product

applications

support

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

magnetic force between coaxial coils, electromagnetic FEA finite element analysis of cylindrical coils

In the lab the forces are measured by electrotic balance on which one of the coils is installed. 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.

**Given**

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.*

**Task**

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

**Solution**

Along the horizontal symmetry axis (line *ab*) B_{n} =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 the coils:

Shield type |
Frequency |
Interaction force, mN |
Problem name |

No shield | 50 Hz | 0.533 | lab2.pbm |

Steel | 50 Hz | 0.098 | lab2_Fe.pbm |

Aluminum | 50 Hz | 0.282 | lab2_Al.pbm |

No shield | - | 0.533 | lab2c.pbm |

Steel | - | 0.138 | lab2c_Fe.pbm |