## 1 Introduction  
A box-type vibration exciter [1] can provide a reciprocating power source for a mine-used linear vibrating screen [2], and the helical gear pair is the key component. It plays an important role in forcing the driving and driven shafts to rotate synchronously and reversely. However, under the coupled excitation of elastic support of the spring seat under the screen body, strong alternating load caused by eccentric block and large clearance of C3 level self-aligning roller bearing [3], the gear center distance of vibration exciter fluctuates violently. As a result, frequent switching is observed between teeth squeezing and large clearance in the process of gear transmission, which increase the fatigue damage of the gear and even causes serious faults such as tooth breakage [4]. Therefore, analyzing the dynamic characteristics of the vibration exciter without and with faulty gear of gear transmission is greatly significant. Clearance is a non-negligible factor in the study of the dynamic characteristics of the gear drive system of the vibration exciter. Many scholars have committed to studying the influence of tooth backlash [5, 6, 7], bearing clearance [8, 9] and their coupled excitation [10, 11, 12, 13] on the dynamic characteristics of gear transmission. [PERSON] and [PERSON] [5] carried out research through experiments. [PERSON] and [PERSON] [8] analyzed the non-linear dynamic phenomenon of planetary gear transmission systems caused by bearing clearance. [PERSON] et al. [11] found that there is a coupling relationship between bearing clearance and tooth backlash. A shorter center distance can cause teeth squeezing and bearing clearance can delay the occurrence of teeth squeezing. At present, research on tooth backlash and bearing clearance concerns rotating machinery. Generally, bearings in rotating machinery have clearance less than C3, and eccentricity is not considered in the rotating machinery model. However, the vibrating screen belongs to vibrating machinery. There are large eccentric blocks and bearings with large clearance in the vibrator rotor system, producing more complex dynamic characteristics and stronger coupling vibration. Excitation is another significant factor in gear transmission. Rotor systems with gear transmission under the working conditions of marine ships [14; 15; 16; 17], wind turbines considering tower elasticity [18; 19], vehicles traveling on the road [20], aeroengines considering stator [21; 22] and so on belong to the typical rotor system under foundation excitation. [PERSON] and [PERSON] [14; 15] studied the dynamic response of the rotor-bearing-gear system with cracks under three periodic foundation angular motions of the ship. [PERSON] et al. [18] and [PERSON] et al. [19] discussed the influence of flexible tower support on a wind turbine's helical gear system and found that the vibration displacement amplitude under flexible support is generally higher. Based on the aeroengine rotor-stator system, [PERSON] et al. [21] found that the influence of foundation vibration on dynamic rotor characteristics is orthogonal. Those works are examples of rotors on moving bases. The foundation of the rotor system of the vibration exciter (i.e., screen body) cannot vibrate by itself, and its working principle is fundamentally different from the rotor system excited by the rotor foundation. In addition, the vibration form of the vibrator rotor is a periodic reciprocating linear motion with a small amplitude in the direction of excitation force, which is also very different from the excitation form generated by waves and wind. Gear mating dynamic analysis has been extensively investigated and reported. [PERSON] et al. [23] built a finite element (FE) model to determine the fault features in the time domain of the ring gear strain signal caused by abnormal mesh force. [PERSON] et al. [24] proposed an analytical-FE method to calculate the time-varying mesh stiffness (TVMS) of gear tooth crack.