planing, hobbing.  Sometimes the bulk is removed with one process, and the profile finished by another. I agree that one looks awkward.


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## RJSakowski (Apr 6, 2020)

I would make the two gears separately and pin them together.  A shaper could make the single piece gear.


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## LEEQ (Apr 6, 2020)

Suzuki that's funny. I figured out how to figure out, and then figured out the module and pa for my gears. Then I took off the one gear I had not and it had the module stamped on the back side of it. So you are not alone at all. As to module and DP, it is accepted that module is called out in mm. It can be called out in inches, but it is then referred to as English module. Such is the system in place. You would probably have as much luck changing that as you would have convincing the whole world to adopt metric and throw away imperial. If I didn't enjoy riddles so much I would wash my hands of this machining business. It seems my time spent on homework way outweighs time spent actually making chips.


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## MrWhoopee (Apr 6, 2020)

With the capabilities you have available to you, the gears will have to be made separately and then joined together. You could cut the smaller gear before assembly, then cut the larger gear after to assure concentricity. If you don't plan to try to harden the teeth, I would try to get some pre-heat treated 4140/42CrMo4 .


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## Suzuki4evr (Apr 7, 2020)

LEEQ said:


> Suzuki that's funny. I figured out how to figure out, and then figured out the module and pa for my gears. Then I took off the one gear I had not and it had the module stamped on the back side of it. So you are not alone at all. As to module and DP, it is accepted that module is called out in mm. It can be called out in inches, but it is then referred to as English module. Such is the system in place. You would probably have as much luck changing that as you would have convincing the whole world to adopt metric and throw away imperial. If I didn't enjoy riddles so much I would wash my hands of this machining business. It seems my time spent on homework way outweighs time spent actually making chips.


For me metric is way simpler than imperial though I work with both, but in my Valley we mostly work with imperial.


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## Suzuki4evr (Apr 7, 2020)

RJSakowski said:


> I would make the two gears separately and pin them together.  A shaper could make the single piece gear.


That is what I thought must happen knowing that I do not have a shaper. I just thought maybe someone else had to do this before without a shaper or making two separate gears.


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## Suzuki4evr (Apr 7, 2020)

MrWhoopee said:


> With the capabilities you have available to you, the gears will have to be made separately and then joined together. You could cut the smaller gear before assembly, then cut the larger gear after to assure concentricity. If you don't plan to try to harden the teeth, I would try to get some pre-heat treated 4140/42CrMo4 .


4140 is a good option yes,then I guess I don't have to harden the teeth. I must say that theese gears are not my primary gears,I am only making them so that I can use the wider apart TPI for cutting grease grooves,if you understand my thinking behind it,like 1TPI or 1/2TPI. The set that is on now is the set I use every day.


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## Suzuki4evr (Aug 12, 2020)

Well I finally started to cut these gears,I just wanted opions on number of passes to make. Is it acceptable to make one pass on 0.1696" depth of cut or a slightly big first cut and the a smaller second cut? I have made a few plastic gears but these are my first metal gears. The material used is 1043.


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## benmychree (Aug 12, 2020)

If you take a heavy cut first and a shallow finish cut, chatter is liable to happen and poor finish resulting, a pitch as fine as that, I would cut it in one pass.  Bottom line, in cutting gears, keep at least two teeth in the cut to avoid chatter.


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## Suzuki4evr (Aug 12, 2020)

Good solid advice and it makes sense. Thank you.


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