Sparse Dictionary Construction For Gear Compound Fault Diagnosis Under Steady Speed And Variable Speed Conditions

Gears are widely used in the mechanical transmission entire mechanical field.Once there exists a failure on the gear,it is easy to trigger a chain reaction and cause serious consequences.Therefore,extracting and diagnosing the gear fault characteristics from the complex gear vibration signals to take timely countermeasures is of great significance for the normal operation of gears and ensuring the stable operation of the equipment.Based on the sparse decomposition theory and combined with the gear compound fault vibration signal mechanism model,feature extraction and diagnosis methods of gear compound fault under the steady speed and the variable speed conditions are deeply studied in this paper.Aiming at the problem of insufficient localized fault signal amplitude extraction accuracy caused by the existing redundant impulse modulation dictionary,an impulse modulation dictionary construction method based on the cepstrum filtering and the least square complex exponential method(LSCE)is proposed,and a gear compound fault diagnosis method under the steady speed condition is formed based on this.The gear distributed fault signal is first extracted with a stationary modulation dictionary in the proposed method,and then the cepstral filtering is utilized to extract the impulse response function from the residual signal.LSCE is used to identify each order of the system modal parameters,combined with the corresponding amplitude information,the atom that contains the multi-order modal information is constructed and time-shifted to obtain an impact modulation dictionary,thereby achieving the localized fault signal extraction.Compared with the existing redundant dictionary construction method based on the correlation filtering,the dictionary constructed by the proposed method is only formed through the time-shifting of a single atom,where the dictionary form is more concise,and the localized fault feature of the gear can be extracted more accurately.The effectiveness of the proposed method in gear compound fault diagnosis under the steady speed condition is further verified through the simulation,experiment,and comparative analysis.For the problem that the existing angular domain quasi-stationary modulation dictionary has insufficient amplitude accuracy in extracting distributed fault features,a gear compound fault diagnosis method under the variable speed condition with the time domain sparse frequency modulation dictionary is proposed.Based on the gear fault signal mechanism model under the variable speed,a sparse frequency modulation dictionary that integrates the timevarying speed information and the gear structure parameters is constructed in the proposed method,and the gear distributed fault signal is extracted directly in the time domain.Then,an impulse modulation dictionary is constructed based on the cepstral filtering and LSCE,and the localized fault feature is extracted from the residual signal.Compared with the sparse decomposition method of constructing a quasi-stationary modulation dictionary in the angular domain,the integration error during the mutual conversion of the time domain and the angular domain is avoided in the proposed method,and the distributed fault signal extraction accuracy of amplitude is improved.The effectiveness of the proposed method in gear compound fault diagnosis under the variable speed condition is demonstrated by the simulation,experiment,and comparative analysis.