Study On Gear Transimission System Active Vibration Control Based On Piezoelectric Actuator

Gearing system is the most important component of rotating machinery and powertransmis-sion device. Due to manufacturing error, meshing impact and some otherinfluence, vibration of the gear pair will be generated in the engaging process. With theexpansion of the tooth surface, the tooth shape error, base pitch error and backlash will bealso increased, which deteriorates the gear transmission. The vibration of the gear systemcan not only produce noise, but also accelerate fatigue of the transmission system.Besides, gear box is the key part of a helicopter of transmission system, which cannotreduce accidents through the redundancy backup, gearbox fault, and it’s a direct threattowards a helicopter flight safety. Typical gearbox vibration contains several tonal signalsmixed with a broadband response. The tonal signals are basically the fundamental gearmesh frequency and their corresponding harmonics generated from the perturbation in thegear meshing process, in which the fundamental gear mesh frequency is the main cause ofthe annoyance problem. In order to suppress this part of the vibration and noise, an activegearbox vibration control structure is developed experimentally to suppress gearboxvibration due to transmission error excitation. At the same time, a filtered-x LMS controlalgorithm is proposed and implemented to generate the appropriate control signals.At first, a gear pair system model is built to assist in the design of the experimentalactive structure, to gain a better understanding of the nature of gear response due totransmission error excitation. Based on an active shaft transverse vibration controlconcept, an active internal gearbox structure, combined with the piezoelectric actuator, isdeveloped to suppress gear pair vibration due to transmission error excitation in a directway.Complex nonlinear hysteresis is present in virtually all piezoelectric actuators. Thesenonlinearities can excite unwanted dynamics which reduced system performance andeven lead to unstable system operation, especially in active vibration control applicationsowing to phase lag. The paper describes a compensator design method for invertiblecomplex hysteretic nonlinearities based on Prandtl-Ishlinskii hysteresis operator. Linearinequality constraints for the parameters guarantee the unique solvability of theidentification problem and the invertability of the identified model. The correspondingcompensator can be directly calculated and thus efficiently implemented from the modelby analytical transformation laws. This allows an efficient implementation of the compensator for real-time control. Finally，the compensator design method is used togenerate an inverse feed forward controller, results of simulation proved the method’savailability.Active vibration control use an active anti-force from secondary path to suppress orattenuate vibration and noises，one of the control algorithms is filtered-x least meansquare (FxLMS) adaptive algorithm. Based on structure of FxLMS algorithm, Level-2S-function is used to build a new FxLMS blocks in MATLAB/Simulink and apply it inoffline vibration active control system simulation. On the condition of convergence,performance analysis is given by adjusting the interior parameters to test the controlalgorithm block. Finally, the custom FxLMS block is downloaded to DSpace as controller,and used in hardware-in-the-loop simulation of active vibration control on a geartransmission system. Results verify the custom FxLMS block’s feasibility built byLevel-2S-function and control algorithm’s efficiency.A gearbox test-bed is also developed with a piezoelectric actuator inside for applyingcontrol forces to the shaft. Lastly, the custom FxLMS block is downloaded to DSpace ascontroller. Experiment results showe that the proposed FxLMS controller performs aneffective performance. Up to35dB of gearbox vibration has been attenuated at somefundamental gear mesh frequency.