Multi stage gear transmission is a system composed of cutting motor, cutting transmission system and cutting roller, which is used to transmit motion and dynamics. The cutting transmission system includes fixed shaft gear, planetary gear train, gear shaft and bearing. Multistage gear transmission is a typical nonlinear system, and the analysis of natural vibration characteristics is for linear system. The common method is to take the average value of the time-varying meshing stiffness of the gear and the rated value of the nonlinear stiffness of the bearing, and obtain the natural frequency and mode vector of the multi-stage gear transmission through eigenvalue calculation.

It is very important to study the vibration mode of transmission system for the design of vibration and noise reduction. According to the characteristics of vibration modes, the vibration modes of multi-stage gear transmission can be divided into four types: translation vibration mode (P), torsion vibration mode (n), yaw vibration mode (b), translation torsion yaw vibration mode (PNB). It should be pointed out that the mode vector of the second torsional vibration mode is not only torsional displacement, but torsional displacement component is significantly larger than other displacement components. For example, the yaw displacement component of the 16th mode vector is three orders of magnitude larger than the other displacement components, so it can be classified as yaw vibration mode; the yaw displacement component of the 15th mode vector is only one order of magnitude larger than the other displacement components, so it can also be classified as yaw vibration mode; and the 28th mode vector can be classified as yaw vibration mode All kinds of displacement components of mode vector are of the same order of magnitude, and there is no obvious dominant displacement component, so it belongs to translation torsion yaw vibration mode.

Translational vibration mode, torsional vibration mode and yaw vibration mode are single vibration modes. Adding the number I after P, N and B indicates that the dominant displacement component is larger than the other displacement components In reference [157], the phenomenon of composite vibration mode is called “unclear vibration mode”, and it is pointed out that under some “special” parameters, when several different natural frequencies are close to each other, the phenomenon of unclear vibration mode will appear. Because the gear system analyzed in reference [157] has only 5 degrees of freedom and less natural frequency, the compound vibration mode only appears under some special parameters; the multi-stage gear system analyzed has 139 degrees of freedom, so the compound vibration mode becomes very common, even the torsional vibration mode contains a small amount of other displacement components. This is because there is correlation among translation, torsion and yaw displacement of transmission system. The more degrees of freedom the dynamic model has, the more likely it is that several different natural frequencies are close to each other, and the more difficult it is to use a single vibration model to classify all vibration modes.

The following phenomena can also be observed

1) The first natural frequency is 0 Hz, which corresponds to the rigid body mode. This is because the torsion degree of freedom of multi-stage gear transmission is unconstrained;

2) There are many natural frequencies with equal values in multistage gear transmission. This is because the bearing model has the same support stiffness in horizontal and vertical directions, which is equal to the radial stiffness. For example, the corresponding vibration modes of the 7th and 8th natural frequencies are that the roller moves in the positive direction of Y-axis and x-axis, respectively, and the displacement of other parts can be ignored;

3) The low frequency region is a single vibration mode (translation, torsion, yaw), and the natural frequency of the composite vibration mode is relatively large.

As shown in the figure, it is a typical vibration mode diagram representing various vibration modes of multi-stage gear transmission. The left column is the top view (x-z plane), and the right column is the front view (X-Y plane). In the figure, the red cylinder represents the fixed shaft gear, the blue cylinder represents the cutting cylinder, the black match line represents the gear shaft, and the green circle represents the motor rotor. Except for the motor rotor and cutting roller, the other parts are drawn according to the actual size; in order to avoid overlapping, the planetary gear train is drawn in a separate area in the front view. As shown in figure (E), the translation torsion deflection compound deformation of the fixed axis gear is caused by the bending deformation of the gear shaft. Because the gear shafts of the rocker arm of the shearer are all short and thick shafts, the translation torsion deflection compound vibration mode appears in the higher order mode.