Multidomain modeling of a variable reluctance transducer.

The variable reluctance magnetic transducer consists simply of a magnetic air gap and a magnetic return path that are supplied with static and dynamic sources of magnetic flux. The dynamic flux is generated by a coil current. The static flux may come either from a permanent magnet or a coil. The attractive magnetic force across the gap is modulated by the dynamic flux to provide the mechanical excitation for the device. The variable reluctance device is fundamentally nonlinear for at least three reasons: (1) the mechanical force across the gap is a quadratic function of the total magnetic flux, (2) the changing gap dimension changes the reluctance in the magnetic circuit so that the flux does not change linearly with coil current, and (3) saturation of the magnetic circuit may be an important aspect of the design that must be included in the modeling. In practical cases, the dynamic variation in gap dimension is large enough that a linearized approximation is insufficient to predict the performance. An approximate model using a set of nonlinear differential and algebraic equations will be discussed that can predict the stability and performance of variable reluctance transducers.