Optimization of magnetic circuits for loudspeakers 1970 and now

One of the largest volume applications of permanent magnet materials are loudspeaker systems. High performant loudspeakers can be obtained by using rare earth permanent magnets with a high residual flux density, as for instance NdFeB. Because such devices are produced in a very large quantity and because the rare earth permanent magnets are quite expensive, it is very important for the manufacturer to keep the volume of the magnetic material used as low as possible. This aim can be achieved by using design methods to optimize the magnetic circuit of the loudspeaker, i. e. to obtain a given flux density in the air gap with a minimum volume of magnetic material. Prof. A. Timotin has done in this respect pioneering work. He and one of the authors of the present work have calculated the magnetic flux in the air gap as well the leakage fluxes of a loudspeaker system by solving analytically the magnetic potential equation with given boundary conditions. Also they have formulated certain constraints on the geometrical parameters of the system to be optimized. However the analytical solution could be obtained only under simplifying assumptions which practically are fulfilled only approximately. Such limitations can be avoided by using numerical methods for computation of the magnetic field. In this work we present the optimization of a large class of magnetic circuits for loudspeaker systems by using high precision numeric finite-elements-method computations.