I am contemplating the construction of a very small tensile force sensor based on the following principle: 1) Use positional feedback to a linear solenoid to maintain a fixed position when the plunger is under tension -- e.g., automatically vary the PWM input to the solenoid as needed to exactly balance that tension. 2) Determine the tensile force based on the required input to the solenoid.
First, let me know if there's any problem with the above concept that I might be overlooking. I realize there probably has to be some kind of damping to control oscillations and to optimize the frequency response of the sensor, but that's for another day.
Now for the main question. I haven't been able to locate a commercial linear solenoid of the size that I think I need, so I'm contemplating fabricating one from scratch. This would be a continuous duty cycle solenoid, and I want to minimize the power draw required to maintain a particular steady state force (order 0.01 to 0.1 N).
My thinking so far:
1) For a given coil radius, solenoid force F is proportional to the number of turns and thus to L*I, where L is the length of the conductor and I is the current.
2) For a given coil volume (excluding the empty interior), the length L is inversely proportional to the square of the conductor diameter D.
3) The resistance R of the conductor is proportional to L/D^2 and thus to 1/D^4 (from 2).
4) The current flow is V/R, proportional to V*D^4.
5) Combining (4) with (1) and (2) gives F proportional to V*D^2
6) Using (4), steady state dissipation of power is proportional to V^2 * D^4.
What (5) and (6) seem to tell me is that, for a given voltage, I can maximize solenoid force AND minimize power consumption by using the thinnest possible conductor (e.g., 44 AWG) and thus the largest possible number of windings in a given volume.
I realize that the inductance goes up with more windings and thus the time response to changes of input, but this strikes me as likely to be important only if one is trying to measure very rapid changes in force.