# Dynamic-Breakdown of the Ball-Screw Inerter in ISD System
## 3 Experiments of DBoBSI in ISD System
### Experimental System of DBoBSI in ISD System  
As an essential prototype of inerters, the ball-screw inerter is widely used in categories of vibration control systems. The diagram of the ball-screw inerter in [16; 17; 18] is shown in Figure 3. The ball-screw inerter comprises a housing, a nut, a screw, bearings, a flywheel, as well as other components. One of the ball-screw inerter's two terminals is the housing, and the other is the screw. When the ball-screw inerter's two terminals are relatively translated, the flywheel and the nut make a coupled rotational motion. The transmission relationship of the ball-screw inerter's two terminals can be expressed by Equation (11) [32]. \[\frac{\omega_{12}}{v_{1}-v_{2}}=\frac{2\pi}{p} \tag{11}\]  
where \(\omega_{12}\) is the angular velocity of the nut as well as the flywheel. The lead of the ball-screw pair is denoted as \(p\). The ball-screw inerter's inertance, \(b\), can be expressed by Equation (12) [32]. \[b=\left(\frac{2\pi}{p}\right)^{2}J_{\rm t} \tag{12}\]  
where \(J_{\rm t}\) is the rotational inertia of coupled rotation components of the ball-screw inerter. \(J_{\rm t}\) is relative to the rotation axes of the coupled rotating components. On account of the model and analysis of the DBoI in the ISD system, the experimental scheme diagram of DBoBSI is shown in Figure 4. The experimental system in [32] is only suitable for the dynamic-breakdown of a single ball-screw inerter. Experiments of DBoBSI in the ISD system cannot be conducted in the experimental system in [32]. Therefore, in this research, the ball-screw inerter is connected with a rectangular spring in parallel, and a novel dynamic-breakdown experimental system is established. Experiments of DBoBSI in the ISD system can be conducted in this newly established experimental system. Considering the system's structural damper, the novel experimental system can be seen as a lightly damped ISD system. One of the ball-screw inerter's two terminals, the screw, is connected to the reference ground. The other terminal of the ball-screw inerter, the housing, can move downward, influenced by the gravity of the components of the inerter, apart from the screw. The weight blocks are fixed with the housing to increase the weight. The weight of these falling components is denoted as \(W_{\rm t}\). The mass of the ball-screw inerter itself is denoted as \(m_{\rm b}\). When the housing moves downward, the gravity potential energy of the falling components is mainly converted into the ball-screw inerter's kinetic energy and the spring's elastic  
Figure 3: The mechanical diagram of the ball-screw inerter in [16; 17; 18]. potential energy. The ball-screw inerter's stroke, \(L\), contains two parts, \(H\) and \(L\)-\(H\), as shown in Figure 4. During dynamic-breakdown experiments, different \(L\)-\(H\) are installed to acquire groups of relative impact velocities, \(v_{\rm 1c}-v_{\rm 2c}\). And then, the two terminals' relative displacement of the ball-screw inerter in the ISD system reaches the limited stroke, and DBoBSI in the ISD system occurs. When DBoBSI in the ISD system occurs, the two terminals impact reciprocally, the ball-screw inerter's kinetic energy is instantly released, and huge impact forces are caused. On account of the experimental scheme, a novel experimental system of the DBoBSI in the ISD system is established, as shown in Figure 5.  
The novel dynamic-breakdown experimental system of the DBoBSI in the ISD system comprises a spring, a ball-screw inerter, two force sensors, a mounting plate, a laser displacement sensor, and other adapting pieces. The ball-screw inerter is connected with a rectangular spring in parallel. Experiments of DBoBSI in the ISD system can be conducted in this newly established experimental system. One of the ball-screw inerter's two terminals, the screw, is connected to the mounting plate. The mounting plate is immovable. The other terminal of the ball-screw inerter, the housing, can move downward, influenced by the gravity of the components of the inerter, apart from the screw.