Reverse Engineered Spur Gear

[nathan.davisFEBT9]

I have two matching spur gears that I'm trying to reverse engineer. No matter what I try I seem to keep getting results from the spur gear generator slightly different than my measurements. I'm also not sure what pressure angle to use.

Here is what I have measured:

Pinion Teeth = 18

Gear Teeth = 69

Pinion Outer Diameter = 1.465in

Gear Outer Diameter = 5.057in

Center Distance = 1.123in (I just meshed the two gears with no clearance and measured the center distance)

I used the following formula to get the diametral pitch (I tried a different formula as well which got 13.92):

Diametral Pitch = (Pinion Teeth + 2)/(Pinion Outer Diameter) = 13.65

If I use the center distance as the design guide, a diametral pitch of 13.65 (not rounding up to 14), a pressure angle of 22.5°, and no unit correction, it gives me a center distance of 3.187in, a pinion outer diameter of 1.465in, and a gear outer diameter of 5.201in.

If I use the unit correction as the design guide, the same diametral pitch and pressure angle, and a center distance of 1.123in, it gives me a pinion outer diameter of 1.457in, a gear outer diameter of 5.074in, and a total unit correction of -0.8169. A little closer, but not quite right still.

No matter what combinations I've tried, I can't seem to get the correct outer diameters and center distance. 

I'm also unsure of the pressure angle. The gear preview of 20° looks a little too narrow at the base. It looks like it should be a 25° pressure angle, but the calculations fail at 25° with a "Tool tip is truncated" error. It passes with a 22.5° angle, which looks closer than the 20° angle, although perhaps still a little narrow at the base (it's hard to tell) and a 22.5° pressure angle seems to be an unlikely design.

Any help on where I'm going wrong would be appreciated. I realize that perhaps some of the difference could be in the manufacturing of the gear, so perhaps that is where I am getting it wrong.

Thanks!

[WHolzwarth]

Hmm. Measurements are never precise. And sometimes a description is misleading.

- In your text, you've told a center distance of 1.123in. But I think, it's 3.123in as in the second calculation.

- Teeth measurements are misleading, too. With equal teeth you'll get different measurements; tip to tip or gap to gap. With unequal teeth you'll end with tip to gap.
- Reverse calculations of diametral pitch (DP) are better, when more teeth are involved. You can get three values:

(18+2) / 1.465 = 13.652
(69+2) / 5.057 = 14.040
(18+69) / 2 / 3.123 = 13.929

Over here in Germany, we're using module instead of DP. It's easier to understand for me. I don't know much about DP standards, but perhaps DP=14 is the right one.

[nathan.davisFEBT9]

Thanks for the tips! You're correct, it should be 3.123in. I attempted to correct for the tip to gap measurement on the large gear, although it could be off a few thousandths.

Using more teeth in the reverse DP calculation makes more sense. I've heard from a handful of sources you typically want to round to a whole number for the PD when reverse engineering, so I think you're right that it's probably 14. 

If I use a PD of 14 and adjust the unit correction on the pinion gear, I can get pretty close to the correct value, with each outer diameter being larger by only .005in. That is probably the design intent and the difference is likely due to manufacturing.

I'm not certain that I have the correct pressure angle, but the tooth profile looks more accurate at 22.5° than at 20°. Seems like an odd angle to design for though.

[JDMather]

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@nathan.davisFEBT9 wrote:

Here is what I have measured:

I'm also unsure of the pressure angle.

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Do you have images of actual gears (perpendicular to the face.)?

Also, do you have mounting shafts - I think I would prefer to measure the center-to-center distances from mounting rather than trying to get from the gears.

And finally, do you realize that without extra work - the gear generator is only going to create simplified "cosmetic" gears only useful for visualization?  (Not true toothforms, in fact - they will interfere rather badly.)

[nathan.davisFEBT9]

Yes, here are a few pictures of the gears.

Unfortunately I don't have the shafts, just the gears. Would you want to include a couple thousandths for backlash if you're just measuring off the gears?

Yes, I've exported the tooth profile to a part in order to get the true toothforms.

Thanks!

[Frederick_Law]

Gear can "only" be cut a certain way.  You can't have half a tooth.  DP or MOD need to be a certain number.

Or else you'll be making complete new custom cutters, hobs, rack to cut 2 gears.

So look up a gear catalog and see what size are available.  DP, MOD, pressure angle.

I usually print the model 1:1 and see how close it is to the part.

Once you have the model, how are you going to make the gears?

[nathan.davisFEBT9]

Gotcha. I was going to have an online machine shop make the gears. I'll have to ask them if that DP will work for them.