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

[Submitted on 29 Aug 2023]

Click here to download a PDF of the paper titled “Modified Lagrangian Formulation of Gear Tooth Crack Analysis using Combined Approach of Variable Mode Decomposition (VMD) and Time Synchronous Averaging (TSA)” by Subrata Mukherjee and 1 other author.

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Abstract: This paper presents a procedure for analyzing gear tooth crack using a combined approach of variable mode decomposition (VMD) and time synchronous averaging (TSA) in the context of a coupled electromechanical gearbox (CEMG) system. The paper also incorporates the modified Lagrangian formulation to model the CEMG system, considering Rayleigh’s dissipative potential. Additionally, an analytical improved time-varying mesh stiffness (IAM-TVMS) with different levels of gear tooth crack depths is included to examine the influence of cracks on the system’s dynamic behavior. The dynamic responses of the CEMG system with different tooth crack levels are used for further investigations. The integrated approach of VMD-TSA is employed to analyze the dynamic behavior of CEMG systems, which experience non-stationary and complex vibration signals with noise due to gear tooth cracks. Two types of nonlinear features, Lyapunov Exponent (LE) and Correlation Dimension (CD), are calculated based on the VMD-TSA approach to predict the level of chaotic vibration and complexity of the CEMG system at different levels of gear tooth cracks. The LE and CD are also used as chaotic behavior features to predict the gear tooth crack propagation level. The results of the proposed approach show significant improvements in gear tooth crack analysis based on chaotic features. This study is one of the first attempts to analyze the CEMG system using chaotic features with the combined approach of VMD-TSA.