Scalar-based finite element modelling of 3D eddy currents in thin moving conducting sheets

A number of electromagnetic devices contain geometries which prove to be challenging when modelled using finite elements. One type of complexity may be a physical dimension which is significantly smaller than the others. For example, a design of maglev coil-track systems may involve the use of relatively thin track sheets of finite widths and extensive lengths. A new set of formulations is presented for the 3D eddy current finite element analysis of thin moving conducting sheets. The conducting sheet, moving at a constant linear velocity in the direction of the sheet plane, is modelled using two scalar quantities, T and the normal component of the magnetic flux density. The second scalar, B·n, is introduced to maintain a second order partial differential equation system. Scalar potentials are used to model the nonconducting regions. This scheme, implemented for time-harmonic cases, is compared with the more usual A-ψ method using a computer model, and force predictions agree favourably. In the DC limit, it is possible to eliminate the T variable, thereby retaining only the B·n scalar in the sheet description. Two experimental test problems serve to illustrate drag and lift force predictions obtained using the two new schemes, T-B·n-ψ and B·n-ψ, and the more usual moving A-ψ formulation