Self-excited oscillation of a closed-engine-governor loop. (1st Report, Negative damping force of linearly approximated single-degree-of-freedom system.

Abstract

As a step toward explaining analytically the mechanism of limit cycle evolution, the present work derives a linearly approximated equation of a single degree of freedom of the closed-engine-governor loop, noting the phenomenon of very slow frequency while considering the results of the previous work. Further it gives a simple physical reasoning to the mechanism of the negative damping force which causes an instability, resulting from a concept of the dynamic feedback torque gain composing a static feedback torque gain and a virtual time constant depending on the phase relations between the feedback torque and the engine speed. Results show that there is energy input during a cycle when the dynamic feedback torque is larger than the inertial torque. This increases the amplitude, and the virtual time constant increases with increasing damping of the governing system due to the presence of a response lag of the speed-sensitive part in the governing system.