Self-Excited Vibration of a Closed-Engine-Governor Loop. Approximate Nonlinear Analysis and Amplitude of Limit Cycle of a Single-Degree-of-Freedom System.

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In a governed engine, the idling speed cannot remain constant and is followed by a low-frequency noise of its own. This fluctuation of engine speed is called low-speed hunting. In order to explain analytically the mechanism of nonlinear damping force and limit cycle evolution, the previous work derived an approximate 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 experimental results. It gave 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. The present work provides the analytical solutions of the amplitude of limit cycle, which agree well with the experimental results and the results of direct numerical integration, and which also gives insight into the effects of the various parameters of the closed loop.