Active vibration control of a gear pair using a direct hybrid adaptive control method

A direct hybrid adaptive control method based on the Lyapunov-like stability theorem is proposed for perforating active vibration control of a gear pair system being subjected to multiple harmonic disturbances. The analysis uses a reduced single-degree-of-freedom definite gear pair representation of the elastic mesh mode, which includes the effect of time-varying tooth stiffness. It is assumed that the resultant actuation force can be directly applied to the gear body along the tooth contact line-of-action employing specially configured inertial actuators for suppressing rotational vibration. The proposed controller simultaneously adapts both the feed-back and feed-forward gains, and only requires knowledge of the instantaneous gear rotational speed and number of gear teeth or equivalently the fundamental gear mesh frequency. The numerical results of this study show that the proposed controller is somewhat insensitive to estimation error at the fundamental gear mesh frequency and the resulting vibration control is better than those provided by the well-known adaptive notch filter and Filtered-X LMS algorithms. Furthermore, the dynamic optimization normalization enhancement is incorporated into the basic controller to optimize performance and improve robustness.