# Dynamic-Breakdown of the Ball-Screw Inerter in ISD System
## 1 Introduction  
Inerter is a novel type of mechanical element, which was proposed by [PERSON] [1]. The dynamic characteristic of the inerter is inertia. The forces applied on the inerter's two terminals are proportional to the two terminals' relative acceleration. Therefore, the proportion's unit is the same as the mass. The proportion is known as the inertance of inerters. Based on the force-current analogy theory, the inerter-spring-damper (ISD) system corresponds to the capacitor-inductor-resistor system [2]. On account of the theory, the network synthesis method used in electrical systems can be applied to mechanical systems.  
On account of the ISD system and the network synthesis method, various mechanical networks have been proposed [3, 4]. For example, the inerter-based vibration isolator [5, 6, 7, 8], the tuned mass damper inerter system (TMDI) [9, 10, 11, 12], the tuned inerter damper system (TID) [13, 14, 15], etc. There are inerters with different categories of physical structures, for instance, the ball-screw based [16, 17, 18], the rack and pinion based [16, 19], the fluid-based [20, 21], and electromagnetic-based inerters [22, 23, 24], etc. The inerter-based vibration control method has been successfully applied in vehicle suspension systems [25, 26], aircraft landing gear suspension systems [27, 28], building vibration control systems [29, 30], etc. The research on modeling, design, analysis, and application of inerter have been persistently focused.  
With the wide applications of the inerter, the operation security issue is becoming increasingly important. For example, the dynamic characteristics of the ISD system with impulsive excitations has been researched [31]. Different from the research in [31], thedynamic-breakdown problem of the inerter is an extreme situation. The definition of the dynamic-breakdown of the inerter (DBoI) is that \"the inerter's two terminals come into contact\". If DBoI occurs, the inerter's two terminals impact reciprocally and the kinetic energy of the inerter is instantly released. DBoI can cause huge impact forces, and destroy the inerter itself and the system. The existence and dynamic characteristics of dynamic-breakdown of a single inerter is studied by [32]. As an essential protype of inerters, the ball-screw inerter is widely used.  
Different from [32], to confirm whether DBoI exists in an ISD system, especially when the inerter is connected with a spring in parallel, the research focuses on the dynamic-breakdown of a ball-screw inerter (DBoBSI) in an ISD system. However, 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, the novelty of the research is that 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. The necessity of the research is to confirm whether DBoI exists in the ISD system, which is quite important for the operation security of the inerter.  
Also, the main objective of this research is to confirm whether DBoI exists in the ISD system, and explore its dynamical characteristics. In Section 2, the dynamic model of the DBoI in the ISD system is established and analyzed. On account of the dynamic model and analysis, in Section 3, a novel experimental system is established, and experiments of DBoBSI in the ISD system are conducted. On account of the experimental data, huge impact forces are caused by DBoBSI. The impact forces collected by experiments are much larger than the weight of the ball-screw inerter itself. In Section 4, the conclusions are that there is a DBoBSI in the ISD system, and the impact force during DBoI in the ISD system ought to be avoided.