# Spring Failure Analysis of Mining Vibrating Screens: Numerical and Experimental Studies
## 3 Spring Failure Analysis
### Discussion  
More analyses with different kinds of spring failure were carried out, and the influence rules among the SVCs and the AVCs were obtained and are listed in Table 3.  
Figure 6: The amplitude variation coefficient (AVC) curves of each spring seat in the \(x\), \(y\), and \(z\) directions in the case of \(k_{1}\) failure.  
Figure 7: The amplitude variation coefficient (AVC) surfaces of four spring seats in the \(x\), \(y\), and \(z\) directions.  
As shown in Table 3, the SVCs under different spring failures have different influences on the AVCs in the \(x\), \(y\), and \(z\) directions. Hence, the influence rules among SVCs and AVCs with six kinds of spring failure can be summarized as follows:  
* Under failure kind 1 condition: In the \(x\) direction, all AVCs will increase. In the \(y\) direction, the AVC \(\Delta\lambda_{1y}\), \(\Delta\lambda_{2y}\), and \(\Delta\lambda_{3y}\) will decrease, while AVC \(\Delta\lambda_{4y}\) will decrease. In the \(z\) direction, the AVC \(\Delta\lambda_{3z}\) and \(\Delta\lambda_{4z}\) will increase, while the AVC \(\Delta\lambda_{1z}\) and \(\Delta\lambda_{2z}\) will decrease;
* Under failure kind 2 condition: In the \(x\) direction, all AVCs will decrease. In the \(y\) direction, the AVC \(\Delta\lambda_{1y}\), \(\Delta\lambda_{2y}\), and \(\Delta\lambda_{4y}\) will decrease, while the AVC \(\Delta\lambda_{3y}\) will decrease. In the \(z\) direction, the AVC \(\Delta\lambda_{2z}\) and \(\Delta\lambda_{3z}\) will increase, while the AVC \(\Delta\lambda_{1z}\) and \(\Delta\lambda_{4z}\) will decrease;
* Under failure kind 3 condition: In the \(x\) direction, all AVCs will be indeterminate. In the \(y\) direction, the AVC \(\Delta\lambda_{1y}\) and \(\Delta\lambda_{2y}\) will decrease, while the AVC \(\Delta\lambda_{3y}\) and \(\Delta\lambda_{4y}\) will be indeterminate. In the \(z\) direction, the AVC \(\Delta\lambda_{1z}\) will decrease, the AVC \(\Delta\lambda_{3z}\) will increase, and \(\Delta\lambda_{2z}\) and \(\Delta\lambda_{4z}\) will be indeterminate;
* Under failure kind 4 condition: In the \(x\) direction, all AVCs will increase. In the \(y\) direction, the AVC \(\Delta\lambda_{1y}\) and \(\Delta\lambda_{3y}\) will decrease, and the AVC \(\Delta\lambda_{2y}\) and \(\Delta\lambda_{4y}\) will be indeterminate. In the \(z\) direction, all AVCs will be indeterminate;
* Under failure kind 5 condition: In the \(x\) direction, all AVCs will be indeterminate. In the \(y\) direction, the AVC \(\Delta\lambda_{2y}\) and \(\Delta\lambda_{3y}\) will decrease, and the AVC \(\Delta\lambda_{1y}\) and \(\Delta\lambda_{4y}\) will be indeterminate. In the \(z\) direction, the AVC \(\Delta\lambda_{2z}\) will decrease, the AVC \(\Delta\lambda_{4z}\) will increase, and the AVC \(\Delta\lambda_{1z}\) and \(\Delta\lambda_{3z}\) will be indeterminate;
* Under failure kind 6 condition: In the \(x\) direction, all AVCs will decrease. In the \(y\) direction, the AVC \(\Delta\lambda_{2y}\) and \(\Delta\lambda_{4y}\) will decrease, and the AVC \(\Delta\lambda_{1y}\) and \(\Delta\lambda_{3y}\) will be indeterminate. In the \(z\) direction, all AVCs will be indeterminate.  
The influence rules listed above indicate that each kind of spring failure leads to one specific influence rule on the AVCs of the four spring seats in the \(x\), \(y\), and \(z\) directions. Hence, a spring failure diagnosis approach can be developed based on the knowledge that the mining vibrating screen dynamic characteristics can reveal certain kinds of spring failure.