Generalized Energy Operator Based Complicated Time-varying Modulation Signal Analysis Method For Machinery Fault Diagnosis

The energy operator can analyze and trace the energy of the signal through the nonlinear combination of signals and their differential.It is a typical application of the theory of generating differential equations.The energy operator can estimate the amplitude and instantaneous frequency of vibration signals,and has the characteristics of simplicity and efficiency.It has been widely applied to the demodulation analysis of mechanical vibration signals in recent years.Complex time-varying modulation often exists in actual engineering vibration signals,and energy operators have limitated applications in this area,such as in dynamic parameter identification and multi-component signal analysis.This paper focuses on how to give full play to the advantages of the energy operator and improve its practicability.This paper has summarized and improved the theory and application of the energy operator.In this paper,we take the limitation of the energy operator and the extended application as the breakthrough point,and take the rolling bearing and the planetary gearbox as the specific research object.Different fault diagnosis methods have been proposed according to the actual problems.The main content and innovation of this paper are summarized as follows:1.Modal parameter identification method via energy operator:a new method for calculating damping ratio based on the energy operator is presented,i.e.,the half-cycle energy operator method.Moreover,we use the energy operator to calculate the modal frequency.We identify the modal order by combining the modal frequency,damping ratio and attenuation waveform.The effectiveness and robustness of the proposed approach is illustrated by simulation and experimental signals.2.The application of the instantaneous damping ratio to fault diagnosis via energy operator:Due to fact that energy dissipation can be described by detecting the changes of instantaneous damping ratio sequences,which can be calculated by differential energy operator,we can identify gear fault by examing.fault characteristic frequency components on damping ratio spectrum.Meanwhile,we proposed two sensitive component selection methods to calculate the damping ratio respectively.3.Due to the fact that generating differential equation(GDE)is the most essential ideology of the energy operator,we proposed a demodulation analysis method via GDE.The original signal can be reconstructed by generating simplified differential equation.Based on the combination of empirical mode decomposition(EMD)and the GDE,the envelope amplitude and instantaneous frequency of sensitive components can be accurately estimated.Thus,we can identify the fault characteristic frequencies according to amplitude demodulation spectrum and frequency demodulation spectrum.4.In order to give full play to the advantages of the GDE,we proposed a new iteration decomposition method,named as iterated generating differential equation decomposition method(IGDE).The method combines with the improved filtering method and GDE demodulation to decompose signal through the iteration,which does not require any prior conditions.We have proved the advantage of the method by comparing the traditional decomposition method via simulation signal analysis.5.Torsional vibration signals analysis in resonance region:planetary gearbox torsional vibration signals are free from the extra amplitude modulation effect due to time-varying transmission paths,and have simpler frequency structure than translational ones.Gear faults lead to modulation on the torsional resonance vibration,and are manifested by the modulation feature.Based on these advantages,we proposed an analysis method of the torsional resonance region signal by the Fourier spectrum,the amplitude demodulation spectrum and the frequency demodulation spectrum.The theoretical derivations and proposed approach are illustrated by numerical simulated signal analysis,and are further validated through dynamics modelling and lab experimental tests.6.A method of fault diagnosis of planetary gearbox by encoder signals is proposed.The encoder signals can not only calculate the rotational speed and control angular displacement,but also contain a large amount of information.The principle of the change of the impulse interval of the encoder signal is given.We proposed a way of extracting gear fault feature by using equal angle resampling and order spectrum of impulse interval.The method has high order resolution and is not affected by the velocity interference.We validated the proposed method experimentally,including the constant-speed condition signal and the varying-speed condition signal of planetary gearboxes.Localized faults on the sun,planet and ring gears are successfully diagnosed.