Vibration Signal Modulation Mechanisim Of Gear System And Sparse Decomposition Method For Its Non-stationary Signal

The gear transmission system is one of the key components of automobile power train and wind turbine transmission.When one fault occurs on the gear system,it will significantly reduce the reliability of the equipment.Moreover,gearboxes often work in variable speed condition,and it is difficult to extract fault features from their non-stationary vibration signals.It is very significant to study vibration signal modulation mechanisms of gear transmission system in healthy and typical fault states and the fault feature extraction method for their non-stationary signals.The meshing point dynamic model considering the displacement error excitation and the impulse sequence excitation is established.By analyzing the characteristic of exciting forces,frequency responses of the shaft-fixed gear system in healthy and typical fault states are deduced.In a healthy state,the vibration response contains the mesh frequency and its harmonics,which are caused by the static elastic deformation and the dynamic mesh stiffness.When there is a steady-type fault,the vibration response will have modulation sidebands around the mesh frequency harmonics whose modulation frequencies are the rotational frequency of faulty gear and its harmonics.And the displacement error excitation is the main reason of modulation sidebands.When there is an impact-type fault,the impact excitation will evoke the resonant modulation sidebands.Owing to the nonlinear feedback,spurious resonant bands will also appear in the signal spectrum.Based on the excitation signal model of the shaft-fixed gear system,signal models of planetary gear system in healthy and typical fault states are deduced theoretically.The influences of the time-varying force direction and the time-varying transmission path in each path signal are analyzed.Frequency characteristics of meshing modulation sidebands and resonant modulation sidebands are summarized.And the fault diagnostic strategy of planetary gearbox is proposed.In the healthy condition without the sun gear floating,the response signal will appear meshing modulation sidebands whose modulation frequencies are the passing frequency of planet gear and its harmonics.When there is a floating sun gear or a steady-type fault on the sun gear,the modulation sidebands whose interval is the absolute rotational frequency of sun gear will appear around the meshing modulation sidebands.The coupling of these two kinds of sidebands will form a special frequency interval of sun gear.When there is an impact-type fault on the sun gear,resonant bands will contain two sets of modulation sidebands whose intervals are the feature frequency of sun gear with impact-type fault.The special frequency interval of sun gear will be formed,which is due to the time-varying force direction function modulating the excitation signal.Furthermore,the time-varying transmission path will cause a series of small amplitude sidebands.When there is a steady-type fault on the ring gear,the characteristic of meshing modulation sidebands will be the same as those in healthy state.But the sidebands will be widened because of the failure excitation force.And the passing frequency of planet gear and its harmonics will also appear in low frequency parts.When there is an impact-type fault on the ring gear,the signal resonant modulation sidebands whose modulation frequencies are the passing frequency of planet gear and its harmonics will appear.Based on the techniques of signal sparse decomposition and order tracking,a novel non-stationary vibration signal processing method for diagnosing gearbox compound faults under time-varying rotation speed condition is proposed.This method contains the separation of quasi-steady modulation component and the extraction of impact modulation component.Firstly,a time domain non-stationary signal is changed into the quasi-steady signal in angle domain by order tracking method.The angle domain quasi-steady modulation component is separated by the quasi-steady sub-dictionary.Then,the angle domain residual signal,in which the signal-to-noise ratio(SNR)of impact-type fault component is enhanced significantly,will be switched back to the time domain.And the impact component will be extracted by the impact sub-dictionary.Two sparse sub-dictionaries are designed according to the characteristics of steady-type fault signal and impact-type fault signal,making those have definite physical meanings.An improved matching pursuit algorithm on segmental signal is designed to solve sparse coefficients and to improve the computational efficiency.The proposed method is able to process the signal with 30% speed fluctuation rate in each segmental signal and-14.6dB SNR of impact-type fault component.