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### Author Topic: Calculating Gear Ratio of Gear Box  (Read 27266 times)

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#### krich

• Robot Overlord
• Posts: 165
##### 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.

Thanks guys (and the occasional gal)!
« Last Edit: January 14, 2009, 12:48:23 PM by krich »

#### ArcMan

• Supreme Robot
• Posts: 519
• 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 »

#### krich

• Robot Overlord
• Posts: 165
##### Re: Calculating Gear Ratio of Gear Box
« Reply #2 on: January 14, 2009, 03:08:44 PM »
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 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?

#### ArcMan

• Supreme Robot
• Posts: 519
• Mmmm... Plasma
##### Re: Calculating Gear Ratio of Gear Box
« Reply #3 on: January 14, 2009, 04:12:17 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.

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

#### krich

• Robot Overlord
• Posts: 165
##### Re: Calculating Gear Ratio of Gear Box
« Reply #4 on: January 14, 2009, 04:33:53 PM »
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!!