# Establishment of finite element model of spiral bevel gear

Three finite element models of gear pairs are established on ABAQUS platform: theoretical tooth surface, only large wheel meshing surface is real tooth surface, and large and small wheel meshing surface is real tooth surface. When the spiral bevel gear is engaged, the convex surface of the large wheel and the concave surface of the small wheel are the meshing surface.

### 1. Division of finite element mesh

The division of finite element mesh is an important part of finite element numerical analysis. The quality of mesh directly affects the accuracy of analysis results. The full hexahedron mesh is used and refined to ensure the convergence of the results. The finite element mesh model is shown in the figure.

### 2. Pretreatment of finite element model

The pre-processing of spiral bevel gear finite element analysis includes element selection, application of load boundary conditions and setting of analysis type. These settings are related to the accuracy of analysis results and are the key technology of finite element analysis.

(1) Definition of material: the material of large and small wheels is alloy steel, and its elastic modulus is 2.09 × 105 MPa, Poisson’s ratio 0.3, density 7.8 × 10 － 9 t /mm3。

(2) Unit type: c3d8r, hexahedral primary reduction integral unit.

(3) Analysis type: ABAQUS implicit dynamic analysis is adopted, and the calculation step is 0.05. Rayleigh damping is selected, and its mass matrix coefficient α The value is 0.03 and the stiffness matrix coefficient is β The value is 3 × 10 － 6.

(4) Definition of contact pair: the tooth surfaces of large wheel and small wheel are defined as nonlinear contact, and the friction coefficient is 0.1. Implicit dynamics generally selects soft contact. In this paper, the contact pressure is set as 1000 n / mm and the gap is 0.001 mm.

(5) Load definition: define different resistance moments for the large wheel according to the actual load, and the small wheel is the driving wheel.

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