# Design, Experiment, and Improvement of a Quasi-Zero-Stiffness Vibration Isolation System
## 1 Introduction
[24] investigated the application of QZS isolators in vibration pickups, a vibration pickups by using of vibration isolation principle of QZS, and the experimental results showed that the QZS isolator pickups has better performance than the linear isolator pickups even if there are physical and geometric errors. Besides, some achievements are obtained mainly focusing on control methodology based on the QZS isolation system [25]. Another way to construct a QZS system is to utilize magnets to construct springs with a negative stiffness. [PERSON] et al. [26] proposed a QZS system that consisted of two vertical mechanical springs and two magnets at the outer edge of each spring. The system could change the characteristics of the magnets to adapt to different working conditions to obtain the best vibration isolation performance. [PERSON] et al. [27] and [PERSON] et al. [28] proposed a novel spring with a negative stiffness that was composed of three cuboidal magnets. They found that the QZS system could reduce the vibration isolation frequency. Other systems with magnets used to create a negative spring were developed by [PERSON] et al. [29], [PERSON] et al. [30], and [PERSON] et al. [31]. Since the magnets mentioned above had a significant spatial distribution and therefore not appropriate for compact situations, another kind of negative spring with magnets was proposed, where two magnetic rings are embedded in each other. In [PERSON] and Bardaweel [32], a vibration system was analyzed, where the nonlinear negative stiffness was carried out using a combination of a magnetic spring and a mechanical oblique spring. The nonlinear damping was introduced to eliminate the undesired frequency jump phenomena. [PERSON] et al. [33] and [PERSON] et al. [34] developed prototypes of a QZS system with magnetic rings, the magnetization of which was along the radial direction. Since the axial magnetization had a high axial stiffness compared to the radial direction, this study investigated the effectiveness of a negative spring with magnetic rings, the magnetization of which was along the axial direction. Furthermore, many methods have been proposed by researchers to improve the feasible load range and its effect on the frequency response performance. [PERSON] and [PERSON] [35] developed a novel method for extending the load range of a vibration isolator using a foldable cylinder consisting of a torsional buckling pattern, where the experimental results show that the initial load range was extended by two to four times that of a conventional vibration isolator. [PERSON] and [PERSON] [36] developeda novel QZS vibration isolator by using flexure-based spring mechanisms, which enables itself to adjust the balance point according to the load weight. In addition, some adjustment methods have been proposed to improve the flexible load [37; 38; 39]. This paper proposes a new negative stiffness spring that uses magnets with an axial magnetization. The negative spring is made up of magnetic rings embedded in each other, which is proper for compacted situations compared to negative springs with mechanisms. Due to the high axial stiffness of magnets with an axial magnetization relative to the radial direction, the magnetic rings are magnetized along axial direction to withstand a greater load. First, the theoretical modeling of the negative stiffness spring was set up and the relationship between the force and displacement of the negative stiffness spring was studied using the equivalent magnetic charge method, thus obtaining the stiffness of the negative stiffness spring. The force-displacement and stiffness-displacement curves were obtained, which met the QZS theory based on finite element analysis. The experimental setup was developed to verify the effectiveness of the QZS system. Experiments with the linear isolation system corresponding to the QZS system were also undertaken. A comparison was made between the QZS system and the linear system regarding the vibration isolation performance.