Vibration Response Modulation Mechanism And Sparse Separation Method For Composite Gear Transmission

When one fault occurs on the gear system, it will trigger and deteriorate other faults. Also influenced by signal transmission path and other normal meshing vibration, vibration signals generated from different sources couple together and increases the difficulty of fault diagnosis. It is important to study the evolution mechanism of vibration response of gear transmission system with different kinds of faults, as well as feature extraction methods.A dynamics model of gear transmission system is established to reveal the characteristic of higher-order mesh frequency harmonics and the mechanism of modulation sideband. The interaction of dynamic mesh stiffness with gear static elastic deformation after loading and the nonlinear feedback of system cause the higher-order mesh frequency vibration. The interaction of dynamic mesh stiffness with displacement error of gear pair’s circular pitch caused by steady-type fault induces modulation sideband, which is characterized by the phenomenon that rotational frequency of fault gear modulates mesh frequency. Impact-type fault generates impulse force sequences, which induce the impact modulations whose carriers and modulation frequencies are natural frequencies of gear system and the rotational frequency of fault gear, respectively. Due to the convolution between nonlinear feedback of impact vibration response and dynamic mesh stiffness, some spurious resonant frequencies are generated. However, all the natural and spurious resonance frequencies are uniformly-spaced discretized by impact frequency of fault gear in whole band.A coupling modulation signal model is established to analyze the vibration response of normal planetary gears. Influenced by transmission paths from time-varying mesh points to fixed-position sensor and time-varying direction of mesh forces, vibration signal collected by the sensor shows a series of modulation sidebands, which are characterized by the phenomenon that rotational frequency of planet carrier modulates mesh frequency of planetary gears. Because the transmission path and direction projection are both periodic functions, they can be expanded by Fourier series with the fundamental frequency be the rotational frequency of planet carrier, and whose expanding order determines sideband’s width. Vibration responses of uniform distributed planetary gears have amplitudes only at frequencies which equal integer multiples of number of planet gears. When the mesh frequency harmonics are integer multiples of the number of planet gears, they get amplitudes, and their sidebands distribute symmetrically. Otherwise, their amplitudes are zero, and their sidebands distribute asymmetrically.A new method based on mesh frequency harmonics and energy centrobaric correction technology was proposed for order tracking analysis on gearbox vibration response. By combining moment estimation and peak searching of time-frequency distribution, the method can overcome not only the drawback of moment estimation which is unavailable to extract multi-component signal but also the limitation of peak searching on time-frequency resolution. For the problem that low frequency components, such as rotational frequency, have small amplitude and difficult to extract directly by acceleration sensor, the proposed method extracts mesh frequency components firstly, and then obtains the instantaneous rotational frequency or speed indirectly. After energy centrobaric correction, instantaneous rotational speed of the gearbox is estimated with high precision, and the frequency and amplitude precisions of order analysis are significantly increased. In simulation analysis of wind turbine gearbox, the greatest relative errors of the estimation values of instantaneous output rotational speed and mesh frequency amplitude are only 0.024% and 2.09%, respectively. Automotive transmission bench tests and actual wind turbine gearboxes experiment verified the effectiveness of the proposed method.Based on the superiorities of sparse representation theory on signal separation and feature extraction, a new method was proposed to separate coupling modulation signal of gearbox hybrid fault, and diagnose gear and bearing faults. Steady modulation dictionary and impact modulation dictionary are designed, which merged the fault mechanism, structure and operation parameters of gearbox, and vibration characteristic of the measured signal. The designed sparse dictionaries have both the advantages of analytical dictionary and learning dictionary, and also have clear physical meaning. To optimized steady modulation dictionary, ratio correction method are applied to obtain exact parameters of harmonic atoms from measured vibration signal. Decomposition coefficients after match pursuit are furtherly disposal through amplitude recovery. The two steps can improve separation accuracy of steady modulation components. Parameters of impulse response atoms are optimized based on correlation filtering method, which significantly reduce the redundancy of impact modulation dictionary. Segmented match pursuit method reduces the calculation cost of inner product in the process of solving sparse coefficients. The two steps can achieve the goal of improving the sparse decomposition speed. Simulation analysis and experimental tests verified that the proposed method is capable of the gear and bearing fault signal separation.