An Improved Coupled Dynamic Modelling for Exploring Gearbox Vibrations Considering Local Defects

Gearbox is a key part in machinery,in which gear,shaft and bearing operate together to transmit motion and power.The wide usage and high failure rate of gearbox make it attract much attention on its health monitoring and fault diagnosis.Dynamic modelling can study the mechanism under different faults and provide theoretical foundation for fault detection.However,current commonly used gear dynamic model usually neglects the influence of bearing and shaft,resulting in incomplete understanding of gearbox fault diagnosis especially under the effect of local defects on gear and shaft.To address this problem,an improved gear-shaft-bearing-housing dynamic model is proposed to reveal the vibration mechanism and responses considering shaft whirling and gear local defects.Firstly,an eighteen degree-of-freedom gearbox dynamic model is proposed,taking into account the interaction among gear,bearing and shaft.Secondly,the dynamic model is iteratively solved.Then,vibration responses are expounded and analysed considering gear spalling and shaft crack.Numerical results show that the gear mesh frequency and its harmonics have higher amplitude through the spectrum.Vibration RMS and the shaft rotating frequency increase with the spalling size and shaft crack angle in general.An experiment is designed to verify the rationality of the proposed gearbox model.Lastly,comprehensive analysis under different spalling size and shaft crack angle are analysed.Results show that when spalling size and crack angle are larger,RMS and the amplitude of shaft rotating frequency will not increase linearly.The dynamic model can accurately simulate the vibration of gear transmission system,which is helpful for gearbox fault diagnosis.

A Noise Reduction Method for Multiple Signals Combining Computed Order Tracking Based on Chirplet Path Pursuit and Distributed Compressed Sensing

With the development of multi-signal monitoring technology,the research on multiple signal analysis and processing has become a hot subject.Mechanical equipment often works under variable working conditions,and the acquired vibration signals are often non-stationary and nonlinear,which are difficult to be processed by traditional analysis methods.In order to solve the noise reduction problem of multiple signals under variable speed,a COT-DCS method combining the Computed Order Tracking(COT)based on Chirplet Path Pursuit(CPP)and Distributed Compressed Sensing(DCS)is proposed.Firstly,the instantaneous frequency(IF)is extracted by CPP,and the speed is obtained by fitting.Then,the speed is used for equal angle sampling of time-domain signals,and angle-domain signals are obtained by COT without a tachometer to eliminate the nonstationarity,and the angledomain signals are compressed and reconstructed by DCS to achieve noise reduction of multiple signals.The accuracy of the CPP method is verified by simulated,experimental signals and compared with some existing IF extraction methods.The COT method also shows good signal stabilization ability through simulation and experiment.Finally,combined with the comparative test of the other two algorithms and four noise reduction effect indicators,the COT-DCS based on the CPP method combines the advantages of the two algorithms and has better noise reduction effect and stability.It is shown that this method is an effective multi-signal noise reduction method.

Gear fault diagnosis using gear meshing stiffness identified by gearbox housing vibration signals

Gearbox fault diagnosis based on vibration sensing has drawn much attention for a long time.For highly integrated complicated mechanical systems,the intercoupling of structure transfer paths results in a great reduction or even change of signal characteristics during the process of original vibration transmission.Therefore,using gearbox housing vibration signal to identify gear meshing excitation signal is of great significance to eliminate the influence of structure transfer paths,but accompanied by huge scientific challenges.This paper establishes an analytical mathematical description of the whole transfer process from gear meshing excitation to housing vibration.The gear meshing stiffness(GMS)identification approach is proposed by using housing vibration signals for two stages of inversion based on the mathematical description.Specifically,the linear system equations of transfer path analysis are first inverted to identify the bearing dynamic forces.Then the dynamic differential equations are inverted to identify the GMS.Numerical simulation and experimental results demonstrate the proposed method can realize gear fault diagnosis better than the original housing vibration signal and has the potential to be generalized to other speeds and loads.Some interesting properties are discovered in the identified GMS spectra,and the results also validate the rationality of using meshing stiffness to describe the actual gear meshing process.The identified GMS has a clear physical meaning and is thus very useful for fault diagnosis of the complicated equipment.