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This paper discusses the possible observation of an integrated gear toothcrack analysis procedure that employs the combined approach of variable modedecomposition (VMD) and time synchronous averaging (TSA) based on the coupledelectromechanical gearbox (CEMG) system. This paper also incorporates themodified Lagrangian formulation to model the CEMG system by consideringRayleigh's dissipative potential. An analytical improved time-varying meshstiffness (IAM-TVMS) with different levels of gear tooth crack depts is alsoincorporated into the CEMG system to inspect the influence of cracks on thesystem's dynamic behavior. Dynamic responses of the CEMG system with differenttooth crack levels have been used for further investigations. For the firsttime, the integrated approach of variable mode decomposition (VMD) andtime-synchronous averaging (TSA) has been presented to analyze the dynamicbehaviour of CEMG systems at the different gear tooth cracks have beenexperienced as non-stationary and complex vibration signals with noise. Basedon the integrated approach of VMD-TSA, two types of nonlinear features, i.e.,Lyapunov Exponent (LE) and Correlation Dimension (CD), were calculated topredict the level of chaotic vibration and complexity of the CEMG system at thedifferent levels of gear tooth cracks. Also, the LE and CD are used as chaoticbehaviour features to predict the gear tooth crack propagation level. Theresults of the proposed approach show significant improvements in the geartooth crack analysis based on the chaotic features. Also, this is one of thefirst attempts to study the CEMG system using chaotic features based on thecombined approach of VMD-TSA.

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