Improving force characteristics of linear oscillatory generator with spring permanent magnet for Stirling engines based on subdomain method

In this paper, an electromagnetic analysis method is proposed to improve force characteristics by using spring permanent magnets (PMs) along the axial and circumferential directions of a linear oscillatory generator (LOG). For accurate electromagnetic analysis, a detailed analysis model of the LOG is developed, and the governing equations of each subdomain are derived based on Maxwell's equations and electromagnetic theory. Analytical solutions of the magnetic vector potential in each subdomain are derived using boundary conditions. The reliability of the proposed method is verified through a comparison with the results of a two-dimensional finite element analysis (FEA). In particular, the force characteristics depending on the spring PM is effectively derived by considering the three-dimensional (3D) circumferential and axial end effects. The proposed analysis method is used to determine the thickness of spring PM that transforms the detent force of the LOG with the spring PM into restoring force. The reliability of the proposed analysis method is verified through comparison with the results of a 3D FEA.