# Analysis of natural frequency and vibration mode of spiral bevel gear transmission

According to the dynamic equation of spiral bevel gear transmission and the calculation method of natural characteristics introduced above, the natural frequencies and corresponding vibration modes of spiral bevel gear transmission with parameters are analyzed. Spiral bevel gear transmission has 7 natural frequencies and 7 vibration modes, representing the free vibration of 7 degrees of freedom respectively.

Natural frequencies of each order of spiral bevel gear transmission; Figure 1 is the vibration mode diagram corresponding to each natural frequency. 1, 2 and 3 represent the transverse degree of freedom of the driving wheel, 4, 5 and 6 represent the transverse degree of freedom of the driven wheel, and 7 represents the degree of freedom in the direction of the meshing line.

(1) Influence of average meshing stiffness of spiral bevel gear on natural frequency

Other parameters remain unchanged, only the value of the average meshing stiffness of spiral bevel gear is changed, and the natural frequency changes with the change of the average meshing stiffness, as shown in Figure 2. As can be seen from Fig. 2, with the increase of the average meshing stiffness, the second, third, fifth and sixth natural frequencies remain basically unchanged, and the first, fourth and seventh natural frequencies continue to increase with the increase of the average meshing stiffness, among which the seventh natural frequency increases greatly.

(2) Influence of support stiffness of spiral bevel gear driving gear on natural frequency

Other parameters remain unchanged, only the value of the support stiffness of the spiral bevel gear driving wheel is changed, and the natural frequency changes with the change of the support stiffness, as shown in Figure 3. It can be seen from Figure 3 that with the increase of the support stiffness of the spiral bevel gear driving wheel, the natural frequencies of the first, second and third orders change little, and the natural frequencies of the fourth, fifth, sixth and seventh orders increase with the increase of the support stiffness of the spiral bevel gear, among which the increase range of the fourth, fifth and sixth orders is large.

(3) Influence of support stiffness of driven gear of spiral bevel gear on natural frequency

Other parameters remain unchanged, only the value of the supporting stiffness of the driven wheel of spiral bevel gear is changed, and the natural frequency changes with the supporting stiffness of the driven wheel, as shown in Figure 4. As can be seen from Fig. 4, with the increase of the supporting stiffness of the driven gear, the natural frequencies of the 4th, 5th, 6th and 7th orders basically remain unchanged, and the natural frequencies of the 1st, 2nd and 3rd orders increase with the increase of the supporting stiffness of the driven gear of spiral bevel gear.

From the above analysis, it can be seen that the average meshing stiffness of spiral bevel gear and the support stiffness of driving wheel have a great impact on the high-order natural frequency (order 4-7) of spiral bevel gear transmission, and the support stiffness of driven wheel of spiral bevel gear has a great impact on the low-order natural frequency (order 1-3) of spiral bevel gear transmission.

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