# Design, Experiment, and Improvement of a Quasi-Zero-Stiffness Vibration Isolation System
## 6 Discussions and Conclusions  
This paper proposes a new kind of QZS system whose negative stiffness was produced using two magnetic rings with axial magnetization, where the negative spring of the magnetic rings was more suitable for compacted occasions and the axial direction for magnetization was more appropriate for greater loads compared to other directions of magnetization. The force-displacement characteristic of the two coupled magnetic rings was derived and the relationship between parameters of the magnetic rings and the stiffness of the system was studied, which provided the direction for the improvement of the system. The dynamic response of the QZS isolation system was analyzed, which showed that increasing the damping ratio was useful for the initial frequency of vibration isolation, but was not appropriate for high-frequency vibration isolation. An experimental prototype was developed to verify the vibration isolation ability of the QZS system. The results of the experiment showed that the proposed QZS system was better than that of a corresponding linear system at vibration isolation. Two methods were proposed for the improvement of the QZS system: changing the axial heights of the magnetic rings and designing a nonlinear spring that was parallel with the linear spring. The dynamic response of the improved QZS system was analyzed. From this analysis, the force transmissibility of the improved system was lower than that of the non-improved system, which indicated that the effect of vibration isolation of the improved QZS system was better than that of the non-improved isolator. Considering the improvement of the QZS system, whether by changing the axial stiffness of the magnetic ring or adopting a flexible nonlinear spring in combination with a linear spring, the QZS system displayed vibration isolation as long as the stiffness met the quasi-zero stiffness characteristics. For the QZS system, the wider the range of the zero-stiffness region at the balance point, the greater the vibration isolation ability. Furthermore, to improve the performance of the QZS system, many structures could be explored in the future for constructing the QZS system different from those schemes mentioned in this paper, which mainly focused on regulating the parameters of the nonlinear flexible structures or the axial stiffness of the magnetic ring. It should be pointed out that the focuses of this paper were the proposed QZS system and how to improve its performance. Some other characteristics, such as stability, the effect of damping performance of the QZS system, the error of the mechanical system, and so on, could be explored in the future, which could be more complicated. [PERSON] and [PERSON] provided the conceptualization; [PERSON] designed experiments and wrote the manuscript; [PERSON] carried out experiments and analyzed experimental results; [PERSON] was the director for the whole article, including the experiments and the structure of the article; [PERSON] proposed the new QZS system and provided  
Figure 20: The comparison between the non-improved system and the improved system with the same excitation amplitude: (**a**) \(\overline{F}_{0}=0.15\) and (**b**) \(\overline{F}_{0}=0.30\). the funding for the experiment; [PERSON] provided project administration. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Key Research and Development Program of China (grant No. 2017 YFB1302200) and the Joint Funds of the National Natural Science Foundation of China (grant no. U1613224). The work was also supported by Key Research and Development Program of Guangdong Province (grant no. 2019B090915001) and the KEY Laboratory of Robotics and Intelligent Equipment of Guangdong Regular Institutions of Higher Education (grant no. 2017 KSYS009), and in part by the DGUT (Dongguan University of Technology)innovation center of robotics and intelligent equipment of China (grant no. KCYCXPT2017006) and the Shenzhen Research and Development Program of China (grant no.