# Trying to calculate (guestimate?) the torque required to backdrive a gearboxed motor in coast mode

I have a situation where I want to actuate an arm with a motor, but after a certain point I want to set the motor to coast and be able to let the arm be pushed back by an external force.

The torques involved to drive the arm are on the order of 5-foot pounds. I need good positional accuracy of about 1 degree, so I figure I need at least 3600 counts per revolution at the arm in order to give enough feedback to the closed loop control circuit to maintain my positional accuracy. I’m considering the Neo 550 since it has 48 counts per rotation. In terms of power it’s way overkill, but I need a lightweight motor with a good encoder, and it fits the bill. That means I need about a 3600/48 = 75:1 gear ratio. At this gear ratio the torque required would be .1 nm, or about 1/10 of the 100A stall torque — so about 10 amps to maintain my position. If the motor stalls current is 100A at 12V, the winding resistance should be .12 ohms, so at 10 amps I’d be burning 10A^2*.12 ohms = 12 watts. So far so good.

My last question is: when I set this motor to coast, am I going to be able to back drive this motor at 1:48? What if I decide I want to go to 1:100 in order to increase the number of counts I give to the motor for maintaining my positional accuracy?

It’s all about friction…which is kind of hard to predict. I expect the arm will fall when it loses power, but there’s one way to find out…try it

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A common rule of thumb is somewhere around 10% torque loss per stage of gearing. When backdriving, though, torque “loss” is actually torque gain. Calculate accordingly.

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Thanks, Oblarg. That’s great info. Maybe I can use that info to get somewhere.

My thought is if I knew how much torque was required to overcome each planetary stage, I should be able to back-calculate the torque required to achieve a particular angular acceleration, but I don’t know where I would look to find values for the that, or what it would be called. Coefficient of static rotational friction? Makes no sense because there’s not really a normal force… in the same sense as there is in linear motion. Static rotational friction? Minimum torque to drive gearbox? It seems like there should be a gearbox parameter that describes what I’m after.

The “apparent static friction” at the shaft is a combination of a lot of things and is probably really really hard to model. An easier (though not perfectly accurate) model is to assume some nominal holding torque at the motor shaft, and propagate that through the gearing (with proportional losses/gains factored in accordingly) to get a holding torque at the output shaft.

If all else fails, get a torque wrench and measure the torque required to move the different gearbox configurations you’re considering.

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Even if it nothing fails, this is good advice. “Trust, but verify”

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