# A Novel Ring Spring Vibration Isolator for Metro Superstructure
## 1 Introduction  
As an important means to alleviate urban traffic pressure, the metro brings convenience to modern life. It also causes noise and vibration pollution in the metro superstructure and for neighboring residents. In recent years, complaints about traffic noise and environmental vibration have become international public issues. The environmental vibration of the underground reduces building comfort, affects human health and hinders the use of sensitive instruments [1]. Furthermore, it even affects the safety of old buildings. To mitigate the negative impact of metro vibration on buildings, many scholars have carried out studies on the method of isolating vibration. [PERSON] et al. [2, 3, 4] presented a 2D impedance model capable of predicting vibration transmission in column- and load-bearing wall-supported buildings. In terms of vibration isolation of buildings, the most commonly used types of vibration isolator are rubber, pneumatic and spring. [PERSON] et al. [5] used a 3D finite element method to study the deformation and stress distribution of rubber dampers which were subjected to strong earthquakes. [PERSON] et al. [6] used thick natural rubber dampers and thick highly damping rubber supports to control the metro vibration. [PERSON] [7] used a bilinear hysteresis model to analyze a series of nonlinear responses of the vibration structure with lead rubber dampers, and studied the response of the lead core self-heating to the lead rubber damper under bidirectional earthquake action. All of them used rubber dampers for vibration isolation. They found that the rubber vibration isolator could have stable performance and low cost, but the vibration isolation effect is limited. The ring spring, a kind of friction spring, is composed of multiple pairs of outer rings with inner cones and inner rings with outer cones (Figure 1) [8]. When axial load \(F\) acts on the ring and the normal component force acts on the conical surface of the inner rings and the outer rings, the outer ring will stretch and its diameter will expand, while the inner ring will compress, with its diameter shrinking. The relative movements of the rings along the conical surface cause them to press against each other and the spring produces axial deformation_f_. When the inner rings and the outer rings undergo a relative motion with each other on the conical surface, the contact surface generates friction. In this relative motion, the characteristic curves of loading and unloading do not coincide. As shown in Figure 2, the characteristic curve of the ring spring, the loading and unloading curves move along OABCO. When the ring spring is unloading, the stress-displacement curve starts from point B instead of point E. This is the reason why friction lags the elasticity of spring. If there is no friction, the loading and unloading will only act along OD. Obviously, the area of OABCO is the energy consumed by the internal friction and friction generated when the spring is working. During the loading process, the area of OABCD is about 60% to 70% of OAGO's, which means the ring spring has a strong damping ability. The pneumatic and hydraulic vibration isolator has excellent performance, but the design is too complicated to maintain [9]. It is not only expensive, but also difficult to promote. Meanwhile, the spring damper has good vibration isolation performance and consumes energy according to its vertical deformation and friction damping [10]. Currently, most spring dampers use helical springs and disc springs. The load-displacement curve of the helical spring is linear without an energy dissipation effect, so it needs to be used with dampers in the design of vibration isolators. [11]. Although disc springs and ring springs are both friction springs, the ring spring is more suitable when space is limited,  
Figure 1: Ring spring. Figure 2: Load–displacement curve of ring spring. thanks to its structural characteristics [12]. Furthermore, the energy storage capacity of ring springs is greater than that of disc springs.