On the nonlinear asymmetric vibrations of the unforced Watt governor: An exact analysis - Akuro Big-Alabo (Advances in Mechanical Engineering)
In this article, the conditions for the asymmetric nonlinear vibrations of an unforced Watt governor were investigated and the exact analytical solutions for its time period and displacement were derived naturally from the first integral of the governing dynamic model. It was demonstrated that the unforced Watt governor can undergo asymmetric vibrations due to bifurcation and the conditions for this to happen were derived based on the dimensionless rotational speed of its spindle and the initial conditions. In contrast to previously published exact solutions that are limited in their scope of application, the present exact solutions are applicable to all conditions of asymmetric vibrations. Simulation results revealed that the unforced Watt governor produces strong nonlinear asymmetric response even for small initial amplitudes and that the expression of the nonlinear effects depended strongly on the initial conditions. The present exact solutions provide benchmark solutions that are useful for calibrating the accuracy of other approximate analytical methods especially under highly stiff nonlinear conditions. The analytical framework develop in this study can be extended to other symmetric oscillators capable of bi-stable and tri-stable vibrations.