Influence of hub deformation on meshing finite element model of star gear reducer

According to the real structure and the above model simplification method, the author establishes the three-dimensional solid models of internal gear ring, planetary gear ring and planetary gear hub in SolidWorks, and imports them into ABAQUS; In ABAQUS, the analytic rigid body model (solid shell) of transmission crankshaft is established, and these solid bodies are assembled according to the original assembly relationship in ABAQUS.

The gear teeth are divided into hexahedral structured mesh, and the mesh of 40 gear teeth in the meshing area of planetary gear and internal gear is refined. Taking the gear tooth of planetary gear as an example, the mesh of tooth surface contact area and tooth root bending area is refined by cutting and seeding. The mesh size of the refined area is 1 mm, the average aspect ratio is 2.12, and the shape is qualified. Through the trial calculation, the difference between the results of further refinement of the grid and the results of this grid model is less than 3%. Therefore, the grid can meet the calculation accuracy and control the calculation time.

(a) Global mesh (b) local details

The hub part is divided into hexahedral swept mesh, and the global mesh size is 3 mm. The overall mesh model and local enlarged display are shown in the figure (the total number of model units is 968756).

The material of internal gear and planetary gear is 42CrMo. The elastic modulus is 206 000 MPa and Poisson’s ratio is 0.29 defined in ABAQUS.

The static general analysis step is selected here. Because of large deformation and contact, check the geometric nonlinearity in the analysis step settings. In the initial analysis step, the global universal contact is defined, and the surface to surface contact is defined between the outer surface of the analytical rigid shaft and the cylindrical surface of the hub shaft hole.

The input end of beam connector is located on the center line of input crankshaft, one end of the hinge connector is connected with the output end of beam, and the other end is connected with the coupling point of the center hole of planetary gear. The definition method of driving support plate of transmission crankshaft is similar, the input end of beam connector is located on the center line of rigid crankshaft, the hinge connector is located on the rotation center line of transmission crankshaft, one end of which is connected with the output end of beam, and the other end is connected with the rotation center point of support plate (i.e. the reference point of applying load) to establish beam connector.

There are five analysis steps (including initial step) defined in the analysis process, which are meshing contact and contact between transmission crankshaft and mating hole (internal gear rotation 0.001 RAD), pre imposed initial load 105 n · mm, applied full torque load 7.58 5107 n · mm, and full load rotation predetermined angle 1 rad.

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