A Novel Gauged Vector Potential Formulation for 3-D Motional Eddy-Current Problems Using Edge Elements

Abstract

The accurate computation of motional eddy currents is essential for the design of electromagnetic devices such as eddy-current brakes. When the conductors are uniform in the moving direction, it is convenient to formulate and solve the problem within a fixed coordinate system without needing to use two or more coordinate systems and connecting the fields in each region. Because ungauged magnetic vector potential (MVP) formulation can be solved using only iterative linear solvers, which are not so robust as direct solvers, it is desirable to impose proper gauge condition to ensure that the formulation has a unique solution. In this paper, a novel gauged formulation for motional eddy-current problems using finite edge element approximation of the MVP is proposed. Both transient and steady-state motional eddy-current problems are studied. A dummy scalar variable is introduced in the non-conducting region to enforce the Coulomb gauge, together with the gauge condition in the conducting region, to ensure that the resultant linear system can be solved using direct linear solvers. Three-dimensional numerical examples are presented to showcase the accuracy and usefulness of the proposed method for practical engineering computation.