Magnetic Equivalent Modeling of Stator Currents for Localized Fault Detection of Planetary Gearboxes Coupled to Electric Motors

Stator current modeling for defective planetary gearboxes based on magnetic equivalent circuits (MEC) is conducted in this article. 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. An 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.