Nonlinear dynamic analysis of spur gear pair for varying crack depth scenario

This paper presents an eight degree-of-freedom dynamic model of a spur gear system under varying crack depth scenarios for nonlinear analysis. Unlike previously reported reduced order models, which fail to capture realistic system behavior, such as chaos in healthy gears observed experimentally, this realistic model offers a more accurate representation. The proposed model is validated against experimental data and used to analyze the effect of varying tooth root crack depth as a bifurcation parameter, a novel investigation in this field. The proposed model incorporates major nonlinearities such as analytically improved time-varying mesh stiffness (AI-TVMS), backlash, static transmission error, and bearing clearances. The AI-TVMS model under healthy and varying crack depth scenarios is incorporated to analyze the nonlinear characteristics of the system. The analysis is presented via different tools such as bifurcation diagrams, phase portraits, Poincare maps, power spectral density, cepstrum analysis, envelope analysis, multifractal spectral analysis, Lyapunov exponents, and approximate entropy. The results demonstrate the chaotic nature of both healthy and defective gear systems. Additionally, the transient nature of the system at fault locations increased with the severity of % the crack depth, due to which the transient chaos phenomenon appeared for defective gear systems. Finally, the evaluation of tools attempts to distinguish between inherent nonlinearity and crack-induced nonlinearity. The findings of this study will aid in more precise gear system failure diagnosis in the future.