Gearbox Fault Diagnosis Based On DDTFA Method

Gearbox fault diagnosis technology plays an indispensable role in the continuous and stable work of gearboxes and related equipments.The traditional time-frequency analysis methods are no longer suitable for gearbox fault diagnosis because of its complex signal components,and the adaptive time-frequency analysis methods have been widely used in gearboxes fault diagnosis in recent years.Data-driven time-frequency analysis（DDTFA）,as an adaptive time-frequency analysis method proposed in recent years,can obtain the sparsest representation of signals by solving the non-linear optimization problem.DDTFA method has rigorous mathematical logic and theory and combines the advantages of Empirical Mode Decomposition（EMD）method and sparse optimization.It can quickly decompose non-stationary signals,and can effectively suppress the problems of modal aliasing and endpoint effect.However,the initial phase function（ θ₀）estimation of this method directly affects the convergence,accuracy and efficiency of the method.Therefore,the study about adaptive estimation of θ₀ is the key to the application of this method in gearbox fault diagnosis.Thesis topics originates from project supported by National Natural Science Foundation of China（Grant No.51605151）.Firstly,the related theoretical research on DDTFA method is carried out.Then,aiming at the problem of the θ₀ estimation,two methods which can accurately estimate θ₀ were proposed for gearbox fault diagnosis.The main contents of this paper are as follows:（1）The theoretical study of DDTFA was carried out and the results show that for the difference between θ₀ and the theoretical phase function,the lower frequency and the smaller amplitude,the more accurate the DDTFA decomposition results are.The analysis verifies that DDTFA method basically follows the the oretical decomposition order of each component energy from strong to weak,but prefers to decompose the signal components similar to the atomic form of its dictionary in decomposition of multi-component non-stationary signals.The adaptability of DDTFA method to time-varying non-stationary signals is also studied and discussed.（2）For solving the θ₀ estimation problem of DDTFA method,Zero Phase Digital Filter（ZPDF）is introduced,with the frequency corresponding to the maximum peak value of Fourier spectrum as its central frequency,a ZPDF-DDTFA method was proposed,which can accurately select the signal components’ θ₀ and then complete signal decomposition.The simulation analysis and gearbox fault diagnosis examples show that the θ₀ and the results which ZPDF-DDTFA method estimates and decomposes are accurate,and ZPDF-DDTFA method can effectively extract the broken tooth fault feature of variable speed gear,which is better than EEMD,and effectively diagnose bearing crack fault with 1.5-dimensional spectrum.（3）Aiming at the θ₀ estimation problem of DDTFA method and the problem that ZPDF-DDTFA method lacks self-adaptation because of bandwidth and ripple,Completely Adaptive DDTFA（CADDTFA）method which can accurately,quickly and adaptively estimate the θ₀ was proposed.Introducing the idea of finding extremum of the function,the θ₀ estimation was transferred into continuous optimization of initial solution set.Through simplifying Gauss-Newton iterative algorithm in the DDTFA,the slope variation of the θ₀ in the initial set before and after one iteration was used as the derivative to obtain the local maximum,then among the local maximums,the θ₀ was optimized with the maximum energy of its corresponding signal component,and then complete the signal decomposition.Simulation analysis and the fault diagnosis of the gearbox（broken tooth fault of variable speed gear and compound fault of gearbox）show that the proposed method can adaptively estimate the θ₀ with high accuracy and efficiency and effectively extract the fault features,which is better than EEMD.In addition,the method shows satisfactory noise resistance.（4）The ZPDF-DDTFA method and CADDTFA method were applied to the fault diagnosis of planetary gearbox respectively.The simulation re sults show that the ZPDF-DDTFA and CADDTFA methods can effectively decompose the single component and multi-components simulated signals for local faults of sun wheel,and the decomposition accuracy is better than EEMD method.The example of broken tooth fault diagnosis of sun wheel shows that the ZPDF-DDTFA method can not effectively diagnose the broken tooth of sun wheel.CADDTFA can effectively diagnose the broken tooth of sun wheel,and the fault characteristics are more obvious than the EEMD method.