wild and crazy gear teeth 2

Tried it, works.

for that application it will work, but it's not a typical to have a full radii at the tips.
what was the rational ?
a standard design would work ,
what was the contact ratio?

I was wondering how hard it would be to cut teeth like that. Is it possible with standard tooling? I suppose the rounded lands could be ground in after cutting an otherwise normal gear, if the cutting allowed for any slight changes in dimensions.

I know my post was too long. I want these rounded lands to allow better meshing in a special application.

If the gear is completely normal except for the rounded lands, as I intend, the contact ratio would not change. The rounded lands must never contact the tooth surfaces. The do not transmit any power.

So aside from wondering whether the gear could be cut that way without a lot of bother, I had to find out whether the rounded lands would ever interfere as the gears rotate. As far as I can see, they wouldn't.

When I say I tried it, I mean that I examined it on AutoCad where it looks OK. I don't have the expertise to set it up on a program that would animate the situation, or any access to such a program.

Then I modified a few teeth on each of two gears to approximate the rounded lands. In my special arrangement, they mesh much better with the modified teeth than they do with the standard lands. As I explained above, a standard gear set does not mesh well in this application.

So, if these gear teeth can be cut without too much trouble, I think they will work for me. That is my main question. Can these gears be cut without requiring some kind of NASA 27-axis robo-rooter that would scare the horses?

Just would like to point out that in conventional auto manual gearbox the gears are in constant mesh and don't slide to mesh.
If you only need a few gears, get them wire cut (if they are not helical).


Politicians like to panic, they need activity. It is their substitute for achievement.

I think such gears could be cut with a standard hobbing machine using a special hob. The basic rack of the cutter would look possibly a bit surprisingly, having a trochoid section which would start even in the middle section of tooth height. The shape and size of the trochoid section would depend on the number of teeth in the gear and the size of the round section.
The making of special hobs would present a challenge with manual machines being ruled out and the CNC machines possibly requiring software updates.

Pud, I didn't know about that one. Wikipedia says the automated manual gearbox by Renault does not have a torque converter like a typical automatic transmission does. That seems to be the main difference between the two. Aside, I suppose, from planetary gears in the typical AT and external gears in the AMT.

Now I am wondering what good the typical automatic transmission is, if this Renault tranny and similar units work OK. They are manual transmissions, but with automated clutches instead of a foot clutch. Without a torque converter, they should be more efficient than the standard automatic type. Although if the gears are always in mesh but most of them idling, that might reduce the efficiency a little. Maybe the typical AT seems more comfortable, smoother or something. What do you think? The Renault website says there is growing demand for the AMT, that it is cheaper and more efficient than the AT:


Thanks for suggesting wire cutting, I hadn't thought of it. That might be the lowest cost for a prototype. If things work out, I would need the cheapest way to mass produce the gears.

Spigor, thanks for the technical analysis. Seems like it might be too expensive to make special hobs, one for each gear size. I would use as many as sixteen sizes in this gearbox. But if I had them, would the cutting process be standard after that, so that it wouldn't cost any more to make these gears than it would standard gears?

I am thinking that it might be cheapest to cut standard gears and then grind in the round lands. I guess that would require some slight adjustments to the standard gear, to leave a little extra tooth length for later grinding.

What about rolling the gears? They will operate at low speed and don't need to be high quality. Could a gear roller make those rounded lands?

Pud, it occurred to me later that you might have been suggesting that I could keep all the gears in mesh all the time and select them some way. This is how the Pinion and Effigear bicycle gearboxes work. I believe I have a better method.

All it takes is to take a standard gear and file or grind a double bevel on the tips. Beveled tips will mesh more reliably than rounded tips. I have seen this done with nip rollers that are geared together, and the nip has to open and close.

I gave you a star for that comment.

All very well given responses, it is possible have a topping cutter to produce the radii at the tips.
it is also possible to wire cut, when it becomes more difficult is when the gears require post gear grind processing.
the material and hardness will become a factor how to produce the radius tip.
a through harden blanks will be easiest wire cut holding .0005 in profile tolerance, however there will be
slight recast layer but can be held .0005 max.

my concern is how much total composite error and Tooth tooth composite error the radii tips will generate.
only way to test, is roll the pinon and gear. in small rolling inspection fixture
T.C.E. is generated because of profile interference. or spacing errors. thus how the profile
is generated(Design) will lessen the error, EDM is surprisingly accurate.

it is true chamfered teeth are machined on tips but to prevent interference. for low RPM this is acceptable.

for high stress applications wire cut is not an approved process or not allowed by most companies.
because of recast and hydrogen embrittlement, but I have never had issue with either, if the EDM is controlled properly.

If you bring two external gears closer together radially, and they have different linear speeds, there will be a collision of two tooth tips, rounded/chamfered or not. All the change of inertia will cause energy concentrate in this single spot.
If you used a clutch instead, having an internal toothing engage an external one, and the tooth chamfering would be provided, there would be many flat surfaces getting in contact simultaneously, so the energy would be dissipated. Such chamfers can be seen here: This solution was still not good enough and so the synchronizers were invented: In some applications where the number of engagements is limited, e.g. racing, simpler and quicker dog clutch designs are used.
Just some basic points for consideration, as this is a very broad subject with many decades of development behind.

Thanks for the good information, mfgenggear. It looks like there are too many uncertainties in wire cutting to keep the cost down, even for a single set of prototype gears.

Excellent post, Spigor. I have been doing a lot of searching but did not find the kristen-goerman website. Those chamfers are for axial meshing so would not apply in my case.

If I use a clutch in that way, instead of radial meshing, it would be an entirely different arrangement. It would be too complicated, heavy and expensive for a bicycle gearbox, at least as far as my imagination goes.

Collision of the tooth tips is the only unknown in my arrangement. As you say, if the gears must transmit high load immediately at the beginning of the mesh, or when approaching at different speeds even if there is no load, it wouldn't work. The teeth would soon be destroyed.

What I have discovered with my prototype gearbox using 14.5 PA gears is that the meshing is almost always smooth if there is no load being transmitted and the gear speeds are low, which is critical. The only problem is when the lands meet and lock, making the gears rotate together on their lands. The chance of that happening depends on how wide the lands are. The wider the lands, the more often they will lock and prevent meshing.

The only way is to make the lands as narrow as possible. Considering the advice offered here and what I have found on my own, I believe it would cost the least to use the highest possible pressure angle for the gears. This will provide the narrowest lands without chamfering. It would not require much special tooling, if any. It would use standard gear cutting methods. It would provide the smallest possible gears, although with increased loads on the shafts and bearings, which I think I can handle.

I base these statements on the paper


by the former chief engineer of Oerlikon Fairfield, Rick Miller. He is consulting now, Innovative Drive Solutions LLC.


But as an earlier post on this forum shows, a land can be too narrow:


Keep your lamps trimmed and burning.

It might be interesting for you to know, that you can get any reasonable PA using a standard hob. It would be like short-hobbing /long-hobbing is also possible/, but used for other purpose.

Since lots of different things can get tricky here, I offer you help with the calculation of the gears according to your specification /like number of teeth, top land width, the size of the gears etc./.

In order to transmit power properly, the contact ratio needs to be greater than one.
If the gears are moved away radially, the contact ratio drops. If you move them into the mesh, at first they will work under insufficient contact ratio condition. Will that be a problem in your application?

Most interesting, Spigor. Not that I understand the details. I never worked in the gear industry and don't know anything about it. My hat is off to those who have a good knowledge of gear design.

In my bicycle gearbox there would be no load on the gears until they are completely meshed and the center distance is fixed. Since the gears will take no load until the mesh is complete, there is no concern about contact ratio before that time.

Keeping the land width to a minimum will reduce, as far as possible, the chance that the gear lands will meet at the beginning of the mesh and stop the engagement. Once the lands have gotten past each other, there will be no more problems.

Land width decreases as PA increases. The greater the PA the stronger the teeth. The stronger the teeth, the lower the gear size and weight. These are all advantages for my bicycle gearbox. The disadvantage is that the higher the PA, the greater the load on the shafts and bearings. I can handle that.

The only question for me now is what pressure angle to use. One of your links above is to a discussion about using differing PAs and DPs for mating gears. Wow. Even though I have a copy of Earle Buckingham's Analytical Mechanics of Gears, I am not going to try to understand those possibilities. I am not young enough to make the effort worthwhile. I would like to have a standard design, at least to begin with.

In the paper I cited earlier, Rick Miller states:

"...If [higher pressure angle gears are] not carefully designed, manufacturing the gears can be difficult and more expensive. Gear cutting tools will usually be non-standard..." You say that a standard hob is good enough for any reasonable pressure angle. There will be no contradiction here if we know what you mean by reasonable.

Miller shows a drawing of a gear with a 35 degree pressure angle. Is it possible to make that gear with a standard hob and standard procedure? The lands are very narrow, looking good to me. But Miller also says:

"...Higher pressure angle designs were typically not considered or used because of the limitations listed above, the most significant being reduced gear teeth top lands and fillet radius..."

and

"...potentially limiting factors are: 1) top land thickness..."

But he does not explain how a top land might be too narrow. I am relying on the eng-tips discussion I cited above, in which it is explained that the narrower the top land, the greater the danger of tooth failure.

What is the highest pressure angle that can be produced using standard hobs and gear-cutting procedures? One of your links is to a paper showing pressure angles up to 45 degrees [Hob Basics Part II].

What is the narrowest land width allowable for my application?

If you can give me some guidance on these questions here I would be grateful.

The gears I want to use would be about 20DP and have tooth numbers from 18-40. Face width would be 3/8" or less. RPM would not exceed 300 for the smallest gear, lower for the rest. Maximum power at least 1/4 HP but might be higher. I can't settle that question until I have a prototype to test. Right now I just have an operating model using the gears I had available. They are 14.5 degree PA change gears of low quality. I can't use them for a prototype, but they have shown this meshing problem I am trying to solve.

Windward said:

I am not going to try to understand those possibilities

Click to expand...

I would not expect you to do so without a reason far better than what we seem to have here, that's why I offered help.
I think we are getting somewhere. We have 20DP and how about we set the land width to .01-.02? This should allow you to use a regular nitriding steel, quench and temper to about 36 HRc, cut the gears and other features and optionally nitride a shallow case for wear resistance (if you used salt bath nitriding you would also get excellent friction properties, corrosion resistance and a nice black finish).

Yes, we are making good progress here. (About the remark you quoted, I didn't mean it as a protest or any offense to you. I appreciated the links. One of them was beyond me, and my comment was only about that. One of those smiley emoticons here for you. I am past the age to actually use one.)

Those land widths are fantastic. I never expected they could be so low. I am sure they would work fine. The other suggestions are also excellent, should give me enough info to specify the gears.

Is 4140 a nitriding steel? That one seems to be commonly used for decent gears.

Not clear to me yet, and the gear supplier would know, but would you cut the gears before or after the quench and temper? What do you suggest for pressure angle?

How about rolling the gears? I am looking for the down and dirtiest way to get gears that work in this low speed, low power, low quality application. Although I want the highest bending and surface stresses I can get for a modest cost. But then, don't we all.

Thanks for explaining and don't worry- my impression is that our conversation has always been constructive and without any bad emotions, which is not always that easy without face to face contact, when I feel like I'm pointing out things that may undermine your plan. I also didn't mean anything bad, just wanted to let you know that I do not expect you to learn everything under those links, and so I offered help.

4140 is ok if you do not plan to nitride the gears or if you plan to salt bath nitride them. But if you plan to gas nitride them you should go for a real nitriding steel like Nit 135M (AMS 6470) /please somebody check this as I'm not familiar with the AMS steel specs/.

I would make the blanks, Q&T them to approx. 36 HRc /if done otherwise you would loose some of the surface hardness, not to mention the stress distribution/, calibrate the bore /other reference surface(s)/, cut the teeth and other features like nuts. You already have decent gears. At this point you need to make a decision if you need to nitride them for much better wear resistance. If so, the dimension changes in nitriding need to be taken into account.

The PA is not set yet. Please let me know the teeth numbers of the first gear set and which one is the driving member.

Rolling with a rack tool? I have experience with the rotary rolling /GROB/ and suppose that the rack tool would have unacceptable narrow top lands, it is almost a topping condition and the face width is small- looks difficult.

AMS-6471,AMS 6470 Nitrolloy 135M (Nitriding steel,
I would take up Spigors offer, free design help is hard to get.

so if I may be of help
start with gear ratios
then center distance
then mod. or DP & Pressure angle
look at profile shift (Recess action)
for the low amount torque I would recommend standard pressure angle, 20 or 25 degrees
when yo get above 30 degree the gear teeth start to apex, and fancy calculations are then required.

Nitriding has good wear resistance, but it also because of it's brittle hardness chips very easily.
17-4 stainless & Nitrided might be a good fit too. shallow case
for some reason, as it use to be know tufftride (salt bath nitride) ( is very shallow and strange dimension changes occurs.
test samples would have to be run.

for cutting proto types I would suggest using a milling form cutter (Standard)& if necessary form grind
for hardness 40 HRc (machine) then nitride. cutters are relatively cheap, sold at ash gear.

if affordable since this is a commercial application, I prefer AISI 9310 machined , then carburized
then close tolerances ground, but quite expensive.

Spigor, the prototype gearbox would have thirteen speeds. The low speed pinion would have 18 teeth. The low speed gear would have 40 teeth. The pinion would rotate at 300 RPM. It must transmit at least 1/4 HP.

The high speed ratio would be the inverse of the low speed ratio. But the RPM and HP of the high speed pinion would be the same as it is for the low speed pinion. In other words, in low speed the 18 tooth gear is driving. In high speed, the 40 tooth gear is driving. In high speed, the 18 tooth gear would be rotating at 667 RPM.

You might deduce from this that the speed range of this gearbox is only 2.22. It is actually about 5. It could be greater than that. It could have a speed range greater than any bicycle gearbox on the market. That is the main innovation of this gearbox. It could also have more or less than thirteen speeds, and it has other important advantages.

About rolling the gears, several weeks ago I got a quote from GROB. Minimum order is a twelve foot bar which would make about 300 of my gears. Using 4140, that bar would cost about $700. Amazing. Of course, after sawing off the gear discs like you were cutting sausage, you would have to true up the sides, might have to chamfer the teeth, then bore the disc.

Still, the cost of these gears would be very low. The quality would also be low, but I think it might be good enough for my gearbox. Can you go into more detail on your doubts about rolling? For cut gears you have suggested a 0.01" - 0.02" land width. Why would such a narrow land be a problem in a rolled gear?

I hope these questions do not seem offensive, as though I were doubting the value of your advice. As mfgenggear says, your free help (and I am glad to have his comments also) is an offer no one could refuse. I certainly appreciate it. If I must use cut gears, you will have given me thousands of dollars worth of information. If I ever manage to produce these gearboxes, I will send you one for free, if you want it.

On that point, I attach a drawing that shows what the gearbox would look like on a bicycle. Maybe it is foolish to publish any details at this point, but what the heck.