Solenoid

[Stephen Dubovsky]

At 02:33 PM 1/29/97 -0800, you wrote:
>Hi,
>
>
>Can anyone tell me the formula for calculating the pull force of a 
>solenoid based on number of coil turns, wire size, voltage, resistance, 
>coil height, coil diameter, plunger material permiability, etc.?
>
>Thanks, Mazda
>
  Ok, we work in power electronics building inductors (for electric cars and
stuff) so magnetics is sort of our specialty (well, kinda).  The quick and
dirty answer is that there isn't one, so here is magnetics 0.101:
  1) field strength will be proportional to number of turns (N) and current
(I).  So, double the N and you can cut I in half to get the same field (or
double both to get 4x the field).
  2) The force will be proportional to field strength.
  3) voltage and resistance have little to do with it (except I=V/R in the
DC case).
  4) Coil height and diameter have very little effect because you are
putting a ferrous material w/ ur>>1 (mu relative)  (Iron is probably
10000-100000) inside of the coil.  This will concentrate almost all of the
field (but the obvious answer is to make them only big enough to house the
plunger comfortably.  The rule of thumb is the length should be 2x the diam,
but this is NOT strictly adhered to)
  5) Wire size only changes the resistance.  I cant remember the rule for
current density (get the metric and inch versions confused).  I THINK its
about 300A/cm^2.  It is usually a little less than a wire in free air
because the turns inside the coil can't be cooled effectively.  Have seen
designs that violate the rule 10:1, but the coil is dipped in conductive
epoxy and glued to a heatsink.  You will definately want to check check this
rule.
  6) The remaining elements are the plunger geometry.  Magnetic fields must
form loops (remember there are no magnetic monopoles in the world - at least
none found yet;)  The field likes to travel in iron (and other ferrous
materials), so for a standard bar/bolt wrapped w/ a coil the field must exit
at the ends, permeate into free space and end up at the other end (duh, an
electromagnet).  The trick is to then put a C shaped piece of iron around
the bolt to almost complete the path (a horse-shoe magnet).  This means the
field must only jump across the gap to the object you are pulling on,
through it a little ways, and back across the gap.  The objective, make the
gap as small as practicle.
  7)  The force is now related to the total gap length (both sides and any
cracks you may have).  I dont think its proportional but instead a 1/x or
1/x^2 relationship (here is where you and I want to do different things).
  8) It is very tough to predict force vs geometry without a finite element
fields program.  The easiest thing to do is to pick a reasonable looking
geometry, put a few turns on it, and run some tests.  Yep, you guessed it -
experiment.  Building an inductor, you usually dont care about the force,
but gap the material instead to control the maximum field and reduce the
effective permeability to something predictable (make the inductor design
repeatable and prevent saturation).
  9) There are ALOT of things I neglect here, so please Mr Maxwell, dont
yell at me.  A also tend to use field and flux interchangeably so plz don't
yell at me their either.  Anyway, have fun.  If anyone has actually read all
of this except Mazda, Im impressed.  If there is anything else I can help
w/, you know how to reach me...

SMD
--
Stephen Dubovsky
dubovsky at vt.edu

95 Yamaha FZR600
83 Porsche 911SC
84 Jeep Cherokee