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