Vibration characteristic analysis of a two-stage spur gear transmission system with tooth crack and profile shifted

Abstract

Gear transmission systems in engineering often involve multiple stages, making vibration and fault analysis critical. This study introduces a revised spur gear time-varying mesh stiffness(TVMS) model using the potential energy method, incorporating nonlinear Hertzian contact stiffness and the coupling effects of healthy and cracked gear fillet-foundation stiffness, along with profile shift coefficients. The analysis shows that cracked gears introduce rotational frequency components into the mesh stiffness spectrum, while the profile shift coefficient influences the amplitude of mesh frequencies and their harmonics. A finite element model of a two-stage spur gear system, incorporating tooth cracks and profile shift coefficients, is developed to analyze the vibration response characteristics of healthy systems, systems with varying profile shift coefficients, and systems with different crack depths. The results indicate that in the frequency domain, a healthy two-stage spur gear transmission system exhibits not only the mesh frequencies and their harmonics but also a rich combination of these frequencies. The fault frequency for cracked gear systems corresponds to the rotational frequency of the cracked shaft and its modulation with two-stage mesh frequencies. Frequency sweeping analysis shows that varying installation positions change natural frequencies and their corresponding amplitude-frequency response, providing strategies to avoid resonance with operational speeds. In amplitude-frequency characteristics, crack depth notably impacts the amplitude at non-resonant peaks, whereas the profile shift coefficient affects the amplitude at resonant peaks. The time-domain statistical indicators(RMS, kurtosis, and IE) do not consistently respond to variations in crack depth across the entire frequency range under consideration; among these indicators, the kurtosis of the displacement signal emerges as the optimal indicator for detecting gear cracks. These findings offer valuable insights for the design and fault diagnosis of two-stage spur gear transmission systems.