Electro-permanent magnet constant force compensation type quasi-zero stiffness vibration isolator and load regulation and control method
By designing an electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator, and combining a three-magnetic-ring module and a semi-active electromagnetic module, the problems of performance degradation and poor load adaptability of magnetic quasi-zero stiffness vibration isolators under low-frequency large displacement are solved. This achieves a wide constant force range and continuous load adjustment, improving the stability and modular expansion capability of the vibration isolation system.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHEJIANG SCI-TECH UNIV
- Filing Date
- 2026-02-03
- Publication Date
- 2026-04-21
AI Technical Summary
Existing magnetic quasi-zero stiffness vibration isolators exhibit reduced vibration isolation performance under low-frequency, large-displacement, or strong-excitation conditions, have poor load adaptability, and lack modular and standardized design, making it difficult to maintain stability and robustness under complex operating conditions.
An electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator is adopted. Through the combination of a three-magnetic-ring module and a semi-active electromagnetic module, a wide constant force range and continuous load adjustment are achieved. By combining passive and semi-active control, a modular structure is formed.
It achieves improved stability under large amplitude excitation, precise load adjustment, modular design for easy expansion, and maintains excellent vibration isolation performance and engineering practicality.
Smart Images
Figure CN121897705A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a vibration isolation device, specifically to an electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator and load control method, applicable to precision instruments, aerospace equipment and low-frequency vibration isolation applications. Background Technology
[0002] With the rapid development of precision manufacturing, aerospace, optical instruments, and high-end equipment, the requirements for low-frequency and ultra-low-frequency vibration isolation are constantly increasing. Traditional linear vibration isolation systems, due to the inherent contradiction between their natural frequency and load-bearing capacity, struggle to achieve excellent low-frequency vibration isolation performance while ensuring a large load-bearing capacity. Therefore, quasi-zero stiffness vibration isolation technology, capable of achieving extremely low equivalent dynamic stiffness under large static load conditions, has become an important research direction in the field of vibration control in recent years.
[0003] Existing quasi-zero stiffness vibration isolators typically achieve this through a nonlinear combination of positive and negative stiffness elements. Among these, magnetic quasi-zero stiffness vibration isolators have attracted widespread attention due to their advantages such as non-contact operation, wear-free operation, compact structure, and high reliability. By rationally designing the spatial arrangement and geometric parameters between permanent magnets, approximately constant force or quasi-zero stiffness characteristics can be formed within a certain stroke range, thereby effectively reducing the system's resonant frequency. However, existing magnetic quasi-zero stiffness vibration isolators still have several shortcomings: on the one hand, their constant force or quasi-zero stiffness range is usually relatively short. Under low-frequency, large-displacement, or strong excitation conditions, the system is prone to entering the nonlinear stiffness hardening region, leading to a significant decrease in vibration isolation performance. On the other hand, these vibration isolators are mostly designed based on specific rated loads. When the actual load changes, the system's static equilibrium point shifts, causing the operating state to deviate from the pre-designed quasi-zero stiffness range, resulting in problems such as increased resonant frequency and increased vibration transmissibility, and limited load adaptability.
[0004] To improve load adaptability, some studies have introduced electromagnetic forces for semi-active or active control, compensating for the system by adjusting the coil current. However, existing electromagnetic control schemes are often incompatible with passive magnetic structures in terms of size or mechanical properties, resulting in complex structures, limited control capabilities, and difficulty in forming a unified and scalable engineering solution with passive quasi-zero stiffness vibration isolation structures. Furthermore, existing vibration isolators mostly adopt an integral design, lacking modularity and standardization, which hinders flexible expansion of load-bearing capacity and application under multiple load conditions.
[0005] Therefore, there is an urgent need for a quasi-zero stiffness vibration isolation device that combines a wide constant force range, continuous load adaptability, unified structure, and easy modular expansion, in order to improve the stability, robustness, and engineering practical value of the vibration isolation system under complex working conditions. Summary of the Invention
[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide an electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator and a load control method to achieve continuous and accurate compensation for load deviation, thereby solving the problems of poor load adaptability, limited constant force range and insufficient control flexibility of the existing quasi-zero stiffness vibration isolator.
[0007] The technical solution provided by this invention is: An electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator includes an upper vibration isolator plate and a lower vibration isolator plate arranged parallel to each other and corresponding vertically, and several vertically movable structures arranged between the upper vibration isolator plate and the lower vibration isolator plate so that the two can only move vertically relative to each other. Its characteristic is that the vibration isolator further includes a three-magnetic-ring module and several semi-active electromagnetic modules disposed between the upper plate and the lower base plate of the vibration isolator; the several semi-active electromagnetic modules are arranged symmetrically to the three-magnetic-ring module; or, The vibration isolator also includes several constant force compensation mechanisms disposed between the upper plate and the lower plate of the vibration isolator and symmetrically distributed; each constant force compensation mechanism includes a passive three-magnetic ring module and several semi-active electromagnetic modules disposed between the upper plate and the lower plate of the vibration isolator; the several semi-active electromagnetic modules are arranged symmetrically to the passive three-magnetic ring module. The three magnetic ring module includes a fixed magnetic ring base fixed to the upper surface of the lower base plate of the vibration isolator, a fixed magnetic ring fixing shell with a fixed magnetic ring installed and fixed to the top of the fixed magnetic ring base, a vertically arranged connecting rod with one end fixed to the center of the upper plate of the vibration isolator, two moving magnetic rings (upper moving magnetic ring and lower moving magnetic ring) installed on the connecting rod, a first linear bearing, and a sliding shaft vertically fixed to the center of the lower base plate of the vibration isolator and inserted into the inner cavity of the connecting rod with the top end to cooperate with the first linear bearing; The semi-active electromagnetic module has a similar structure to the three-magnetic-ring module, except that the fixed magnetic ring in the three-magnetic-ring module is replaced with a coil with the same outline.
[0008] The fixed magnetic ring base is a shell with a cylindrical cavity. The bottom end of the cavity is open to the outside, and the top end is open to the outside through a through hole. It is fixed to the upper surface of the lower base plate of the vibration isolator by a three-magnetic ring base plate.
[0009] The fixed magnetic ring fixing shell has a cylindrical cavity for installing the fixed magnetic ring. The bottom end of the cavity is open to the outside, and the top end is open to the outside of the cavity through an opening.
[0010] The connecting rod is a cylindrical two-moving magnetic ring connecting rod with an external thread at one end and a flange at the other end. The flange ends of the two moving magnetic ring connecting rods are coaxially connected by bolts, while the first linear bearing is clamped and fixed between the flange end faces of the two moving magnetic ring connecting rods.
[0011] One of the moving magnetic ring connecting rods is fitted with an adjusting pad and an upper moving magnetic ring in sequence, and then threadedly connected to the upper plate of the three magnetic rings fixed on the bottom side surface of the upper base plate; the other moving magnetic ring connecting rod is fitted with a lower moving magnetic ring, and the provided nut is tightened to push the lower moving magnetic ring upward and secure it, so that the lower moving magnetic ring is suspended in the cylindrical cavity of the fixed magnetic ring base.
[0012] The sliding shaft is vertically fixed at the center of the three magnetic ring base plate. The top of the sliding shaft is inserted into the inner cavity of the two moving magnetic ring connecting rods and the first linear bearing, so as to make vertical sliding contact with the first linear bearing during operation.
[0013] By adjusting the thickness of the adjusting pad, the vertical height of the upper and lower moving magnetic rings can be adjusted, so that the midpoint of the distance between the upper and lower moving magnetic rings is on the same horizontal plane as the midpoint of the height of the fixed magnetic ring.
[0014] The aforementioned vertical moving structures are arranged symmetrically to the passive three-magnetic-ring module.
[0015] The method for load regulation using the aforementioned electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator is carried out according to the following steps: (1) Select the number of passive three-magnetic ring constant force modules according to the target rated load, and construct a foundation quasi-zero stiffness vibration isolation platform; (2) Select several semi-active electromagnetic modules to be connected in parallel according to the load variation range; (3) When the load deviates from the rated value, calculate the required compensation constant force according to the magnitude of the load deviation, adjust the control current of the semi-active electromagnetic constant force module, so that the output electromagnetic constant force can offset the load deviation, and bring the working point of the vibration isolation system back to the quasi-zero stiffness center range, thereby restoring excellent vibration isolation performance.
[0016] The beneficial effects of this invention are: 1. Flexible design of wide constant force range: Through the coordinated design of three magnetic ring structural parameters, the length of the constant force range and the height of the magnetic ring are matched, which significantly improves the stability of the system under large amplitude excitation.
[0017] 2. Achieve continuous load regulation by using the current control of the electromagnetic constant force module to achieve continuous and precise compensation for load deviation.
[0018] 3. It is highly modular and versatile. The passive and semi-active modules have the same size and mechanical properties, which facilitates array expansion and engineering integration. At the same time, while maintaining the high reliability of passive vibration isolation, it introduces semi-active control capability, taking into account both performance and engineering feasibility. Attached Figure Description
[0019] Figure 1 This is a schematic diagram of the main structure of an embodiment of the present invention.
[0020] Figure 2 yes Figure 1 Schematic diagram of the inner side structure of the upper plate of the vibration isolator (only five three-magnetic-ring upper plates are installed).
[0021] Figure 3 yes Figure 1 A schematic diagram of the disassembled state of the embodiment (only the upper plate of the vibration isolator is removed).
[0022] Figure 4 yes Figure 1 Enlarged top view of the main structure of the three magnetic ring modules.
[0023] Figure 5 yes Figure 1 A top-view enlarged schematic diagram of the three magnetic ring modules.
[0024] Figure 6 yes Figure 1 A three-dimensional schematic diagram of the three magnetic ring module.
[0025] Figure 7 yes Figure 5 A schematic diagram of the assembly structure of the moving magnetic ring and the connecting rod of the moving magnetic ring.
[0026] Figure label: 1. Vibration isolator lower base plate; 2. Linear bearing seat; 3. Semi-active electromagnetic module; 4. Passive three-magnetic ring module; 5. Vibration isolator upper plate; 6. Moving shaft; 7. Coil; 8. Three-magnetic ring base plate; 9. Rubber; 10. Nut; 11. Lower moving magnetic ring; 12. Fixed magnetic ring fixing shell; 13. Fixed magnetic ring; 14. Adjusting pad; 15. Upper moving magnetic ring; 16. Three-magnetic ring upper plate; 17. Sliding shaft; 18. Moving magnetic ring connecting rod; 19. First linear bearing; 20. Fixed magnetic ring base. Detailed Implementation
[0027] The implementation is further explained below with reference to the accompanying drawings.
[0028] like Figures 1 to 3 The electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator shown includes an upper isolator plate and a lower isolator plate arranged parallel to each other and corresponding vertically, and several vertically moving structures (preferably four vertically moving structures in this embodiment) vertically positioned between the upper and lower isolator plates, allowing only vertical relative movement between them. Each vertically moving structure includes a second linear bearing and a moving shaft 6 that cooperates with the second linear bearing. As shown in the figure, the second linear bearing is mounted on the lower isolator plate via a linear bearing seat 2, and the top end of the moving shaft 2, which cooperates with the second linear bearing, is fixed to the upper isolator plate via a support. Both the upper and lower isolator plates are square, and the lower isolator plate has sidewalls connected to the four edges of the square plate and extending upwards to equal heights. These features are similar to existing vibration isolators.
[0029] The improvement of this invention involves setting a passive three-magnetic ring module 4 and several semi-active electromagnetic modules 3 between the upper plate and the lower base plate of the vibration isolator. The number of semi-active electromagnetic modules is typically two to six; in this embodiment, four semi-active electromagnetic modules are arranged symmetrically to the passive three-magnetic ring module. The passive three-magnetic ring module 4 is mounted in the center of the lower base plate 1 of the vibration isolator via a three-magnetic ring base plate 8, and the four semi-active electromagnetic modules 3 are fixed at the four corners of the lower base plate 1. Four first linear bearings 10 are fixed to the middle of each edge of the upper surface of the lower base plate 1 via linear bearing seats 2, while the sliding shaft 6 is vertically arranged and its top end is fixed to the lower surface of the upper plate 5 of the vibration isolator. The sliding engagement between the sliding shaft 6 and the first linear bearings 19 ensures that the upper plate and the lower base plate are parallel to each other. The passive three-magnetic ring module and the semi-active electromagnetic modules are connected to the bottom surface of the upper plate of the vibration isolator via a three-magnetic ring upper plate 16.
[0030] Figure 4 The structure of the passive three-magnetic-ring module is shown. The fixed magnetic ring base 20 is a shell with a cylindrical cavity, the bottom of which is open to the outside and the top of which is open to the outside through a through hole. The fixed magnetic ring base is fixed to the upper surface of the lower base plate of the vibration isolator by the three-magnetic-ring base plate 8. The fixed magnetic ring fixing shell 12 is also a shell with a cylindrical cavity, the bottom of which is open to the outside and the top of which is open to the outside of the cavity through an opening. The fixed magnetic ring 13 is installed in the cylindrical cavity of the fixed magnetic ring fixing shell and thus fixed to the top of the fixed magnetic ring base 20.
[0031] The two moving magnetic ring connecting rods 18 have the same structure, both being cylindrical with external threads at one end and flanges at the other. The flanges of the two moving magnetic ring connecting rods are coaxially connected by bolts, while the first linear bearing 19 is clamped and fixed between the flange end faces of the two moving magnetic ring connecting rods 18. The two moving magnetic ring connecting rods 18 are arranged vertically. One moving magnetic ring connecting rod has an adjusting pad 14 and an upper moving magnetic ring 15 sequentially fitted onto it, and its external threaded end is then threadedly connected to the upper plate of the three magnetic rings fixed to the bottom side surface of the upper base plate. The other moving magnetic ring connecting rod has a lower moving magnetic ring 11 fitted onto it, and after the external threaded end is screwed into a nut 10, the lower moving magnetic ring is pushed upwards and tightened, so that the lower moving magnetic ring 11 hangs in the cylindrical cavity of the fixed magnetic ring base 20, maintaining a distance from the upper moving magnetic ring. Thus, the two moving magnetic ring connecting rods 18, the three magnetic ring upper plate 16, the adjusting pad 14, the upper moving magnetic ring 15, the first linear bearing 19, the lower moving magnetic ring 11, and the nut 1 together form an assembly that slides axially with the sliding shaft. Its structure is as follows: Figure 7 As shown.
[0032] A sliding shaft 17 is vertically arranged at the center of the three magnetic ring base plate 8. The bolt passes through the stepped hole at the center of the three magnetic ring base plate 8 from bottom to top and engages with the screw hole at the bottom of the sliding shaft to fix the sliding shaft. At the same time, the top of the sliding shaft 17 is inserted into the inner cavity of the two moving magnetic ring connecting rods and the first linear bearing 19 so as to perform vertical sliding engagement with the first linear bearing 19 during operation.
[0033] By adjusting the thickness of the adjusting pad 14, the vertical distance between the upper moving magnetic ring 15 and the lower moving magnetic ring 11 can be adjusted, so that the midpoint of the distance between the upper moving magnetic ring 15 and the lower moving magnetic ring 11 is on the same horizontal plane as the midpoint of the height of the fixed magnetic ring (that is, the horizontal plane symmetrical to the upper moving magnetic ring 15 and the lower moving magnetic ring 11 can bisect the fixed magnetic ring).
[0034] The aforementioned vertical moving structures are arranged symmetrically to the passive three-magnetic-ring module.
[0035] Furthermore, a passive three-magnetic-ring module 4 and several (preferably two to six) semi-active electromagnetic modules 3 can serve as a constant force compensation mechanism; therefore, several constant force compensation mechanisms (the specific number is determined as needed) can be symmetrically arranged between the upper plate and the lower plate of the vibration isolator to form the electro-permanent magnet constant force compensation quasi-zero stiffness vibration isolator described in this invention, thereby significantly increasing the load that the vibration isolator can withstand.
[0036] In this embodiment, a constant axial magnetic force output can be generated through the repulsion and attraction between the magnetic rings; by adjusting the axial height, radial thickness, and gap parameters of the magnetic rings, the length of the constant force range can be designed and expanded. A rubber 9 is also placed inside the fixed magnetic ring base 20 to mitigate the impact. Figure 7 The assembly shown vibrates due to instability when its movement exceeds the constant force boundary (the rubber can cushion the impact generated when the assembly becomes unstable and falls).
[0037] The structure of the semi-active electromagnetic module is similar to that of the passive three-magnetic-ring module. It only requires replacing the fixed magnetic ring 13 with a coil 6 of the same profile and adjusting the size of the adjusting pad 14 (increasing the sliding axial thickness by 2mm). The coil lead-out connector is connected to an external controller, which controls the coil current to generate an adjustable constant electromagnetic force. The force-displacement characteristics of the semi-active electromagnetic module are consistent with those of the passive three-magnetic-ring constant-force module, achieving structural and functional unity. Furthermore, both modules share the same external dimensions and installation interfaces, facilitating rapid replacement and expansion.
[0038] This invention allows for the selection of the number of passive three-magnetic-ring constant force modules based on the target rated load to construct a basic quasi-zero stiffness vibration isolation platform. Furthermore, it allows for the parallel connection of several semi-active electromagnetic modules based on the load variation range. By combining multiple passive three-magnetic-ring constant force modules or semi-active electromagnetic constant force modules in parallel with current regulation, a load adaptability combining discrete and continuous characteristics can be achieved.
[0039] The working principle of this invention is as follows: Under rated load, the restoring force of this quasi-zero stiffness vibration isolation is provided solely by the passive three-magnetic-ring module. When the vibration isolation system is subjected to axial loading in the sliding direction, the spacing between the magnetic rings changes, and the magnetic interaction force exhibits nonlinear characteristics with displacement. However, through the nonlinear magnetic coupling between the two moving magnetic rings and the fixed magnetic ring, the magnetic force remains approximately constant within a certain displacement range, thus forming a stable constant force range, providing the vibration isolation system with a low natural frequency and high load-bearing capacity. When the load deviates, the semi-active electromagnetic constant force module outputs current to perform real-time constant force compensation on the system, allowing the vibration isolation system to return to the target standard zero stiffness operating range. Therefore, the system can flexibly switch between passive and semi-active modes, achieving stable maintenance of vibration isolation performance under multiple load conditions.
[0040] The specific control method includes the following steps: First, select the number of passive three-magnetic-ring constant force modules based on the target rated load to construct a basic quasi-zero stiffness vibration isolation platform. Second, select a certain number of semi-active electromagnetic modules in parallel according to the load variation range. When the load deviates from the rated value, calculate the required compensation constant force based on the magnitude of the load deviation, adjust the control current of the semi-active electromagnetic constant force modules, and make the output electromagnetic constant force offset the load deviation, so that the operating point of the vibration isolation system returns to the quasi-zero stiffness center range, thereby restoring excellent vibration isolation performance.
[0041] Finally, it should be noted that the above examples are merely specific embodiments of the present invention. Obviously, the present invention is not limited to the above embodiments and many variations are possible. All variations that can be directly derived or conceived by those skilled in the art from the disclosure of this invention should be considered within the scope of protection of this invention.
Claims
1. An electric-permanent magnet constant force compensated quasi-zero stiffness vibration isolator, comprising a vibration isolator upper plate (5) and a vibration isolator lower base plate (1) arranged parallel to each other and corresponding vertically, and several vertically movable structures arranged between the vibration isolator upper plate and the vibration isolator lower base plate so that the two can only move vertically relative to each other. Its features are: The vibration isolator also includes a passive three-magnetic ring module (4) and several semi-active electromagnetic modules (3) disposed between the upper plate and the lower base plate of the vibration isolator; the several semi-active electromagnetic modules are arranged symmetrically to the passive three-magnetic ring module; or, The vibration isolator also includes several constant force compensation mechanisms that are symmetrically distributed between the upper plate and the lower plate of the vibration isolator; each constant force compensation mechanism includes a passive three-magnetic ring module (4) and several semi-active electromagnetic modules (3) disposed between the upper plate and the lower plate of the vibration isolator; the several semi-active electromagnetic modules are arranged symmetrically to the passive three-magnetic ring module. The passive three-magnetic-ring module includes a fixed magnetic ring base (20) fixed on the upper surface of the bottom plate of the vibration isolator, a fixed magnetic ring fixing shell (12) with a fixed magnetic ring (13) installed and fixed at the top of the fixed magnetic ring base, a connecting rod arranged vertically and fixed at one end to the center of the top plate of the vibration isolator, two moving magnetic rings and a first linear bearing (19) installed on the connecting rod, and a sliding shaft (6) fixed vertically in the center of the bottom plate of the vibration isolator and inserted into the inner cavity of the connecting rod with the top end cooperating with the first linear bearing. The semi-active electromagnetic module structure is similar to that of the passive three-magnetic-ring module, except that the fixed magnetic ring (13) in the passive three-magnetic-ring module is replaced with a coil (6) with the same outline.
2. The electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator according to claim 1, characterized in that: The fixed magnetic ring base (20) is a shell with a cylindrical cavity. The bottom end of the cavity is connected to the outside, and the top end is connected to the outside through a through hole. It is fixed to the upper surface of the lower base plate of the vibration isolator by a three magnetic ring base plate (8).
3. The electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator according to claim 2, characterized in that: The fixed magnetic ring fixing shell (12) has a cylindrical cavity for installing the fixed magnetic ring. The bottom end of the cavity is connected to the outside, and the top end is connected to the outside of the cavity through an opening.
4. The electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator according to claim 3, characterized in that: The connecting rod is a cylindrical two moving magnetic ring connecting rod (18) with an external thread at one end and a flange at the other end. The flange ends of the two moving magnetic ring connecting rods are coaxially connected, and the first linear bearing (19) is clamped and fixed between the flange end faces of the two moving magnetic ring connecting rods.
5. The electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator according to claim 4, characterized in that: One of the moving magnetic ring connecting rods is fitted with an adjusting pad (14) and an upper moving magnetic ring (15) in sequence, and then threadedly connected to the upper plate of the three magnetic rings fixed on the bottom side surface of the upper base plate; another moving magnetic ring connecting rod is fitted with a lower moving magnetic ring (11), and the provided nut (10) is tightened to push the lower moving magnetic ring upward and tighten it, so that the lower moving magnetic ring is suspended in the cylindrical cavity of the fixed magnetic ring base.
6. The electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator according to claim 5, characterized in that: The sliding shaft (17) is vertically fixed at the center of the three magnetic ring base plate (8). The top of the sliding shaft is inserted into the inner cavity of the two moving magnetic ring connecting rods and the first linear bearing (19) so as to make vertical sliding cooperation with the first linear bearing during operation.
7. The electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator according to claim 6, characterized in that: By adjusting the thickness of the adjusting pad, the vertical height of the upper moving magnetic ring (15) and the lower moving magnetic ring (11) can be adjusted, so that the midpoint of the distance between the upper and lower moving magnetic rings is on the same horizontal plane as the midpoint of the height of the fixed magnetic ring.
8. The electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator according to claim 7, characterized in that: The aforementioned vertical moving structures are arranged symmetrically to the passive three-magnetic-ring module.
9. The method for load regulation using the electro-permanent magnet constant force compensated quasi-zero stiffness vibration isolator as described in claim 1 shall be performed according to the following steps: (1) Select the number of passive three-magnetic ring constant force modules according to the target rated load, and construct a foundation quasi-zero stiffness vibration isolation platform; (2) Select several semi-active electromagnetic modules to be connected in parallel according to the load variation range; (3) When the load deviates from the rated value, calculate the required compensation constant force according to the magnitude of the load deviation, adjust the control current of the semi-active electromagnetic constant force module, so that the output electromagnetic constant force can offset the load deviation, and bring the working point of the vibration isolation system back to the quasi-zero stiffness center range, thereby restoring excellent vibration isolation performance.