According to the standard tooth profile geometric relationship of GB / T 12759-1991, according to the gear parameters (z = 51, M = 4 mm α = 24°、 β = 20. 263 °, B = 60 mm), using croe software to establish the parametric solid model of double circular arc gear. The geometric model is imported into the workbench software, and the model material is defined as the default structural steel of the software. Because the low-order frequency is grid independent, that is, the grid type and density have little effect on the results of low-order frequency and vibration mode in modal analysis, the tetrahedral large-size mesh is adopted for the model.
According to the actual motion constraint state of the gear kinematic pair, the radial, axial and normal displacement and rotation components of the gear inner hole surface are fully constrained. The first six modes are extracted without considering the influence of external excitation. The first 6-order modal characteristics of double circular arc gear are shown in the table, and the vibration modes of the first 6-order modes are shown in the figure.
| Order | Natural frequency / Hz | Vibration mode |
| 1 | 1 075.2 | Circumferential vibration |
| 2 | 1 361.3 | 1st order half vibration |
| 3 | 1 384.7 | 1st order half vibration |
| 4 | 1 789.3 | Umbrella vibration |
| 5 | 2 252.2 | Second order half flexural vibration |
| 6 | 2 254.1 | Second order half flexural vibration |