Making replacement gear

[JeffB]

Without knowing the pressure angle and the pitch circle diameter, I'm afraid one is still guessing.  The pressure angle is what determines to tooth tangent to pitch resulting in tooth curvature; OD and number of teeth is simply not enough to know the true mesh.  As the pressure angle decreases the contact face of the tooth becomes more pitched.

Also one cannot measure the diameter of an ODD number of teeth.  Liken it this way, if you measure a three legged stool, you will measure from the tangent of one leg to a line between two tangents of the other two legs, I.e, a flat spot, which will skew the measurement.

Not saying you can't come close, but you really are just guessing, and there really is no way to determine if the mesh is English or Metric without an optical comparator, or measuring across pins of a very specific diameter.

Yes, I used to design Ford Tractor (now New Holland) transmissions many moons ago.

See the image below to truly understand all the the dimensions that are necessary to 3D model a properly meshed (teeth actually touching at the pitch circle) spur gear.

You're not wrong, but it doesn't require that much precision.  A fairly close measurement of the OD is enough, plus the number of teeth plus 2 is all you need.  We're talking about models here, not precision transmissions, gearheads or the like, with high loads and long lifespans.

The only time you run into trouble if the gear is some mongrel pitch (DP or Mod), or a non-standard tooth profile or just plain manufactured poorly.  Which is entirely possible.

Some might also argue that helical gears (RH and LH, sometimes called "worm and reverse worm" gears) require a complex calculation...  Maybe it does, but I've built many gearboxes using both and the simple calculation for gear spacing, plus a little clearance has always worked without issue. 

Jeff

[Lemosteam]

You're not wrong, but it doesn't require that much precision.  A fairly close measurement of the OD is enough, plus the number of teeth plus 2 is all you need.  We're talking about models here, not precision transmissions, gearheads or the like, with high loads and long lifespans.

The only time you run into trouble if the gear is some mongrel pitch (DP or Mod), or a non-standard tooth profile or just plain manufactured poorly.  Which is entirely possible.

Some might also argue that helical gears (RH and LH, sometimes called "worm and reverse worm" gears) require a complex calculation...  Maybe it does, but I've built many gearboxes using both and the simple calculation for gear spacing, plus a little clearance has always worked without issue. 

Jeff

In reality a helical gear is not much more than a spur gear with a twist on is axis for its width, and a lot more difficult to machine.  Not so sure I agree with you on the accuracy here in N.  Lash (tooth mesh gap) is a huge contributor to perceived locomotive noise, as well as slow speed performance, not to mention any clearance from the center of the hole to the pin its riding on.  Everything is negatively impacted in N scale when variation and clearances are loose. 

My main point was this- if you cannot reasonably accurately determine what gear you have in your hands, it just makes it more difficult to find a replacement that is not form a second, same model.

[woodone]

To answer a few questions—
Pete- I think we were talking about how to figure the gear ratio of a planatary gear set up. Lots of info but I do not recall tooth design.
I have sleep since then and did not go back and read that post again-
I learned about making gears 60 years ago at an industrial art school, and I do not think the math has changed.
I can get the OD by making a go-no-go gauge so getting the correct OD does no present a problem.
The gear I need made has been removed from the gear case. There are two of the same gear used in the drive and only one is destroyed.
I can measure six ways from Sunday of said gear. Except the root diameter. I guess that I could use the wire method and a micrometer
but handling such a small gear with wires takes more hands than I have.
SkipGear you stated you had made some gears, would you care to take a stab at doing one of these for me?
I can furnish all the data you said you needed.
Thanks for all the feed back.

[peteski]

Well then Jerry, sounds like you knew exactly what you've talking about all along. Good luck with the replacement gear.

[turbowhiz]

I'd look into the several openscad files available for generating gears if I was trying to come up with a 3d gear model for printing.

Put in the parameters for your gear, and it generates your model.

Openscad I have used with good success. Its a totally programmatic way of designing 3d models, and for certain applications, its really super powerful. Obviously good if you have programming experience.

Gears seem like sort of design application it would do well with. You shouldn't need any programming experience just to take an existing gear generating program and run it for your purpose, assuming that it satisfies your requirement out of the box.

Again, not attempted using this for generating gears on N scale models, but I'd start there...

[SkipGear]

To answer a few questions—
Pete- I think we were talking about how to figure the gear ratio of a planatary gear set up. Lots of info but I do not recall tooth design.
I have sleep since then and did not go back and read that post again-
I learned about making gears 60 years ago at an industrial art school, and I do not think the math has changed.
I can get the OD by making a go-no-go gauge so getting the correct OD does no present a problem.
The gear I need made has been removed from the gear case. There are two of the same gear used in the drive and only one is destroyed.
I can measure six ways from Sunday of said gear. Except the root diameter. I guess that I could use the wire method and a micrometer
but handling such a small gear with wires takes more hands than I have.
SkipGear you stated you had made some gears, would you care to take a stab at doing one of these for me?
I can furnish all the data you said you needed.
Thanks for all the feed back.

message me with a couple good pictures of the gear that is still in tact, measurement of overall diameter and the diameter of the compound smaller gear, overall thickness, and the thickness of each gear in case there is a bushing/standoff built in, and finally the bore. I can see what I can come up with.

[woodone]

SkipGear—- sent you a PM

[railnerd]

-Dave

[sd80mac]

This is a good resource for generating gear profiles:

https://geargenerator.com/

Also, Inkscape has a gear generating extension.  Go to Extension>Render>Gear>Gear...

Donnell

[narrowminded]

That gear generator is an outstanding tool to visually demonstrate to anybody, technically astute or not, the things I've described any of a number of times in some of my posts on the subject.  It's also why I had decided early in the effort that for the tiny loco chassis' I wanted to make, a key would be to have the ability to live hob the gears myself.  That capability affords some luxuries not available when trying to buy small quantities of really miniature gears from reliable sources and in the custom sizes desired.

The model shows a fairly standard 20 degree pressure angle (PA) gear.  If you play with the model and settings you can see the whole point of the involute shape.  You can stop the motion and if you change the number of teeth you can watch that involute shape change to accommodate the changing profile needed to mesh properly.  That will also demonstrate why the gear cutter profile used with an indexing head to generate a single tooth at a time is so critical and why each tooth count change requires a new cutter with a different profile.  What you find when ordering that style of cutter is that one cutter will be used for several tooth counts, rounding the numbers to close enough but the fact is, one will be right and the next few, +/-, will be less than perfect.  That means noise, too.

The next thing you'll recognize is why most gear manufacturers don't make a gear with fewer than 12 or 14 teeth.  As the number of teeth are reduced the undercut required for mesh clearance at the tooth base weakens the tooth beyond reasonable.  Make rather large changes and watch what happens.  In our applications the loads are low enough to accept the undercut of a ten or maybe even eight tooth gear as adequately strong but that, as well as tolerances in general, dictates that the gears remain relatively large for the service.  I needed really small components so that wasn't an option if I was ever to accomplish my desires.

And one more really important detail is what a change in the pressure angle makes and how it can be useful.  The more that you increase the pressure angle the less undercut you get at the tooth base.  This allows some reasonable tooth profiles if you really must make small gears.  Select the eight tooth pinion gear and change the pitch angle setting to 14 degrees, observe the tooth profile, and then to 30 degrees and observe the change in the tooth profile.   This demonstrates beautifully what happens to the tooth base as the pressure angle changes. 

And this is why the only hob I've made to this point is a 30 degree for small gears.  And as a result, all of my gears to this point are 30 degree pressure angle which requires the mating gear to be 30 degree as well.  But with the more optimum tooth profile I can get the tooth strength needed in a smaller diametral pitch (mod) gear, even for high tooth count gears that don't have the bad undercut problem.  This means I can make all of my gears physically smaller or get a bigger gear reduction in the same envelope dimensions as a larger DP (mod) gear. 

And finally, this begs the question, why aren't the PA standards higher than 14.5 degree and 20 degree PA?  Tolerances!  The tolerances are tighter on the tooth profiles and shaft centerlines but if you can hold them (you must) then there's little reason not to.  Further, the single tooth hobs used when cutting one tooth at a time with an indexer will not be useable on different numbers of teeth.  Live hobbing uses one cutter for as many teeth as you want to make... except worm gears that envelope the worm.  In that case, the hob must be the size of the worm.  Think about it.

More than any modeller needs to know but there it is.   All of the theory understood!

[Chris333]

So do you have an index plate to rotate on each slice or do you have a rotary table dial and just count out the degrees?

[Lemosteam]

Great commentary @narrowminded .

Alas hobs to make gears aren't always used, particularly on very small gears.  Extrusion dies are very inexpensive, accurate and the process is simple.  You can bet your bottom dollar that all of the small metal gears made for models are cutoff extrusions.  This makes the parts very inexpensive to manufacture and why places like NWSL can (could?) offer specialty gears so cheaply.

[JeffB]

Great commentary @narrowminded .

Alas hobs to make gears aren't always used, particularly on very small gears.  Extrusion dies are very inexpensive, accurate and the process is simple.  You can bet your bottom dollar that all of the small metal gears made for models are cutoff extrusions.  This makes the parts very inexpensive to manufacture and why places like NWSL can (could?) offer specialty gears so cheaply.

All of NWSL's gears are machined/hobbed.  The worms/worm stock is pressure rolled from 12L12 or 12L14 steel stock.  I know this for a fact because I've purchased several thousand dollars worth of their gear stock and had spoken at length about gears/gearing with the first owner of NWSL (Raoul "Fred" Martin).

Good info narrowminded.  Undercut is definitely a problem with gears smaller than 12-15tooth.  Some manufacturers (like NWSL) will alter the OD/PD a bit (make it larger) to compensate, as well as using a special hob (or at least that's what Fred Martin of NWSL had told me).  Tooth strength is a consideration in larger applications, where there's higher loads involved.  But for our model trains, it's not really an issue so long as you select the appropriate gear pitch for the scale you're building in. 

Wear is more of a problem than anything, more specifically, wear of the worm/worm gear, where friction is highest (in gearboxes we use at least).  If you look at the majority of the NWSL gearboxes, the worm is polished steel and the worm gears are Delrin/Nylon.  This is to minimize friction/wear.  It's not the only option, lubricated Delrin/Nylon worm/worm gears are fine too. 

"Precision" is a relative term...  I don't know how precise most commercial gears (for model train applications) really are.  I would assume that the steel gears in Faulhaber or Maxon gearheads have a very high degree of precision due to what they're used for (in industry).  Gears in our locomotives...  Probably not as "precise" as you might think, but I don't know that for sure.  I've seen some decent running locomotives that have lower quality gearing.  They may not last long, but so long as they gear train and rest of the mechanism is smooth running, and the motor is of decent quality, they'll run OK. 

Jeff

[Lemosteam]

All of NWSL's gears are machined/hobbed.  The worms/worm stock is pressure rolled from 12L12 or 12L14 steel stock.  I know this for a fact because I've purchased several thousand dollars worth of their gear stock and had spoken at length about gears/gearing with the first owner of NWSL (Raoul "Fred" Martin).

Good info narrowminded.  Undercut is definitely a problem with gears smaller than 12-15tooth.  Some manufacturers (like NWSL) will alter the OD/PD a bit (make it larger) to compensate, as well as using a special hob (or at least that's what Fred Martin of NWSL had told me).  Tooth strength is a consideration in larger applications, where there's higher loads involved.  But for our model trains, it's not really an issue so long as you select the appropriate gear pitch for the scale you're building in. 

Wear is more of a problem than anything, more specifically, wear of the worm/worm gear, where friction is highest (in gearboxes we use at least).  If you look at the majority of the NWSL gearboxes, the worm is polished steel and the worm gears are Delrin/Nylon.  This is to minimize friction/wear.  It's not the only option, lubricated Delrin/Nylon worm/worm gears are fine too. 

"Precision" is a relative term...  I don't know how precise most commercial gears (for model train applications) really are.  I would assume that the steel gears in Faulhaber or Maxon gearheads have a very high degree of precision due to what they're used for (in industry).  Gears in our locomotives...  Probably not as "precise" as you might think, but I don't know that for sure.  I've seen some decent running locomotives that have lower quality gearing.  They may not last long, but so long as they gear train and rest of the mechanism is smooth running, and the motor is of decent quality, they'll run OK. 

Jeff

Good to know then.

[DMetz]

There has been a lot of good information about gears in this thread.  I have worked with miniature, precision instrument gears for many years.  And also larger power transmission gears.  I have worked on the design and manufacturing of gears, and also teaching classes on gears.  All of the info in this thread so far is very accurate.  But gear design can go much, much deeper than this.  I will add a little to the conversation, but the info on gears goes much farther than even this.

The pressure angle for most modern gears is 20 degrees, with a lot of older designs being 14.5 degrees, and more newer designs at 22.5, 25 and even 30 degrees.  There is no right answer for which is better, all have tradeoffs, with tooth strength and surface sliding friction being the two main concerns.  A good gear design will consider a lot of info, and choose from many options for the gear.  The choices includes the tooth count, tooth shape, helical or straight, manufacturing method, and gear material.  (And dozens of additional options)

When a gear rotates in mesh with another gear, the interaction between the teeth is both rolling and sliding.  At the line of centers, the interaction is only rolling, so the friction is practically zero.  As the point or line of contact between the teeth moves away from this line, the sliding motion increases.  The friction from the sliding motion leads to wear on the tooth face.  A proper gear design would choose appropriate gear pressure angle, gear material, lubrication, and rotation speed to minimize or resist the sliding wear.  A 14.5 pressure angle gear will have the lowest sliding friction, and a higher pressure angle will increase the sliding concerns. 

But sliding wear in not the only concern.  Tooth strength is very important in higher performance gear designs.  A wider pressure angle changes the tooth shape to make the base of the tooth wider, and more resistant to breaking.  A 25 degree pressure angle gear tooth has a wider base than a 14.5 P.A. gear.  So the 25 P.A. gear is much more resistant to fatigue, and breaking off.  If you look at the end of a tooth, it looks a little like a pyramid.  A larger pressure angle for the gear tooth with make the base of the pyramid shape wider.  A wider base is much more resistant to tipping over, or in this case, breaking off.

So the different pressure angles of gears are chosen mainly as a trade off between sliding friction and tooth strength.  There are other concerns, such as smooth transmission speed, manufacturing methods, undercut, etc.  It is very true that lower tooth counts can have severe undercutting of the tooth.  In my company, we usually use the "increase the gear size" method to partially control this.  Basically the smaller gear is made with the same tools, but just oversize by a specific amount.  The mating larger gear is made smaller by the same amount to compensate.  In some cases, either or both gears can be made oversize or undersize to achieve a different center distance for the gear pair.  There are limits to how much the size can be changed, and there are also tradeoffs for negative affects.  One of the biggest concerns is this can increase the sliding friction, and gear wear.

The video above is excellent to show a single tooth manufacturing method.  I am also too familiar with multi-tooth hobbing machines.  In this case, both the part and cutter rotate in time with each other, and all of the gear teeth are made with the same tool pass.  These hobs have cutting teeth with straight sides, and automatically produce the proper involute gear shape, regardless of tooth count.  But the lower tooth count gears can have severe undercut.  The single tooth type hobs shown in the video is also an excellent way to reduce the undercut for smaller gears.  But the trade off is slower manufacturing times, and it can introduce position errors in the gear teeth.  And you need a different tool for each group of tooth counts.

Dan M