Study On Active Vibration Control Of A Gear Pair System Based On Online Secondary Path Modeling

As a universal part, gear is an important transmission device in mechanical system.It plays a very key role in mechanical industry, traffic, chemical industry, aviation,spaceflight, shipbuilding, etc. But the manufacture and installation errors areunavoidable in practical application of the gear, of which the deformation is producedby the load. The mesh relation of gear pair is damaged by these errors and thedeformation. It causes the gear position is different from the theory location, and alsothe instantaneous drive ratio is changed. The internal incentive, engendered by collisionand impact between the teeth, causes the vibration and noise.In this paper, active control technology is applied for the gear pair system vibrationcontrol. An active vibration control structure in the internal gearbox, combined with thepiezoelectric smart material, is developed to suppress gear pair vibration due totransmission error excitation in a direct way. The approach is based on an active shafttransverse vibration control concept. In the control structure, a piezoelectric stackactuator is employed, which is constructed by some piezoelectric elements in the way ofseries connection in mechanics and parallel connection in electrics. The force generatedby the actuator can attenuate bending vibration of the shaft. So the vibration of gear pairsystem is suppressed. The main contributions of the dissertation include the following:1) A three-degree-of-freedom vibration mathematical model of the spur gear isestablished by using the lumped mass method in order to analyze dynamicresponse of the gear system, which lay the foundation for the active control.The influence of excitation frequency, load and damping on the gear vibrationstate and meshing form is discussed; Difference between linear and nonlinearmodels, time-varying stiffness model and time-invariant stiffness model forkinetic analysis is compared.2) An active control structure based on active shaft transverse vibration controlconcept is proposed. A mathematical model of the active control structure isconstructed by using the finite element method to lay the foundation for thesimulation study. The basic principle of adaptive filtering algorithms isexplained, and simulation study of active control based on the FxLMSalgorithm. The influence of the secondary path estimation error and referencesignal on the convergence performance and stability of FxLMS algorithm is analyzed.3) The reasons for online identification of the secondary path are analyzed.Several online identification algorithm by using additional random signals andits performance characteristics is discussed, the active control simulation is alsodone to verify the correctness of the algorithms. DLMS algorithm on themethod of secondary path adaptive delay estimation is applied to activevibration control, and simulation, the simulation results prove its correctness.4) An active vibration control rig is constructed based on a direct drivepower-absorbing-type test gearbox, and the software and hardware ofexperimental system are integrated. Firstly, the secondary path model is studiedin off-line conditions and experimental results prove the correctness of usingadaptive notch filter to obtain a reference signal. And then the appropriatecontroller is designed, the active vibration control experimental study isperformed by using adaptive filtering algorithm based on online secondary pathidentification，The result verifies the effectiveness of the active controlalgorithms and structure.