Dynamic simulation framework for single-tooth crack detection in spur gearboxes: modal analysis and vibration indicator sensitivity

Abstract

This study introduces an efficient dynamic simulation framework for a single-stage spur gearbox with an induced single-tooth crack, aimed at evaluating vibration-based health indicators for early crack propagation detection. Building upon the conventional lumped parameter approach, the model incorporates an advanced continuous mesh stiffness function, capturing crack-induced variations in stiffness and damping while integrating torsional degrees of freedom. The dynamic analysis, focusing on y-axis motion and neglecting frictional effects, employs a six-degree-of-freedom model to compute natural frequencies, lateral mode shapes, receptance and phase responses, mobility and accelerance characteristics, and Nyquist plots to comprehensively characterize system dynamics. Relative damping ratios are determined using the peak picking method, while the Ibrahim Time Domain method yields time-domain responses and refined natural frequencies. Health indicator analysis demonstrates that Root Mean Square (RMS) values, extracted from residual signal segments corresponding to the first three meshing cycles, exhibit superior sensitivity to early crack propagation compared to Kurtosis. Discrete Wavelet Transform (DWT) preprocessing significantly enhances RMS sensitivity, with an optimal decomposition level identified; exceeding this level results in diminished monotonicity and sensitivity. The methodology proves robust under noisy conditions, though elevated noise levels reduce both sensitivity and the optimal DWT level. Validation across diverse gearbox sizes and input shaft frequencies confirms the approach’s generalizability. This framework establishes a highly effective, robust strategy for vibration-based condition monitoring, offering substantial potential for early fault detection and strategic maintenance planning in critical industrial gear systems.