# Gear formulas question.



## hobby

Hi everyone,

I looked on the innernet, to find out about making gears, a lotof info, out there, but I'm not grasping the main concepts, yet,

Could someone please explain in detail, what formulas and procedures do you use to make a gear.

To make a gear from a blank, with a specified number of teeth, do you have to know diametral pitch and things, or just divide the circumfrence by the tooth number.

Just for example, if you were to make a gear with 40 teeth on a blank that is 2" diameter, is it as simple as dividing the teeth into the circumference, or what procedure from start to finish would you do to accomplish this.

Excluding the actual machining, with a hob, or gear cutter.

Thankyou...

PS.
I'm not making gears yet, but always wondered about the formulas involved.


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## John S

Look for a book called Gears and Gear-cutting by Ivan Law.
It's in the workshop practice series and isn't expensive, plenty of copies on both sides of the Atlantic as you haven't said where you come from. This book is based on simple home shop gear cutting and doesn't try to cover loads of extended maths that you have no control over anyway.


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## Richard1

This website seems to have most of the formulas listed that you would need.
http://www.engineersedge.com/gear_formula.htm

In your example of a 40 tooth gear on a 2 inch diameter blank the formula for DP is Number of teeth (N) + 2 = 42 divided by the OD of the gear so 
P= (20 + 2) ÷ 2 so you would have a DP of 21.

Depth to cut = 2.2 ÷ P +0.002" 
Depth is 2.2 ÷ 21 + 0.002 = 0.107"

You would however be better working from a known DP and number of teeth and making the blank to the right size in which case the formula is 
OD = (N+2) ÷ DP

The above is just very basic and assumes ordinary spur gears in DP pitches.


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## hobby

Thanks guys.

Using the formula DP = ((N) +2) / OD

Then I could rework the formula back and forth to solve for gear blannks and OD's.

And I could then take a ready made gear, count the number of teeth, and measure its outside diameter, to be able to calculate the DP so as to make mating gears.

That's simple enough.

Thanks again...


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## mklotz

You might want to get a (free) copy of my GEARSPUR program. Given any two facts about a spur gear, it will calculate everything else you need to know - including whole depth which you'll need to cut gears.

Here's a sample output using your example data...



		Code:
	

[I]mperial or (M)etric units?

Enter whatever data you know. Enter zero (0) for unknowns
You must enter two data items to obtain an answer.

OD of gear [2.35 in] ? 2
Number of teeth [45] ? 40

Diametral Pitch = 21.0000
Module = 1.2095
Number of teeth = 40
Outside Diameter = 2.0000 in = 50.8000 mm
Pitch Diameter = 1.9048 in = 48.3810 mm
Addendum = 0.0476 in = 1.2095 mm
Dedendum = 0.0571 in = 1.4514 mm
Whole Depth = 0.1048 in = 2.6610 mm
Circular Pitch = 0.1496 in = 3.7998 mm
Tooth Thickness = 0.0718 in = 1.8239 mm

B & S cutter number used to cut this gear = 3


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## hobby

Marv
Thankyou for the link.

A lot of good info on that site.

I'll be sure to use it from time to time.

Thanks again...


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## Mainer

What John said..... Get "Gears and Gear Cutting" by Ivan Law.


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## tel

I'll third that, that book is pure gold.


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## hobby

Thanks guys.

That book must be excellent, according to amazon.coms customer reviews, it got a 5 star rating, no one had a bad review.

I'll get that book when I am ready to pursue gear making.

Thanks again...


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## precisionmetal

Hobby,

Learning/understanding the basics will get you through 95% of anything you'd probably ever need, especially if the plan is to cut typical/standard gears using standard cutters (e.g. involute form cutters using a dividing head in a milling machine).

Beyond that, just fire away if you have questions. There's plenty of people here that will jump in and help. 

PM


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## Cedge

Surfing on Youtube, I stumbled onto an interesting series of videos on making homemade hobs for gear cutting. http://www.youtube.com/user/Hobbynut . He shares enough information to get started, if you're interested enough to have a go at it.

He also offers a neat little windows friendly freebie on his web site, called "gearcodit" for calculating all the needed gear cutting data, as well as G-coding for CNC. His web site is located at www.leatherwoodplayground.com . The gear utility is located in his "machine shop" area.

After having gone the single tooth cutter route, I'll be making up a few gear hobs of my own when I go back into the shop. 

Steve


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## Maryak

Cedge  said:
			
		

> After having gone the single tooth cutter route, I'll be making up a few gear hobs of my own when I go back into the shop.
> 
> Steve



Took the words right out of my mouth. I'm currently on the scrounge for a decent lump of drill rod. ;D

Best Regards
Bob


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## shred

I've seen a fair bit of debate online about HobbyNut's methods, but it looks like they work well enough. I'm plotting to try them at some point in the future as well.


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## Cedge

Jose Rodriguez shows the same basic technique in his instructional DVD "Making Gears the Easy Way"..... if you can stay awake long enough to get through it. He notes that once you have the created the hob for a given classification, you can cut any tooth count of that size with the same hob. With a matter of creating a few profiles, one can cut nearly any gear needed. Sure sounds cheaper than buying a full set of involute cutters.

Steve


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## putputman

Steve, that was a very good video. Thanks for posting it. I watch the complete series on cutting gears. Haven't watch all the series on making the hobb yet.
I have a question that maybe you can answer. When he cut the gear, he cut .005 depth at a time until he finally reached his .090 depth. He mentioned that you had to do it in steps to accomplish the profile. 
I don't understand why you can't cut to the full depth the first time around. I wonder if his light cut where due to the fast he was using light equipment.
It just seems to me the profile would be generated as you rotate the gear.
All those .005 passes are fine with CNC equipment but would take forever manually.
I just can't get my head around it.


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## Cedge

Putput
He was working with Taig or Sherline sized machines, so lighter cuts were required. I'm sure, heavier equipment would have allowed him to be a bit more aggressive.

I was amazed that he's gotten so much negative response to doing the videos. Reading between the lines it seems he almost decided to stop doing them after "the experts" went at him. Being nibbled to death by ducks still means you're just as dead. I'm glad he got over the shock and went forward.

Steve


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## shred

Cedge  said:
			
		

> Putput
> He was working with Taig or Sherline sized machines, so lighter cuts were required. I'm sure, heavier equipment would have allowed him to be a bit more aggressive.
> 
> I was amazed that he's gotten so much negative response to doing the videos. Reading between the lines it seems he almost decided to stop doing them after "the experts" went at him. Being nibbled to death by ducks still means you're just as dead. I'm glad he got over the shock and went forward.
> 
> Steve


I'm not sure you don't need the steps to create the shape, but it's worth a try both ways if you've got more rigid equipment. Likewise, I was kinda surprised by how the keyboard commandos were (though he does throw out a blooper or two). For most of our purposes we don't need a perfect tooth form anyway, just something that will mesh and deliver power reasonably well.


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## Cedge

Shed
After the single tooth thing, I'm convinced model engineering doesn't always require NASA standards...LOL. I'd do it again, but getting that tiny cutter profile right was a bear.

Give the guy his due.... his gear change box for the Sherline lathe isn't something you'll see just everyday....LOL. He's obviously hobbed a few gears that worked.

Steve


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## Blogwitch

I am looking at the moment at cutting internal module gears by making a spur gear and grinding it up to make an internal hob. I will also be cutting external gears by using commercially produced gear hobs, and using them in a slightly modified way to how Jose Rodriguez does with his home made ones.

http://www.arceurotrade.co.uk/Catalogue/Cutting-Tools/Gear-Hobs

I have found this program very useful for getting all the data I require, for all types of internal and external gears, for both DP and Module. All the inputs aren't required, just the size of the cutter and number of teeth, plus how you want the output, metric or imperial. You don't have to input your name for the program to work, that is only if you want to send the data to Berg so that they can make the gear for you.

Go to here

http://www.wmberg.com/tools/

and download the program 'GearSpec' and unpack and install it.

Blogs


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## Cedge

Putput
My last response was a bit quick on the trigger and made an assumption that wasn't justified. I had only reviewed his videos on making the hobs. In his CNC gear hobbing collection he explains that the movement in .005 increments assures that you'll have a smooth "rounded" transition on the involute surfaces. 

Makes sense, I suppose, but I'd have to give things a try to be sure....(grin)

Steve


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## putputman

Steve, I am trying to picture this in my mind. When you take the final cut at .090 depth, you remove all the metal that was left from the previous cut at .085 depth. I think you get your "involute profile" from the cutting tooth above & below the primary cutting tooth of the hobb. It will not be a true involute profile, but would be suitable for our type of use.

I think someone with good 3D drawing skills could show this. I may try to draw it up with my 2D system.


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## Cedge

Putput
Yeah.... I'm trying to visualize it too. I keep coming up with the last cut erasing things. As you say, it isn't going to be a "true" involute, but close enough for any foreseeable needs I'd have. Some things are just hard to get one's head wrapped around without seeing it happen.

Steve


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## ksouers

Try this site.

http://www.metallmodellbau.de/GEAR-CUTTING.php

It's in German, but he has drawings. That should unwarp things a bit.


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## Cedge

Kevin
Excellent site!! The one thing I immediately noticed is that he's taking full dept of cut. The second was that what I was seeing in my mind's eye is correct. The next tooth over on the hob only clearances the bottom of the gear tooth. Made sense, but nice to see it confirmed. 

Definitely high on my to do list..... if the sunny South ever becomes so again. I'm now in full withdrawal from getting no shop time.

Steve


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## putputman

Kevin, Thanks for that post. I will bookmark it. I can't read it but the photos tell the story pretty good. 

That is pretty much how I imagined it would look. I thought the cutting tooth would be on center instead of straddling center. When I cut gears with an involute cutter, I always put the center of the cutter on the center of the gear. I wonder if the profile that he illustrated would look just a little differant if he put his cutter tooth on center of the gear.


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## Cedge

As long as the cutter is dead on the center line of the gear blank I don't suppose it would really matter much. One trick Duclos shared was to leave a tiny tip on the end of the mandrel to make setting the cutter height easier. 

I can see where a small tapered point could make this guy's way work quite nicely. When both sides of the hob tooth touch the little taper, you have to be dead on centerline.

Steve


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## ksouers

Cedge  said:
			
		

> As long as the cutter is dead on the center line of the gear blank I don't suppose it would really matter much. One trick Duclos shared was to leave a tiny tip on the end of the mandrel to make setting the cutter height easier.
> 
> I can see where a small tapered point could make this guy's way work quite nicely. When both sides of the hob tooth touch the little taper, you have to be dead on centerline.
> 
> Steve



He has a picture doing just that. He has a point held in a three-jaw chuck setting the cutter height.

Take a look around his site. I can't figure out if the guy just does amazing work or is just such a good photographer that it looks great. Maybe a little of both. There are online German translators you can use but most have problems with the compound words so prolific in the German language.


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## gmac

Run the site thru Google Translate and it makes even more sense.... :big: I'd been to the site before and had to find a German speaking friend to help me out, not much  though, he's not too technical. Google did well enough.

Cheers
garry


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## precisionmetal

After the part has made one full turn, the cutter could be shifted half a tooth in Z, and the gear could be indexed half a tooth... then run around one more time. Eventually if this is done enough, it begins to approach what is accomplished in a hobbing machine.


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## shred

After looking at HobbyNut's videos and that German site, I'm noodling on the idea there's an easier way to set the geometry for the 'straight-hob' of any given DP/PA combo (yes, I know it might not truly be a 'hob' per-se, but I'm calling it one for convenience)

I started thinking about it when grinding the 40-degree bit (an otherwise fairly mindless task on a T&C grinder)-- I think the need to precisely grind the tip width as Hobbynut does is to set the infeed depth and thus generate the size of the flats on the outer diameter of the hob teeth. So, why not grind a pointed tool and just infeed it into a slightly oversize blank until it's all nice sharp crests and valleys? Then measure it and go back over it with a turning tool and turn off the peaks to get the right size flats.

Since the 40 degree angle is known, the spacing of the V's is known, and the size of the desired flat is known, the actual OD change required should be easy to figure out. Time to wrestle with some geometry.


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## bob ward

shred  said:
			
		

> After looking at HobbyNut's videos and that German site, I'm noodling on the idea there's an easier way to set the geometry for the 'straight-hob' of any given DP/PA combo (yes, I know it might not truly be a 'hob' per-se, but I'm calling it one for convenience)
> 
> I started thinking about it when grinding the 40-degree bit (an otherwise fairly mindless task on a T&C grinder)-- I think the need to precisely grind the tip width as Hobbynut does is to set the infeed depth and thus generate the size of the flats on the outer diameter of the hob teeth. So, why not grind a pointed tool and just infeed it into a slightly oversize blank until it's all nice sharp crests and valleys? Then measure it and go back over it with a turning tool and turn off the peaks to get the right size flats.
> 
> Since the 40 degree angle is known, the spacing of the V's is known, and the size of the desired flat is known, the actual OD change required should be easy to figure out. Time to wrestle with some geometry.



I was thinking along these lines as I watched the videos. Another thought is to grind a sharp tool, do the sums and plunge it in the right distance to form the correct crests as you go. 

Gear cutting from scratch is one of the things I want to try, and I'm starting to think that making a straight hob (or whatever it is more correctly called) will be easier than producing a single point cutter. Which probably means I'm overlooking something. 

It was also interesting to learn that the pressure angle of a gear is more than a just an abstract concept, it actually has a physical counterpart, ie the hob for a 20° PA gear is cut with a 40° point.


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## ironman

On one of the sherline forums on Yahoo Groups is a guy named hobbynut. He has many videos on YouTube about cutting gears both ways. Under Sherline Gear cutting. He also has a program he wrote in the files section (of the forum) called Gear Code It. I have been using that program for over a year. Just put in a couple of things and it does the rest, including making the G-code to run on cnc mill. ironman


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## Richard1

I think these ideas were first documented by J A Radford of New Zealand in the 1960s and published in the Model Engineer. I have a book of his called "modifications and improvements to your lathe" or something like that and he goes into quite a bit of detail about making the hobs and form relieving them. If you could find a copy of the book or the articles it might be helpful.
Richard


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## shred

I finished up a quick 'straight-hob' the other day and tested it. Watching it cut was tedious, but the resulting gear-shaped-object would actually run against a 'real' 24DP gear, though it didn't engage all that well; I attribute this to a rather sloppily made hob. 

That got me thinking again...

Not only could you (with CNC) use a simple 40-degree double-bevel cutter (think a T-slot cutter with the teeth beveled off to a <> shape as seen from the side) to shape each gear tooth (well, tooth gap), about as perfectly as you wanted, but you could use it to emulate the multi-tooth straight hob with or without CNC--

Run it around the blank (well, rotate the blank, but you get the idea) at center height, then move it up the CP and run it around again, and move below center by the CP and run it around again. Same cuts as if you had a 3-tooth straight hob.  More cutting passes, but less work making the cutter, and a 40 degree cutter could easily be ground from HSS toolbits and used flycutter-style (which might make for a longer-lasting tool than hardened drill rod), or turned directly on the lathe without needing the intermediate 40-degree lathe tool. One flycutter would do for any gear size of a given DP, but I suspect you'd have to have the proper flat on the tip, preventing use of one flycutter for many different DPs.

A 40-degree V- engraving cutter might also work (and those are available off the shelf) applied to the top of the blank rather than one side, but it would have to spin faster than my machine is keen to. It would seem such a thing could cut helical gears on a CNC.


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## Maryak

Shred,

I've been following this with much interest as I intend to try the straight tooth hob method for the gears on my hit and miss.

Maybe I've missed something but you seem to have gone full circle and perhaps defeated the purpose of a hob as opposed to a single point flycutter.

I accept that straight sides are much easier to grind than an approximation of the involute curve; but it seems to me you end up with a series of ridges on the sides of the teeth, similar to using the hob and have introduced more potential for error moving up an down the Z axis and bringing backlash into the equation.

Just my thoughts on it. :-\

Best Regards
Bob


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## Jasonb

The gear cutting machine in this set of photos shows how using a cutter like a hob will be cutting several teeth in one go to create the involute and saves having to buy a full set for each profile, you just need to index the blank for the required number of teeth

Jason


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## John S

Not quite Jason,
That's a Sunderland gear shaper and it rolls the gear as the cutter moves down to create the true involute.
It then retracts, steps back and does the next few teeth.

John S.


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## Jasonb

Ah, missed the bit in teh middle, thinking about it now if the wheel was only indexed you would just get maybe three facets to teh involute curve.

Jason


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## bob ward

Maryak  said:
			
		

> I accept that straight sides are much easier to grind than an approximation of the involute curve; but it seems to me you end up with a series of ridges on the sides of the teeth, similar to using the hob and have introduced more potential for error moving up an down the Z axis and bringing backlash into the equation.



Thinking about it a bit more, I can see that a straight cut hob is not going to cut good gears on a manual mill. But, as I understand it, a spiral hob will do that? 

Is making a DIY spiral hob as simple as combining straight hob techniques with single point threading?


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## shred

bob ward  said:
			
		

> Thinking about it a bit more, I can see that a straight cut hob is not going to cut good gears on a manual mill. But, as I understand it, a spiral hob will do that?
> 
> Is making a DIY spiral hob as simple as combining straight hob techniques with single point threading?


Maybe... except the "thread" pitch required usually involves numbers that can't be generated with the typical lathe. I read a discussion on it over on the HSM forum a while back. Seemed like PI was involved. Perhaps a decent approximation can be created. A proper spiral hob ought to be able to make 'correct' gears of any size.

Straight-hob cut gears will be 'good enough' for many if not most ME purposes, similar but with different tradeoffs to the traditional commercial or fly-cutter gear-cutters; even with a perfect grind, it's only 'correct' for one tooth count.

With a CNC (or manual and lots and lots of patience), and one 40-degree cutter (or straight hob) you could make the approximation go as many rounds as you'd like, though I think it will always remain an approximation of some sort.


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## Lew_Merrick_PE

Two things:

1) I have a PDF copy of the Sterling Products/Stock Drive Products _Handbook of Gears_ that I am allowed to distribute (SP/SDP charges you for the paper version -- but even that is cheap). I have not uploaded anything here yet, but it should not be that hard to do (I built my first microcomputer in 1967).

2) I am in the process of redoing my spurgear marcos for _General CADD_ (http://www.GeneralCADD.com -- plug, plug for some friends of mine) to comply with the recent changes in ISO gearing. Part of this, still "in-work." is a document explaining the macro in particular and spur gearing in general. The big thing is that I use a 2-arc approximation of an involute. [AGMA recommends using a 3-arc approximation.] The 2-arc system is reasonable for most hobbyist applications and fairly easy to grind a cutter for using Bob Porter's custom toolbit grinding set-up.

The SP/SDP _Handbook of Gears_ gives you most all of the information in the ($90) _AGMA Handbook_.


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## jodhner

Get obsessed, or get a machinist.


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## tornitore45

bob ward and shred

A real helical hob can not be used on a simple mill.
The gear must be positively driven around as the hob is carving.
The hob is acting as a endless screw but is not supposed to self drive the gear.
Some folks say that after gashing the blank is possible to let the hob drive the blank along but is a recipe for overcutting the spaces.
As stated in the thread, the first round of cuts gives you a segmented (faceted) tooth but if you re-index 1/2 a tooth or as many time as your patient allows you end up with a practical involute.
Plus as shred said the real (helical) hob has a pitch that can only be approximated since is not an integral TPI.


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## jodhner

I make small brass gears (1/8" to 2") for mechanical instruments and models. The gears need to be what they need to be, so I design them from scratch, choosing the center to center distance and tooth ratio that suits the application. I pick the pressure angle mostly for looks, and I try to use the involute tooth profile because it is easy to form. I don't have to worry about strength or power or many of the other things that real machinists do. I also don't have to worry about economics. I try to make the gears operate as smoothly as possible, with as little backlash and binding as possible. I am able to make low tooth count gears that run without any noticeable cogginess.

The method I have been using could be called "CNC single point fly cutter rack generation". It's nothing new, but I don't see much about it on the Web. It is suited to my needs. I can cut just about every gear I need with one V-shaped fly cutter bit. The bit is cheap (< $2) and easy to sharpen (< 1 minute). I do all of my work on a sewing machine, er, I mean a Sherline Mill (I always get those machines mixed up).

--Justin


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## Lew_Merrick_PE

Burr-cutters and sand-crabs,

I have finally uploaded the Sterling Instrument/Stock Drive Products _Handbook of Gears_. It turns out if the file extension is "PDF" (as in all capital letters) the file system here rejects it. The extension has to be "pdf" to be valid. As *I* date to the days when *all* filenames were *all* capital letters, it threw me for a loop.

But then, I believe in the square root of -1, so I already *know* I am an irrational number!


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## shred

Lew_Merrick_PE  said:
			
		

> Burr-cutters and sand-crabs,
> 
> I have finally uploaded the Sterling Instrument/Stock Drive Products _Handbook of Gears_. It turns out if the file extension is "PDF" (as in all capital letters) the file system here rejects it. The extension has to be "pdf" to be valid. As *I* date to the days when *all* filenames were *all* capital letters, it threw me for a loop.
> 
> But then, I believe in the square root of -1, so I already *know* I am an irrational number!


Cool, thanks. Lots of good info there.

I note the 'straight-hob' method is pretty much an approximation of rack-generation, less so proper hobbing.


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## bob ward

bob ward  said:
			
		

> Is making a DIY spiral hob as simple as combining straight hob techniques with single point threading?





			
				shred  said:
			
		

> Maybe... except the "thread" pitch required usually involves numbers that can't be generated with the typical lathe. I read a discussion on it over on the HSM forum a while back. Seemed like PI was involved. Perhaps a decent approximation can be created. A proper spiral hob ought to be able to make 'correct' gears of any size.



This is the thread cutting table on my generic 14 x 40 lathe. I've used the top half of the table but have not yet learned about the bottom half. Does having the Module and DP settings get me any closer to cutting an accurate spiral hob?


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## djc

bob ward  said:
			
		

> Does having the Module and DP settings get me any closer to cutting an accurate spiral hob?



Yes. The pitch of the hob is the circular pitch of the gear (see http://www.homemodelenginemachinist.com/index.php?topic=7990.0 another thread running alongside this one).

Hence, for a 1 MOD gear, your hob needs to be 3.14mm pitch; for a 1DP (big!) gear it needs to be 3.142 inches pitch (or the inverse of this in tpi). Multiply the metric pitch by your actual MOD to find the corresponding hob pitch. Divide the imperial pitch by your actual DP to find corresponding hob pitch.


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## black85vette

Been following this with interest. Thanks for all the good info.  :bow:


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## black85vette

Went out to the shop to play tonight. Used some HSS 1/4" stock to make a 40 degree cutter. Grabbed a piece of 1/2" delrin rod. Went through the process of cutting the groves and then milling the flats on the mill and made what looks like a hob.  woohoo1

Wanted to kind of get a feel for the process before doing it for real. Still a little foggy on some of the math. 

Appreciate all the posts and links. Watched all of Shorty's videos. Downloaded the booklet from our area. Got Marv's program (thanks for another one Marv!!). Read all of Dean's post (several times). Dang, if I hang out here long enough I might even learn something. Don't feel totally clueless now. 

Now I need to locate some drill rod.

I do have one question; how do you calculate the width of the flat spot on the end of the gear tooth? I kind of get the spacing and depth part but don't recall seeing this anywhere.


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## Maryak

black85vette  said:
			
		

> I do have one question; how do you calculate the width of the flat spot on the end of the gear tooth? I kind of get the spacing and depth part but don't recall seeing this anywhere.



B85V,

The tool width can be calculated as follows:

Tool Width at Tip = Circular Pitch/2 - (Tan Pressure Angle x Dedendum x 2)

Difficult to measure accurately. The tool infeed must equal the whole depth and not the working depth of the rack when making the hob. If it's a little wider it will increase the backlash and if it's a little narrower binding may occur.

Hope this helps

Best Regards
Bob


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## black85vette

Maryak  said:
			
		

> The tool width can be calculated as follows:
> 
> Tool Width at Tip = Circular Pitch/2 - (Tan Pressure Angle x Dedendum x 2)
> 
> Difficult to measure accurately. The tool infeed must equal the whole depth and not the working depth of the rack when making the hob. If it's a little wider it will increase the backlash and if it's a little narrower binding may occur.



Bob;

Thanks. This is just what I was looking for.  

Just to be sure I am understanding; when making the hob, the flat on the end of the hob tips and the tool tip should be the same if you have made the cut to the right depth and your tool is cut correctly. Is that right?


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## Maryak

black85vette  said:
			
		

> Bob;
> 
> Thanks. This is just what I was looking for.
> 
> Just to be sure I am understanding; when making the hob, the flat on the end of the hob tips and the tool tip should be the same if you have made the cut to the right depth and your tool is cut correctly. Is that right?



B85V,

I think that is correct because the hob is the reverse of the gap between the gear teeth, so when it cuts the gear blank to full depth the OD/tip of the hob should equal the width at the root diameter of the gear, (the result of the formula I gave you).

Thanks for your help in this, so far your doing all the work and we are learning this together.

Best Regards
Bob


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## black85vette

Bob; Thanks again. I think it is you guys doing the real work with understanding the theory, figuring out the math and finding all the links. I'm just the lathe monkey cranking out some pieces.  :big:

Odd day today. We are in a climate zone that produces tornados. But we also sit between the really cold weather and the warmer weather to the South. So it snows to our North, rains to our South and we get a drizzle that freezed after it falls. It coats the trees, cars, power lines and roads. So our office shut down and sent everyone home to be safe. Not a bad deal, a day in the shop mid-week!

So I ran to the metal supplier and picked up some .5" drill road. Made another 40 degree cutter out of some better material and made a 32 pitch straight hob. Rather than heat treat it I just turned some Delrin and mounted it in the rotary table and made a couple of quick gears. The teeth appear to be a little thin.  I think I did not get my depth quite right on the hob.

Anyway, I did make a couple 24 tooth plastic gears that look like they would probably function OK. Not too bad considering two days ago I had no idea how to go about this. It does confirm for me that the method is feasible, not very difficult, and pretty cheap.

As usual, I did come up with another question.  This is my first time to use drill rod. Turning it was not too bad. Just a little chatter doing a plunge cut.  But then I tried to cut the right angle cuts for the hob teeth and dulled two end mills pretty quickly.  Is there something I need to know about working with drill rod?


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## black85vette

putputman  said:
			
		

> I thought the cutting tooth would be on center instead of straddling center. When I cut gears with an involute cutter, I always put the center of the cutter on the center of the gear. I wonder if the profile that he illustrated would look just a little differant if he put his cutter tooth on center of the gear.



It does appear to make a difference. I tried it both ways and putting a cutting tooth on center did not produce a good profile for me.  

On another note: On Shorty's website someone asked him why he did not cut the 40 degree notches in the hob on an angle with the compound like cutting a thread. I wondered about that and tried it tonight and had much less chatter and a smoother cut. So I guess I will do it that way from now on. Just have to do a little math to refigure the depth.


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## Maryak

black85vette  said:
			
		

> On another note: On Shorty's website someone asked him why he did not cut the 40 degree notches in the hob on an angle with the compound like cutting a thread. I wondered about that and tried it tonight and had much less chatter and a smoother cut. So I guess I will do it that way from now on. Just have to do a little math to refigure the depth.



B85V,

If you cut the teeth at an angle you will have to tilt the hob or the gear blank to the same angle, so that the cutter and the blank are at right angles, to get a spur gear out of it. Blogwitch is working on a system to use a spiral hob so it may pay you to ask him the ins and outs of it.

Best Regards
Bob


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## black85vette

Maryak  said:
			
		

> If you cut the teeth at an angle you will have to tilt the hob or the gear blank to the same angle, so that the cutter and the blank are at right angles, to get a spur gear out of it. Blogwitch is working on a system to use a spiral hob so it may pay you to ask him the ins and outs of it.



Bob;

I didn't explain it well. The end result of the cut stays the same. Rather than plunge straight in I tried advancing the cutter at 20 degrees with the compound while held perpendicular to the work and the carriage not moving. Just like single point threading, the cutter is only cutting on one edge instead of two. At least that's my theory.

Regards,
Rick


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## Maryak

Rick,

AH HA or Abracadabra ;D

All is revealed and understood. :bow:

Best Regards
Bob


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## black85vette

Maryak  said:
			
		

> AH HA or Abracadabra ;D
> 
> All is revealed and understood. :bow:
> 
> Best Regards
> Bob



Bob, I just attribute it to the difference in our versions of English.  :big:


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## black85vette

I have been out in the shop cutting some more "practice" hobs out of aluminum and think I have all my dimensions where I want them for a 32 pitch hob. Drew up 5 and 6 tooth .5" diameter profiles in CAD.  I think the 6 tooth will not leave enough on each tooth. The flat spot on top ends up about .015" the 5 tooth is about .060"

Got "Gears and Gear Cutting" by Ivan Law in today. Looks like lots of good info for not too much money.

Here are the profiles for the cutters.


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## black85vette

Here is some info for standard pitches I hope you find useful. When making a straight hob you first need to make a 40 degree cutter.  The cutter is a mirror image of the tooth you want on the cutter so it is designed to have a flat tip and you measure your depth of cut from that flat.  It is somewhat difficult to measure that flat so I did some quick math to find out how much length was being removed. The Width Column is how wide the tip needs to be. The Length Column shows how much length to remove from the 40 degree cutter to get the tip you want.

Alternately, if you know the length of the tip you need to remove you can just increase the depth of your cut by that much.  So the Depth Column shows the standard depth of cut and the W/tip Column shows how deep to cut if your cutter is ground to a point and the tip still in place.

Finally, the 20 Degree Column adds a factor for making your cut using your compound set at 20 degrees just as you would do a 29 degree angle for a 60 degree thread cutting tool.  So using a factor of 1.06 for a 20 degree angle use this column so you can read the dial on your compound to get the correct depth.

I have only verified the 32 pitch by making actual cuts and checking the results.



		Code:
	

Pitch  Width  Length Depth  W/tip  20 degrees
48   0.015  0.0221 0.0449 0.067  0.07102
32   0.023  0.0336 0.0674 0.101  0.10706
24   0.03  0.0439 0.0899 0.1338 0.141828
20   0.036  0.0526 0.1079 0.1605 0.17013
18   0.04  0.0585 0.1198 0.1783 0.188998
16   0.046  0.0672 0.1348 0.202  0.21412
12   0.061  0.0892 0.1798 0.269  0.28514


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## Cedge

tornitore45  said:
			
		

> A real helical hob can not be used on a simple mill.
> The gear must be positively driven around as the hob is carving.



Oddly enough, I just finished watching the DVD of Jose Rodriguez do exactly that. He managed it quite easily, while noting that you have to take care on the first round of cutting to allow the hob to seat properly. From there on, the hob cut and drove the emerging worm wheel throughout the process. End product was impressive and appeared to be quite adequate for the average home shop project.

Steve


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## black85vette

Had to wait for a new end mill to make a new gear cutter. Attached is a picture of the results. The gears are 32 pitch 24 tooth gears. They match up fine with a commercially made 32 pitch gear and the tooth profiles are almost exact.  I did end up with a new question about a calculation. I understand the total depth of the tooth, but when you make the cutter it does not cut straight in from the tip because you center a gap in the cutter with the center of the gear blank.  I made a bunch of trial and error cuts until I found a depth that worked and produced a good profile.  I found that if I moved the cutter into the gear blank by .087" it produced a good profile. The gear depth for a 32 pitch is .067". So I am wondering how to calculate how far the cutter should should advance into the blank.


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## Lew_Merrick_PE

black85vette  said:
			
		

> I did end up with a new question about a calculation. I understand the total depth of the tooth, but when you make the cutter it does not cut straight in from the tip because you center a gap in the cutter with the center of the gear blank. I made a bunch of trial and error cuts until I found a depth that worked and produced a good profile. I found that if I moved the cutter into the gear blank by .087" it produced a good profile. The gear depth for a 32 pitch is .067". So I am wondering how to calculate how far the cutter should should advance into the blank.



The OD of your gear blank will be (N+2)/DP (32 in your case). The total depth of the gear tooth (most often 2.25/DP) will be the same wherever you start plunging. The total depth goes from the OD to the Clearance Diameter -- assuming that you have ground your cutter properly. Back in the dark ages, I used to make 4-bar mechanisms for a local gear company to guide grinding of single-point cutters. I believe that Robert Porter published the ratios and sizes for such mechanisms in a booklet form a few years back (Lindsay Publications carried it the last time I was aware of it). Some of the HP calculator books (HP-67 and HP-41, if memory serves me) had exercises for their 4-bar mechanism generator program to do the same. I have found several of the old HP calculator programming books on-line as PDF.

Does this help?


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## shred

Cedge  said:
			
		

> Oddly enough, I just finished watching the DVD of Jose Rodriguez do exactly that. He managed it quite easily, while noting that you have to take care on the first round of cutting to allow the hob to seat properly. From there on, the hob cut and drove the emerging worm wheel throughout the process. End product was impressive and appeared to be quite adequate for the average home shop project.
> 
> Steve


Hobs and worms are fairly easy. Hobs and gears (where the hob drives the gear as it cuts) are quite a bit harder-- creating the hob is much more difficult. This one took me quite a while to sort out.


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## black85vette

Lew_Merrick_PE  said:
			
		

> assuming that you have ground your cutter properly.



Well that would be an assumption. I was pretty careful in all my cuts.  I made each cut at .067" depth per Marv and Shorty's calculators for whole depth. Then moved the carriage over by the Circular Pitch which is .0982". The resulting flat on the peaks was difficult to measure but seemed to be close to the .023" called for.  So I "think" the cutter is correct, but then again have nothing to compare it to.


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## precisionmetal

black85vette,

Here are some numbers for you that might come in handy: span measurement over 3 and 4 teeth on a 24 tooth, 32 DP 20° gear cut to standard dimensions (circular tooth thickness of .0491").  If you'd like the DXF of this, I'd be happy to make it available.


Lew,

If I'm not mistaken, on anything finer than 20DP, a whole depth of (2.2/DP + .002") is the modern accepted number. It just so happens to work out nearly identical in this example.


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## black85vette

Went back and had a closer look at the cutter and thought about the geometry of the cut.  I believe I understand this better now.  The teeth on the cutter were a little too long requiring a deeper cut to get the too profile right, but making the cut too deep. Also this left the tip a little too narrow making the space at the bottom of the gear teeth too narrow.  I ground a little off the tips and things started to come together. The tip is wider and the resulting space at the base of the gear teeth looks better and I was able to make a good profile with a total depth of .071 which is where the calculations say it should be. 

Thanks Lew and Precisionmetal for the formulas and for questioning the assumption about the cutter.

Lew; had to go Google 4-bar linkage to find out what the heck you were talking about!


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## Lew_Merrick_PE

precisionmetal  said:
			
		

> If I'm not mistaken, on anything finer than 20DP, a whole depth of (2.2/DP + .002") is the modern accepted number. It just so happens to work out nearly identical in this example.



The standards for spurgearing went through a revision in 1999. I know because I was just "caught" on that on a job I did for the Navy and had to rewrite all my CAD-based gear generation routines. The whole tooth depth is 2.25/DP since then (except for stub gears). Most of the changes are changes in terminology (and I spent *hours* digging through them!) rather than physical changes. It was such a mess that I even broke down and spent the $90 for the current Gear Association handbook.


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## precisionmetal

Lew,

Thanks for the update on that.


Blackvette,

If you have some .060" measuring wires (or gage pins), you should be seeing .8452" over wires at (std. tooth thickness).

Or... if you don't have a pair of .060" wires, you can take a measurement over any pair (e.g. a .059" pin and a .060" pin if you're using out of a pin gage set) I can give you the tooth thickness of your gear which will tell you if you are at the correct depth with your cutter.

PM


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## black85vette

Found some good info over at Standard Drive Products web site. They have a reference library on line with lots of gear, pulley and belt info. Plenty of formulas, standards and information.

http://sdp-si.com/web/html/reference_library.htm


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## Lew_Merrick_PE

black85vette  said:
			
		

> Found some good info over at Standard Drive Products web site. They have a reference library on line with lots of gear, pulley and belt info. Plenty of formulas, standards and information.
> 
> http://sdp-si.com/web/html/reference_library.htm


Black85Vette -- I uploaded (with permission) the SDP/SI _Handbook of Gears_ to the library here. It gives you the most complete set of gear information you can get without shelling out $90 to the AGMA.


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## Clockmaker94

Hello excuse me for disturbing you in the group.

I changed watchmaker in Austria I now operational on CNC and would need a page where I can find Gercodit to download.

I hope I came to you right specialists. 

Best greetings from Austria.
wishes Masterwatchmaker

Sebastian D.


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## Jasonb

You have made a slight error in the spelling

Gearcodit should be easy to find with Google

http://gearcodit.software.informer.com/


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## Mainer

It seems to me that the "straight hob" method may at times be more accurate than using an involute gear cutter, which is strictly correct only for one tooth count. Except for the ridges, the tooth form produced by a straight hob should be exact for any tooth count it cuts.

It may help to visualize the straight hob as a section of rack, and it's being used to produce a mating gear.


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## Hopefuldave

This is an interesting thread, particularly as I need to make a few gears...

It.occurs to me (but may be a stupid idea) that if the gear blank could be progressively indexed as it moved relative to the cutter (and the rack cutter were long enough), a correct involute would be cut. Easy on a CNC mill, if you have one, but harder on a manual lathe...

I thought that the blank could be coupled to a pulley of the pitch diameter with a tensioned wire? attached to the tailstock, as the carriage advanced the blank would rotate in time with its movement along the hob making the progressive cuts to form the involute. It may be a stupid idea, though...


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## Flopearedmule

hey guys,
Is there a place you can purchase these hobbs? or will I have to make my own? This looks like the easiest way to make gears that I have seen, but I can't find anywhere that makes the hobb, so I don't have to worry about making it myself.
Thanks


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## pgp001

Hi Guys
I think you are talking about Sunderland cutters when you mention straight hobs.
My late father rigged up the Alexander Master Toolmaker milling machine to cut gears by that method. I still have the machine but not used it for cutting gears recently as I also have a conventional Mikron hobbing machine.





















Hope these are of interest. I have a procedure written by my dad for indexing and rolling the blank round for different tooth counts, he cut a full set of change gears for the Myford lathe going up in increments of one tooth, the stack of change gears is about  two feet tall.














Phil


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## cidrontmg

black85vette said:


> Found some good info over at Standard Drive Products web site. They have a reference library on line with lots of gear, pulley and belt info. Plenty of formulas, standards and information.
> 
> http://sdp-si.com/web/html/reference_library.htm


There's also an excellent treatise for "ESCAP® Ironless Rotor D.C. Micromotors
  and Step Motors". They're wonderful motors, small, powerful, Swiss made - and expensive  .


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## Cogsy

dmh13433 said:


> hey guys,
> Is there a place you can purchase these hobbs? or will I have to make my own? This looks like the easiest way to make gears that I have seen, but I can't find anywhere that makes the hobb, so I don't have to worry about making it myself.
> Thanks


 
I haven't seen them for sale anywhere (and I suspect they're not sold) but this link has all the info on making them and using them, they're really not that hard to make. I've made several gear sets this way that work perfectly on my latest builds. Good luck.


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