The setting of finite element preprocessing is very important, which not only determines whether the spiral bevel gear can converge in the analysis, but also determines whether the analysis result is reliable.
1. Mesh generation based on HyperMesh
Import the model into HyperMesh and mesh manually, which is of higher quality than the mesh automatically generated by arranging seeds in ABAQUS. In order to facilitate grid division and reduce the number of grids, the central part of the wheel blank is perforated, and then the model is segmented. The hexahedral grid type is adopted, and the grid density should be moderate. Because the model is more complex, you can divide the mesh by generating 2D mesh and then 3D mesh. The check elems module of HyperMesh is used to check the mesh quality. It is found that the mesh quality is good. The two spiral bevel gear mesh models are assembled as shown in Figure 1. The mesh model is generated into an InP file and imported into ABAQUS for spiral bevel gear analysis.
2. ABAQUS pretreatment
Firstly, the properties of spiral bevel gear material 20CrMnTi are defined. The elastic modulus is 209 000 MPa and the Poisson’s ratio is 0.3. The solver is static and general. The constraint condition is set to coupling type, and the coupling point is placed on the axis of the large and small wheels to couple with the inner ring of the spiral bevel gear. The contact mode is face-to-face contact. It is defined that the small wheel is the driving surface and the large wheel is the driven surface. The friction coefficient of the contact surface is set to be 0.1. At the initial stage of contact, all loads cannot be applied to the small wheel at one time, which may cause drastic changes in the contact state and lead to non convergence of iterative calculation. Therefore, small loads need to be added in the first analysis step, and all loads need to be loaded in the second analysis step. This method is also adopted for the output of spiral bevel gear angle. First, a small angle is applied to make the tooth surface contact, eliminate the assembly clearance, and then enter a large angle after the balance relationship is established. The resistance torque of the large wheel and the load along the rotation direction of the spiral bevel gear axis are set as 500 nm, 1000 nm and 1500 nm for light, medium and heavy loads respectively.
3. Finite element analysis results
3.1 Contact analysis
Select the big wheel as the observation object, select the analysis results of different rotation angles of the big wheel, get the contact lines at different times in the meshing cycle, and get the contact area of spiral bevel gear. Figure 2 shows the contact line during the meshing cycle. As can be seen from Fig. 2, the shape of the contact line is basically oval, and the contact area is basically in the middle of the spiral bevel gear. From the direction of tooth length, the contact area is located in the middle of tooth length. From the direction of tooth height, the contact area is located in the middle of tooth height, which is reasonable relative to the ideal contact area.
3.2 Extraction and analysis of transmission error curve
A large number of research results have confirmed that transmission error is the excitation source of spiral bevel gear vibration. Therefore, the angular output of large wheel and small wheel is extracted, and then the transmission error curve under different resistance torque is synthesized, as shown in Figure 3.
According to the transmission error curve, it is found that the transmission error of spiral bevel gear fluctuates sinusoidal. With the increase of load, the amplitude of spiral bevel gear transmission error curve decreases gradually, but the absolute value of deviation from zero line increases gradually. It shows that the transmission of spiral bevel gear is more stable under large load, but the transmission accuracy decreases. This conforms to the dynamic performance law of spiral bevel gear. Through the contact spot and transmission error curve, it shows that the simulated spiral bevel gear has good performance, and the simulated machining can provide a more efficient model for the research of spiral bevel gear. Finite element method can predict and evaluate the contact performance and transmission error of spiral bevel gear in the design stage of spiral bevel gear.