Quote:
Originally Posted by kklokreach
How exactly do you calculate the gear ratio for a gearbox by hand?
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The gear ratio of a gearbox is usually expressed in turns of the input to turns of the output. To find this you divide the number of teeth on the bull gear (the gear on the output side) by the number of teeth on the pinion gear (the gear on the input side). For each additional stage you multiply the ratios of each stage together. So if your first stage was 12:48 (input : output) and the second stage was 20:40, your overall gear ratio would be (48/12)*(40/20):1 which is equal to 8:1.
For gears in series like this:
You only need to use the number of teeth on the first gear and the number on the last gear as the intermediary gear(s) do(es) not affect the ratio. For example if the above picture was a 12 tooth gear connected to a 40 tooth gear connected to a 72 tooth gear the ratio would be (72/12) = 6:1 which is the same as if you calculated each pair's ratios and multiplied them together; (40/12)*(72/40) = 6:1
Quote:
Originally Posted by kklokreach
I understand that it is Input gear/Output gear but I don't understand which constants to use and what to do when converting because when I do the math I get FPS and Torque output to be in the thousands.
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First lets define some variables:
tau(i) = your motors' stall torque
tau(o) = your gearbox's max torque output
omega(i) = your motor's free speed (unloaded rpm)
omega(o) = your gearbox's max rpm output
r = you gearbox's overall gear ratio
R = your wheel radius (in feet)
v(o) = your robot's maximum translational velocity
To get the maximum torque the gearbox will output you simply multiply your motor's stall torque by the gearbox's gear ratio:
tau(o) = tau(i) * r
To get your robot's maximum speed you first need your max rpm which is:
omega(o) = omega(i) * (1/r)
Then to get the max speed you need to convert the rpm (angular velocity) to translational velocity, which is:
v(o) = omega(o)*(2piR)/60
(note you're robot will never be traveling at that speed as you will have energy loss due to friction and other sources and your motors will always have some amount of load on them as well which will make them rotate more slowly than they do at their free speed)
The simplest way to do all of these calculations would be to just use a premade excel spread sheet like JVN’s design calculator which can be found here:
http://www.chiefdelphi.com/media/papers/2755