Cutting non standard (low tooth count) gears

[petertha]

I am new to this (involute spur) gear cutting business & want to confirm my understanding (or lack thereof). I'm cutting metric/module gears but I believe same issue for Imperial/DP involute gears.

Here is an example: Module = 0.8, Pressure Angle = 20-deg, number of teeth = 12. Note I am using commercial gear cutters like this set, not hobbing them. So as is typical with these sets, the lowest recommended number of teeth is stamped 12-13 on the #1 cutter. My understanding is the involute profile is tweaked or optimized a bit for each cutter towards one end of the tooth count range or the other, I can't recall off hand. So as long as I'm not trying to cut lower than 12 tooth with #1, at least I have the right tool. So far so good.

If I use the standard or maybe I should say simplified gear equations it yields: gear blank OD (tip dia) = 11.2mm, pitch circle (reference dia) = 9.6mm. For cutting, if I followed the 'standard' DOC formula 2.25 * m = 1.800mm. But using what I think is the proper methodology accounting for low tooth count (non-standard) gears like this online calculator, a warning message pops up: 'gear has undercut, increase xE value to ... 

https://ondrives.com/gear-calculator

Now this is confusion point #1. I always assumed undercut was a byproduct of hobbing, a well established commercial manufacturing process. The gear blank is rotating so the hob cutter action removes an enlarged chunk around the root area, more or less as a consequence? Therefore tooth is weaker, only runs on a portion of involute & other disadvantages. So I wondered out loud if I'm using the aforementioned cutter set where we in-feed to a stationary gear blank it obviously will not reproduce that enlarged undercut, how does that pertain to me? Just use the #1 cutter & all is good? But after much Googling & YouTubes showing graphic illustration, I now think the standard gear recipe (OD & DOC) runs the risk of mating gears actually interfering with one another because its related to the same phenomena? Maybe this is common knowledge, I see a lot of 10,12 tooth gears around this size, but its worth me asking here.

[petertha]

So my understanding: To fix the issue for non-standard gears involves something called profile shifting which involves effectively enlarging the gear blank by some amount. This results in a different addendum & dedendum distances compared to the standard gear formula, but AFAIK the DOC is the same as standard gear. And the important bit which was hard for me to visualize, the pitch diameter is the exact same even though the gear OD is larger.

There is a formula to calculate 'x' (profile shift coefficient). What I did was use the same online tool to progressively increment x from zero (standard gear or default) until the warning popup went away. This screen grab shows the end result assuming x1=0.5. Gear blank OD (tip diameter) is now 12.0mm. Note the same 9.6mm reference diameter. So laying out gear centers on reference diameter circles does not change. I tabulated the standard & non-standard. So does this look right? Obviously big ramifications for my gear pump because it has what qualifies as non-standard / low tooth count. The gear cavity in the pump housing must be a small offset distance to gear OD.

[Jasonb]

Using a hob or gear planer which have rack form cutting edges produces gears that will run including any required undercut that happens on the smaller tooth counts. They also give the correct involute whatever the tooth count

Involute cutters have short commings and cannot produce these required undercuts so things like profile shift are used to get around that but the ivvolute profile will still not be optimum. Which for low loads like your pump is not really going to be an issue.

less than 1.0 MOD is often cut with a larger dedendum like 1.4 than gears over 1.0 MOD at 1.25

[Charles Lamont]

A 12-13 tooth cutter may well (I don't know without doing some work) produce an undercut because the blank is rotated 30° (for 12 teeth) between each radial cut.

[Jasonb]

Involute cutters can't physically produce an undercut as the blade would need to be wider than the narrowest gap between teeth and unlike a planer or hob only cut one gap at a time. They can cut a modified profile that eliminates the need for undercut which is whare the profile shift comes into it.

[Vixen]

The British company HPC Gears know a thing or two about cutting gears. If you look at their catalogue for 0.5 MOD gears, you find they apply the profile shift as follows:

14 teeth   7.0 PCD   8.0 OD     (normal)
13 teeth   6.5 PCD   7.5 OD     (normal)
12 teeth   6.0 PCD   7.0 OD     (normal)
11 teeth   6.0 PCD   7.0 OD    (shifted centres)
10 teeth   5.5 PCD   6.5 OD    (shifted centres)

I would be inclined to follow their teaching, unless you think you know better.

Mike

[Jasonb]

Thats a lot of shift Mike  I think those are for 0.5MOD.

Also if you look at the technical section they detail what they allow for correction

https://www.hpcgears.com/pdf_c33/27.48-27.60.pdf

[Vixen]

Quite correct Jason. I used the wrong bookmark. I should have given

The British company HPC Gears know a thing or two about cutting gears. If you look at their catalogue for 1.0 MOD gears, you find they apply the profile shift as follows:

14 teeth   14.0 PCD   16.0 OD     (normal)
13 teeth   13.0 PCD   15.0 OD     (normal)
12 teeth   12.0 PCD   14.0 OD     (normal)
11 teeth   12.0 PCD   14.0 OD    (shifted centres)
10 teeth   11.0 PCD   13.0 OD    (shifted centres)
9 teeth     10.0 PCD   12.0 OD    (shifted centres)

The point is, they modify the PCD, and therefore the OD, for tooth counts below 12 teeth

Mike

[john mills]

funny term i have not heard before.
if you use involute cutters and cut the number of teeth on the cutters that will work only if you use a generating process such as hobbing or shapping like a fellows machine then sizes can be altered to not have undercut  the details are in machinery hand books early ones mines a 17th edition.they still have the proper involute form but you don't have to.
i hade a job cutting 5 tooth pinions  2.5 mod with undercut.but i also cut 5 tooth 3.5 dp stub form which were increased in size no undercut so centre distances are altered the sizes can be more than you might think .only applies if using hobs on
hobbing  machine or a generating process   i have cut other sizes too  plenty whith altered sizes i wondered why the
sizes never matched the stanared formulas  then i found it in machinery hand book and the figures worked out.
john

[Charles Lamont]

Involute cutters can't physically produce an undercut as the blade would need to be wider than the narrowest gap between teeth and unlike a planer or hob only cut one gap at a time. They can cut a modified profile that eliminates the need for undercut which is whare the profile shift comes into it.

Poppycock:

[crueby]

Involute cutters can't physically produce an undercut as the blade would need to be wider than the narrowest gap between teeth and unlike a planer or hob only cut one gap at a time. They can cut a modified profile that eliminates the need for undercut which is whare the profile shift comes into it.

Poppycock:

Except that involute cutters are not parallel at the tip...

[Jasonb]

Charles 12T is not the problem so why use 12 T as your example? As stated in the first post the involute cutters will do 12T like your sketch and that is why you can buy a cutter for 12-13T

It is when the tooth count gets smaller than 12T that the root width shown with the green arrow becomes wider than the mid point so the wider end of the cutter needed can't fit through that narrower distance. Think of it like a TCT tipped saw blade the red width would be the disc and the green bit the width of the teeth. The blade cuts a parallel cut the width of the teeth

But it looks like you may be trying to apply some form of cutter offset like is done on the parallel depth gear cutting method. This is a bit like a gear planer which moves the rack cutter relatibe to the gear centre line as the blank rotates an dthat is what allows it to generate a full involute for a cutter that is not an involute form.

[petertha]

Jason's last picture shows the undercut quite clearly. My understanding of this is 1) its a byproduct of using a 'true' involute cutting process, typically hob but there are other production method 2) its not a feature its an unfortunate byproduct because it reduces tooth strength, reduced contact area, puts the contact area more on the rub vs roll region... on & on. So to compensate for this, manufacturers use profile shift which effectively enlarges the gear blank diameter by some specified amount, but carry on using the very same cutting process.

That's all fine & good if one buys a commercial gear or pinion wire, they know what they are doing. But if my tools are the typical numbered cutter set which are in-fed to a stationary blank, it does not 'cause' the same enlarged undercut as the hob process. I have read that these cutters are not a true involute, their profile shape has somehow been compensated to be a 'mostly true ' involute, but I think what they are getting at there has nothing to do with this undercut issue. It has to do with the range of teeth a cutter can do. They could make a cutter for a Mod 0.8 14T and another for a 15T, but they have somehow done the math & grouped them into ranges where the difference is small. Hence #1 does 12-13T, 32 does 14-16T, #3 does 17-20.... the range gets larger as it approaches a rack. But for any one cutter its not geometrically perfect for any one tooth. maybe it favors the lower tooth count if its more critical, I don't know. So I guess this is one discussion point to be clarified.

But to reiterate my bigger question, even though its a complaint 12T cutter for a 12T gear, it appears as though the gear falls in the range of what they call non-standard where I should be profile shifting. Now this is another rabbit hole. If I have a 12T meshing a 12T (gear pump) would I have interference or running problems on that basis? As opposed to a 12T running with a 60T. I saw another calculator where both gears are defined but it was unclear to me what the profile shift implications were. I think you could share some compensation between them, but my take-way guess is they still need 'something'.

Here are some links (there are many). They assist with the visualization, but not necessarily a definitive workflow for making them the way I have to make them

<a href="https://www.youtube.com/watch?v=Af3ZKjpP2B4" target="_blank">http://www.youtube.com/watch?v=Af3ZKjpP2B4</a>

<a href="https://www.youtube.com/watch?v=1K_0Ha3-YGY" target="_blank">http://www.youtube.com/watch?v=1K_0Ha3-YGY</a>

[petertha]

Some screen grabs of the addendum & dedendum math of standard & non-standard gears. This is what led to my understanding that DOC is the same in both cases, but the resultant gear tooth profile is different because of the relative proportion of addendum vs dedendum applied to the profile shifted diameter. When I ran the 2 cases using the online calculator & tabulated, it supports this result. There are some minor-minor differences in the suggested x1 shift parameter but according to Gemini The Fibber, this may have to do with the online calculator (a gear manufacturer & gear cutter supplier) making other compensations for root fillet, tip radius & other factors. But bottom line if I set x1 = 0.5, the popup warning goes away & it provides me resultant enlarged profile shifted blank diameter (tip diameter). And I think I can just infeed the same amount h = 2.25 * m, h = 2.25* 0.8=1.80mm. Not sure if I am home free quite yet but hope this clarifies how I arrived to this point.

[Jasonb]

Thats it, you feed in the same amount. However as you are now using a larger overall diameter the PCD will also increase so your gear ctrs will be further apart.

One other way to overcome undercut is to increase the pressure angle but you would likely have to make your own say 30pa cutter. And from that comment it should be easy to see that undercut was greater with old 14.5pa angles than with todays more common 20pa.