Finite element model of variable hyperbolic arc gear

In the finite element calculation, the choice of mesh type is very important to the accuracy of the results. According to different types of problems and solving requirements, the most suitable element should be selected for the model. The finite element analysis software ABAQUS has abundant continuous elements based on stress and displacement. The typical ones are: linear complete integration, quadratic complete integration, linear reduced integration element, quadratic reduced integration element and so on. The shear self-locking problem occurs when the linear fully integrated element is subjected to bending load, and the calculation accuracy is poor.

Although the calculation of stress is very accurate, it can not be used in contact analysis. Similarly, the quadratic reduced integral element can not be used for contact analysis, and the quadratic element can not be used to discretize the model because it can cause the contact force of the equivalent node to oscillate between the corner node and the middle node.

The results show that the linear reduced integral is more accurate for the displacement, the accuracy of the analysis will not be greatly affected when the mesh is distorted, and the shear self-locking is not easy to occur under bending load. The tooth profile surface of the variable hyperbolic arc gear is a complex surface, and the mesh will be distorted to a great extent when meshing. After comprehensive consideration, the linear reduced integral element c3d8r is adopted.