Direct Hybrid Adaptive Control of Gear Pair Vibration

A direct hybrid adaptive approach based on the Lyapunov stability theorem is proposed for performing active vibration control of a rotational gear pair subject to multiple-harmonic, transmission error disturbances. The analysis applies a reduced single-degree-of-freedom gear pair model of the elastic mesh mode with time-varying tooth mesh stiffness. It is assumed that the resultant actuation force for suppressing the rotational vibration of the gear pair can be directly applied along the tooth contact line-of-action by employing a set of suitably configured inertial actuators. The proposed controller simultaneously adapts both the feedback and feed-forward gains, and only requires knowledge of the fundamental gear mesh frequency that is given by the product of the instantaneous gear rotational speed and the number of gear teeth. The analysis indicates that the proposed controller is insensitive to the gear mesh frequency estimation errors, and the resulting vibration control is more effective than those provided by the adaptive notch filter and filtered-x LMS algorithms. The control theory also incorporates dynamic normalization and leakage enhancements in order to optimize performance and improve robustness. Finally, the salient features are demonstrated in several numerical examples.