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Motor Calculations - some help

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Hello all,

I have been attempting to do some calculations based on the link and I'm a bit unclear about some aspects of it. 

The parameters I am using are:

Mass = 27 lbs.
Acceleration = 10 in./s (or .83 ft/s)
Velocity = 20 in./s (or 1.67 ft/s)
Efficiency = .75

So I do the equation:

Torque * rps = 27 * .83 * 1.67 * (1 + .75) / 2 * pi

The answer I get is ~:


Since I am using differential drive I will be using two motors.  So the RMF for one motor should be:


So that is saying some rps times some torque (in lb-in.) equals 5.22 right?

So now I am looking around a various motors and it occurs to me that I'm obviously going to have some gears between the motor and the axle (assuming a non-geared DC
motor).  So how do you factor gear reduction into the equation?  For instance, look at the motor on this page called "Mabuchi Speed-550 motor".

It's specs are:

Stall Torque: 91.65 oz-in
RPM: 24,000 rpm

I don't want to stall the motors so let's say operating torque would be 45 oz-in or .234 lb-ft.  RPS would be RPM/60 so RPS would be 400.  So this particular motor would give me an RMF of:


So it seems this motor is massively over powered right?  However, I wouldn't be hooking the motor up directly to the wheel.  So how does gear reduction play into this?  Or is it somehow already taken into account?  Any info on whether or not my calculations/conclusions are right would be greatly appreciated.


ok two things . . .

first, i found an error in my equation. instead of:
Torque * rps > = Mass * Acceleration * Velocity * (1 + efficiency) / (2 * pi)

it should read:
Torque * rps > = Mass * Acceleration * Velocity * (2 - efficiency) / (2 * pi)

sorry!!! ill correct that as soon as i can . . .

ok so your RMF with the correction should be 7.44 ft lb / sec (the RMF for one motor should be half that, since its differential drive)

referring to this datasheet:

now looking at the motor . . . so for torque, you dont want to calculate for stall torque, what you want is torque between maximum efficiency (58mNm at 21840rpm) and maximum power (407mNm at 12000rpm), depending on your application. If power or motor overheating is a problem, you want maximum efficiency. If torque or motor cost is an issue, you want maximum power.

So the RMF for the motor would be either 15.57 lb ft / sec at maximum efficiency or 59.99 lb ft / sec at maximum power. It looks like you can run at maximum efficiency with no problem. What happened was the speed you listed is for zero torque, and the torque you listed is for zero speed (not possible¬  :P).

Now for your other question about gear reduction . . .
Gearing is when you change the torque to speed ratio, so the RMF is unaffected. If your output will have half the rpm, but twice the torque, RMF doesnt change. However, since you have added gears, you have decreased the efficiency (reducing effective RMF). In my experience, homemade gear setups are low efficiency, so its better to buy a motor with a built in gear head.

in case you havnt seen this, here is where I give efficiency estimates for different types of gearing:

hope that helps!

Thanks for the great explanation! 

I had a sneaking suspicion that the RMF would be unaffected by gearing.  I do have one more question though.   Your revised calculations indicate that I would need an RMF of 3.72 per motor.

So at maximum efficiency, the motor I was looking at would have an RMF of 15.57.  Almost 5 times the RMF I need.  Am i right in thinking that this motor is excessive for this application, or is it a "meets or exceeds" the RMF situation I am looking for?  I want my robot to have motors that are "big enough" as opposed to "PLENTY big!"  if you know what I mean. 


Calculating RMF is just to find motors that will do the job . . .

but there are really even more issues to consider:
cost of the motor
power requirements of the motor (lower voltages are better)
weight of the motor (lighter robots are always better)
motor size and space requirements (does your robot need to be small?)
terrain (robot going uphill or over bumps?)

and even deeper questions:
how easy is it to mount the motor to wheels and the chassis? when you are finished this project, and scrap this robot, would the motors be useful in the future?

I perfer to rate my motors with a 1.5 safety factor, meaning multiply the required RMF by 1.5. This gives me play room in case of design changes, unexpected flaws, or a miscalculation - each occuring often in the prototyping stage.

I feel dumb for not doing this before . . .

an excel sheet to do the calculations for you has been added to the tutorial:

Also, I used your robot as the example . . .
I added in calculating for inclines too, and it turns out your robot needs an RMF of ~30 to go up a 5 degree slope.


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