Abstract
Gears are the most important parts of rotating machinery and power transmission devices. When gears are engaged in meshing transmission, vibration will occur due to factors such as gear machining errors, meshing rigidity, and meshing impact. The traditional FxLMS algorithm, as a common active vibration algorithm, has been widely studied and applied in gear transmission system active vibration control in recent years. However, it is difficult to achieve good performance in convergence speed and convergence precision at the same time. This paper proposes a variable-step-size multichannel FxLMS algorithm based on the sampling function, which accelerates the convergence speed in the initial stage of iteration, improves the convergence accuracy in the steady-state adaptive stage, and makes the modified algorithm more robust. Simulations verify the effectiveness of the algorithm. An experimental platform for active vibration control of the secondary gear transmission system is built. A piezoelectric actuator is installed on an additional gear shaft to form an active structure and equipped with a signal acquisition system and a control system; the proposed variable-step-size multichannel FxLMS algorithm is experimentally verified. The experimental results show that the proposed multichannel variable-step-size FxLMS algorithm has more accurate convergence accuracy than the traditional FxLMS algorithm, and the convergence accuracy can be increased up to 123%.
Highlights
As a general-purpose part, gear is an important transmission device in various mechanical equipment systems and plays a very key role in equipment in machinery, transportation, chemical, aviation, aerospace, shipbuilding, and other industries
Guan et al [27] proposed a direct hybrid adaptive control method based on the Lyapunov stability theorem to simultaneously adjust feedback gain and feedforward gain to control gear vibration, and the results showed that this method was not sensitive to gear meshing frequency error
Design and Verification of Experiments e experimental platform of the active vibration control system of the gearbox system can be divided into three parts, namely, the gear transmission system, the vibration measurement processing system, and the active control system
Summary
As a general-purpose part, gear is an important transmission device in various mechanical equipment systems and plays a very key role in equipment in machinery, transportation, chemical, aviation, aerospace, shipbuilding, and other industries. E experiment showed that stiffness modulation factor is proportional to the load on the gear,and the torsional vibration damping is about 7 dB at meshing frequencies of 150–350 Hz. Guan et al [27] proposed a direct hybrid adaptive control method based on the Lyapunov stability theorem to simultaneously adjust feedback gain and feedforward gain to control gear vibration, and the results showed that this method was not sensitive to gear meshing frequency error. Li et al [28, 29] installed the actuator on the gear shaft with additional support bearings, combined with the phase-locked loop for frequency estimation of reference signals, and used the filtered LMS algorithm to control the gear vibration. The adaptive control method is less dependent on prior knowledge and does not depend on specific models, so it is an ideal choice to apply the adaptive control method to the active control of gear vibration
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