I'm building a simple 20:1 reduction gearbox for a project. I pulled some solid looking gears out of a beefy old electric drill, and I'm kind of worried about the strength of one of them. I had to heat it up to push it out of a super tight press fit. After it turned a bluish color I stopped heating, but it's settled on a darker color now. I'm hoping I didn't anneal it or otherwise affect its properties. I need all the strength I can get pushing 2200W through these gears. What do you guys think?
Funky one on the right:
http://i27.tinypic.com/1zwyfqh.jpg

Probably did change something, but they look pretty strong anyhow.

What did they come from, and what are you putting them into?

Power is likely to be irrelevant, how much torque will you be putting through them, and how much torque went through them originally?

I pulled them out of an old AC electric drill motor. I'll be casting a new gearbox for these guys for my electric bike project. I didn't show the input shaft, which drives the gear on the left. Input is a high power R/C brushless motor at 8000ish RPM, rated for 2200W. I won't be using more than 300W continuous I don't think, and peak for not more than 10 seconds at a time for acceleration. Torque (N.m) = speed (rad/s) / power (W); I'll do the math some other time.

using the gear ratios you can find the torque handled by both gears, and assume that is their maximum (this will leave you a safety margin), then depending on how you install them on your bike, you should be able to work out the stresses on them from your motor.

If you don't have data on your motor, you could alternately work out a maximum acceleration, and see if that sounds reasonable to you. If it is very high (e.g. 1 gee) there should be no problem.

I would do this for you, but I don't know how you are installing them.

I'm actually not so confident in their strength anymore. The ony laying flat looked 10cm in diameter to me, which made me think it was strong, but from what you've told me, I think I have my sense of scale out there.

Ha, no, they're not quite that big. That's why I'm concerned about the torque. I know steel gears are strong but they're not indestructible. Comparing these to gears I've seen in car/bike transmissions which are designed to handle 100x the power I'm working with, though, I think these have a chance of standing up. Here's the layout and some data:
..........#.......dia.
input: 8T 6.4mm
gear1: 37T 23.7mm
gear2: 13T 9.6mm
gear3: 55T 34.1mm

ratio: (37/8)*(55/13) = 19.57:1
http://i32.tinypic.com/k54qvr.jpg

It's 4am so I'm going to sleep.. I'll figure out more stuff tomorrow. Thanks.

Hmm. should this be in DIY instead?

Possibly. Argon moderates both DIY and GH so I figure he knows better than anyone which it should be in, so I left it for him.

If you want it moved, just ask and I shall do.

Sorry I haven't helped you more, you should post how your bike will be powered, how the gears are set up in it, and how the drill was powered, and how the gears were set up in it.

Then its easy enough to get the two torque levels and see if there is a concern.

Alright. I did some calculations. Everything is SI for sanity's sake.

I figured the bike + me + equipment weighs a total of about 87 kg. To accelerate from 0-12 m/s (about 0-28 mph) in 10 seconds means 1.2 m/s^2. Since F = ma, that means a constant force of about 104 N.
If my rear wheel has a diameter of 26", the radius is 13" or about .33m. Torque = r x F, (104)(.33), about 34.3 N.m.

If I'm going 12 m/s, that means my wheel is spinning at 36.4 rad/s. Power = torque x angular velocity, so at 12 m/s, still accelerating at 1.2 m/s^2 I'm using (34.3)(36.4) = 1247 W of power at the wheel. Sounds about right.

Now I'm not sure about how torque and gear ratios work together. But say I've got my output gear at a 1:1 ratio with the rear wheel. That means it's spinning at the same angular velocity, and is experiencing the same torque, 34.3 N.m. It has a radius of 17 mm. If T = r x F, then force = T/r. (34.3 N.m) / (.017 m) = 2012 N at the teeth of the output gear.
That's... hefty. Assuming I did that right. Input appreciated...

Now I could calculate the surface area of the gear teeth, figure out how many are meshed at any given instant, derive the maximum pressure exerted per tooth and see if exceeds typical Young's modulus for steel, assuming the gear is made of steel... maybe another day. For now, I'm just going to assume these teeth can withstand 2,000 N.

Yeah. That was fun.

Oh, and I've decided I think this thread would do better in DIY. If you would be so kind, Argon.

Thank the lord!

I'm pretty sure this method will work just fine assuming the last gear in line is the one you are worried about, and that acceleration is what you are going for, etc. I would also recommend doing the same thing for your drill to find out the torque it experiences.

If you want to model it further, assume only 1 tooth is in contact, and use the yield stress of some common steel as a failure point (try and get some factor of safety, though). Normally they are modeled as cantilevers IIRC.

Off it goes to DIY, then.

I think you're worrying too much. Try it, see if it breaks, and rebuild it if you have too. Chances are you'll think of lots of improvements that you want to include in the second build anyway.

What does your casting setup look like?