Modal Analysis of a High-Speed Train Gearbox Housing Using Smoothed Finite Element Method

The gearbox is a crucial component of the power transmission system in high-speed trains, and realistically calculating its natural frequency is vital in avoiding system resonance. In recent decades, numerical techniques have become essential in designing engineering structures, and the finite element method (FEM) has gained widespread recognition and acceptance for its robustness and effectiveness. However, the FEM technique using linear 4-node tetrahedral elements (T4) performs poorly, leading to low accuracy and unreliable results. Consequently, complex hexahedral or second-order elements are often required for better performance. In this paper, we employ the smoothed finite element method (S-FEM), which combines the gradient smoothing technique with the standard FEM to improve calculation accuracy while still using linear tetrahedral elements. We apply S-FEM to accurately obtain the natural frequencies and mode shapes of a high-speed train gearbox using automatically generated linear tetrahedral elements. A test of tolerance to mesh distortion is also carried out on the gearbox. The results demonstrate that S-FEM can significantly enhance the computational accuracy of low-order 4-node tetrahedral elements without altering the mesh topology. It is expected that S-FEM can be an alternative to FEM in the modal analysis of complex structures in the railroad industry.