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I need enough electric power to produce about 0.289 Nm with a rack and pinion system and compress 24 mm of a 110 mm x 21.6 mm, 0.99 N/mm steel spring.

What I have so far is that for a 10mm pitch diameter gear with ten 1mm gear modules and an angular velocity of about 15rpm (or 1.571 rad/s) I could use a 12 V power supply to deliver 37.8 mA and do this job with a DC motor:

I didn't know where to start from so I arbitrarily decided that the rack would slide the 24 mm with 3/4 of the gear full rotation in 3 s. That brought me to a 10 mm pitch diameter gear with ten 1 mm gear modules. The angular velocity I obtained is:

$$ \theta =\frac{3}{4} 2 \cdot \pi \cdot \text { rad } \quad w =\frac{\theta}{3}=1.571 \frac{\text { rad }}{s} \\ $$ Is that reasonable? Should I reconsider this decision?

Then, I assumed the torque on the gear to be the same as the work done by compressing the spring and set this to be the electrical power consumed:

$$E \cdot w=0.454 W$$

$$ V=12 V \quad I =\frac{(E \cdot w)}{V}=37.837 \mathrm{~mA}$$

Are these last equations correct? If so, how do I go about combining an adequate DC motor with the optimal gear ratio?

Any corrections, comments and/or suggestions are welcome!
For a more thorough description of my problem go to here

curioso
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  • The motor must be able to supply the peak torque. It can not be selected based on average torque. The friction of the drive train must also be considered. A motor of the power in question will not be very efficient. The electrical input power will be something like twice the mechanical output power. The speed reduction gear for the motor will also be very inefficient. –  Feb 23 '21 at 12:57
  • Such a low speed motor will be highly geared (like 200:1 for a 3000rpm motor), and tiny motors are pretty inefficient in the first place. I recommend allowing about 50% efficiency for each, or 25% overall, as a reasonable first guess. So multiply that current by about 4. –  Feb 23 '21 at 13:29
  • Alright, I will note that down. So I should look for DC motors with a maximum output torque above ~0.29Nm (29Ncm) and avoid relying too much on gear reduction? Would something like [this](https://befr.rs-online.com/web/p/dc-motors/9211460/) be a safe option? I'm working with a low budget. – curioso Feb 23 '21 at 14:48
  • That one is 300:1 geared and meets your speed and torque goals, so looks OK at first glance. –  Feb 24 '21 at 00:39

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