The setup: I'm trying to mount a leadscrew powered by this motor Tetrix Max Torquendado Motor on a 40ish pound robot, in order to lift it 4" off the ground. I already have the linear motion, latching mechanism, etc. I'd like it to go as fast as possible, but for now, let's just say that it can take 4 seconds to lift the robot. There will be 40ish pounds of tension acting on the screw when the robot is hanging, and minimal compression. Also, resolution is unimportant. It seems like there's a simple way to calculate the pitch/diameter leadscrew needed based on the torque, motor, and time requirements. What leadscrew should be used, and generally how could I calculate this sort of thing?
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$\begingroup$ You may be able to simplify the system to a pair of gears with a ratio of the the pitch to the mean circumference. Given that for every rotation the thread will move it's pitch. But I'm not sure how to get it from torque to linear force and make the units balance without making stuff up. This would allow you to calculate a maximum pitch to diameter ratio required to lift a load with a certain torque, which you then need to compare to the material strength to minimise the diameter. This also doesn't consider friction, but you may be able to get away with grease and a fudge factor in real life. $\endgroup$– KagekibaJan 9, 2019 at 17:07
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1 Answer
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The relationship between torque and force for a frictionless single-start leadscrew is [1]:
$$ \frac{F}{\tau} = \frac{2 \pi}{p} $$
where $F$ is linear lifting force, $\tau$ is torque, and $p$ is pitch.
You can choose a suitable torque which that motor is best operated at, you know the force is the weight of the robot, so you can calculate pitch.
The speed of lifting is determined by the power delivered by the motor. So you can get maximum speed by operating the motor at a torque that maximizes its power output. That's typically half its stall torque (700 oz-in) so choose $\tau$ = 350 oz-in.
[1] https://en.wikipedia.org/wiki/Screw_(simple_machine)#Torque_form
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$\begingroup$ What units should force and pitch be in? Also, does the diameter of the lead screw mater? $\endgroup$ Jan 10, 2019 at 2:27
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$\begingroup$ You can use any units as long as you carry them through the calculations (see high school physics textbook for how to do that). Or, to take a shortcut, choose a consistent system like (in, lb_f, lb_f-in) or (m, N, N.m). Diameter turns out not to matter at this level of idealization (frictionless, static, weightless rod). $\endgroup$ Jan 11, 2019 at 3:23