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Main >> Applications >> Sample problems >> Cylindrical coaxial coils interaction force

Cylindrical coaxial coils interaction force

Task
Find the force between the coils carring current with and without the shield between them.

Experiment
Forces are measured by use of digital balance on which one of coils is installed (see the right picture below). Tests are performed with currents varying, and different conductors and ferromagnetics are placed between coils.

Problem type
Plane-parallel problem of DC magnetics, AC magnetics.

Geometry
Due to symmetry of the formulation only upper half of the problem (above ab line) is defined, and at the axis of symmetry (line ab) the boundary conditions are set.
Cylindrical coaxial coils interaction force >Find the force applied to the coils with current with and without the shield between them. O a b Metal disc 150 mm 25 mm 27 mm Ø300 mm Ø90 mm Ø160 mm

Given data
Current density in the coil j = 0.1 A/mm2.
Relative magnetic permeability of the steel disc μ= 1000.
Electrical conductivity of steel disc σ= 10 MS/m.
Electrical conductivity of aluminum disc σ=37 MS/m.
Coils are wound by insulated wire, so cross-section conductivity in coils σ= 0 S/m.

Boundary conditions
Along the horizontal symmetry axis (line ab) Bn =0.
Equation B=rot A in cylindrical coordinate system leads to A=const at the axis ab. The field fades at the infinity, so due to the condition of continuity of the potential A=0 at the line ab.

Results:
Field distribution around coils:

two cylindrical coaxial coils magnetic simulation

  • Time-harmonic magnetic field, f=50 Hz.

    Shield type

    Interaction force, mN

    Problem

    No shield

    0.533

    lab2.pbm

    Steel

    0.098

    lab2_Fe.pbm

    Aluminum

    0.282

    lab2_Al.pbm

  • DC magnetic field

    Shield type

    Interaction force, mN

    Problem

    No shield

    0.533

    lab2c.pbm

    Steel

    0.138

    lab2c_Fe.pbm

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    QuickField 6.4