Error Analysis of Instantaneous Frequency Estimation of Second-Order SST and Its Application on Analyzing Gear Meshing Stiffness From Motor Current

Motor gearbox systems are widely used in industrial production, and the variations of gear meshing stiffness generate transient frequency modulation (FM) effects on motor current. The 2nd-order synchrosqueezing transform (SST) is effective for revealing the time-varying frequency characteristics of motor current, thus enabling the monitoring of the condition of the electromechanical system; however, the selection of the window parameter in 2nd-order SST analysis is subjective and lacks specific theoretical guidance. To quantify the analytical limits, this study derives the instantaneous frequency (IF) estimation error function of the 2nd-order SST. The function demonstrates that the factors affecting the IF estimation are the window parameter and the 2nd-order and 3rd-order derivatives of the signal phase. To validate the practical application of the IF estimation error function, a rotating vector (RV) gearbox test bench is constructed. First, the motor current model of the test bench that contains the meshing stiffness is established, which allows the definition of the phase and FM amplitude of the signal. In the analysis of the model simulation, the optimal window parameters for identifying the FM characteristics are determined by comparing the FM amplitudes with the calculated IF estimation errors. With the window parameter determined by model analysis as previous knowledge, the healthy and faulty meshing stiffness characteristics are successfully extracted from the experimental motor currents. As a result, local gear faults in the RV gearbox can be diagnosed intuitively and accurately.