The Effectiveness of Using Fourier Series to Solve the Simulation of Gearbox and Rotor Dynamics using MATLAB and Simulink Software

Abstract

This research explores the application of Fourier series as a mathematical tool to simulate the intricate dynamics of mechanical systems, specifically gearboxes and rotors. By leveraging MATLAB and Simulink, the study decomposes periodic mechanical forces into their harmonic components to analyze vibrational behavior. The methodology integrates signal generation, Fast Fourier Transform (FFT)-based frequency analysis, and noise simulation to validate real-world operational conditions. The findings demonstrate the precision of Fourier series in modeling gear mesh and rotor imbalance frequencies, offering engineers an advanced framework for vibration analysis, predictive maintenance, and mechanical system optimization.