Finite Element Stress Analysis For Loxodrome Normal Circular-arc Spiral Bevel Gear

Loxodrome normal circular-arc spiral bevel gear transmission is a typical engineering application based on the principle of Betrand conjugate surface. It is likely to be the hi-tech prototype for the middle or large spiral bevel gear. Researchers generally pay more attention to its intensity property because it is just on the stage of research. But the stress distribution of this new kind of gear is 3D state and the intension is very complex, it cannot be calculated by the current formulas. And the contact intensity of the circular-arc is greatly higher than the involute gear, so it does not need to be calculated. Therefore, 3D FEM is presented to lay stress on bending stress analysis.Mathematics Equations of actual gear alignment lines and tooth profile lines are developed on the basis of Bertrand conjugate surface. The difficulty to make the profile and the fillet on tangent is solved through simulating process in practice. According to the equations, the solid models of a pair of loxodrome normal circular-arc spiral bevel gear are given by using APDL language and the modeling function in ANSYS. Boundary is located on the solid model and the mesh is denser in contact zones, taking into account the limit of the computer memory and stress property. The rigid constraints are applied along boundaries of the finite element models.According to the property of Bertrand, the main curvature on the mesh point is calculated by using the frame. Based on the Hertz theory, it can be work out that the contact force is spread over an elliptical area whose center is the theoretical point of contact and the distribution of pressure is a semi-ellipsoid on the contacting surface.The variational trends of bending stress of the gear and pinion are analyzed based on the FEM results. For the gear and pinion, the bending stress increase steadily along the gear alignment line, and reaches the maximum on the small end. At the same mesh point, the bending stress on the gear is bigger than that on the pinion. The reasons for these trends are discussed farther.Above all, the meaning and value of the paper are as follows. By using FEM the stress of 3D finite model is analyzed. The trend of stress in different parts of the tooth is got and questions about the intensity of the loxodrome normal circular-arc spiral bevel gear are answered. Results of this paper give the important bases for applying the new gear into practice.