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Relay dynamics simulation using GNU Octave and ActiveField (QuickField Object Model) - QuickField simulation example

Relay-plunger motion under electromagnetic and spring forces, with GNU Octave integrating the mechanical equation while field force changes with position..
To combine the electromagnetic field analysis with the moving core dynamics both GNU Octave and QuickField are used. Interaction between QuickField and GNU Octave is performed using ActiveField application programming interface.

Engineering question

How is the relay's plunger motion calculated using QuickField and GNU Octave?

Answer
Set up an axisymmetric QuickField DC Magnetics problem and replace the multi-turn coil with an equivalent total current. Use GNU Octave to integrate the plunger's equation of motion, invoking QuickField at each step to get the electromagnetic force.

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Typical applications
electromagnetic relays, relay armatures, electromechanical switching devices

Relay dynamics simulation using GNU Octave and ActiveField (QuickField Object Model)

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Simulation problem

Problem Type
Axisymmetric problem of DC magnetics.

Geometry
Relay dynamics simulation The electromagnetic and spring forces act on the plunger. Both forces depend on the plunger position Coil Plunger Spring 20 mm x Ø 7.2 mm

Given
Current I = 400 Ampere*turns;
Plunger pull-out position xmax = 10 mm.
Plunger pull in position xmin = 6 mm.
Plunger weight m = 4.5 g;
Spring constant k = 4 N/m
Spring free position xspring.free = 15 mm.

Task
Relay-plunger motion under electromagnetic and spring forces, with GNU Octave integrating the mechanical equation while field force changes with position..

Solution
The multi-turn winding is replaced with the equivalent total current.

The motion function can be found from second-order differential equation
m · d²x/dt² = f(x),
where m - is a plunger weight (kg),
x - is a plunger position (m)
f(x) - is the force acting on the plunger (N).
The force acting on the plunger is a sum of spring force fspring(x) = k·(xspring.free - x) and electromagnetic force.

The equations are solved in GNU Octave. The dynamic link is used to invoke QuickField and calculate the electromagnetic force at each step.

The calculations are stopped when x=xmin (pull in position, plunger hits damper).
GNU Octave to QuickField link The equations are solved in GNU Octave. The dynamic link through COM is used to invoke QuickField and calculate the electromagnetic force at each step GNU Octave QuickField Initial conditions x0 = xmax, v0 = 0 m/s Invoke QuickField to calculate Force(xi) vi+1 = vi + Force/mass*Δt xi+1 = xi + vi+1* Δt x>xmin ? true false EXIT

Results
The plunger hits initial position after 55 ms.
GNU Octave plot of the plunger position in meters vs time in seconds.

Video

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