Nonlinear characteristics analysis of encased differential gear train containing tooth crack fault

Abstract

The encased differential gear train features a high speed-ratio and a compact structure, enabling coaxial reverse rotation of twin rotors. However, gear cracks can reduce stability and may lead to safety incidents. Additionally, nonlinear factors complicate vibration responses, posing challenges for fault diagnosis. Therefore, investigating the nonlinear behavior and stability of the cracked system is crucial and significant. The dynamic model of the encased differential gear train is proposed and validated through an experiment, considering nonlinear factors involving time-varying mesh stiffness, tooth backlash, and comprehensive transmission error. Responses of sun gears in both stages, under healthy and cracked conditions, are analyzed using bifurcation diagrams, phase diagrams, Poincaré diagrams, time series, and FFT spectra at different input speeds. Results show that the system exhibits chaotic, quasi-3-periodic, and 3 T-periodic motions with varying speeds under healthy conditions. Impacts of crack on system responses vary with input speeds, and stable motion rather than chaotic is preferable for fault diagnosis. Crack propagation destabilizes the system. Moreover, the differential stage is more sensitive to the encased-stage crack than the encased stage itself. The influence of transverse stiffness of the intermediate shaft on the system stability is also examined, indicating that the system becomes more stable with increased stiffness under both normal and fault conditions. Notably, with a 50 % increase in stiffness, the sun gear in the differential stage becomes stable under fault conditions. This study investigates crack-induced responses in this single-input, dual-output planetary gear train, providing valuable insights for mechanical design from the perspective of reliability and fault diagnosis in multi-stage gear systems.