# Analysis of inherent characteristics of spiral bevel gear transmission with additional damping ring

The key to the influence of the damping ring on the dynamic characteristics of the system lies in the positive pressure and contact stiffness. Here, the positive pressure N1 of the damping ring is taken as 323n, and the contact stiffness A3 K of the damping ring is taken as 6.13 × 108n / m, at the same time, under the basic parameters shown in Table 3.1, and the radius of spiral bevel gear groove, take three-quarters of the radius of indexing circle at the small end of spiral bevel gear, and the friction coefficient between damping ring and groove μ = 0.3. According to the dynamic equation of the spiral bevel gear transmission system with additional closed damping ring and the calculation method of natural characteristics introduced in Chapter 3, the natural frequencies and corresponding vibration modes of the spiral bevel gear transmission system with additional damping ring are analyzed. The transmission system has 11 natural frequencies and 11 vibration modes, representing the free vibration of 11 degrees of freedom respectively.

Natural frequencies of spiral bevel gear transmission with additional damping ring; The vibration mode corresponding to each natural frequency is shown in Figure 1. In Figure 1, the abscissa represents each degree of freedom, 1, 2 and 3 represent the transverse degree of freedom of the pinion, 4, 5 and 6 represent the transverse degree of freedom of the large gear, 7, 8 and 9 represent the transverse degree of freedom of the damping ring, 10 represents the degree of freedom in the direction of the meshing line, and 11 represents the relative displacement freedom between the damping ring and the groove.

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

The influence of the average meshing stiffness of spiral bevel gear on the natural frequency of the system is analyzed, as shown in Figure 2. It can be seen from Figure 2 that with the increase of the average meshing stiffness of spiral bevel gear, the 8th and 11th natural frequencies increase with the increase of the average meshing stiffness of spiral bevel gear, among which the 8th increase is large. It has little effect on other natural frequencies except the 8th and 11th order.

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

The influence of support stiffness of spiral bevel gear driving wheel on natural frequency is analyzed, 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 5th-8th natural frequencies increase with the increase of the support stiffness of the spiral bevel gear, among which the 6th and 7th natural frequencies increase greatly. It has little effect on the natural frequencies of orders other than 5-8.

(3) Effect of radial contact stiffness of damping ring on natural frequency

Other parameters remain unchanged, only the radial contact stiffness of the damping ring is changed, and the natural frequency changes with the change of the contact stiffness, as shown in Figure 4. As can be seen from Fig. 4, with the increase of radial contact stiffness of damping ring, the 9th, 10th and 11th natural frequencies increase with the increase of support stiffness of spiral bevel gear, which is obvious. It has little effect on other natural frequencies.

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