# Research on the method of gear crack propagation

There are many methods to study the crack propagation of gears. The following summarizes four common methods to simulate the crack propagation.

1) Boundary element method based on Franc 3D

The concrete steps of crack simulation by Franc 3D are as follows: firstly, the gear 3D model is established in the modeler OSM, or in other CAD software, and the model is imported into OSM through the interface between software and software; Then the boundary conditions and material parameters are set in the franc 3D module; The initial crack is set in the gear, and the gear is meshed and saved in. FYs file format; Open the bes module of the boundary element system, and calculate the stress intensity factor of each node at the crack leading edge according to the displacement results; The propagation step of each node in the crack front is calculated; The new crack leading edge node is determined. The least square method is used to fit the new node, and a new crack front curve is obtained; Finally, the crack surface and the whole model are meshed again, and the above steps are repeated.

2) Boundary element method based on ANSYS

The main idea of ANSYS for crack simulation is as follows: after the initial crack is inserted into the mesh divided by the gear, the incremental method is used to simulate the crack growth, calculate the stress intensity factor and the crack growth angle, and then calculate the crack growth angle again and define the crack length at the new crack location, and re grid the calculation again. This process is repeated many times, Finally, the crack propagation path is obtained.

3) Boundary element method based on Franc 2D

The main idea of the boundary element method based on Franc 2D to solve the crack propagation is: Based on linear elastic fracture mechanics, the dynamic calculation of gear meshing process is linearly equivalent to the static analysis of multiple meshing positions, the stress intensity factors of different positions are solved, the crack propagation is judged according to K criterion, and the crack propagation is calculated by Paris criterion, The maximum circumferential stress criterion is used to calculate the crack propagation angle, and the fatigue crack propagation path is obtained.

4) Extended finite element method based on ABAQUS

The main idea of XFEM based on ABAQUS to solve the crack propagation is: the main idea of XFEM is to define the fatigue crack, the crack propagation path can be solved by using XFEM to define the fatigue crack, and the leading edge stress intensity factor can be solved by using contour integral to define the fatigue crack.

This method can solve the problem of crack propagation accurately, efficiently and quickly without re meshing. This is because the extended finite element method allows the crack to pass through each element, uses the enhancement function to construct the discontinuity at the crack tip, adds additional degrees of freedom to the element near the crack tip, and uses the shape function to capture the singular field at the crack tip.

To sum up, the extended finite element method solves the problem of crack propagation which is difficult to predict. Therefore, the extended finite element method is mainly used to solve the problem of crack propagation in this study.

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