Diagnosis of damage in spiral bevel gear models using Lagrange-Wavelet method

This study integrates the Lagrange method and wavelet analysis to create a comprehensive approach to detect damage in spiral bevel gears within transmission systems. The Lagrange method is employed to accurately model the motion equations of the gears during operation, thereby creating a mathematical model that includes dynamic variables, structural components, and boundary conditions, allowing for the calculation of vibration parameters such as frequency and amplitude. Meanwhile, wavelet analysis is applied to analyze the vibration signals of the gears, helping to detect spatial and temporal variations in the signals and identify signs of damage within the system. The combination of these two methods enables a precise and comprehensive diagnosis of damage problems and prediction of mechanical system vibrations, particularly in complex meshing models. This not only improves efficiency and accuracy in the research and handling of gear-related problems, but also makes significant contributions to the field of mechanical engineering, especially in gear maintenance and damage diagnosis, thereby improving the reliability and lifespan of transmission systems.