Electromagnetic simulation of Duffing lock

Duffing's electromagnetic lock is a kind of elecromagnet used to permanent attraction of magnet keeper (5) and it fast releasing when additional coil (3) will be energized.

A holding coil (1) is constantly supplied with properly chosen current that saturates relatively thin iron core in the surroundings of releasing coil (3). If additional current flows there, a magnetic field will be significantly reduced in parts (4)+(8) and only slightly increased in parts (2)+(7) - because of the saturation effected by holding coil. If the force of keeper attraction is comparable with the stretching force of the spring, even small demagnetizing current will release the magnet keeper.

Problem type:
Plane parallel nonlinear magnetostatic.

Geometry of the electromagnetic lock:

                           / 
                           \
                           /  <-- spring                            
                   ________\________
                  |        5        |<- magnet keeper
                  |_________________|
                 /  ___   | |   ___  \
                | 8| 3 |7 |6| 4| 3 |2 |
                |  | + | /   \ | - |  |
                |  |__/ /     \ \__|  |
                |      /  air  \      |<- core
                |     /_________\     |
                |    /|    +    |\    |  
                |   |_|____1____|_|   | 
                |                     |   
                |_____________________|
                      |    -    |
                      |_________| <- holding coil

Depth of electromagnetic lock: 5 cm.

Given:
Core and keeper material: iron
magnetic permeability: nonlinear
Holding coil current I_h = 20 A;
Holding coil turns n_h = 5000;
Releasing coil current I_r = 20 A;
Releasing coil turns n_r = 5000;
Force of stretching spring F = 200 N/m

Results:
When releasing coil is not energized (I=0, edlock_1 case) then the force of keeper attraction is about 215 N/m. Otherwise (I>0, edloc_2 case) the attraction force decreases to 180 N and becomes less then stretching force of the spring, and magnet keeper will be unlocked. The force was calculated by means of "Integral calculator" tools.

I_h, A·turns	I_r, A·turns	F, N/m
100000	0	215.1
100000	50000	179.9

Student's version	Professional version
-	Model6s.zip (4648 nodes)