The pre-processing of finite element analysis of variable hyperbolic arc gear includes: the selection of element, the setting of analysis type, the application of load, the determination of boundary conditions, etc. These settings directly determine the accuracy of the analysis results, which is the key technology of finite element analysis.
(1) Material definition: set the elastic modulus of main and driven wheels to 208 GPA and Poisson’s ratio to 0.3.
(2) Element attribute definition: hexahedral integral element (c3d8r) is used.
(3) Definition of analysis type: the implicit and static analysis algorithm is adopted, and the calculation step of the analysis process is set to 0.1.
(4) Definition of contact pair: the analysis tooth surface of driving wheel and driven wheel is defined as face-to-face contact, and the friction coefficient in tangential contact attribute is set to 0.15.
(5) Meshing: the size of the whole gear unit is divided into 1 mm. In order to make the stress and deformation of the meshing contact area more accurate, the actual meshing contact area unit of the gear should be subdivided locally. It is verified that when the mesh size of the refined area is 0.03 mm, the mesh size will no longer affect the analysis accuracy.
(6) Boundary condition definition: the driving wheel only retains the rotational degrees of freedom along the axis of the reference point, and all the degrees of freedom on the reference point of the driven wheel are limited.
(7) Boundary condition exertion method: the reference point is established at the center of the axis of the driving wheel and the driven wheel, and the MPC coupling constraint is established between the reference point and the inner ring and profile of the driving wheel and driven wheel, so as to connect the load and boundary condition with the reference point. The boundary conditions and loads applied on the reference points are equivalent to those applied on the coupling nodes, and then transferred to each node of the gear. Of course, the coupling constraints can also simulate the boundary conditions after the loads are applied on the driving gear.
（8） Definition of analysis step: in order to ensure the convergence of gear contact analysis process, the analysis process is divided into the following two steps: ① since there may be backlash on the contact tooth surface at the initial position, a small torque should be applied on the driving gear and a fixed boundary condition should be applied on the driven gear to eliminate the backlash and ensure the convergence of contact iterative calculation; ② remove the driving gear In order to complete the contact analysis under a certain load, a small torque is applied on the driving wheel and a specific working load is applied on the driving wheel.
(9) Load definition: the torque of driving wheel is defined as 20 N · m, and the load increases from 0 N · m to the maximum during the whole analysis process.