# Spring Failure Analysis of Mining Vibrating Screens: Numerical and Experimental Studies
## 2 Finite Element Model
### Modeling  
In this paper, ANSYS is adopted to establish the finite element model of a mining vibrating screen. The main modeling contents include the following aspects:  
* Beam model. The vibrating screen has one exciting beam, two reinforcement beams, and a dozen bearing beams. In order to ensure that the calculation is accurate and it is easy to load the alternating forces, SOLID elements are adopted for the beam models, as shown in Figure 2a-c;
* Lateral plate model. The mining vibrating screen has a pair of lateral plates. The dimensions of a single lateral plate are 7010 mm \(\times\) 3174 mm \(\times\) 10 mm; thus, the thickness is far smaller than the length and height. In this paper, SHELL181 elements are used to model the lateral plate, as shown in Figure 2e, to ensure the calculation accuracy and efficiency;
* Bolted connection model. The beam flanges, lateral plates, and spring seats are connected by bolts in practice. In this paper, beam elements are adopted to simulate bolts for improving the calculation efficiency, as shown in Figure 2d. Hard points are created at the bolt positions of all structures, and multiple linear BEAM188 elements are used to connect the mesh nodes around the hard points so as to maintain the same degree of freedom of these hard points, which can reflect the bolted connection relationship;
* Spring seat and spring model. The mining vibrating screen has two loading side spring seats and two unloading side spring seats. Four elastic supports comprised of linear metal cylindrical helical springs are mounted under the spring seats. In this paper, the SHELL181 elements are adopted for modeling the spring seats, and the linear SPRING elements are adopted to simulate each elastic support. The SPRING elements are established at the centre of the spring seat baseplate in three mutually perpendicular directions (\(x,y,z\)), and the other end of each SPRING element is fixed, as shown in Figure 2f,g;
* Exciter model. In practice, the mining vibrating screen has two exciters, which are bolted on the exciting beam (region A and region B). Since the exciter mass is much lower than the mining vibrating screen, the inertia of the whole system is not affected by the exciters. Therefore, the point mass units are adopted to simulate the exciter mass of region A and region B in this paper. Meanwhile, the stiffening caused by the exciters is negligible, because it is far less than the system alternating forces. In this paper, the alternating forces are applied on region A and region B.  
Figure 1: Structures of the SLK3661W mining vibrating screen (lateral view). The left side is the loading side and the right side is the unloading side. According to the above modeling method, the overall finite element model of a mining vibrating screen can be established, as shown in Figure 3. In this finite element model, the number of finite elements is 39,214, the number of nodes is 127,932, the whole system mass is 11,303 kg, and the damping coefficient is 0.04. According to the system technical descriptions, the elastic support parameters can be obtained, as shown in Table 1. The alternating forces are loaded as simple harmonic forces on POINT MASS in the \(x\)-\(y\) plane, the amplitude of each sinusoidal force is 450 kN, and the force frequency is 14.82 Hz, which is typical of vibrating screen operations. \begin{table}
\begin{tabular}{c c c c c} \hline Parameters & \(k_{1x}\)/(N/m) & \(k_{2x}\)/(N/m) & \(k_{3x}\)/(N/m) & \(k_{4x}\)/(N/m) \\ value & 353,010 & 470,680 & 353,010 & 470,680 \\ \hline parameters & \(k_{1y}\)/(N/m) & \(k_{2y}\)/(N/m) & \(k_{3y}\)/(N/m) & \(k_{4y}\)/(N/m) \\ value & 931,800 & 1,242,400 & 931,800 & 1,242,400 \\ \hline parameters & \(k_{1z}\)/(N/m) & \(k_{2z}\)/(N/m) & \(k_{3z}\)/(N/m) & \(k_{4y}\)/(N/m) \\ value & 353,010 & 470,680 & 353,010 & 470,680 \\ \hline \end{tabular}
\end{table} 
Table 1: Elastic support simulation parameters table. Figure 3: The overall finite element model of the mining vibrating screen.