# Dynamic-Breakdown of the Ball-Screw Inerter in ISD System
## 3 Experiments of DBoBSI in ISD System
### Dynamic-Breakdown Experiments and the Results  
On account of the experimental system of the DBoBSI in the ISD system, dynamic-breakdown experiments are conducted, and the results are analyzed. The relative displacements as well as velocities during the processes of the DBoBSI in the ISD system are shown in Figure 6. \(L\)-\(H\) are installed as 204.5 mm, 202.1 mm, 196.2 mm, 189.3 mm, and 185.7 mm, respectively. For example, Figure 6(1.a) shows the relative displacements during dynamic-breakdown, measured by the laser displacement sensor. Figure 6(1.b) shows the relative velocities,  
Figure 6: The relative displacements as well as velocities during the processes of the DBoBSI in ISD system. (**1.a–5.a**) Displacements; (**1.b–5.b**) Velocities. which are valid and calculated by the displacements. When \(L\)-\(H\) is installed as 204.5 mm, the housing moves downward, the relative displacement \(z_{1}-z_{2}\) decreases and the falling components' gravity potential energy is mainly converted into the ball-screw inerter's kinetic energy and the spring's elastic potential energy. Then, the relative displacement reaches the limited stroke and dynamic-breakdown occurs. When DBoBSI in the ISD system occurs, the housing and the two force sensors impact each other. The two terminals' relative velocity increases dramatically and suddenly. Meanwhile, the inerter's kinetic energy is instantly released and causes a huge impact force. Then the two terminals disconnect and may rebound several times. Figure 6(2.a) shows the relative displacements during dynamic-breakdown, and Figure 6(2.b) shows the relative velocities which are calculated by the displacements, when \(L\)-\(H\) is installed as 202.1 mm. Figure 6(3.a) shows the relative displacements during dynamic-breakdown, and Figure 6(3.b) shows the relative velocities which are calculated by the displacements, when \(L\)-\(H\) is installed as 196.2 mm. Figure 6(4.a) shows the relative displacements during dynamic-breakdown, and Figure 6(4.b) shows the relative velocities which are calculated by the displacements, when \(L\)-\(H\) is installed as 189.3 mm. Figure 6(5.a) shows the relative displacements during dynamic-breakdown, and Figure 6(5.b) shows the relative velocities which are calculated by the displacements, when \(L\)-\(H\) is installed as 185.7 mm. Results here, are similar in these dynamic-breakdown experiments of the DBoBSI in the ISD system. The impact forces, which are measured by one of the two force sensors during dynamic-breakdown, are shown in Figure 7, when \(L\)-\(H\) are installed as 204.5 mm, 202.1 mm, and 196.2 mm. Figure 7 shows that the peak impact forces of one of the two force sensors are more than 3000 N. That means that the peak impact forces of the two force sensors are more than 6000 N. The impact forces collected are much larger than the force \(k(z_{1}-z_{2})\) and the weight \(W_{\text{t}}\). The maximum value of the supporting force of the spring connected in parallel with the ball-screw inerter is no more than 400 N. The weight \(W_{\text{t}}\) is 166 N. Therefore, the dynamic-breakdown experiments here, are suitable for the dangerous situation that the inerter causes almost the entire impulse. The huge impact forces may destroy the ball-screw inerter as well as the system. The dangerous situation should be mainly concerned and researched, when designing inerters as well as the system. It can be verified that there is a DBoBSI in the ISD system, and the impact force during DBoI in the ISD system ought to be avoided. Results of the experiments of the DBoBSI in the ISD system are shown in Table 2. When DBoBSI in the ISD system occurs, the coefficient of restitution \(e_{\text{t}}\) changes slightly, and the variation of momentum \(M_{\text{c}}\) is nearly equal to the impulse \(P_{\text{t}}\). The error is within 15%.