Proposal of Maxwell Stress Tensor for Local Force Calculation in Magnetic Body

Local force distribution is required to evaluate the deformation and vibration of a core in an electrical machine using the mechanical analysis. In the local force calculation, the Minkowski and Chu models with linear and nonlinear energy expressions are often used for the Maxwell stress tensor in linear or nonlinear condition, respectively. In the nonlinear magnetic field analysis, the volume forces, which move a magnetic body, obtained by using the above two models coincide with each other, whereas their local forces, which deform the magnetic body, are different. In this paper, a new expression of Maxwell stress tensor derived from Fleming's left-hand rule is proposed. Then, the local forces of a simple magnetic body obtained by using various expressions of Maxwell stress tensor are compared with that obtained from the equivalent magnetizing current method. The surface force obtained from the proposed Maxwell stress tensor coincides with the equivalent magnetizing current method, and it is much different from those obtained by using the Minkowski and Chu models in this simple analytical model. Finally, the local force distribution in a 2-D finite element model is also demonstrated to show the necessity of the proposed model.