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I'm trying to understand solenoid behavior through the magnetic saturation region.

Most solenoid charts show a linear force vs current:

enter image description here

This doesn't seem to show any saturation. I assume that's because the currents on the chart are too low.

What happens when parts of the magnetic circuit start to become saturated?

Does the graph level off, or does the force continue to increase, but at a reduced rate?

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  • \$\begingroup\$ At saturation, the differential \$μ_r\$ of the plunger asymptotically approaches 1. I think this would mean the force would asymptotically approach a constant, but I'm not certain and can't be bothered to do the math on it right now. Hence why this is a comment and not an answer. \$\endgroup\$ – Hearth Oct 28 '18 at 23:39
  • \$\begingroup\$ With as much air gap as there is in a solenoid, does the iron even saturate to a significant degree? \$\endgroup\$ – TimWescott Oct 28 '18 at 23:48
  • \$\begingroup\$ @TimWescott Well, if you put a truly ridiculous current through it... \$\endgroup\$ – Hearth Oct 28 '18 at 23:50
  • \$\begingroup\$ The "solenoid" in this case will be a coil gun. So there may be lot of current. \$\endgroup\$ – Drew Oct 29 '18 at 0:01
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Your assumption is correct. As you approach saturation, B-H curve flattens out, meaning that a further increase of magnetic field strength does not result in an increase in flux density. So, the solenoid force will drop just as you predict for a given gap length.

Solenoids designers are generally concerned with starting force, because it takes less magnetic field strength to get the steel magnetized as the gap becomes smaller. As a result, solenoid drive circuits are often often designed to charge capacitors to provide high initial current to get the load moving, or start with a high current and use PWM to drop the current after closing.

An annealed low-carbon steel like 1018 will have a maximum flux density in the 1.5-1.8 Tesla range, and exotic cobalt alloy materials like VACOFLUX achieve 2.4 Tesla. You should design such that the starting (full gap) flux density in the flux path at the point of lowest cross sectional area is below these values. Otherwise, you will be supplying more current than necessary to magnetize the steel to its maximum.

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  • \$\begingroup\$ So the force doesn't increase at all beyond saturation? \$\endgroup\$ – Drew Oct 29 '18 at 22:39
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    \$\begingroup\$ The force does increase, but you have dramatically diminishing returns. If you are aiming for velocity, you should concentrate on providing enough magnetic field strength to get you near saturation over a long length of time. Applying the force over a longer period will get you more velocity more economically than trying to get high localized currents. \$\endgroup\$ – John Birckhead Oct 30 '18 at 14:10

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