Finite element method (fem) is to the gear body and tooth discrete into tiny unit elastic body, and through the related mechanics theory under the action of external loading amount of elastic deformation response to calculate TVMS gears, the calculating numerical model to simulate the gear real physical model geometry and boundary conditions and the scholars are widely used to verify the proposed analytical method to calculate TVMS model and the validity of the results and the accuracy, such as Zhou, etc., Ma, Ma, Sdnchez, Luo, etc., Yang, Sim etc. The algorithm model and the results.
Liang et al. established a general finite element analysis model, but through three different measurement methods of internal hole node displacement, the displacement of internal hole node was output and its related meshing stiffness effect was deduced. Finally, the influence of meshing stiffness under different internal hole diameter effect was studied. Du et al. established a three-dimensional FE model of a single gear tooth, introduced an improved transmission error (TE) model, studied and analyzed the influence of single tooth stiffness changing with the load point on the transfer error, and deeply studied the major contribution of tooth deflection component to TE. Saryazdi et al. also established a 3D FE model, and performed regular mesh division and node demarcation on the meshing tooth surface. The flexibility matrix of the gear teeth was calculated by 3D boundary element analysis. Then the load distribution in the contact area is calculated using Hertz theory and the flexibility matrix of the meshing gear teeth. This method is used to predict the meshing force distribution and meshing stiffness values of straight orunder different meshing conditions.
Kiekbusch et al. proposed the development of detailed 2D and 3D finite element models for calculating gear meshing torsional stiffness. In this paper, the advanced parametric design language of ANSYS is used to realize the parametric modeling without thepair, and the adaptive contact algorithm is realized for the contact area. Derivation of 2 d finite element analysis results can be used for rapid straight gear meshing is derived when the combination of the torsional stiffness of simple formula, can the 3 d model derived from the tooth surface is derived in detail under the geometric features of torsional rigidity calculation, and finally combined with the model to compare the torsional rigidity of lead simplify the related calculation formula used for fast prediction and evaluation of torsional rigidity. Based on the linear FE method, Hedlund et al. calculated the tooth deformation and used it to evaluate the excitation caused by the variation of meshing stiffness in design. By combining Hertz contact analysis with structural analysis, the variation of rodent stiffness in time domain and frequency domain was obtained. Based on the fracture mechanics (LEFM) finite element method, Pandya et al. carried out the prediction and verification of time-varying meshing stiffness. When the gear teeth crack exists, the meshing stiffness decreases, and the larger the percentage of meshing stiffness changes with the increase of crack length, the more obvious the gear with high failure rate detected in the early stage is.
FernandezdelRincon etc to establish direct contact force and deformation of gear transmission Guo level model of each gear contact deformation is formulated as the combination of global and local items, each of them all through the finite element model for gear contact, and strengthen its compatibility and complementarity conditions, to carry on the tooth meshing stiffness of Gui quantitative and qualitative research. Guo et al., Gu et al., established a FE model to verify and modify the simplified stiffness calculation formula proposed in the paper. Cooley et al., based on finite element method, proposed the application of two statistical methods for calculating meshing stiffness. The first method is the average slope method (the ratio of meshing force and meshing deflection), and the second is the local slope method of nominal deflection. The results of the two methods show that they are consistent for static stiffness evaluation, but different for dynamic mesh stiffness calculation. Therefore, the adaptability and reliability under actual meshing conditions should be properly considered no matter which algorithm is adopted. Based on the CAD-FEM-QSA series modeling method and the quasi-static boundary setting analysis method, Zhan et al. carried out the simulation calculation of the mesh stiffness of three-dimensional spur gear pair. Verma et al. used the extended finite element method (EFEM) to study the gear tooth meshing stiffness with cracks and verified it by comparison with the analytical model.