Research On Radial Basis Function Collocation Meshless Method For Moving Conductor Eddy Current Electromagnetic Problems

Many devices in the modern electrical engineering field contain moving conductors, such as the electric machine, electromagnetic switch, coil gun, maglev train and so on. To analyze and optimize their parameters, the electromagnetic field in these devices must be calculated. The moving conductor eddy current problem has always been an attractive and difficult problem in the computational electromagnetics. The traditional numerical method, for example, the finite element method needs to mesh the solving domain to construct the shape function. This leads to a great difficulty when the model varies because of the movement of the conductor. The newly developed meshless method, which is free from domain meshing, shows a deep potential to deal with motion coupled electromagnetic problems. The radial basis function (RBF) collocation method, which is a kind of pure meshless method, is studied and applied to solve two dimensional moving conductor eddy current problem in this paper. The structure of the paper is as follows.1. A novel superposition RBF collocation method is presented. This method, which is based on the source superposition principle and the linear property of the governing equations of RBF collocation method, could conveniently decouple the unknowns in the electromagnetic field equations. The arbitrary movement of the conductor is expressed through introducing moving coordinate systems to build the node model. The governing equations of the field are discretized through time domain iteration, which enable us to analyze the magnetic field and eddy current in the system at any time.2. The equality of the proposed method and the normal RBF collocation method is examined in both static and transient electromagnetic problems. According to numerical examples, we also prove that the proposed method is effective to solve moving conductor eddy current problems. Furthermore, a global model combined the magnetic field, electromagnetic force, conductor movement and the circuit equations is presented to simulate the dynamic process of a practical engineering device containing moving conductors. The model parameters are also analyzed for optimization.3. The application of the RBF collocation method in complex media electromagnetic problems is presented. First, an iterative RBF collocation scheme on the basis of Newton iteration and continuation optimization of the initial value is presented to deal with nonlinear media electromagnetic problems. The convergence property of this method is analyzed with a numerical example. Moreover, the domain decomposition method (DDM) combined RBF collocation method, which has been used to solve electrostatic problems, is extended to compute transient electromagnetic field. Through combining the proposed superposition RBF collocation method and the DDM, a time domain iterative scheme for multi-media moving conductor eddy current problems is presented. One advantage of this method is that the dimensions of the matrix equations solved in each iteration step could be reduced and the efficiency of computation could be greatly improved.