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

To investigate the noise reduction of an electrical machine, the deformation and vibration of the cores are evaluated by using the coupled magnetic and mechanical analyses [1]. In these analyses, the local force calculated by using the flux distribution obtained from the magnetic field analysis is required in the mechanical analysis. In the local force calculation [2], the Maxwell stress tensor is usually used. The Maxwell stress tensors are often represented by the Minkowski and Chu models with linear and nonlinear energy expressions, respectively. In the nonlinear magnetic field analysis, the volume forces, which move the magnetic bodies, obtained from both models coincide with each other, whereas their local forces, which deform the magnetic bodies, are different. Therefore, more investigation is required to clarify the suitable expression of the Maxwell stress tensor. In this paper, to clarify the proper expression of the Maxwell stress tensor for the local force calculation of a nonlinear magnetic body, the Maxwell stress tensors are derived from the Fleming’s left hand rule because the volume current density can be used to determine the magnetization in the nonlinear magnetic body. As a result, a new Maxwell stress tensor is derived. The surface force obtained from the new Maxwell stress tensor is compared with those obtained from the ordinary Minkowski and Chu models, and the equivalent magnetizing current method [3] to show the effectiveness and validity of the proposed Maxwell stress tensor.