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.

Integrated Approach of Gearbox Fault Diagnosis

Gearbox fault diagnosis is one of the most important parts in any industrial systems. Failure of components inside gearbox can lead to a catastrophic failure, uneven breakdown, and financial losses in industrial organization. In that case intelligent maintenance of the gearbox comes into context. This paper presents an integrated gearbox fault diagnosis approach which can easily deploy in online condition monitoring. This work introduces a nonparametric data preprocessing technique i.e., calculus enhanced energy operator (CEEO) to preserve the characteristics frequencies in the noisy and inferred vibrational signal. A set of time domain and spectral domain features are calculated from the raw and CEEO vibration signal and inputted to the multiclass support vector machine (MCSVM) to diagnose the faults on the system. An effective comparison between raw signal and CEEO signal are presented to show the impact of CEEO in gearbox fault diagnosis. The obtained results of this work look very promising and can be implemented in any type of industrial system due to its nonparametric nature.