# Spring Failure Analysis of Mining Vibrating Screens: Numerical and Experimental Studies
## 4 Validation of Developed Diagnosis Approach  
Experiments were conducted on a SLK3661W vibrating screen with YHJ(C) mining portable vibration data acquisition instruments and GBC1000 mining intrinsically safe vibration sensors, as shown in Figure 8. Three acceleration sensors were mounted orthogonally on each spring seat to obtain the longitudinal vibration (in the \(y\) direction), horizontal vibration (in the \(x\) direction), and lateral vibration (in the \(z\) direction) acceleration signals individually. Meanwhile, all acceleration signals were acquired and saved with data acquisition instruments. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Failure** & \multicolumn{8}{c}{**AVCs**} \\ \cline{2-13}
**Kind** & \(\Delta\lambda_{1x}\) & \(\Delta\lambda_{2x}\) & \(\Delta\lambda_{3x}\) & \(\Delta\lambda_{4x}\) & \(\Delta\lambda_{1y}\) & \(\Delta\lambda_{2y}\) & \(\Delta\lambda_{3y}\) & \(\Delta\lambda_{4y}\) & \(\Delta\lambda_{1z}\) & \(\Delta\lambda_{2z}\) & \(\Delta\lambda_{3z}\) & \(\Delta\lambda_{4z}\) \\ \hline
1 & \(+\)\(The main parameters of data acquisition are shown in Table 4.  
Then, the acquisition data were loaded into a computer in the laboratory for data processing with MATLAB. The displacements were calculated from the accelerations by using numerical double integral and detrend operations. For example, the acceleration and displacement curves in the \(x\), \(y\), and \(z\) directions of spring seat 2 under normal conditions are shown in Figure 9. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value/Range** \\ \hline Sample frequency & 2500 Hz \\ Sampling resolution & 16 \\ Frequency range & 1–10 kHz \\ Signal amplification ratio & 1:3 \\ Output voltage range & \(\pm\)5000 mV \\ Acceleration range & 0–50 g \\ Sensor sensitivity & 5 mV/ms\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The main parameters of data acquisition. Figure 8: Experimental setup. (**a**) The SLK3661W vibrating screen applied in the coal washery. (**b**) Acceleration sensors and data acquisition instruments used in experiments. Figure 9: Acceleration and displacement curves in the \(x\), \(y\), and \(z\) directions of spring seat 2 under normal conditions, including the steady state displacement curves during 20–21 s.  
As shown in Figure 9, the vibrations of the mining vibrating screen include three states:  
* Start state. The driving motor causes the mining vibrating screen to vibrate, and the accelerations and displacements rapidly increase. In this state, as the motor speed increases, the mining vibrating screen passes through the resonance region quickly;
* Steady state. The accelerations and displacements gradually change into stable ranges. In this state, the system does not resonate, so it is suitable for long-term stable working;
* Outage state. The accelerations and displacements decrease gradually at first, then increase for a period of time, and finally decrease to zero. In this state, as the motor speed decreases, resonance occurs when the system passes through the resonance region. The mining vibrating screen halts at last. After data processing, the steady state amplitudes of the four spring seats in the \(x\), \(y\), and \(z\) directions under normal conditions were obtained, as shown in Table 5.  
Furthermore, springs with different sizes were adopted as the failure springs with a 20% decrease in longitudinal (\(y\) direction) stiffness; that is, the SVC was 20%. According to Table 2, six spring failure kinds were selected for conducting the spring failure experiments. After data acquisition and data processing, the steady state amplitudes of four spring seats in the \(x\), \(y\), and \(z\) directions under the spring failure condition were obtained. Meanwhile, the AVCs of each spring seat in the \(x\), \(y\), and \(z\) directions could be calculated as experimental results according to Formula (2). Therefore, the experimental results could be compared with the simulation results, as shown in Figures 10-15.