Design of Electrical Solenoid

The information you ask for is VERY complicated and depends on the specific design of the product you are dealing with.

We manufactured 12V DC solenoids for some years.

Total air gap in the magnetic circuit (armature/core/yoke) is significant to determine closing forces.

Air gap in the magnetic circuit is significant to determine holding force once activated.

Number of turns in the coil is important as is total coil resistance (More important than length of coil wire) as the magnetic attraction is determined by "amp turns" of flux created.

Remnant magnetism in the non-energised magnetic circuit is important. Wrong material selection and the solenoid will become permanent magnet and stay closed.

Relative cross section of magnetic path material is important so as to avoid "saturation" of the flux path.

Coil wire purity is VERY important. Cannot use just any old wire.

Bobbin winding (coil density) is also critical as it affects the coil resistance and thus the current flow.

Friction in the moving part (armature to yoke) is also important. Pressed parts need to be "square" and true.

Generally we treated the two states as separate "static" conditions and did the calculations to check that both were stable.

Determination of the magnetic attraction you require for "snap shut" of contacts was something that we experimented with basically a ratio of theoretical magnetic force to "off" condition spring strength.

Hopefully some of the others will be able to give you more empirical information.

Hi,

temperature rise will rise the resistivity of the coil by 0.4%/degreeC, so if constant current operation the force will not be changed but the resistive heating.

Air-gaps are explained in a post above.

Stroke to bobbin length is not a valid parameter.

What you would have to do:

Solve three equations that are fairly complicated:

1. The magnetic flux in a magnetic circuit is constant. Relation of stray-flux (wasted) to useful flux can be determinated only by FEM or guessed.

2. The magnetic field-strength x length increment, integrated along a flux line is zero in a permanent magnetic circuit and = (turns) x (current) in an electromagnetic circuit.

3. The material gives a relation: Flux density = (relative permeability) x (vacuum permeability) x (field-strength)

Equation 3 to be taken for the typical 3 (2) materials in this magnetic circuit: iron, (magnet), air.

From this you get the flux and flux-density in iron and air as a function of position.

Flux density can be recalculated to give magnetic energy.

Derivative of magnetic energy with respect to movement gives the force.

I have the basic equations at hand but to convert these into a readable form would require a full day working time (if hand written), if done in a program (Mathcad) around 10 to 14 days. This would incorporate a simplified calculation of the relation of useful flux to stray flux.
This will neglect the eddy currents in the electrically conducting iron parts.

RHABE

(Formal offer available if you need extended help)