Self-excited oscillation of a closed-engine-governor loop. 2nd Report, Non-linear damping force and limit cycle evolution of an approximated single-degree-of-freedom system.

Abstract

In order to explain analytically the mechanism of non-linear damping force and limit cycle evolution, the present work derives an approximated differential equation of a single degree of freedom system with the closed-engine-governor loop, noting the phenomenon of very slow frequency while considering the results of the previous work. It gives a simple physical reasoning to the mechanism of the nonlinear negative damping force which causes an instability and a limit cycle evolution, resulting from a concept of the dynamic feedback-torque gain composing a nonlinear 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 inertia torque. This increases the amplitude, and at the final amplitude the energy put in by the negative damping force in the part the quantity of fuel injection is large is neutralized by the energy dissipated by the positive force in the part the quantity of fuel injection is small because of the nonlinearity of the torque characteristics.