## 4 Current Progress of Magnetic Negative Stiffness in QZS Isolators
### QZS-Based Hybrid Magnetic Negative Stiffness Elements
The findings demonstrate that as the control current increases, the vibration isolation system can effectively isolate vibrations in all three directions (x, y, and z). Both the isolation onset frequency and amplitude decrease. Additionally, the paper conducts motion and dynamics analyses of the six-degrees-of-freedom vibration isolation system. It employs the harmonic balance method to derive linear algebraic equations and validate the stability of the corresponding solutions. Functioning as a passive HSLDS vibration isolator, the system demonstrates robust load-bearing capabilities across a broad spectrum of vibration isolation requirements. Moreover, the system efficiently achieves vibration isolation in six directions: x, y, z, \(\alpha\), \(\beta\) and \(\gamma\). With increasing control current, the peak shape shifts toward lower frequencies, leading to a corresponding decrease in the response peak. Augmenting the electromagnetic coefficient Cm expands the frequency band of the vibration isolation. Specifically, elevating Cm enhances the vibration isolation efficiency in the QZS state and shifts the vibration isolation start frequency to a lower range, consequently diminishing the resonance amplitude in the \(\alpha\) and \(\beta\) directions. Nonetheless, the isolation efficiency diminishes in the translational directions (x, y, z) and at high frequencies. Moreover, the isolation efficiency proves sensitive to changes in the start distance, and augmenting the start distance may  
Figure 30: The orthogonal six-DOFs vibration isolation with tunable HSLDS: (**a**) the three-dimensional design structure of the six-DOFs isolation system; (**b**) the schematic diagram of the tunable electromagnetic HSLDS spring; (**c**) the experimental configuration; (**d**) photograph of the experimental rig; (**e**) curve of the force versus displacement of the electromagnetic spring; and (**f**) curve of the stiffness versus displacement of the electromagnetic spring. lead to a reduction in the isolation efficiency. The impact of the electromagnetic coefficient diminishes as the start distance increases. For instance, when the start distance is (d = 0.4 m), the vibration isolation start frequency remains constant despite an increase in the electromagnetic coefficient in the translational direction. [PERSON] [76] presented an HSLDS vibration isolator featuring an adjustable electromagnetic mechanism. In Figure 31, this system's distinguishing feature lies in its capability to adjust the stiffness characteristics by varying the current in the coil. At zero current, the HSLDS system reverts to functioning as a passive vibration isolator. Moreover, this system can expand the isolation bandwidth and enhance the isolation performance near the natural frequency of the passive system when compared to conventional passive vibration isolators. The system exhibits a more compact structure, greater load capacity, and enhanced efficiency in negative stiffness generation compared to certain other electromagnetic vibration isolation systems. Additionally, the paper introduces an analytical model for computing the electromagnetic force and displacement transmission rates, and it experimentally validates the performance of the vibration isolation system and its tuning strategy. This innovative adjustable electromagnetic negative stiffness mechanism enables the vibration isolation system either to function as a passive vibration isolator or to adjust its dynamic stiffness characteristics as necessary to accommodate various vibration environments. This new breed of vibration isolator offers enhanced compactness, greater load-bearing capacity, and increased efficiency in negative stiffness generation. The non-contact characteristic of this electromagnetic device yields not only a more compact mechanical structure but also a longer fatigue life compared to conventional mechanical and magnetic variable stiffness systems.