## 2 Dynamic Model of Vibrating Screen Excitation System  
### Construction of Dynamic Model of Excitation System  
The purpose of building the overall model of the virtual prototype of the vibration excitation system is to simulate the boundary conditions of the gear pair and accurately reflect dynamic characteristics. The model should first be able to complete the normal gear mesh movement; secondly, it should be able to correctly reflect the reciprocating movement in the direction of the excitation force; finally, it must be able to accurately simulate the coupling effect of various components inside the exciter. Therefore, the overall model must consider the following components: gear pair, shaft, bearing, eccentric block, screen body, and spring. The spatial position relationship between the components is shown in Figure 1a. The rotating shaft connects the gear, bearing, and eccentric block. Fixed pair constraints are used between the rotating shaft and the gear, as well as between the rotating shaft and the bearing's inner race. Speed is applied to the inner race of the driving bearing, and torque is applied to the driven shaft to complete the drive of the gear. The action of the exciting force is simulated using the particle and the force with a constant magnitude that changes direction with the rotation axis. The bearing's outer ring is fixed on the screen body. The screen body is considered a rigid body, and only its mass characteristics are considered. The springs in the x and y directions are set at the bottom of the screen body. The excitation force, spring stiffness, and mass of each component are comprehensively considered to make the whole system reciprocate in the direction of excitation force [33]. Considering the shaft flexibility and bearing clearance, it can more truly reflect the coupling effect between components. This paper uses ADAMS software to establish the virtual prototype dynamic model of a mine-used linear vibrating screen with a processing capacity of 260 t/h. The main modeling contents include the following aspects listed in Figure 1b. 1. [label=(0)]
2. Eccentric blocks: four eccentric blocks of the vibration exciter are equivalent to the mass point fixed at the four ends of the rotating shaft. The centrifugal force generated by the movement of the eccentric block is considered a force (i.e., 7800 N) whose direction changes continuously with the rotating shaft. 3. Bearings: the 22232-el-xl-k bearing model provided in ADAMS is adopted, the bearing clearance grade is C3 (i.e., 0.195 mm), and the whole screen body is directly set as the bearing support. 4. Shaft: considering the flexibility of the shaft, the shaft support is an elastic support with a fixed inner circumference, and the MNF format file of the shaft generated by ABAQUS is imported into the ADAMS assembly. 5. An accurate gear pair model is established by parametric modeling with Pro/E software: gear diameter \(d_{r}\) is 330.002 mm; normal modulus \(m_{n}\) is 3; number of teeth \(Z\) is 93; reference circle pressure angle \(\alpha_{n}\) is 23.29\({}^{\circ}\); addendum coefficient \(han^{*}\) and backlash coefficient \(c^{*}\) are 1 and 1.25; helix angle of pitch circle \(\beta\) and normal pressure angle \(\alpha_{n}\) are 32.28\({}^{\circ}\)and 20\({}^{\circ}\); foot width \(B\) is 100 mm; center distance \(d_{0}\) is 330.0024 mm. Considering the problem of operation efficiency, the rigid model of helical gear pair is adopted in ADAMS. * (5) Gear contact coefficient: the meshing force and friction force of gears are calculated by impact function and Coulomb friction in ADAMS. According to [PERSON] elastic collision theory, the gear meshing stiffness coefficient \(K\) is 9.47e + 05 N/mm and the force index \(e\) is 1.5; the damping \(C\) is 947 N-s/mm, and the penetration depth \(d\) is 0.1 mm. The lubrication of the gear is considered in the setting of the friction coefficient.