Quickest way to work out gears to suit ratios for gear hobber

Macsbig · Oct 27, 2013

Hi again all,

Another hobber question, so I opologise in advance!

Obviously the closer I can get my ratios the better, but my gear ratio's book must have - I don't know a million or so gear combinations, but not always "spot on" to the ratio's I require.

The formula I use is: (A/b) x (c/d) to get my ratio's manually - e.g 0.845029

It can take me an absoulute age to get to my required 6 decimal places using my change gear combinations (20 to 100 teeth in 1 tooth graduations, and some duplicated gears), and then sometimes I have to alter it if the combination doesn't physically fit in to the gear case, or I can't fit an idler in etc - if the set-up requires it.

I have to do this for both the index and differential on each job.

Is there a quick and simple way to work things out, or maybe some software I could purchase/download made for this very purpose. I can't believe all you gear cutters out there are math genious's!

Any suggestions would maybe stop me going insane with all these numbers! :confused:

Thanks in advance,

Mark

alonzo83 · Oct 27, 2013

I am no gear hobber, and I am certainly no math genius. I am more like an idiot savant with excel.

Can you make a formula in an excell spreadsheet?

you can use (if then) statements to weed out false combinations that will not work or fit by entering the number of teeth and the dimensions to your gears in the spreadsheet.

Macsbig · Oct 27, 2013

alonzo83 said:
I am no gear hobber, and I am certainly no math genius. I am more like an idiot savant with excel.

Can you make a formula in an excell spreadsheet?

you can use (if then) statements to weed out false combinations that will not work or fit by entering the number of teeth and the dimensions to your gears in the spreadsheet.

-------------------------------------------------------------------------------------------

Ah right alonzo83,

I dont use Excell, but I'm sure I can find someone who can, or mayb a quick Google search can help me with a "crash course" in it!

Can Excell be configured to only use integers?

Cheers,

Mark

Conrad Hoffman · Oct 27, 2013

You can grab my gear ratio program here. It's easier than using a book once you get the hang of it. Expect a few seconds or more load time.

alonzo83 · Oct 27, 2013

Macsbig said:
-------------------------------------------------------------------------------------------

Ah right alonzo83,

I dont use Excell, but I'm sure I can find someone who can, or mayb a quick Google search can help me with a "crash course" in it!

Can Excell be configured to only use integers?

Cheers,

Mark

Excell can be made to display intergers. Pick up an excel for dummies. I was still in school and was interning where I now work. when I saw the owner and the foreman crunching numbers to get the degrees minuets and seconds for a gear. I made them a spreadsheet where they enter in the number of teeth and it spits out the deg min and sec for every movement. turned a 45 min job into a quick trip to the printer with not having to worry about errors.

Forrest Addy · Oct 27, 2013

I''ve tried many times to automate this problem if determining tooth counts for compounded meshing gear pairs for a trageted ratio accurate to five signiificant figures.

My best effort was when I designed a double circular slide rule where it has two rotary scales and a single index cursor. The guy who designed the "InfiniRule" app with its adjustable precision has the solution in his grasp; I've been arguing with him but he wants money to add another rule to his app. 5 significant figure accuracy is possible with this app.

I can't make Excel work because I can't get it to automatically increment and compare within limits. However it will calculate and manually increment quickly and conveniently.

So far as I know the only methods that work are manual recursive trail and repeat using continued fractions or logs of gear pair tables.

Here's a search: https://www.google.com/#q=logarithms+of+gear+ratios

Machinery - Google Books

There are still logs of gear ratios available some in the above links.

This would seem to be a problem ideally suited for a computer program but I'm not smart in that direction. I've never been able to find one although the need is there. The reason why is obvious. There is no problem more unexciting or rarely needed than lead gear calculation. Not a single sword, laser, castle, terrorist, gorilla, monster to be conquered/killed/destroyed; maid in peril rescued: or geek esteem, or dollar to be had. The geeks ignore it in droves.

Peter Colman · Oct 27, 2013

The easiest way to get over this is via the book for the machine which may be available either new or as a copy, try lathes website. The other way is to post on meshing with gears site, the moderator is most helpful and knowledgable, he has a software system to sell but with the ratio of your machine you can get there yourself.
I also think that Ivan laws book on gears is very useful in that it helps with things like turning lead into feed on worms.
PM me with details of your machine if you need any more help.

Macsbig · Oct 27, 2013

Many thanks for your replies guys, it's time for me to hit the sack here, I'll digest it all a little more when I hit the factory tomorrow!

Did have a quick look at your program Conrad, seems awsume - only problem I had on my windows 7 pc at home was I couldn't find how to change the gear limits (no command line start-up?)

Anyway I'm knackered can't think straight, I'll look again in the morning on my work pc which runs XP!!

Thanks again guys.

Forrest Addy · Oct 27, 2013

Conrad's program works great.

Macsbig · Oct 28, 2013

Forrest Addy said:
Conrad's program works great.

Yeh looks just what I needed!

Just PM'd Conrad, as I still can't work out how to change the gear limits

Great program tho'!!!

Zahnrad Kopf · Oct 28, 2013

Macsbig - short answer? No, not really. Not to my knowledge. Welcome to gear making... I think it's one of the reasons that most souls avoid it like pox. Conrad has a few utilities that will be of good assistance to you and there are books you will find helpful as well. Gear making is one of those things that one doesn't get really good at by dabbling and giving casual attention. It demands a certain amount of reckless abandon and embracing of the mental instabilities inherent with its practice ...

A lot of reading and math, too...

Good luck.

JB @ C and L Machine · Oct 28, 2013

Our 100'' Fellows has 6 change gears to ( plus work and no. teeth in the cutter ) play with. Most of the time I get right away after 12 years, but there are some I have to rack my brains out and curse like a drunken sailor !!

Macsbig · Oct 28, 2013

Zahnrad Kopf said:
Macsbig - short answer? No, not really. Not to my knowledge. Welcome to gear making... I think it's one of the reasons that most souls avoid it like pox. Conrad has a few utilities that will be of good assistance to you and there are books you will find helpful as well. Gear making is one of those things that one doesn't get really good at by dabbling and giving casual attention. It demands a certain amount of reckless abandon and embracing of the mental instabilities inherent with its practice ... A lot of reading and math, too... Good luck.

JB @ C and L Machine said:
Our 100'' Fellows has 6 change gears to ( plus work and no. teeth in the cutter ) play with. Most of the time I get right away after 12 years, but there are some I have to rack my brains out and curse like a drunken sailor !!

Haha, seems like I'm not QUITE as dumb as I thought, do enjoy the challenge of it I must admit, but it can be taxing on the old grey cells! :crazy:

The problem is that I DO dabble, thats the nature of my job I'm afaid, running a team of maintenance engineers I have to have a reasonable knowlage of most disciplins, but a master of none I guess!

At least its good to have you guys to bounce off, does help, and I am gratefull!

The more I do it, the more I'll learn about it I'm sure, its just I don't have the time to spend a couple of hours finding out a couple of gear ratio's.

Conrads program I'm sure will help alot, mayb I'll see if I can get one of our I.T guys to write me a program that will do all the math for me hehe - wishfull thinking ay??

Cheers guys.

Dan from Oakland · Oct 28, 2013

One thing to remember- your index ratios need to be exact- not an approximation- even to 6 places. Teach yourself to factor your index constant 24/N etc to get your 4 (or 6) gear ratio.

Dan

Conrad Hoffman · Oct 28, 2013

My little program came about when I got a copy of "14000 Gear Ratios" by Page. It seemed like such a simple thing to work out. Right. Since I don't like delays, the program creates a huge array and then lets you step through it. For two compounds it's reasonable for up to about 130 teeth. For three compounds, six gears, it's a completely idiotic way to do it, as the arrays quickly get out of hand. Hopefully one can break the problem down and just use the program twice.

I'd think that for any given machine there would be a very small number of combinations needed to produce a full range of gears, just as I have a simple table for my lathe, covering every known (and a few unknown) metric threads. Just as with the lathe, one has to check the fit of each combination, since what works by the math might not fit under the cover, or the compounds might not engage.

I only know XP, so to change the gear limits, create a desktop shortcut. Then, right click and edit properties of the shortcut. Under the tab "Shortcut" append the lower number and upper number to the program name- whereever\GearRatios.exe 24 62

The lower limit is 6 and the upper is 130. When you start the program, if you did it right, you'll get a little dialog confirming the numbers. If you go up to 130 be sure to wait a few minutes to load- it will appear dead, but it's just thinking (that's what I tell people about me!)

jCandlish · Oct 28, 2013

What kind of hobs are these, and how can I work out a sensible tool/workpiece ratio to cut something that ends up with teeth, with only the hobs themselves and the diameter of the gear blank to calculate from?

Does there exists a textbook 'reverse engineering hobs'? Or maybe 'practical hob design'???

The OPs question does not take into account that the hob itself is a gear and may generate more than one sensible workpiece.

On edit: picking gear ratios from sets of gears is a type of problem in number theory known has Diophantine equations. There are some some (sub)optimal algorithms to speed and narrow the search.

Macsbig · Oct 28, 2013

Dan from Oakland said:
One thing to remember- your index ratios need to be exact- not an approximation- even to 6 places. Teach yourself to factor your index constant 24/N etc to get your 4 (or 6) gear ratio.

Dan

Conrad Hoffman said:
My little program came about when I got a copy of "14000 Gear Ratios" by Page. It seemed like such a simple thing to work out. Right. Since I don't like delays, the program creates a huge array and then lets you step through it. For two compounds it's reasonable for up to about 130 teeth. For three compounds, six gears, it's a completely idiotic way to do it, as the arrays quickly get out of hand. Hopefully one can break the problem down and just use the program twice.

I'd think that for any given machine there would be a very small number of combinations needed to produce a full range of gears, just as I have a simple table for my lathe, covering every known (and a few unknown) metric threads. Just as with the lathe, one has to check the fit of each combination, since what works by the math might not fit under the cover, or the compounds might not engage.

I only know XP, so to change the gear limits, create a desktop shortcut. Then, right click and edit properties of the shortcut. Under the tab "Shortcut" append the lower number and upper number to the program name- whereever\GearRatios.exe 24 62

The lower limit is 6 and the upper is 130. When you start the program, if you did it right, you'll get a little dialog confirming the numbers. If you go up to 130 be sure to wait a few minutes to load- it will appear dead, but it's just thinking (that's what I tell people about me!)

Thanks Dan, I try to make both ratios right to 6 decimal places, if the index I can say only get to 0.000002 accuracy then I'ill make the differential -.000002 (hope that makes sense!)

Thanks alot for the PM on changing the gear limits of the program Conrad - works a bloody treat!! even in windows 7

( I'm at home now and use W7 at home and the soon to be defunct XP at work)

I'm well chuffed, and all the guys at work will think I'm a right clever sod when I work it out in minutes. hehe

Also I'll keep all my own hair for a bit longer as I wont be pulling it out - you've done a great service to mankind Conrad. haha

Macsbig · Oct 28, 2013

<jbc> said:
Does there exists a textbook 'reverse engineering hobs'? Or maybe 'practical hob design'???

The OPs question does not take into account that the hob itself is a gear and may generate more than one sensible workpiece.

Sorry jbc, really don't understand what you'r trying to say there!

Maybe I should try Google translate? :confused:

Or maybe Conrad has a program to spell it out for me! hehe

Conrad Hoffman · Oct 28, 2013

I'm still a bit baffled. I would have thought that ratios needed to work out exactly for gear cutting. Where would any error come into play? I do use a 37/47 pair to get close to metric threading, bit that's sort of a special case with a 0.02% error considered close enough for most work.

Macsbig · Oct 28, 2013

Conrad Hoffman said:
I'm still a bit baffled. I would have thought that ratios needed to work out exactly for gear cutting. Where would any error come into play? I do use a 37/47 pair to get close to metric threading, bit that's sort of a special case with a 0.02% error considered close enough for most work.

Sometimes it appears you can't get the exact ratio.

For instance the Ratio I'm currently working with is 0.835039 - can't get it exactly with four gears (try your program), so I error correct with the Diff ratio - unless I'm missing something?

Quickest way to work out gears to suit ratios for gear hobber

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