Cutting non standard (low tooth count) gears

[internal_fire]

2) its not a feature

Undercut IS a feature if you want to mesh with a perfect involute gear or a rack at the ordinary calculated center-to-center spacing. That is why it shows up when cutting with a hob.

The shortcomings are well-known, but in some cases the tooth strength (for example) is not a concern.

Of course it is not a useful feature for most ordinary home shop users who do not possess fancy gear cutting machines.

Gene

[petertha]

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.

Assuming you mean Pitch Circle Diameter (aka reference diameter, aka pitch diameter)?  Actually not, which is what I initially assumed. You can see the profile shifted gear (blue shade) is 9.60mm, exact same dimension as the uncorrected gear (yellow shade). Therefore the gear centers would be the same distance apart in both cases. But the increased diameter may well factor into things. Specifically my gear pump where the cavity bore must be a very close offset to gear OD (aka tip diameter).

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.

That's a good point. I now want to go back to some of those workbooks that show how involute cutters are made with circular buttons or whatever the process is. I gather tha 14.5 PA had some historical significance but largely (or maybe its predominantly metric/module) 20-deg PA seems to be the norm.

One other thing of note, this particular link has an input cell for you own measurement dowel or bearing ball. Input the size & it calculates the pin over pin dimension confirming correct pitch diameter has been achieved. Kind of like MOW (measurement Over Wires) for screw threads. I'm not quite clear how it factors odd numbered teeth where the pins would not be 180-deg apart. I have a generic CAD application that spits out a 'pretty close' involute & i confirmed the pin-to-pin matches, this reminds me I need to check how it compares.

[petertha]

Undercut IS a feature if you want to mesh with a perfect involute gear or a rack at the ordinary calculated center-to-center spacing. That is why it shows up when cutting with a hob.

I think I worded that poorly. How about - it is a natural BYPRODUCT or RESULT of the exact same hob process as conventional involute spur gears. They don't do anything special to achieve the enlarged undercut, the exact same tooling setup just gouges deeper as a function of the low tooth count geometry. So perhaps it may be fine to leave it this way in certain applications, but I think the reason the warning flag shows up on commercial calculators, or at least more rigorous calculations, is they probably don't leave it at that. They have the means to correct the gear by profile adjustment & probably do so?

[Charles Lamont]

I thought we were talking about a gear of at least 12 teeth. I do know the cutter tip is generally not parallel sided, I was just illustrating, rather crudely, how a standard type of cutter can produce a degree of undercut, which Jason said it could not. Actually, I suggest the tip portion of a 12-13T cutter might well be parallel sided and that this is what determines the 12T minimum tooth count for form cutters.  I take the point that with even smaller tooth counts cut without profile shift, the gap may be wider at the root than at the pitch circle.
 

[john mills]

it does not matter what method you use small numbers of teeth look thin at the base
they will still be the involute shape the teeth still roll properly.

[petertha]

I don't think I agree, John. If the gear making method is confined to using the typical numbered cutter set, it does not produce an enlarged root area the way a hob does. Because in hobbing the gear blank is turning as the hob cutter rotates & that action path removes the root area as a byproduct (see YouTube videos posted). Whereas the numbered cutter enters a stationary gear blank perpendicular from the side, then repeats for the next tooth. The cutter profile is what it is, skinny at tip & curved thicker with some kind of compromised involute curve optimized for that specific tooth count range.

But AFAIK it is a moot point if you want to cut a 10T gear on the smallest cutter which specifies 12-13T. I have read a #1 cutter could be employed with specific setup modifications but its even more of an involute approximation getting progressively worse the smaller the tooth count, so not recommended. Like 8T seems to be a hard stop limit. Interestingly the 12T minimum is universal despite the module, because its the same involute geometry problem. Maybe commercial dedicated cutters are available for <12T I don't know. Either that or I guess you must hob which is a completely different setup. But from what I'm gathering of all this, profile shifting may still be desirable if not required for a 12T using numbered cutters.

[internal_fire]

I think I worded that poorly. How about - it is a natural BYPRODUCT or RESULT of the exact same hob process as conventional involute spur gears.

I do not see it as a byproduct. It is required if a low-tooth-count gear is going to mesh without interference with a large gear or a rack.

The alternative is to make adjustments as noted here, including in some cases changing the center-to-center gear spacing.

Gene

[Jasonb]

I thought we were talking about a gear of at least 12 teeth. I do know the cutter tip is generally not parallel sided, I was just illustrating, rather crudely, how a standard type of cutter can produce a degree of undercut, which Jason said it could not. Actually, I suggest the tip portion of a 12-13T cutter might well be parallel sided and that this is what determines the 12T minimum tooth count for form cutters.  I take the point that with even smaller tooth counts cut without profile shift, the gap may be wider at the root than at the pitch circle.

I think it comes down to what "undercut" is taken as. I have always seen it as where the root gap is wider than the pitch gap.

Yes the tip of a 12T cutter will be almost parallel. If you think of the buttom method of making cutters then the infeed is almost half the button dia so at the tip of the cutter the curve is almost tangent.

Extreme example here the 12T on the right is almost parallel, the 4T on the left would not work as a cutter with a root width of 1.18 would just make a 1.18mm wide slot and cut off the contact areas at the pitch dia.

[Jasonb]

Does your calculator do the calcs for a pair of gears? I also see the note that it is valid for 1MOD and above.

This is Gearotic which gives the data for each where the 9.6 stays the same as addendum and dedendum get altered which effectively changes where  the circle passes but when put together as a pair the ctr distance often referred to as the PCD of the pair goes up when shift is applied.

Easy enough to check, just rough out a pair in aluminium with the shifted OD and try them together

[Jasonb]

What KHK have to say

https://khkgears.net/new/gear_knowledge/abcs_of_gears-b/gear_profile_shift.html#:~:text=When%20the%20number%20of%20teeth,gear%20cutter%20xm%20(mm).

And if you want to believe AI that also says ctr distance alters when you shift the profile

[Minh Thanh]

Interesting topic ! 

[petertha]

Hmmm... the plot thickens. Well MY AI (Gemini) says the reference diameter remains unchanged. Is it really too much to expect our AI's would collaborate behind the scenes & come up with a mutually agreeable answer?   So as I often due when it hallucinates, I provide contrary evidence & ask to re-evaluate the answer. Here is what it says

Q) This article seems to contradict what you said that center distance remains unchanged. Can you diagnose why that would be https://khkgears.net/new/gear_knowledge/abcs_of_gears-b/gear_profile_shift.html#:~:text=When%20the%20number%20of%20teeth,gear%20cutter%20xm%20(mm

A) That is an excellent point. The article is correct, and the apparent contradiction is due to the two distinct applications of profile shifting in gear design. The KHK article is referring to the use of profile shift to intentionally change the operating center distance. My previous answer assumed you were using the profile shift in its most basic application: to correct undercutting while maintaining the standard center distance.

Here is the diagnosis of why both statements are true:

1. Profile Shift for Correction Only (Standard Center Distance)
This is the scenario we discussed and is often used to fix undercutting on a small pinion.

Goal: Prevent undercutting on the small gear (14T) and improve tooth strength, without altering the distance between the shafts.

Method: You calculate a positive correction factor (x1 >0) for the pinion and zero correction for the wheel (x2=0).

Result:

The Reference Diameters (d) remain fixed (11.2 mm and 64.0 mm).
The gears are mounted at the Standard Center Distance (a0 37.6 mm).
The meshing works because the involute tooth form allows the gears to mesh at an automatically increased Operating Pressure Angle (α w >20∘) to accommodate the pinion's thicker teeth, thus keeping the center distance the same. In this case, the center distance is unchanged from the uncorrected standard calculation.

2. Profile Shift for Center Distance Adjustment (Extended Center Distance) This is the application highlighted by the KHK article. It uses the exact same gear geometry but mounts them farther apart.

Goal: To achieve a precise, non-standard distance between two shafts, or to reduce backlash and smooth operation. Method: The designer intentionally spaces the shafts apart to an Extended Center Distance (a>a
0). A total positive correction (x 1 +x2 >0) is then required to ensure the gears mesh correctly at this new distance.

Result:

The Reference Diameters (d) are still fixed by m and z.
The Operating Center Distance (a) is enlarged from the standard a 0 .

The KHK article correctly states that profile shift is a powerful design tool that gives you the freedom to enlarge (positive correction) or reduce (negative correction) the center distance if desired.

Key Takeaway The presence of a profile shift does not automatically require a change in center distance. You can mesh a corrected pinion with a standard wheel at the Standard Center Distance (a
0 ), but you can also use profile shift to deliberately set an Extended Center Distance (a) if your design requires it.

[petertha]

Does your calculator do the calcs for a pair of gears? I also see the note that it is valid for 1MOD and above.

This is Gearotic which gives the data for each where the 9.6 stays the same as addendum and dedendum get altered which effectively changes where  the circle passes but when put together as a pair the ctr distance often referred to as the PCD of the pair goes up when shift is applied.

For paired gears, I was flipping back & forth between another free online app but I believe Ondrive, the one I have been referencing screen grabs for this example discussion gear, does have provisions for a mating gear. What I am less clear on is how to utilize it depending on relative size between them. Can one share the total profile shift coefficients between 2 gears, or confine it to the smaller pinion gear so the larger gear remains standard? My guess is to increment the correction until the red warning pop up disappears & maybe the end result is for the designer/gear maker to decide?

I see that Gearotic is a purchased app? Maybe you could do a comparison to Ondrive since its free.

https://ondrives.com/gear-calculator

[crueby]

Gearotic can be used for free, but you can't  save setups or export unless you buy it. At least thats how it was when I  got my copy.

[petertha]

I tried 2 identical 12T as before which would correspond to my pump gears. Using the same 0.5 profile shift correction applied to both. No warning popup arose, same 9.6mm reference diameter & same 12.0mm tip diameter. Any attempt to vary x1, x2 like 0.4,0.6 resulted in a different error / warning diagnostic. So perhaps they ideally want to be equal for equal gears?