Relevant parameters of hypoid gear. It is defined that the axis of the small wheel is parallel to the x-axis direction of the global coordinate system, the axis of the large wheel is the Y-axis of the global coordinate system, and the small wheel is positively offset to the z-axis of the global coordinate system.

Based on the meshing principle and machining principle of hypoid gear, the surface point coordinates of hypoid gear teeth are obtained, the nodes and element data files of hypoid gear finite element model are generated, and the finite element model of hypoid gear is obtained by importing the finite element software ABAQUS. The element type adopts 8-node 6-surface element, and the material parameters adopt the real material parameters of hypoid gear. Considering the calculation accuracy and efficiency, 5 pairs of tooth models are used for calculation and analysis, and the established finite element model is shown in the figure.

(1) Definition of contact pair: under the normal driving condition, the concave surface of small wheel is meshed with the convex surface of large wheel. Five pairs of concave surface of small wheel and convex surface of large wheel participating in meshing are defined as face-to-face contact pairs respectively, and the friction factor of 0.1 is considered.

(2) Boundary conditions and loads: reference points are respectively established at the center of the hypoid gear and coupled with the nodes on the hypoid gear body. The boundary conditions are applied to the reference point at the center of the hypoid gear. The load step is defined as follows.

Initial load step: respectively constrain the other 5 degrees of freedom except the rotational degrees of freedom of the central reference point of the two hypoid gears along the axis.

Load step 1: constrain the axial rotation freedom of the central reference point of the large wheel, and apply a small axial rotation angle at the central reference point of the small wheel to make the hypoid gear enter the contact state.

Load step 2: constrain the axial rotation freedom of the central reference point of the small wheel, release the axial rotation freedom of the central reference point of the large wheel and apply a small torque to make the hypoid gear reach the ideal initial meshing state.

Load step 3: apply the axial rotation displacement uniformly varying with time in the positive x direction on the center reference point of the small wheel to realize the change of the meshing orientation of the hypoid gear, and apply the axial constant torque in the negative Y direction on the center reference point of the large wheel to simulate the loading meshing process of the hypoid gear under the positive driving condition.

(3) Analysis type: use implicit algorithm to simulate the quasi-static meshing process of hypoid gear, and finally obtain the meshing parameters corresponding to each small wheel orientation.