Finite element modeling of static loading contact analysis of spiral bevel gear

According to the geometric characteristics of spiral bevel gear, the gear can be divided into multiple independent teeth with the same shape according to the number of teeth along the circumferential direction. Firstly, the single substructure is meshed, and then the complete spiral bevel gear mesh model is obtained through array, merging and other commands, which can reduce a lot of repetitive work and improve efficiency. Using its excellent surface modeling technology in CATIA software, a smooth cutting surface is drawn between the tooth root centerline and the axis of a single tooth. A complete spiral bevel gear is cut into a single complete tooth at the center line of two adjacent tooth root surfaces. Fig. 1 is a single tooth cutting model.

The complexity of spiral bevel gear tooth surface brings difficulties to mesh generation. It is difficult to obtain hexahedral finite element mesh directly using structural mesh or sweeping mesh. In order to obtain high-quality finite element mesh model, solid segmentation technology must be used to segment the spiral bevel gear geometry into simple geometric areas that can use structural mesh. According to the characteristics of the geometric model of spiral bevel gear, the free cutting surface is composed of auxiliary cutting curves in CATIA, and the single tooth geometric model is divided into six simple geometric areas with these cutting surfaces, as shown in Figure 2. It provides good conditions for obtaining high-quality structured hexahedron mesh.

Meshing is one of the most important parts of finite element analysis. The form and number of grids directly affect the calculation accuracy and time. Therefore, make a reasonable choice in the actual analysis. Finite element analysis software ABAQUS is good at nonlinear analysis and has powerful meshing technology. Structured grid technology is to apply standard grid to areas with simple shape. Swept mesh technology first generates mesh on the edge or face of the solid model area, and then stretches along the swept path to obtain the overall mesh model. Free mesh generation technology has the widest applicability and the most flexible application. In practical application, sometimes it is impossible to mesh the model with extremely complex structure. The solution is to divide the complex shape model into multiple simple shape models, so that an ideal mesh model can be divided. Swept mesh technology and structured mesh technology are the preferred mesh generation technology for finite element analysis of three-dimensional geometric model, and their analysis accuracy is high. Because the tooth profile of spiral bevel gear is complex, the sweeping path can not be found, so the sweeping mesh technology can not be applied. After the region division of spiral bevel gear teeth, it can be meshed by using structured meshing technology. In finite element analysis, hexahedral mesh has many advantages, such as small number of elements, strong deformation resistance and high solution accuracy. Hexahedral mesh is the first choice in numerical analysis. Hexahedral mesh should be used as much as possible in the three-dimensional geometric model to reduce the calculation time and improve the calculation accuracy. For the three-dimensional finite element model of spiral bevel gear, after considering various factors, the three-dimensional solid reduced integral element, namely c3d8r, should be selected.

In the finite element software ABAQUS, the spiral bevel gear model after region segmentation is imported through the data interface. According to the extremely complex characteristics of spiral bevel gear tooth surface, through the topology optimization technology in ABAQUS software, each segmented area of a single spiral bevel gear can be transformed into a structured mesh model. Using virtual topology technology, short edges or small faces can be combined, and some edges or points can be ignored at the same time. After topology optimization, each region of a single tooth is divided into structured hexahedral meshes. The element type used is a linear reduced integral element conducive to large strain analysis, as shown in Figure 3.

The high-quality structured hexahedral mesh single tooth area model can be obtained by combining the finite element mesh models of each single tooth area through the merging command in the software, as shown in Figure 4. After the single tooth mesh model is obtained, the finite element models of multiple teeth are obtained through circular array command and merge command in assemby module. In order to improve the calculation efficiency and give consideration to the calculation accuracy, the mesh of 8 teeth of spiral bevel gear is refined, and the other gears use coarse mesh. Figure 5 shows the full tooth finite element mesh model of spiral bevel gear and small spiral bevel gear created by the above method.

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