Escape through parametric instabilities in a non-ideal motor driven geared rotor shaft driveline

Abstract

Periodically-varying gear mesh stiffness is a source of parametric excitation, which causes torsional instabilities in geared rotor systems. Unbounded amplitude growth at instability requires energy to be continuously pumped into the torsional modes from some ideal source of infinite power. However, real or non-ideal drives can only provide a limited amount of power; hence, the amplitude growth of torsional oscillations is bounded even at the unstable regions. In this paper, the coupled electro-mechanical dynamics of a geared rotor system driven by a non-ideal DC motor is investigated. It is shown that the system exhibits symptoms of Sommerfeld effect when driven through a torsionally unstable zone. As the system transitions through an unstable speed range, harmful torsional vibrations of the rotor-shafts consume a major part of the motor power, thereby reducing the power available to spin the rotor-shafts. Under some conditions, the spin speed gets captured at the instability zone, from where an escape occurs in the form of a speed jump on supplying a certain minimum threshold power. The design guidelines to suppress this harmful Sommerfeld effect are then proposed.