Modified Lagrangian Formulation of Gear Tooth Crack Analysis using Combined Approach of Variable Mode Decomposition (VMD) and Time Synchronous Averaging (TSA)

This paper discusses the possible observation of an integrated gear tooth crack analysis procedure that employs the combined approach of variable mode decomposition (VMD) and time synchronous averaging (TSA) based on the coupled electromechanical gearbox (CEMG) system. This paper also incorporates the modified Lagrangian formulation to model the CEMG system by considering Rayleigh's dissipative potential. An analytical improved time-varying mesh stiffness (IAM-TVMS) with different levels of gear tooth crack depts is also incorporated into the CEMG system to inspect the influence of cracks on the system's dynamic behavior. Dynamic responses of the CEMG system with different tooth crack levels have been used for further investigations. For the first time, the integrated approach of variable mode decomposition (VMD) and time-synchronous averaging (TSA) has been presented to analyze the dynamic behaviour of CEMG systems at the different gear tooth cracks have been experienced as non-stationary and complex vibration signals with noise. Based on the integrated approach of VMD-TSA, two types of nonlinear features, i.e., Lyapunov Exponent (LE) and Correlation Dimension (CD), were calculated to predict the level of chaotic vibration and complexity of the CEMG system at the different levels of gear tooth cracks. Also, the LE and CD are used as chaotic behaviour features to predict the gear tooth crack propagation level. The results of the proposed approach show significant improvements in the gear tooth crack analysis based on the chaotic features. Also, this is one of the first attempts to study the CEMG system using chaotic features based on the combined approach of VMD-TSA.