Loaded tooth contact analysis for helical gears with surface waviness error

Meshing characteristics are crucial for the transmission performance of vibration noise and strength of gear systems. Gear transmission error has been acknowledged as a prominent excitation in vibration systems, but the surface waviness deviations that directly affect it in contact analysis are generally ignored. This study proposes a comprehensive model for quasi-static analysis of tooth surfaces with waviness error. The model reconstructs the actual tooth surface in reverse based on the gear Fourier measurement principle. Instead of solving the meshing equations to pre-assume contact position, the problem of normal contact between surfaces with deviations is solved by an innovative multiscale grid and a local iterative numerical algorithm. Combining the finite element numerical method and surface integral of the Boussinesq solution determines gear deformation and develops a loaded contact model. The validity of the model is verified through numerical examples. Furthermore, the proposed model is applied to discuss the tooth surfaces with different waviness amplitudes, frequencies, and distribution angles for the first time. It explains the interaction between local microscale and global scale introduced by waviness error on tooth surfaces and reveals the mechanism of the waviness error on meshing performance.