## 3 Comparison of Dynamic Response Characteristics under Fault-Free State
### Dynamic Response of Gear Transmission of Vibration Exciter  
Two local coordinate systems are established at the geometric center of the driving wheel and the driven wheel. The position curve can be obtained by measuring the position changes of the two local coordinate systems in the global coordinate system of the system. As shown in Figure 5, the displacement range of the rotation center reaches the maximum of the bearing clearance in the x' direction. The dynamic fluctuation of gear center distance is strong because of the combined action of big clearance and eccentric block, which is easy to lead to frequent teeth squeezing and large tooth backlash.  
Figure 4: (a) Normal meshing force and (b) x-direction vibration acceleration.  
In Figure 6a, the red line \"\(F_{n}\)\" represents the normal meshing force of the gear, and the blue line \"ZXJ\" represents the difference between the actual gear center distance and theoretical center distance. The gear meshing force fluctuates periodically with the change of center distance. The main reason for the \"wave crest\" at position I is gear squeezing. Figure 6b shows the gears meshing in and out clearly. Compared with the spectrum of Figure 4a, except for GMF and its multiples, Figure 7a shows the obvious rotational frequency \(F_{r}\), which is mainly caused by periodic teeth squeezing. It is noteworthy that the side frequency modulated by \(F_{r}\) is symmetrically distributed on both sides of GMF and its multiples, resulting in significant amplitude-modulated vibration. It is indicated that exciter gears are subjected to more complex alternating excitation.  
In Figure 8a, the vibration acceleration of the gear in three directions shows obvious periodic vibration, in which the vibration in the x and y directions is similar to simple harmonic vibration. Figure 8b has the same frequency components and distribution as in Figure 7. Compared with ordinary rotating machinery, gear transmission of the excitation system has more complex dynamic response characteristics. The stronger vibration and shock further explain the reason for the high failure rate of the exciter gear.  
Figure 5: Position curve of gear rotation center in x\({}^{\prime}\) y\({}^{\prime}\) coordinate system. (**a**) Driving gear and (**b**) driven gear.  
Figure 6: Fault-free condition: (**a**) relationship between meshing force and center distance fluctuation; (**b**) zoom magnified image of position I.  
Figure 8: (**a**) Vibration acceleration in x, y, and z directions; (**b**) frequency spectrum in x, y, and z directions.  
Figure 7: Fault-free condition: (**a**) frequency spectrum of normal meshing force; (**b**) zoom magnified images of positions 1–4 of (**a**) (position 5 has the similar distribution).  
The statistical results in Table 2 quantitatively show the differences in meshing force and vibration response between the exciter gears and the rotating machinery gears. It can be concluded that the fault mechanism of the exciter gears is the strong alternating excitation and complex vibration mode resulting from the different working principles.