Advancements in Key Technologies for Vibration Isolators Utilizing Electromagnetic Levitation

Abstract

With the advancement of manufacturing, the precision requirements for various high-precision processing equipment and instruments have further increased. Due to its noncontact nature, simple structure, and controllable performance, electromagnetic levitation has broad application prospects in ultra-precision instruments and ground testing of aerospace equipment. Research on vibration isolation technology using electromagnetic levitation is imperative. This paper reviews the latest research achievements of three types of passive isolators and five active isolation actuators. It also summarizes the current research status of analytical methods for passive isolators and the impact of isolator layout. This study explores current isolators’ achievements, such as the development of passive isolators that generate negative stiffness and require mechanical springs for uniaxial translational vibrations, single-function actuators, and control systems focused on position and motion vibration control. Based on the current isolators’ characteristics, this review highlights future developments, including focusing on passive isolators for heavy loads and multi-axis isolation, addressing complex vibrations, including rotational ones, and developing methods to calculate forces and torques for arbitrary six-DOF movements while improving speed. Additionally, it emphasizes the importance of multifunctional actuators to simplify system structures and comprehensive control systems that consider more environmental factors. This provides significant reference value for vibration isolation technology using electromagnetic levitation.

1. Introduction

Vibration is a ubiquitous form of disturbance encountered across various industries and engineering fields. Vibration isolation applications show promise in long-span structures [1,2], particularly bridges and railways. These methods help identify damage and support maintenance in steel bridges [3]. In railways, vibration analysis detects track faults, ensuring safe train operation [4]. Vibration isolation systems in structures like sea-crossing bridges mitigate environmental and operational effects [5]. These techniques enhance performance, reduce costs, and extend infrastructure lifespan. In addition to the need for vibration control in large-span structures, the management of micro-vibrations, characterized by low-frequency and small-amplitude oscillations, is equally crucial in many high-precision applications. Low frequency, lacking a strict definition, typically refers to oscillations or vibrations occurring at rates below several tens of Hz, which are particularly challenging to mitigate in precision engineering and sensitive equipment applications. As technological progress accelerates and industrial manufacturing evolves, the precision requirements for various high-precision instruments have increased [6]. For instance, in ultra-precision instruments such as photolithography machines, the workpiece stage and mask stage must maintain high accuracy during large-scale movements [7]. The supportive mechanisms must provide gravitational compensation and vibration isolation to achieve precise positioning. These mechanisms can reduce power loss and temperature rise, as well as effectively mitigate external environmental interferences. Compared to mechanical spring and air flotation isolation systems, electromagnetic levitation technology offers significant advantages, including noncontact, simple structure, controllable performance, and compatibility with vacuum environments [8]. Electromagnetic levitation gravity compensation technology can achieve excellent performance with large load capacity and low power consumption, with broad application prospects in advanced manufacturing equipment. This technology is crucial for driving the advancement of the ultra-precision manufacturing industry.

Meanwhile, some large precision payloads in aerospace require ground testing before launch. Electromagnetic levitation gravity compensation technology can provide a noncontact, six-DOF, vacuum-compatible, low-parasitic-force ground simulation platform, ensuring the reliability of performance tests for large precision payloads. When designing, manufacturing, and testing aerospace equipment, it is essential to consider the space environment’s impact on the equipment [9,10]. Since most aerospace equipment operates far from Earth, changes in the gravitational field are a critical factor [11,12]. To ensure proper functioning, support or levitation devices are needed to simulate the microgravity environment of space during ground testing. Traditional levitation methods typically use hydraulic or rope to support [13]. However, due to contact between the equipment and the test object, these methods often result in coupling, directly affecting test results’ accuracy [14]. In contrast, electromagnetic levitation vibration isolators offer noncontact and frictionless advantages, and they are more suitable for supporting aerospace equipment during ground testing [15].

With electromagnetic isolators offering unparalleled benefits, many researchers have focused on designing and studying their structures [16]. However, these isolators generally have low levitation forces. As aerospace technology develops, the mass of large precision optical equipment for space applications will increase. Low levitation force density isolators may not meet the requirements for ground testing support [17]. Therefore, research on electromagnetic levitation and vibration isolation technologies, particularly for large-load applications, is imperative.

Controlling the impact of undesirable vibrations in production and daily life has long been a popular topic [18,19]. Isolators and dampers are the primary tools used for this purpose [20]. Unlike dampers, which reduce the amplitude of mechanical oscillations, isolators work by establishing a barrier between the vibration and the protected component to minimize adverse effects. Typical isolators include mechanical, air flotation, and electromagnetic isolators [21]. Compared to other types, electromagnetic isolators have unique advantages [22,23].

2. Passive Isolators

Based on whether energy is consumed, electromagnetic vibration isolators are classified into two types. Passive isolators typically employ PMs to generate the working magnetic field, providing noncontact levitation force through the interaction between PMs. This type boasts no external energy requirement, load-bearing solid capacity, excellent low-frequency isolation performance, and simplicity. However, it often falls short in high-frequency isolation applications. Depending on the topology and structural forms of the PMs, passive isolators are classified into various types. The following parts will introduce the current research status of these types.

2.1. Permanent Magnet Springs

These isolators generally use one or more pairs of PMs arranged face-to-face, generating magnetic forces for NS. A few researchers have also used them to achieve PS. Most of these isolators need to be combined with mechanical structures of opposing stiffness, which compromises the noncontact of magnetic levitation.

2.1.1. Single-Pair Permanent Magnet Springs

Li, Q. [24] and Zhu, Y. [25] designed a series of single-pair magnetic ring MSs combined with various shapes of rubber mechanical springs. The objective is to combine MSs with rubber membranes for reducing the inherent frequency and vibrations in the low frequency. Unlike the common MS forms, the authors in [26] configured the MSs to generate PS, while the rubber springs provided NS. In [27], the authors compared the effects of combining different mechanical springs, including linear bearings, rubber O-rings, and rubber membranes. Experimental results demonstrated that the isolators could achieve lower natural frequencies with rubber membranes.

To address the challenge of mitigating low-frequency vibrations while transporting newborns, researchers [28] suggested an innovative incubator incorporating a QZS isolator for reducing the transfer of mechanical disturbances. The designed MS is shown in Figure 1a. For a 2.2 kg payload, the isolator achieved a low vibration isolation onset frequency of 2 Hz, qualifying it for ultra-low frequency applications. When implemented in the incubator with four QZS isolators supporting a 10.5 kg payload, the system exhibited a vibration isolation onset frequency of 3.2 Hz. Under random excitation with 2–15 Hz bandwidth and 2 mm amplitude, the mean square root acceleration transmissibility was 0.3230, indicating substantial vibration attenuation. These results suggest that the QZS isolator-based incubator offers an effective solution for mitigating mechanical vibrations during neonatal transport.

In [18,28,29], a pair of repulsive ring PMSs and wave springs were connected in parallel. The authors fabricated prototypes and evaluated the vibration isolation performance through displacement and acceleration transmissibility.

Zheng, Y. S. [30] investigated MSs with HSLD stiffness. The NS MSs consist of two concentric PM rings positioned alongside mechanical springs to counteract PS, as shown in Figure 1b. Furthermore, they utilized NS MSs as HSLD stiffness struts to construct a passive Stewart platform. This platform effectively reduces resonance frequency without compromising load-bearing capacity. They demonstrated that the proposed NS MS effectively reduces the resonance frequency and peak transmissibility of the system. Experimental results reveal that the resonance frequency decreased from 9.0 Hz without NS MS to 7.2 Hz with 8-tile NSMS and further to 5.8 Hz with 10-tile NS MS. This reduction in resonance frequency, coupled with the introduction of eddy current damping, contributed to a decrease in peak transmissibility. The NS MS’s performance is characterized by its ability to lower the system’s natural frequency and enhance vibration isolation effectiveness. However, it is notable that excessive base excitation can lead to a high jump-down frequency, potentially compromising isolation performance.

Other researchers have also designed similar MSs [31,32,33], using a pair of attractive magnetic rings as NS-generating elements, aiming to achieve QZS for the overall isolator.

2.1.2. Multiple-Pair Permanent Magnet Springs

The MSs used by Nguyen, H. T. comprise a pair of stationary PM rings, with an additional PM suspended in the intervening space [34]. They innovatively combined MSs with nonlinear PS and mechanical oblique springs with geometric nonlinear NS [35]. By introducing nonlinear damping, the vibration isolation performance was enhanced. The authors found that nonlinear damping eliminated the undesirable jump phenomenon in QZS vibration isolation systems.

Kamaruzaman, N. A. combined PMs with mechanical lever arms to construct a novel planar QZS magnetic levitation isolation system [36]. In Figure 2b, the depiction of forces is illustrated with dark blue arrows indicating the primary forces and light blue arrows representing the secondary forces. They created a pole map of the dynamic system to analyze its stability. A new parameter was found that is advantageous in eliminating rotational instability. However, with greater stability, the rotational resonance frequency increases and consequently decreases the range of frequency over which vibration attenuation occurs. Therefore, the authors argue that an appropriate level of stability must be chosen based on the system requirements. In [37], they also proposed a six-DOF isolator achieved by stacking multiple pairs of ring MSs. This system uses magnetic suspension to bear the load, achieving QZS along the vertical axis and zero stiffness in others.

Similarly, Dong, G. X. researched combining MSs with mechanical beams [38]. The proposed isolator parallels NS MSs with Euler–Bernoulli beams. The NS MSs consist of four PM pairs to reduce the isolator’s natural frequency. Sun, X. T. has also conducted similar research [39]. Additionally, Dong, G. X. designed HSLD stiffness magnetic isolators with multiple pairs of parallel helical bending springs [40].

Other researchers have designed similar nonlinear magnetic isolators using multiple pairs of PMs [41,42,43], analyzing and experimentally verifying the vibration isolation performance of HSLD stiffness magnetic isolators.

2.1.3. Specially Shaped Permanent Magnet Springs

Zhang, F. has designed a uniquely shaped MS based on Maxwell normal stress [44,45], as shown in Figure 3. This device has a magnetic mechanism that provides high magnetic NS to offset static stiffness. The system comprises an NS MS utilizing variable reluctance stress. And this MS comprises PMs, a mover, and two stators, generating NS parallel to the system’s axis. This NS is combined with the PS generated by mechanical springs.

In [44], the authors found that when employing positive acceleration feedback with equivalent mass < 0, the system exhibited a sharp increase in dynamic stiffness from low frequencies, significantly exceeding its static stiffness. This resulted in excellent dynamic stability and substantial attenuation of the vibration response. Conversely, with negative acceleration feedback or positive feedback control where equivalent mass > 0, the system’s dynamic stiffness fell below its static stiffness in the low-frequency band, potentially leading to resonance when the external disturbance frequency aligns with the system’s natural frequency. However, in the high-frequency range, the vibration response diminished due to the dynamic stiffness surpassing the static stiffness.

In [45], the root mean square value of vibration acceleration response decreased from 4.8430 m/s² to 2.4350 m/s², while the natural frequency reduced from 72.5 Hz to 45.2 Hz, thus broadening the vibration isolation band. Additionally, the acceleration transmissibility peak in the resonance region was reduced by 50.5%, from 75.8 to 25.3. The implementation of isolators with NS MS has been shown to effectively reduce the system’s natural frequency, broaden the isolation frequency band, and enhance damping characteristics. This configuration improves the relative damping coefficient and further suppresses the resonance peak compared to linear isolators.

2.2. Planar Isolators

Most existing passive isolators are designed for vertical direction isolation, with only a few researchers having developed passive magnetic isolators for in-plane vibration isolation. Unlike horizontally oriented PMSs, planar isolators can simultaneously achieve vibration isolation in two DOFs. Research in this area remains limited.

Zheng, Y. S. [46] employed an MS composed of a pair of annular PMs parallel to a traditional pendulum to isolate ultra-low frequency vibrations, as shown in Figure 4. The MS generates a torque to offset the gravitational torque, thereby reducing the resonance frequency. They examined the dynamic characteristics of the isolator. By adjusting the parameter ${\mathsf{\chi }}^2$, various transmission characteristics could be achieved. When ${\mathsf{\chi }}^2=0.700$, $\mathsf{\beta }$ became negative (−0.0036), resulting in a flattened transmissibility curve in the high-frequency domain due to the center of percussion effect. At ${\mathsf{\chi }}^2=0.500$, $\mathsf{\beta }$ turned positive (0.0103), introducing a dip in the transmissibility curve alongside the flattening phenomenon. The flattening phenomenon disappeared when ${\mathsf{\chi }}^2=0.619$, corresponding to $\mathsf{\beta }=0$. Numerical analysis demonstrated that the resonance frequency could be reduced to as low as 0.11 Hz by setting ${\mathsf{\chi }}^2$ to 0.500. However, the isolation performance in the high-frequency domain was limited to −40 dB due to the center of percussion effect, despite the significant reduction in resonance frequency.

To expand the application range of QZS isolators, Liu, C. R. proposed an in-plane QZS isolator [47] to mitigate oscillations in all horizontal directions, as shown in Figure 5. It includes two radially magnetized rings and eight pre-tensioned cables. Magnetic interactions provide NS, while the cables act as mechanical springs providing PS, thus achieving QZS characteristics through superposition. Transmissibility analysis demonstrated the superior vibration isolation performance of this isolator in both directions, being characterized by an expansive isolation bandwidth and reduced peak and high-frequency transmissibility. Experimental results corroborated these findings, revealing low transmissibility across a broad frequency spectrum. Notably, the isolation frequencies were observed at 7.23 Hz for 0° experiments and 6.39 Hz and 4.75 Hz for 30° experiments. Peak transmissibility values were recorded at 11.22 dB, 9.41 dB, and 3.99 dB for the respective configurations. These outcomes not only validate the isolator’s exceptional performance but also underscore its efficacy under varying excitation directions, thereby demonstrating its robust and versatile isolation capabilities.

2.3. Permanent Magnet Array Isolators

These passive magnetic isolators can effectively enhance levitation force and load capacity by arranging PMs in a specific array pattern. This arrangement also increases force density per unit volume. Additionally, these isolators rely on magnetic forces for levitation, eliminating the need for additional mechanical structures and maintaining the advantage of noncontact magnetic levitation. However, achieving nonlinear stiffness and reducing stiffness magnitude is more challenging than for permanent MSs. This difficulty arises because the simple superposition of PS and NS to reduce stiffness is no longer feasible.

2.3.1. Horizontal Air Gap Permanent Magnet Isolators

In [48], Zhou, Y. H. introduced a ring-shaped Halbach isolator with an intervening space. It generates levitation force through an annular Halbach array, with the air gap oriented horizontally, resulting in greater static load-bearing density. In [49], the authors described a planar horizontal air gap passive isolator, as shown in Figure 6. It employs a double stator configuration and an exceptional PM array, effectively lowering its natural frequency and enhancing its isolation capability.

Other researchers have also designed similar structures. In [50], a magnetic levitation isolator with four sets of repulsive rectangular PMs was proposed.

2.3.2. Vertical Air Gap Permanent Magnet Isolators

Hsieh, W. H. has achieved significant results in this isolator type. In [51], the authors described a tubular vertical air gap isolator and proposed four typical topologies of tubular horizontal air gap isolators, as shown in Figure 7. They analyzed the force characteristics of different topologies. Compared to traditional ones, the proposed isolator exhibited higher force density.

In [52], a cylindrical vibration isolator with the Halbach secondary array was proposed, being characterized by compact structure, high thrust linearity, good isolation performance, and low surface temperature rise. Similar designs include those in [53]. Zhou, Y. H. and Li, J. Z. have also designed topologies using Halbach arrays to enhance levitation force [54,55].

Additionally, Shan, J. Z. proposed an innovative subsystem combining eddy current damping and NS MSs [56] to elevate isolating efficiency. They combined eddy current damping mechanisms with nonlinear NS springs for the first time to achieve better energy conversion behavior under seismic excitation. The eddy current–magnetic NS spring significantly enhanced isolation performance regarding base drift and structural acceleration.

2.3.3. Inclined Air-Gap Permanent Magnet Isolators

Van Casteren, D. T. E. H. designed a conical PM isolator for microbalances [57,58], as shown in Figure 8. This isolator can achieve a QZS region, making it advantageous for vibration attenuation. The researchers employed a three-dimensional analytical model to calculate the force, stiffness, and resonance frequency for various cone angles in order to determine the optimal configuration. The results indicate that 4° and 90° represent two optimal angles. However, when considering force output and spatial constraints, a 90° angle may prove more practical for implementation.

Zhou, Y. H. proposed a diamond-shaped PM isolator [59] to enhance levitation force performance. This structure aims to reduce levitation force fluctuations and increase levitation force density. The authors maintained levitation force fluctuations at a low level by analyzing and optimizing the levitation force characteristics.

2.4. Impact of Isolator Arrangement

Due to individual passive isolators’ generally low load-bearing capacity, multiple isolators are often used together to support the load in practical applications. The arrangement of these individuals can significantly affect the overall isolation performance.

Fang, H. N. and other researchers [60,61,62] have investigated the placement impact on overall isolation performance. In multi-DOF magnetic levitation isolation systems, changing the number and arrangement of isolators alters the stiffness matrix of the entire system, thereby affecting its isolation performance. Therefore, they studied the arrangement schemes to achieve the desired isolation effect with the minimum number of isolators and optimal placement. The authors analyzed one isolator’s stiffness characteristics and the total stiffness characteristics when active and passive isolators were connected in parallel. They established a multi-DOF system model and compared the effects of different parameters, resulting in an optimal arrangement scheme that provides better isolation performance.

2.5. Analytical Methods for Passive Isolators

The analysis of passive isolators essentially involves the examination of interactions between PMs.

2.5.1. Equivalent Magnetic Charge Method

The equivalent magnetic charge method for computing inter-magnet forces has been a subject of significant research since the 1980s. The pioneering work in this field was conducted by Yonnet, J. P. and his team in France, with their seminal findings published in 1984 [63]. Yonnet achieved a three-dimensional calculation of the interaction force between two cubic PMs using purely analytical methods. Despite the complexity of the analytical expression for magnetic force, its computation speed significantly outpaced the FEM. Moreover, Yonnet derived an analytical expression for stiffness, enabling rapid optimization of magnetic device topologies. This groundbreaking work has had a profound impact and has been widely cited [50,64].

Building on Yonnet’s work, Charpentier, J. F. introduced an approach in 2001 for calculating PM synchronous couplings’ performance based on magnetic pole theory [65]. In the same year, Yonnet expanded his research by developing three-dimensional precise calculation formulas for forces exerted by cubic PMs with aligned and orthogonal magnetization [66]. This advancement facilitated the analysis of interaction forces between linear Halbach arrays.

Yonnet further addressed the challenge of torque calculation in [67], enabling the representation of energy, force, and torque vectors through formulas. He achieved this by replacing magnetization with magnetic charge distribution on the magnetic poles, assuming only that each PM’s magnetization should be rigid and uniform. Yonnet continued his research in this area until 2011 [68].

Parallel to Yonnet’s work, Rovers, J. M. M. in the Netherlands conducted extensive research on analytical methods. In 2009, Rovers calculated the interaction forces between PMs in Halbach arrays used in moving magnet planar actuators [69]. The following year, they proposed improved formulas for cubic PM torques applied to magnetic bearings [70]. These innovative equations apply universally, regardless of PM position and particularly when their faces are coplanar, and they obtain torques relative to any reference point.

In 2011, Rovers presented equations for directly calculating the torques between vertically magnetized cubic PMs in free space [71]. These equations are suitable for designing and analyzing coreless structures and offer short computation times. In the same year, Janssen, J. L. G.’s dissertation further explored the surface magnetic charge modeling technique, and the work proposing novel analytical equations for forces, stiffness, and torques [72]. These equations apply to any combination of magnetization vectors and relative positions.

Recognizing the limitations of assuming the equal relative permeability of PMs and air, researchers in 2013 considered the permeability of PMs as redistributed magnetic surface charges, obtaining accurate solutions for magnetic fields under low relative permeability [73]. This method was also applied to analytically calculate the aforementioned conical PM isolator [57].

Throughout this period, other researchers have widely adopted and applied this method [18,25,28,74]. Sun, X. T. and Shan, J. Z. [39,56] employed it to calculate the mechanical properties of NS MSs.

In recent years, some researchers have further refined the method by considering changes in the operating points of PMs, thereby improving calculation accuracy [53]. This ongoing research continues to enhance our understanding and application of the equivalent magnetic charge method in various magnetic systems.

2.5.2. Equivalent Current Method

The Equivalent Current Method, based on the Amperian current model, has become a powerful analytical tool for studying magnetic levitation systems. This approach represents permanent magnets as equivalent surface currents or current loops, enabling precise calculations of magnetic forces and stiffness characteristics. By integrating over magnet surfaces or volumes, researchers obtain comprehensive expressions for magnetic forces and stiffness, providing a more accurate representation of magnetic field distributions in three-dimensional space compared to simplified dipole models.

Zheng, Y. S. and Dong, G. X. [30,38,40] have extensively applied this method to analyze NS MSs. They derived analytical expressions for the axial magnetic force and stiffness of NSMS composed of coaxial ring PMs and cubic magnets. By representing the PMs as equivalent current-carrying coils or surface currents, they calculated the magnetic forces between the components through integration. Following an examination of how magnet dimensions influence stiffness, they proposed design processes for magnetic springs, enabling efficient parametric analysis and optimization.

The Equivalent Current Method has been applied to analyze complex levitation systems. Ref. [32] used this approach to derive a mathematical model for the NS MS using PMs as current loops. Similarly, ref. [40] treated magnetic rings as current-carrying coils. In both cases, the method facilitated the evaluation of axial magnetic forces and the derivation of expressions for magnetic negative stiffness, supporting the optimization of these vibration isolation systems.

Extending the application to other vibration isolation systems, ref. [41] applied the Equivalent Current Method to nonlinear isolators of varying stiffness levels. This facilitated the derivation of nonlinear magnetic stiffness and the establishment of governing equations for the VSNI system. The method proved particularly effective in capturing the intricate nonlinear behavior of the magnetic forces, making it crucial for understanding the isolator’s performance characteristics.

Bao, Y. Y. [75] employed the Equivalent Current Method in the analysis of Permanent Magnetic Levitation systems. They combined the Sine method for expressing the magnetic field of Halbach array magnet rails with the equivalent current model for PM V-shapes. This approach enabled the precise calculation of the levitation and lateral forces generated by the system, providing a solid foundation for PML design optimization.

2.5.3. Equivalent Magnetic Circuit Method

In general, due to the direct spatial interaction of PMs, the magnetic flux pattern is intricate, leading to relatively large calculation errors when using the equivalent magnetic circuit method. Consequently, this method is not commonly employed for analytical calculations of magnetic forces. However, in the isolators designed by Zhang, F. [44,45], the presence of an iron core guiding the magnetic circuit created a scenario where the equivalent magnetic circuit method proved effective for analytical modeling. This method, rooted in Ampère’s circuital law, establishes magnetic circuit equations by considering the impedances of various components, including air gaps, moving parts, stators, and grippers. It integrates geometric shapes and material properties, encompassing relative permeability and dimensions, to comprehensively evaluate magnetic flux distribution and the resulting forces.

In Zhang, F.’s isolator [44], the equivalent magnetic circuit method plays a crucial role in modeling variable reluctance stress principles, which are fundamental to isolator design. As shown in Figure 9, by constructing a magnetic circuit model, researchers can represent magnetic flux paths through PMs, moving parts, stators, and air gaps, as well as applying Kirchhoff’s laws to derive equations describing magnetic flux relationships throughout the system. The calculation process involves considering the impedances of various components, which are expressed in terms of their geometric and material properties. A key step in determining the magnetic force acting on the moving part is calculating the magnetic flux density in the air gap. By examining the change in magnetic energy with the displacement of the moving part, researchers derive expressions for the magnetic force and negative stiffness characteristics of the isolator.

This approach enables parametric studies of the isolator, examining how factors such as air gap thickness, moving part thickness, and pole face area influence magnetic negative stiffness [45]. The equivalent magnetic circuit method provides a solid theoretical foundation for isolator design and optimization, allowing researchers to predict and enhance performance in vibration isolation applications without resorting to computationally intensive finite element analysis for each design iteration.

In essence, while the equivalent magnetic circuit method may have limitations in some magnetic force calculations, it has proven particularly effective in the context of Zhang, F.’s isolator designs. This method offers valuable insights into the behavior of magnetic systems with guided flux paths, providing a balance between analytical simplicity and predictive accuracy in specialized magnetic isolation applications.

2.5.4. Semi-Analytical Method

Beyond the three analytical approaches outlined, several researchers have explored semi-analytical methods for developing ultra-accurate electromagnetic actuators and couplings with extensive multi-axis PM configurations. These methods offer significant advantages over the FEM, including reduced computation time and improved force distribution calculations within PMs.

Jansen [76] introduced two semi-analytical modeling techniques: the magnetic surface charge model for efficient 3D magnetic flux density solutions in coreless magnet assemblies and the harmonic model based on Fourier series for analyzing planar actuators. These approaches enable rapid design iteration and optimization by circumventing time-consuming 3D finite element simulations.

Elies [77,78] developed complementary semi-analytical methods for synchronous couplings. They proposed a hybrid approach combining analytical expressions with numerical integration to analyze forces between PMs in flat air gap configurations [77]. In a subsequent study [78], they applied these methods to optimize the torque of permanent-magnet coaxial synchronous couplings, considering various parameters such as pole pairs and airgap dimensions.

Both research groups validated their models through experimental results, demonstrating high accuracy in predicting force and torque characteristics. These semi-analytical techniques offer a balance between analytical precision and the flexibility to incorporate complex geometries and material properties, facilitating efficient optimization within practical constraints.

3. Active Isolators

Due to its excellent properties, passive isolators have garnered increasing attention in semiconductor and high-precision equipment fields. However, the instability of PMs means that they alone cannot achieve stable six-DOF control of levitated objects. In such cases, active isolators are required to stabilize the levitation, which can maintain noncontact and vacuum compatibility advantages.

Meanwhile, passive isolators, while effective in many applications, present limitations that warrant careful consideration, particularly in complex multi-mass systems. As Stosiak, M. [79] demonstrate in their study on hydraulic valve vibrations, the effectiveness of passive isolation is typically confined to a specific frequency range, which is determined by the natural frequency of the isolated object. They note that the proposed model and ‘black box’ approach can be used to evaluate the effectiveness of reducing directional control valve body vibration using materials with known stiffness and damping. This approach, while useful, highlights the challenges in achieving optimal vibration isolation across a broad frequency spectrum, especially in systems with multiple components exhibiting diverse vibration characteristics. Recent studies [80,81] have also emphasized these challenges, exploring both nonlinear vibration isolation systems and novel structural approaches to address the complexities of multi-frequency vibrations. Such limitations underscore the need for more advanced isolation strategies in complex systems, potentially incorporating adaptive or active vibration control methods to address the full range of vibration frequencies encountered in practical applications. These findings show active isolators’ indispensable role in addressing complex vibrational challenges.

This section introduces the current research status of active electromagnetic isolators. It is important to note that while standalone active isolators offer advantages such as a wide controllable frequency band and reasonable control performance, they often require substantial external energy and tend to have a complex structure. Therefore, combining active and passive isolators can effectively isolate impacts over a broader frequency range, enhancing efficiency. This hybrid approach represents the future direction of electromagnetic isolation development. Many researchers have focused on balancing performance with energy efficiency, particularly in electromagnetic levitation systems. The integration of active and passive isolation techniques has emerged as a promising solution to this challenge. Zhang, F. [44] demonstrated that an active–passive hybrid magnetic negative stiffness isolator could significantly improve low-frequency isolation while maintaining high static support stiffness, reducing the initial isolation frequency by 80% compared to passive systems alone. Similarly, Yang, B. B. [61] optimized isolator arrangements in multi-freedom systems, considering both passive and magnetic suspension isolators to minimize power flow while maximizing isolation effectiveness. These hybrid approaches, combined with advanced control strategies such as fuzzy PID control [82], have shown potential in achieving superior vibration attenuation across a wide frequency range while minimizing energy consumption, addressing the inherent power demands of purely active electromagnetic levitation systems [15,83].

3.1. Electromagnet Actuators

Active isolators designed using electromagnets are structurally simple and have been widely adopted by researchers. However, controlling these actuators can be relatively complex and highly nonlinear, making precise position control challenging.

3.1.1. E-Shaped Electromagnet Actuators

Unilateral E-Shaped Electromagnet Actuators

Hoque, M. E. has proposed a series of zero-power control magnetic levitation systems for unilateral E-shaped electromagnet actuators and has extensively applied this control method. In [84], an enhanced zero-power levitation control system with adjustable stiffness was proposed, as shown in Figure 10a. The authors modified the fundamental system to modify stiffness through the incorporation of a small displacement proportional response element to the controller. They developed a vibration attenuation mechanism by integrating a PS spring in sequence with the improved zero-power controller’s NS levation. Their isolation system demonstrated exceptional performance, particularly in the low-frequency domain. At 0.1 Hz, the isolation table exhibited a remarkably low displacement of −122 dB [m/N], which is indicative of its high stiffness against low-frequency dynamic direct disturbances. The system effectively suppressed direct disturbances, as evidenced by both static and dynamic responses. In step response tests utilizing an electromagnet-generated 0–10 N disturbance, the isolation table displayed a transient increase in gap relative to the middle mass, while the middle mass’s displacement relative to the base decreased. Notably, the isolation table returned to its initial position within 0.6 s, further substantiating the system’s efficacy in vibration isolation and disturbance mitigation.

In [85], they proposed an improvement scheme using elastic ferromagnetic materials, which reduced magnetic reluctance, increased levitation force, and improved damping characteristics. In [86], a six-DOF apparatus utilizing a parallel configuration was designed, with each unit consisting of a sequential arrangement of dual isolators, with one acting as a motion nullification isolator and the other as a PS isolator. In [87], a modular three-DOF mechanism employing improved zero-power control was proposed. The authors in [88] proposed a hybrid mechanism employing linear zero-power control incorporating load-bearing springs, combining mechanical springs in series with NS springs achieved through zero-power control to isolate ground vibrations. Yu, X. W. has also researched unilateral E-shaped electromagnets [89].

Bilateral E-Shaped Electromagnet Actuators

Sun, L. F. designed a metal mesh magnetic levitation isolator [90], where the active isolation component is a bilateral E-shaped electromagnet, as shown in Figure 10b. They established a theoretical formula of the electromagnetic actuator and studied its isolation characteristics. The system allows for adaptive control, making it particularly effective in managing high-frequency vibrations. This feature enhances the isolator’s versatility across a broader frequency spectrum. Duan, X. S. researched the isolation performance and active control of their bilateral electromagnet magnetic levitation isolator [91]. Yang, Z. G. constructed a six-DOF Stewart platform using electromagnets [92]. Yang, B. B. compared different arrangement schemes of bilateral E-shaped electromagnet actuators and passive isolators [61], proposing a hybrid vibration system. Zhang, B. designed a hybrid system using this actuator and proposed a two-tier fuzzy PID isolation control approach integrating position and current differentials [82].

Figure 10. E-shaped electromagnet actuators. (a) Unilateral. (b) Bilateral.

Figure 10. E-shaped electromagnet actuators. (a) Unilateral. (b) Bilateral.

In addition, Meng, K. [93] proposed a specially shaped E-shaped electromagnet actuator. It can be directly used as an adjustable NS spring based on Maxwell normal stress.

3.1.2. U-Shaped Electromagnet Actuators

Chen, F. [94] introduced the development of an innovative electromagnetic composite isolator equipped with a U-shaped electromagnet actuator, as shown in Figure 11. The actuator and rubber element are arranged in parallel, with the rubber element embedded within the actuator’s mover. This configuration linearizes the actuator’s magnetic force. When the controller is turned on, the acceleration amplitude of the base plate drops dramatically, and the frequency spectrums of the base plate vibration signals at 55 Hz and 155 Hz are suppressed by 21.2 dB and 27.9 dB, respectively. Compared to passive isolators, this isolator can not only damp the high frequency vibrations, but also obtain better performance in the low frequency region.

3.1.3. Cylindrical Electromagnet Actuators

Cylindrical electromagnet actuators, which are the standard shape of electromagnets, have been frequently used as the primary actuating components in systems by Su, P. and Ma, J. G. [95,96,97]. These were designed as new QZS nonlinear magnetic isolators by paralleling them with linear PS springs and airbags. The isolator [95] shown in Figure 12 revealed two pseudo-resonant peaks in the amplitude–frequency curve, occurring in low- and high-frequency bands, respectively. While the first peak remained constant, the second exhibited a notable frequency shift towards the natural frequency. Increasing the current resulted in decreased peak amplitudes and significant alterations in the backbone curve of the second resonant crest. Furthermore, the system demonstrated a chaotic parameter region, with the potential for chaos control through the isolator. These findings offer valuable insights for the design and optimization of nonlinear vibration isolation systems, highlighting the isolator’s effectiveness across different frequency ranges and its capacity for enhanced vibration control. As the most common and practical electromagnetic actuator, cylindrical electromagnets have also been widely applied in other studies [98,99,100,101,102,103].

3.1.4. Specially Shaped Electromagnet Actuators

Some specially shaped actuators fundamentally operate on the same principle as electromagnets. Chen, S. Q. [104] studied an innovative isolation system and dynamic control challenges. Chang, K. N. [105] developed a compact magnetic pneumatic isolation platform, using electromagnetic coils to produce attractive interactions counteracting the pneumatic thrust load. The platform minimizes axial bearing stiffness and precisely controls the platform’s axial position. Mofidian, S. M. M. [106] proposed an isolation system combining elastic and MSs with viscous and magnetic damping, as shown in Figure 13, where the arrangement of magnets results in a negative linear stiffness. The dynamic characteristics of the vibration isolator were extensively analyzed through both experimental measurements and model simulations. Displacement transmissibility versus frequency was evaluated at acceleration levels of 1.0 g and 0.25 g [m/s²], employing both the harmonic balance method (HBM) and the 4th-order Runge–Kutta (RK) numerical method for model simulations. The results demonstrated the isolator’s efficacy in attenuating vibrations above 11.91 Hz when subjected to an excitation of 0.25 g [m/s²]. Notably, the isolator incorporated a novel eddy current damper, rendering it both oil-free and leakage-free, thus enhancing its practical applicability and maintenance profile.

3.2. Linear Motors

Linear motor actuators are excellent for active vibration isolators, effectively performing single-DOF actuation tasks. Currently, coreless voice coil motors are widely adopted.

3.2.1. Traditional Dual-Sided Voice Coil Motors

Wu, Q. Q. has frequently applied traditional bilateral voice coil motors as Lorentz force actuators in magnetic levitation isolation platforms. In [107], a magnetic levitation actuator with excellent linearity was designed, and its essential characteristics were obtained through the FEM, as shown in Figure 14. By altering the actuator‘s arrangement, active isolation platforms for different payload scales were designed, and actuator characteristic verification experiments were conducted. The linearity of the actuator and the mechanical dynamic response of the platform were obtained. The experimental results highlight the effectiveness of the proposed design. In [108], the motor’s structure was designed to achieve better performance, and a optimization was devised to maximize thrust while minimizing conductor mass.

Kremers, M. F. J. and Janssen, J. L. G. have also conducted relevant research. In [109], the influence of crucial design variables on the motor’s characteristics with vertically magnetized magnets and quasi-Halbach magnetized arrays was studied, modeling performance through formulations for spatial magnetic flux distribution. In [110], the designed voice coil motors operated parallel with passive isolators, providing the necessary stability and active isolation.

Additionally, studies [111,112,113,114] have also employed traditional bilateral voice coil motors as actuators for active isolation systems.

3.2.2. Special Voice Coil Motors

Zhou, Y. has designed several voice coil motors with diamond-shaped PM arrays for magnetic levitation positioning systems [115,116], as shown in Figure 15. The unique stator magnetic structure gives the mover a hyperbolic magnetic field, offering superior force consistency, enhanced thrust density, and favorable production feasibility. They introduced the basic structure and working principle of the proposed motor. Using the equivalent current model, they derived expressions for the flux distribution, force, and torque. Experimental results demonstrated the excellent performance of this voice coil motor.

3.2.3. Other Configurations

Chen, C. H. [117] proposed a highly integrated and modular structural design for a magnetic levitation microgravity isolation system, as shown in Figure 16. This actuator, similar to the voice coil motor, utilizes the Lorentz force principle. Using Matlab’s multi-objective optimization function, they optimized the parameters to achieve a lightweight, low-power design. They experimentally studied the voice coil motor’s static output and dynamic response characteristics, obtaining the spatial distribution state and variation trend of the static output force. Analysis of the acceleration auto-power spectra revealed that the magnetic levitation microgravity vibration isolation system demonstrates excellent vibration control performance. Within the frequency range of 1 Hz to 20 Hz, the acceleration amplitude of the floating platform is significantly lower than that of the base platform. This effective attenuation is achieved through the implementation of a cascaded PID control method, which successfully mitigates indirect acceleration disturbances of varying frequencies originating from the base platform. These findings indicate that the vibration isolator maintains its effectiveness across a broad spectrum of low-frequency vibrations, making it particularly suitable for applications requiring precise vibration control in the 1–20 Hz range. Zhao, Y. M. [118] also conceived a configuration featuring a similar magnetic circuit.

Meng, K. [93,119] developed a novel NS spring. The spring features controllable stiffness, which is suitable for low resonance frequency isolation systems. The spring consists of concentric PMs and a current loop, with stiffness adjustment through the current. They established a theory derived from the filament method.

3.3. Rotary Platforms

Rotary platforms serve specialized conditions, typically requiring in-plane angular positioning and rotational motion. Zheng, T. [120] proposed an optimization for sizing electromagnetic suspension devices in rotating systems, as shown in Figure 17. This method allows for directly determining the dimensions of windings and PMs in a Halbach system instead of deriving a unique geometric parameter through mathematical analysis.

Dyck, M. [121] proposed a six-DOF magnetic levitation precision rotational platform. It employs a mobile magnetized motor design, featuring Halbach arrays positioned along the periphery. Its driving force is achieved through Lorentz forces, with coils fabricated using a printed circuit board. Eight independent controlled forces are generated in total by utilizing four three-phase amplifiers. Optical encoders and capacitive sensors enable closed-loop motion control. Testing of the fabricated platform confirms its capability to achieve sub-micron accuracy in applications.

3.4. Planar Motors

Compared to linear motors, planar motors offer higher integration and efficiency. However, their topologies and control systems become more complex.

Wang, W. R. [122] designed an electromagnetic planar actuator for logistics, which addresses the requirements through arbitrary combinations of unit modules. This planar motor features frictionless and fast dynamic response, as well as the ability to modify the goal in real time according to demand. Sun, H. B. [123] proposed a feedforward compensation method to reduce torque ripple errors for motors with similar topologies. Zhang, S. G. [124] proposed a mathematical approach that was developed to calculate the winding dimensions based on the pole pitch.

Jansen, J. W. [76] designed a high-precision actuator containing a large multi-dimensional PM array intended for applications in the lithography industry. Zhu, H. [125] proposed a magnetic levitation planar positioner that is smaller in mass compared to existing designs. It uses four low-order moving magnet linear motors with single-pole Halbach arrays. Lei, J. [126] designed a Lorentz planar motor. This novel motor comprises three Lorentz linear motors (Y1, X, and Y2) capable of achieving three-DOF planar positioning motions.

3.5. Multi-Degree-of-Freedom Actuators

Some researchers have designed fully active electromagnetic isolation actuators. This section introduces the current state of research on these platforms.

3.5.1. Single-Degree-of-Freedom Superposition

Gong, Z. P. has researched active isolation platforms with single-DOF actuators. In [127], a magnetic levitation actuator with six-DOF motion capabilities was proposed, as shown in Figure 18, achieving precise positioning and vibration reduction, thus providing a favorable environment for scientific experiments. The system’s dynamic characteristics and vibration isolation performance were experimentally evaluated using an electromagnetic shaker to produce multi-frequency vibration disturbances. The results demonstrated significant attenuation across various frequencies, with approximately 15 dB reduction for disturbances around 18 Hz and 20 dB attenuation for those near 55 Hz. The system exhibited a bandwidth of 5 Hz characterized by a −40 dB per decade slope at higher frequencies. These findings collectively underscore the system’s efficacy in mitigating vibrations across a broad spectrum of frequencies. In [128], a six-DOF magnetic levitation isolation platform was proposed to meet the requirements in quasi-static environments. The design considered nonlinearity, precision, and minimal energy consumption and employed optimization to design actuators for noncontact with large travel. In [129], a noncontact active control method according to the Lorentz force principle was utilized. The force constant, which meets the current resolution of the electrical system, was used as a verification index, while maximizing magnetic induction intensity and minimizing coil mass and thermal consumption were the goals. The dimensions of PMs and windings were optimized to design a highly linear actuator, leading to the establishment of the total system.

Sundaravadivu, K. [130] proposed a voice coil motor that generates a constant upward force within the nonexcitation working range, where the force magnitude matches the effective load on the armature. Thus, it does not consume energy, minimizing thermal expansion caused by Joule heating and improving the precision of semiconductor equipment. Ding, C. [131] designed a control strategy combining H-infinity control and feedback linearization for actuators with similar structures.

Wu, Q. Q. [132] proposed a standard structure, as shown in Figure 19. A vibration isolation performance in the frequency range of 0.01–100 Hz and a tracking performance below 0.01 Hz were obtained. The percentage of vibration isolation was more than 80% in six DOFs, and the system can effectively suppress the disturbance within the frequency band of 0–70 Hz. Similar platforms were also designed by Chen, C. H. [133].

Unlike the studies above, Guo, Z. X. [134] installed single-DOF actuators on a Stewart platform, achieving active magnetic levitation isolation.

3.5.2. Multi-Degree-of-Freedom Superposition

Liu, R. Q. and Li, S. Z. [135,136], addressing the need for active vibration isolation technology in microgravity environments, proposed a multi-dimensional isolation platform based on a two-DOF electromagnetic actuator. This design comprehensively considers the configurations of existing microvibration isolation platforms and electromagnetic actuators.

Bozkurt, A. F. [137] proposed a flexible transportation device based on magnetic levitation principles. They analyzed the levitation force and torque characteristics using the 3D FEM. By combining the magnetic equivalent circuit method with the FEM results, they established a dynamic model representing the multi-DOF motion characteristics.

Takahashi, M. [138] proposed a suspension system utilizing only a single motor that integrates gravity and torque compensation functions, as shown in Figure 20. This system includes a self-regulating magnetic circuit design, minimizing the influence of current and temporal disturbances on operational dynamics, and it does not require cables and sensors. They showed the frequency responses from the motor thrust to the position and tilt angle of the developed maglev stage. In each system, the characteristics described by the mass inertia model of 1/Ms² in series with a lag system were measured; the gain characteristics were inclined at −40 dB/dec. The levitated condition results did not show a resonance peak with a phase delay under 200 Hz. Similar actuators and stacking methods were used in [139,140,141].

Raab, M. [83] introduced a magnetic levitation linear actuator with integrated active gravity compensation. The gravity compensation combines permanent magnets with a novel hybrid shape memory actuator. The magnetic levitation system uses nine unipolar linear reluctance actuators to levitate a passive armature with no mechanical connection. Active gravity compensation adjusts the air gap to achieve the required gravity compensation force, helping to maintain low power consumption and temperature rise, thereby improving system precision.

Lahdo, M. [142,143] proposed a single-PM device producing both lift and thrust, providing an economical and space-efficient scheme for magnetic levitation. Utilizing this mechanism, an innovative magnetic levitation planar positioning system was proposed. It utilizes the least amount of PMs and actuators to achieve six-DOF motions.

Recent advancements in control methods for multi-degree-of-freedom active magnetic levitation vibration isolation systems have led to the emergence of innovative technologies. These new approaches address the complex challenges associated with controlling such sophisticated systems, offering improved performance and efficiency.

Several studies have contributed to these advancements. Liu, C. N. [144] proposed a physics-driven control strategy that prioritizes low computational load and ease of implementation, potentially enhancing vibration isolation quality by over 10%. In another study, Yang, Y. [145] explored phase deviation compensation in semi-active suspension control, which could improve system stability and vibration isolation across a wider frequency range. Wu, D. [146] presented an optimization approach for control unit configuration, potentially leading to more energy-efficient operation. Additionally, recent research has introduced active composite control strategies integrating feedforward and feedback control with Kalman filtering [147], which could provide robust performance across various operating conditions in multi-DOF magnetic levitation systems.

These emerging technologies of active isolators offer the potential for more precise control, improved energy efficiency, and enhanced vibration isolation performance.

4. Summary

4.1. Passive Isolators

Researchers have been striving to diversify and complicate structures to better adapt to specific working conditions for passive isolators, specifically passive or semi-active electromagnetic isolators. Essentially, this process involves transitioning passive isolators from general use to more specialized and refined classifications to enhance required performance. Due to the widespread demand for vibration isolation across various industrial fields, the external environments, vibration sources, and required isolation effects and precision inevitably differ. Therefore, this trend toward specialization is inevitable.

Based on current findings, electromagnetic passive isolators can be broadly categorized according to their structural characteristics into several types: PMSs, planar isolators, and PM array isolators. PMSs generally have lower load capacities and typically require mechanical springs. Their magnetic structures are relatively simple but easier to achieve QZS. Most researchers use permanent magnets as elements to generate NS. Research and design on planar isolators are still relatively limited but have vast application prospects. Compared to other types, PM array isolators have stronger load capacities, diverse magnetic structures, and do not require mechanical springs.

The two most important performance indicators for passive isolators are levitation force and stiffness. These two indicators of the isolators referenced above are statistically summarized in Figure 21. Since the levitation force and stiffness of PMSs are generally zero at their initial positions, they are not included in the statistics. In Figure 21, numbers 1 to 8 correspond to references [48,49,50,52,53,55,56,57].

In terms of the performance of passive isolators, many researchers have achieved better isolation effects by endowing them with specific nonlinear mechanical properties. This means that, unlike traditional mechanical springs, the function curve of levitation force versus displacement is not linear. Nonlinear isolators can reduce dynamic stiffness, thereby improving isolation performance. Many studies have pursued QZS systems, where the NS generated by the electromagnetic structure is almost equal in magnitude to the PS, and there is a region near the zero position with a sustained near-zero overall stiffness. Such isolators perform better in response to low-frequency excitations, which traditional isolators cannot achieve. This is just one type of nonlinear isolator. In recent years, some researchers have proposed the principle of HSLD stiffness to surpass the limitations of linear isolators. As the name suggests, such systems have high stiffness in static conditions, making them capable of independently supporting loads, but they exhibit low stiffness when low-frequency vibrations are present. Essentially, these isolators are an evolution of QZS isolators, where the stiffness is sufficient to bear the load’s weight but becomes softer in response to dynamic motion. In other words, HSLD stiffness isolators exhibit highly nonlinear isolation characteristics based on system parameters and the magnitude of foundation oscillation. Additionally, there is a trend toward designing isolators with variable stiffness and adjustable parameters. This paper also lists several examples of isolators with variable stiffness, aiming to broaden the application range.

Furthermore, for the performance analysis of passive isolators, the forces are generated through interactions between permanent magnets, since they do not contain coils. Standard analysis methods include the equivalent current method, equivalent magnetic charge method, and equivalent magnetic circuit method. Through continuous improvements to basic formulas by predecessors, there are now numerical analysis methods for calculating the forces and torques between PMs that are faster than the FEM and more accurate than classical methods.

4.2. Active Isolators

Currently, research on single-DOF and two-DOF electromagnetic actuators for active isolators is relatively mature. These actuators come in various types and principles, which can be broadly categorized as follows: electromagnets, linear motors, rotary platforms, and planar motors. Among them, electromagnet actuators can be further divided into various forms based on the shape of the core. Their simple structure has led many researchers to adopt them as active components in magnetic levitation isolation platforms. However, owing to the pronounced nonlinear characteristics of the levitation force, their control systems are relatively complex. Additionally, their position states are essentially binary, which is disadvantageous for vibration control and necessitates using a core to ensure actuation force.

Many researchers prefer linear motors, primarily voice coil motors. Voice coil motors have a simple structure, no cogging effect, fast dynamic response, high acceleration, direct drive capability, and linear force control proportional to the input current. These characteristics make them highly suitable for vibration control. Rotary platforms are akin to horizontally placed rotary motors, wherein they are capable of effectively controlling the rotor’s rotational motion and position angle within a plane while achieving levitation. These actuators are used in specific conditions. Planar motors can achieve two-dimensional planar motion, allowing for multi-DOF control and improving efficiency and reliability. However, their structure is more complex than linear motors, increasing maintenance difficulty, and their control systems are also more complicated, leading to higher energy consumption and heat generation.

Most researchers achieve this for multi-DOF or even six-DOF actuators by superimposing single-DOF actuators and planar actuators, essentially creating a purely active magnetic levitation isolation platform. Additionally, a form combines magnetic bearings with linear motors, but these actuators generally have fewer DOFs and must include at least one rotational DOF. If only translational vibration isolation is needed, these actuators may not be effective.

Beyond the structural design of the actuators, some researchers have specifically analyzed the heating conditions of the actuators and designed cooling structures. Excessive temperature rise can affect the dynamic response and other performance and potentially lead to the demagnetization of the permanent magnets and failure of other components. Therefore, these research findings are highly significant for the future design of magnetic levitation isolation platforms.

5. Challenges and Developments

For passive isolators, most current designs use electromagnetic structures to generate NS. Innovations in purely permanent magnetic isolator structures remain relatively rare without combining them with other mechanical structures. Additionally, most isolators discussed in the literature are unsuitable for heavy-load conditions, and there is almost no research on high-load ones. Although the force output level by isolators is important, the size constraints often present significant challenges in applications. The future direction is not only focused on increasing force levels but also on enhancing force density. This aims to provide effective vibration control in confined spaces, addressing the demand for compact, high-performance isolation across various industries. The designed isolators are predominantly single-axis, with relatively few studies having been conducted on multi-axis isolation. Furthermore, most researchers focus on translational vibration sources, whereas real-world vibrations are complex, and addressing rotational vibrations remains unresolved.

For passive isolators’ analysis, there is still a lack of methods to calculate the magnetic forces and torques between PMs for arbitrary six-DOF movements in space. Although the equivalent magnetic charge method based on the working point has high accuracy, its computational speed is still low, making it unsuitable for optimization.

Most existing designs achieve only single functions for active actuators, with few designs and studies on actuators that simultaneously achieve multiple functions. Multiple single-axis actuators are usually combined to realize six-DOF motion controls, resulting in relatively complex system structures.

For the entire magnetic levitation isolation system, most researchers design isolation control systems that focus solely on position and motion vibration control. However, in practical use, factors such as the working environment also significantly affect the final performance of the isolation system, yet there is little related research that has been conducted.