# Life analysis of internal meshing modified gears with cracks

ABAQUS software and FRANC3D software will be used to analyze the fatigue life of internal gear plate crack [4-6]. The main analysis steps are as follows:

## 1. Sub model of internal plate denture

Firstly, the *. InP model is imported and divided into global model and sub model; The finite element models of sub model and global model are output respectively, and two *. InP files are generated for subsequent crack growth analysis.

## 2. Adding initial cracks to the sub model

Firstly, the crack is established, and the crack type is selected as elliptical crack. Secondly, the size of the crack is defined. The radius of the long axis of the elliptical crack is a = 1 mm, and the radius of the short axis of the elliptical crack is b = 0.25 mm. The third is to define the coordinates of elliptical crack as (73.5018, 3.091, – 20) and rotate 90 degrees around x, y and Z axes °。 Finally, the mesh is divided again. In order to ensure the accuracy of calculation, the mesh at the crack is densified automatically.

## 3. Solving the stress intensity factor

Relevant parameters and stress intensity factors are calculated by computer, as shown in Fig. 1 ~ Fig. 3.

In Figure 1, it can be seen from the figure that the stress intensity factor ki is symmetrical, and the stress intensity factor in the middle of the crack tip is larger than that at the edge; The change trend of stress intensity factor Ki in the edge is larger than that in the middle, which indicates that the expansion speed of the edge is larger than that in the middle; The stress intensity factor at node 0 is smaller than that at node 1, which is mainly due to the larger tensile stress in the middle of the crack. The KIC of relevant materials can be found by consulting relevant manuals.

In Figure 2, the stress intensity factor Kii appears negative values at node 0.2 and node 0.8, which means that the expansion direction is opposite. The stress intensity factor Kii is also symmetrical, and the stress intensity factor near node 0 is greater than that at node 1; The crack tip edge propagates in the positive direction, and the crack tip node 0.2 and node 0.8 propagate in the opposite direction; Although the crack tip node 0.2 and node 0.8 propagate in the opposite direction, compared with the crack tip edge propagation speed, the middle part is still very small. This is also because the mode II stress at the edge of the crack tip is greater than that in the middle of the crack tip.

It can be seen from Figure 3 that the stress intensity factor kiII is approximately a straight line, which is bounded by 0.5 of the node. The left half of kiII is expanding in the positive direction, and the right half is expanding in the opposite direction. The expansion speed is similar, and 1.89mpa/mm is the maximum stress intensity factor.

After solving the stress intensity factor, we will judge the main crack types according to the stress intensity factor, and analyze the crack propagation of the main crack types. 