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# Relay dynamics simulation using Tcl/Tk and Parametric command line

The relay consists of the solenoid with moving core, which disconnects the electric switch contacts when the control current is running in the solenoid. The spring keeps the core in the pull out position with switch contacts connected. When the current is turned on, the magnetic field acts on the ferromagnetic core, overcomes the resistance of the spring, and pulls the core inside the solenoid to the pull in position where it is stopped by damper ring, which absorbs the shock. Operating time of this relay and the plunger motion function should be calculated.

To combine the electromagnetic field analysis with the moving core dynamics both Tcl/Tk and LabelMover are used. Interaction between LabelMover and Tcl is performed using parametric command line interface.

Problem Type:
Axisymmetric problem of DC magnetics.

Geometry: Number of turns N = 2000;
Current I = 0.2 A;
Plunger pull out position xout = 10 mm.
Plunger pull in position xin = 6 mm.
Plunger weight m = 4.5 g;
Spring constant k = 4 N/m
Spring free position xspring.free = 15 mm.

Problem:
The electromagnetic and spring forces act on the plunger. Both forces depends 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 fspring(x) = k·(xspring.free - x) and electromagnetic force.

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

The calculations are stopped when x=xin (pull in position, plunger hits damper).  View TCL file in the separate window: relay_control_script.tcl.

Results:

The plunger hits initial position (0.006 m) after 0.06 s. The plot was created using plotchart library.  Download simulation files (files may be viewed using any QuickField Edition)..