Gear Box Eff

7/30/2019 Gear Box Eff

1/6

krich

Robot Overlord Posts: 165 Helpful? 0

Calculating Gear Ratio of Gear Box

on: January 14, 2009, 12:06:57 PM

I've got a chassis/gearbox off a RC car that I'm going to be using for one of my projects. I'd like

to calculate (estimate) the gearbox ratio so that I can do things like determine max weight,

acceleration, of the robot as I'm building it.

I read the gears tutorial and it's helped quite a bit, but I think I'm missing a key part of the

equation. The gearbox (as most do) uses compound gears. The tutorial goes into calculating

torque for a compound gear, but I'm not sure how to apply this to my particular gearbox.

I've drawn up a diagram of what the gearbox looks like. It starts with a pinion gear attached to

the motor. It ends by driving two output shafts which go to the wheels. There are two levels in

the gear box, so I've labelled them top (blue) and bottom (red). The pinion gear and the bottom

of the first compound gear in the gear box have a different pitch. I'm not sure how this changes

my calculations, if at all.

Here is how I was thinking about solving this, so let me know if I've gone astray from reality. I

can cut the entire gearbox in half to simplify because it is a mirror image, making sure I take this

into account later when using the ratio for other calculations. Then, calculate the gear ratio of

each "stage" of the gearbox. Then, calculate the torque generated by each stage of the gearbox

and use that as the input for the next stage. This, I think, reduces down to simply multiplying

the ratios of each stage together to get the final ratio and then you can use that to get the final

torque, RPM, etc.

Hopefully this makes sense. Does it sound like I'm on the right path here?

The diagram is attached.
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2/6

Thanks guys (and the occasional gal)!

gearbox.png(26.16 kB, 809x366 - viewed 1015 times.) Last Edit: January 14, 2009, 12:48:23 PM by krich

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ArcMan

Supreme Robot

Posts: 519 Helpful? 4 Mmmm... Plasma

Re: Calculating Gear Ratio of Gear Box

Reply #1 on: January 14, 2009, 02:29:11 PM

You are correct in your thinking.

As you suspected, pitch does not play into torque or speed conversion - only the ratio of the

number of gear teeth.

Don't forget that your spur gears are not 100% efficient, either. The effective torque at the

output will be reduced by the gear inefficiency. You need to multiply your efficiencies together

just like you do with the gear ratios. I believe spur gears are about 98% efficient. You have 4

gear interactions per axle, so that's an efficiency of about 92%. Last Edit: January 14, 2009, 02:31:04 PM by ArcMan

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krich
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3/6




Thanks ArcMan.

I forgot to mention that the numbers inside the circles on the diagram are the number of teeth

on the gear.

Anyway, so here's my calculations:

Stage #1: 9/52

Stage #2: 15/38 (ignoring the middle 38 tooth gear as suggested in the tutorial)

Stage #3: 20/38

multiplies out to 2700/75088, or roughly 1:27.8 ratio.

For efficiency, I would use similar calculations, right?

Eff = gearTypeEffeciency ^ (# of Gears - 1) equation from the tutorial, I have

Stage #1 (2 gears) = ~90% efficiency for spur gears

Stage #2 (3 gears) = 0.90 ^ (3-1) = 0.81 = ~81%

Stage #3 (2 gears) = ~90%

multiplies out to 65.6% efficiency.

On a related note, I disassembled the gear boxes, removed the dirt and ground up leaves that

were hanging around in there, and then lubricated the gears with some Servo Lubricant that I

had laying around. Once I reassembled the gearbox, it moves much less freely than when it did

before (although probably still acceptable). There's not any room for physical issues related to

the reassembly of this gear box, so it has to do with the cleaning and lubrication. What could
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4/6

cause this? Is my lubricant too viscous, or did I use too much, or is this normal and is a trade off

between slow, goopy, long-life gears and fast, dry, self-distructing gears?

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ArcMan

Supreme Robot

Posts: 519 Helpful? 4 Mmmm... Plasma



Quote from: krich on January 14, 2009, 03:08:44 PM

Eff = gearTypeEffeciency ^ (# of Gears - 1) equation from the tutorial, I have

Stage #1 (2 gears) = ~90% efficiency for spur gears

Stage #2 (3 gears) = 0.90 ^ (3-1) = 0.81 = ~81%

Stage #3 (2 gears) = ~90%

multiplies out to 65.6% efficiency.

No, that's not correct. What the tutorial is saying is that you have 4 gears in the train so your

efficiency is 90% ^ (4-1) = 72.9%.

As far as lube goes, I always lube my spur gears with (just a little) light white lithium grease.

Don't put any goopy grease on them. All the servos I've worked on also had white lithium grease

as well. Perhaps yours don't. Anyway, you can get that grease at any hardware store.
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5/6

Last Edit: January 14, 2009, 04:12:52 PM by ArcMan

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krich




OMG, I feel like a complete dufus. Now that I've actually spent the time to understand the

equation, it is essentially multiplying the number of "contacts" between gears with the gear's

efficiency rating. Very straight forward.

As it turns out, that's what I was doing in my example, but (in typical Krich form) making it more

difficult than it needed to be. If you look at my first crack at this, I was simply multiplying 0.9 by

itself 4 times.

Interestingly enough, ArcMan, your answer is correct too, with the exception that I think you

forgot to count one of the gears. On the one side of the gearbox we're discussing, there's the

pinion gear, the three intermediate gears, and the drive shaft gear. This discussion makes me

wonder about both sides of the gear box and if the other side affects the total efficiency as well.

Probably so. So, that's 8 gears, 0.9^(8-1)=48%. Blah!

About the grease, you guessed it. It's the white lubricant found in servos. It's not marked, but

pretty sure its the same stuff you're talking about. My example was to show the extremes,

gooped vs. dry. Mine are lubricated somewhere in between those extremes; closer to the dry, I

figure. I'm hoping that as the excess lubricant is thrown off the gears by centrifugal force, the

action will get looser. I have yet to run the gearboxes with the motors.

Thanks ArcMan!!

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6/6

Admin

Administrator Supreme Robot

Posts: 11,492 Helpful? 165o


Reply #5 on: January 27, 2009, 12:35:55 AM

Since you have compound gears its a little more complicated - you need to account for the 52/15

stage and the 38/20 stage too!

And yeap you are right, there are four different locations that the gears mesh. So if it has 98%

efficiency at each mesh, it'll be .98^4 = ~92%. But if your gears were contaminated then you

probably have more like ~90% at each mesh, giving more like 66% total efficiency.
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