# Magn2: Solenoid actuator

A solenoid actuator consists of a coil enclosed in a ferromagnetic core with a plunger. Calculate the magnetic field and a force applied to the plunger.

Problem Type:
A nonlinear axisymmetric problem of magnetics.

Geometry:

All dimensions are in centimeters.

Given:
Relative permeability of air and coil μ = 1;
Current density in the coil j = 1 000 000 A/m2;
The B-H curve for the core and the plunger:

 H (A/m) 460 640 720 890 1280 1900 3400 6000 B (T) 0.8 0.95 1 1.1 1.25 1.4 1.55 1.65

Problem:
Obtain the magnetic field in the solenoid and a force applied to the plunger.

Solution:
This magnetic system is almost closed, therefore outward boundary of the model can be put relatively close to the solenoid core. A thicker layer of the outside air is included into the model region at the plunger side, since the magnetic field in this area cannot be neglected.

Mesh density is chosen by default, but to improve the mesh distribution, three additional vertices are added to the model. We put one of these vertices at the coil inner surface next to the plunger corner, and two others next to the corner of the core at the both sides of the plunger.

A contour for the force calculation encloses the plunger. It is put in the middle of the air gap between the plunger and the core. While defining the contour of integration, use a strong zoom-in mode to avoid sticking the contour to existing edges.

The calculated force applied to the plunger F = 374.1 N.

Comparison of Results:
Maximum flux density in z-direction in the plunger:

 Bz(T) Reference: 0.933 QuickField 1.0183

Reference:
D. F. Ostergaard, "Magnetics for static fields", ANSYS revision 4.3, Tutorials, 1987.

See the Magn2.pbm problem in the Examples folder.