How to Measure and Model a Curved Gear Rack

[Lotaxi]

I now get a diametral pitch of 34 (or .75 Mod).

That's the closest to what I was calculating off the measurements I pulled, yes.

The scan, I believe, is noticeably more accurate. However, including x and y known-length references with the part would have been nice.

I can rescan, I suppose, I typically just use physical measurements to line up points.

It will be interesting hearing about the pinion measurements and the possibility of an addendum modification. The likelihood will be low if the pinion is steel with the plastic sector.

Here's what I pulled from the pinion. I don't know enough about gear design to come close to thinking that I got the tooth profile perfect and I'm assuming the pitch diameter and the 20 degrees, but the measurements for OD, root diameter, and tooth width included are reasonably correct. It's aluminum, by the way. 15 Teeth.

 

[Lotaxi]

Even if you are off by 2dp the customer probably would not notice.

But now that you have asked the gear perfection Gods, they will notice.

Honestly now that I have access to the pinion, I was just going to try and make replacements for both. No mismatch if they're designed as a set XD

Going for 17-4 PH for both sides, and just hardening to H950. Should be more than enough for years of play so long as the gears are greased to prevent galling.

 

[David_M]

Lotaxi,

Attached is a zip file containing a DXF of the gears. It should be good enough to burn into first-trial gears, but no guarantees.

.75 mod for the gears.
I moved the mounting holes on the sector less than 0.001" so they matched 2 holes on a 96mm diameter, 24-hole bolt circle.

 

[Lotaxi]

Attached is a zip file containing a DXF of the gears. It should be good enough to burn into first-trial gears, but no guarantees.

Thank you! I'll try these out! Probably going to be smoother than the ones I've come up with so far

I moved the mounting holes on the sector less than 0.001" so they matched 2 holes on a 96mm diameter, 24-hole bolt circle.

Why is the bolt hole circle important? I'm assuming it's for proper locating according to convention?

 

[David_M]

Why is the bolt hole circle important? I'm assuming it's for proper locating according to convention?

To me, it is reassuring that the scan came that close to what makes sense for locations.

I think, at this point you could wire-cut a sector out of scrap (just the locating holes and the teeth) and try it with the old pinion for fit in the machine.

 

[Lotaxi]

To me, it is reassuring that the scan came that close to what makes sense for locations.

That makes sense!

I think, at this point you could wire-cut a sector out of scrap (just the locating holes and the teeth) and try it with the old pinion for fit in the machine.

I have a couple that I have 3D printed. My version seems to be a little bit off because it seems to be hitting the root of the teeth on the pinion as it turns. They're fairly rough and they have a tendency to lose teeth after a bit. It's about what I expected out of a prototype run. I haven't tried yours yet, but it's in the printer now. I'll let you know how it works

 

[David_M]

...My version seems to be a little bit off because it seems to be hitting the root of the teeth on the pinion as it turns. They're fairly rough and they have a tendency to lose teeth after a bit...

The teeth need an involute shape to roll correctly. The low tooth count pinion also needs undercutting, typically as a trochoid (to leave as much material as possible).

 

[Lotaxi]

The teeth need an involute shape to roll correctly. The low tooth count pinion also needs undercutting, typically as a trochoid (to leave as much material as possible).

So many things I don't know. I love this forum. Can you point me at some resources to learn more about gear mechanics and design, especially as it pertains to reverse engineering? Machinery's handbook has a fair bit of info, but it presupposes a certain degree of knowledge that I don't have yet.

Gear seems to fit flawlessly with the adjusted profile, by the way. We'll see how they stand up to the rougher use I'm expecting they'll receive.

 

[Halcyon]

Do you still need help with this? I have access to gear modeling tools if you need.

 

[David_M]

There is a lot of information to be found by searching the forum. Look for posts from Dan from Oakland, Emanuel Goldstein, Zahnrad Kopf, and others.

The following lists some good books:

5 Books to Improve Your Gear Cutting Operations - Practical Machinist

Dive deeper into gear cutting with these recommended books. You may be surprised to discover your project requires an approach you did not expect.

www.practicalmachinist.com

 

[Lotaxi]

Do you still need help with this? I have access to gear modeling tools if you need.

For the purposes of the prototype run I'm going to install for testing, I think I'm ok after the help from David there. I might reach out as I design the ground-up replacement gear set, though. Thanks!