Establishment of finite element analysis model of variable hyperbolic arc gear

In order to calculate the stiffness of variable hyperbolic arc gear, it is necessary to calculate the normal contact force FN of tooth profile surface and the comprehensive elastic deformation UN of meshing area. Because the middle section of variable hyperbolic arc gear belongs to involute section, and the other sections except the middle section are hyperboloid with curvature change, it will be very complex to determine the comprehensive deformation of the meshing area. Therefore, the accurate results can be obtained by using the finite element software for mechanical analysis. Taking a pair of variable hyperbolic arc gear as an example, the finite element analysis model of variable hyperbolic arc gear is constructed by digital modeling, and the contact finite element analysis is carried out by applying load. The comprehensive elastic deformation of tooth surface is obtained by finite element post-processing, and then the normal contact force of tooth surface is calculated by combining torque formula, and the variable hyperbolic arc gear is calculated based on the two The meshing stiffness of the system.

The 3D model of gear pair is imported into ABAQUS finite element software for preprocessing, and the finite element mesh model can be obtained after meshing. According to the contact mechanics, the contact pressure is highly concentrated near the contact area and decreases sharply with the increase of the distance from the contact point. Therefore, the contact pressure and comprehensive deformation of the tooth surface in the contact area do not depend on the geometry and boundary conditions far away from the contact area. The research focuses on the single tooth meshing stiffness, which should avoid the unnecessary influence of the edge rigid body coupling contact on the calculation results; at the same time, without affecting the calculation accuracy, the calculation time should be reduced as much as possible and the model should be simplified. After comprehensive consideration, the three tooth model should be used for analysis. The three tooth finite element model of the meshed variable hyperbolic arc gear pair is shown in the figure.