Relay dynamics simulation using MATLAB and ActiveField (QuickField Object Model)

QuickField simulation example

The electromagnetic and spring forces act on the plunger. Both forces depend on the plunger position. Calculate plunger motion function.
To combine the electromagnetic field analysis with the moving core dynamics both MATLAB and QuickField are used. Interaction between QuickField and MATLAB is performed using ActiveField application programming interface.

Problem Type
Axisymmetric problem of DC magnetics.

Geometry

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

Task
The electromagnetic and spring forces act on the plunger. Both forces depend on the plunger position. Calculate plunger motion function.

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 f_spring(x) = k·(x_spring.free - x) and electromagnetic force.

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

The calculations are stopped when x=x_min (pull in position, plunger hits damper).