An internal active vibration control system is developed and verified experimentally to suppress gearbox housing vibrations due to gear transmission error excitation. The approach is based on an active shaft transverse vibration control concept. The system contains a piezoelectric stack actuator for applying control forces to the shaft via a rolling element bearing. A modified filtered-x LMS control algorithm with frequency estimation is developed to generate the appropriate control signals. The experimental results show 5-20 dB reduction in the housing vibration at the first two gear mesh harmonics over a wide gear rotation speed range. However, under certain narrow conditions, vibration amplifications at other locations are observed in the experiments, which might be attributed to the system un-modeled dynamics. In spite of this limitation, the approach developed is fairly promising. Studies are being performed to improve the overall performance of the prototype active control system.
Four actuation concepts for the active suppression of gearbox housing mesh frequency vibrations caused by transmission error excitation from the gear pair system are modeled and compared by computing the required actuation force and amplifier power spectra. The proposed designs studied consist of (i) active inertial actuators positioned tangentially on the gear body to produce a pair of reactive force and moment, (ii) semi-active gear-shaft torsional coupling to provide tuned vibration isolation and suppression, (iii) active bearing vibration control to reduce vibration transmissibility, and (iv) active shaft transverse vibration control to suppress/tune gearbox casing or shaft response. Numerical simulations that incorporate a transmission error term as the primary excitation are performed using a finite element model of the geared rotor system (dynamic plant) constructed from beam and lumped mass/stiffness elements. Several key comparison criteria, including the required actuation effort, control robustness and implementation cost, are examined, and the advantages and disadvantages of each concept are discussed. Based on the simulated data, the active shaft transverse vibration scheme is identified as the most suitable approach for this application.
KEYWORDS: Error analysis, Active vibration control, Actuators, Control systems, Adaptive control, Linear filtering, Teeth, Digital filtering, Vibration control, Analytical research
A direct hybrid adaptive control method based on the Lyapunov-like stability theorem is proposed for performing 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.
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