Parametric oscillatory motion in electromechanical devices

An analysis is presented which explains the mechanism of parametric motion in electromechanical devices. The implications of the mechanism, in the unstable operation of a wide range of electrical machines, are indicated; for example, in stepper motors where, under certain combinations of system parameters and operating conditions, oscillations superimposed on the synchronous rotary motion are observed. The simplest possible device in which parametric oscillations occur, the magnetically-maintained pendulum, is considered in detail and the conditions necessary for maintenance of motion are given. Expressions are derived for (a) the boundary frequency above which the damping torque is negative, and (b) the frequency at which peak negative damping occurs.