In this study, a novel time–frequency (TF) analysis method, referred to as the scaling-basis chirplet transform (SBCT), is developed by extending the conventional chirplet transform. This method includes a replacement kernel function that can vary the chirp rate with frequency and time by scaling the TF basis at and around the corresponding time center. This enables the corresponding chirplets to accurately match the targeted slopes for every trajectory of a multicomponent signal and within any window length. Therefore, the TF representation obtained via the SBCT can achieve significantly higher energy concentrations even for multicomponent signals with close-spaced frequencies and high levels of background noise. The effectiveness of the proposed SBCT approach was demonstrated by analyzing a numerical multicomponent signal and a vibration signal obtained from a gearbox test rig. Both numerical and experimental results showed that the SBCT can satisfactorily handle multicomponent signals with nonlinear frequency trajectories, close-spaced frequencies, and noisy backgrounds, demonstrating its superiority.

Traditional signal postprocessing methods suffer from the repeated assignment problem (RAP), which can result in inaccurate instantaneous frequency (IF) estimation and signal recovery. In this article, to solve this problem, a novel time-frequency (TF) analysis (TFA) method called the synchro-reassigning transform (SRT) is proposed. This method aims to obtain the ideal TF representation (TFR) by utilizing derivatives of the constructed amplitude function and a three-step selection rule to adaptively extract the TF coefficients on the IF trajectories in the TF plane, and reassigning these TF coefficients into a new TFR. In this way, SRT can eliminate the RAP, thus obtaining an approximately ideal TFR that helps to realize more accurate IF estimation and signal reconstruction. Furthermore, SRT shows satisfactory performance on signals with high nonlinear IFs or relatively close IFs, even under strong noise conditions. Two simulated signal and three real-life signals were used to demonstrate the performance of SRT.

Stator current modeling for defective planetary gearboxes based on magnetic equivalent circuits (MEC) is conducted in this study. A lumped parameter torsional model of the motor-planetary gearbox coupling system is established to obtain the nonlinear time-variable torsional response of the rotor numerically. A MEC model of an induction motor is established by connecting the equivalent flux tubes with nodes. After considering the time-variable rotor torsional response, the nonlinear magnetic field intensity of the iron material and magnetic saturation, an iterative numerical integration method is presented to solve the MEC model. Both a finite element analysis and dynamic tests on a planetary gearbox driven by an induction motor are carried out for verification. Based on these, the fault characteristic components in the stator current spectra are, respectively, identified when the tooth chipping defect appears at sun/planet/ring gears. Fault-related frequencies are essentially represented by the combinations between the meshing frequency, sun/planet/ring gear fault passing frequency, its harmonics, and the power supply frequency. Owing to the electromechanical coupling effect, high-order harmonics of the power supply frequency also participate in the fault-related frequencies of the planet and ring gears. By quantitatively analyzing the influence of chipping size on the amplitudes of fault characteristic frequencies, suitable spectra for planetary gearbox condition monitoring are recommended.