Quasi-zero Stiffness Vibration Isolator Research Articles

An approach for realizing lightweight quasi-zero stiffness isolators via lever amplification

Quasi-zero stiffness (QZS) vibration isolators exhibit excellent performance in low-frequency vibration isolation but require the negative stiffness to be consistent or close to the positive stiffness, which may lead to an excessively large volume or weight of the negative stiffness mechanism. In this paper, a lightweight QZS (L-QZS) vibration isolator using the lever amplification mechanism is developed, theoretically investigated, and experimentally verified. The negative stiffness can be amplified by one order of magnitude through the amplification effect of the lever structure, enabling a lower negative stiffness to compensate for the positive stiffness. Meanwhile, the lever increases the inertia effect of the negative stiffness structure, leading to an increase in the system’s effective mass and further reducing the resonance frequency. Results indicate that with a small negative stiffness, the isolation bandwidth of L-QZS isolators is significantly enlarged. The transmissibility at high frequencies of the L-QZS isolator tends to a certain value, which is mainly determined by the lever ratio and the tip mass of the lever. Furthermore, the negative stiffness can be controlled by adjusting the lever ratio, providing a viable method for matching various positive stiffnesses in engineering applications.

Design and Vibration Isolation Investigation of a Load-Adjustable Quasi-Zero Stiffness Isolator

Quasi-zero Stiffness (QZS) isolators offer significant advantages in low-frequency vibration isolation. Nonetheless, the complexity of the structure and the limited load adaptability hinder the practical application of such isolators. Therefore, this paper proposes a novel load-adjustable QZS isolator based on a compliant mechanism. By integrating the positive stiffness of the curved beam and the negative one of the inclined beam, a comprehensive design strategy for the QZS flexible beam is introduced. The optimal geometric parameters of the structure are determined using a genetic algorithm, and the finite element simulations are employed to numerically validate the QZS characteristics of the structure as well as the low-frequency vibration isolation performance. Leveraging the same structural design and a kind of temperature-sensitive materials-Thermoplastic Polyurethane (TPU), a unit cell of load-adjustable QZS isolator controlled by electric heating is developed and fabricated via 3D printing. Static and dynamic tests are conducted to explore the QZS platform characteristics and vibration isolation performance of the isolator subjected to various voltage inputs. The results demonstrate that the QZS characteristics of the isolator can be effectively regulated by adjusting the input voltage, ensuring effective low-frequency vibration isolation under different loads. Moreover, the incorporation of serial and parallel arrangements of unit cells could further enhance the range of load adjustability. This study offers novel insights into the design of load-adjustable QZS isolators.

A nonlinear low frequency quasi zero stiffness vibration isolator using double-arc flexible beams

There is an increasing demand for integrated small vibration isolators in precision sensing instruments and medical equipment. Therefore, a quasi-zero stiffness (QZS) vibration isolator with double-arc flexible beams (D-AFB) is proposed. The QZS isolator consists of D-AFB units, the base, platform, fixture, guide rail, and linear bearing. The static performance of D-AFB is analyzed using the FEA method, and the QZS condition is obtained. The harmonic balance method (HBM) and the pseudo arc length method (PALM) are used to solve the dynamic equations of the nonlinear system, and the analytical solutions of displacement transmissibility and Force transmissibility are derived. In theory, the initial frequency is 77.6 % lower than that of the equivalent linear system. The QZS characteristic of D-AFB is verified by static experiment, and the low-frequency isolation performance of the QZS isolator is verified by dynamic experiment under constant amplitude and constant acceleration excitation. The D-AFB has a simple structure and can easily satisfy QZS conditions. So the D-AFB can be customized according to load requirements. Multiple vibration isolation loads can be obtained by adjusting the assembly of the D-AFB. The QZS isolator can adapt to load changes within 10 % and has an isolation effect on vibrations above 4 Hz. The idea of designing a QZS isolator with D-AFB as an array unit has a good research prospect and great application value in meeting the requirements of miniaturization and integration.

Design and test of a quasi-zero stiffness isolator with machinable springs

Quasi-zero stiffness (QZS) vibration isolators are widely used for vibration isolation due to their high performance, but their low load-carrying capacity limits their applications. In this paper, a heavy-load-bearing QZS vibration isolator consisting of three compression springs is investigated for isolating ultra-low frequency vibrations. From the theoretical aspect, parameter optimization considering both load mass and isolation performance metric (IPM) is implemented, and a parameter guidance diagram is proposed for parameter design. From the practical point of view, two innovative springs are designed and fabricated by wire-electrical discharge machining (W-EDM), referring to the idea of compliant mechanism. These creative designs are endowed with precise stiffness, large compression and buckling avoidance, which further improve the system properties. Finally, a prototype is made and experiments are carried out to verify the effectiveness of the design. Compared with linear isolators, the experimental results of QZS isolator show better isolation performances in a wider frequency range.

Analytical study of quasi-zero stiffness vibration isolator with uncertain parameters based on arbitrary polynomial chaos expansions method

Analytical study of quasi-zero stiffness vibration isolator with uncertain parameters based on arbitrary polynomial chaos expansions method

Novel modular quasi-zero stiffness vibration isolator with high linearity and integrated fluid damping

Novel modular quasi-zero stiffness vibration isolator with high linearity and integrated fluid damping

Tunable stiffness design of curved-crease origami and extended quasi-zero stiffness vibration isolator

A kind of origami tube based on the curved crease, which has a tunable stiffness, was designed, fabricated, tested, and extended to the concept of a quasi-zero stiffness (QZS) vibration isolator. The regulating function of crease stiffness on the overall origami stiffness without changes in the crease pattern was verified by single-crease models. With various opening ratios along the creases, three tubes composed of mirrored single-crease origami were designed, fabricated by 3D printing, and compressively tested. The test results present the potential of the approach of QZS. Further, the elastic-frictionless origami tubes were redesigned and simulated to obtain the target stiffness. The cubic term fitting of the load curve was adopted by the harmonic balance method to solve the steady-state vibration response, and then the simulation results obtained by the finite element method (FEM) were compared. The study shows that the designed elastic-frictionless isolator has a good low-frequency vibration isolation performance. The concept of the simple stiffness control method of curved-crease origami provides more practice options for high static and low dynamic stiffness systems.

Research on flexible beam-type nonlinear vibration isolators suitable for low frequencies

Ship vibration not only causes safety issues, but also easily generates noise pollution. Therefore, this paper introduces the quasi-zero stiffness (QZS) vibration isolator to solve the problem of low-frequency vibration. In terms of static analysis, this paper proposes a discretized beam constraint model (DBCM) to study the static properties of flexible beams with large deformation, and the finite element analysis (FEA) verifies the accuracy of DBCM. Regarding dynamic analysis, this paper combines the harmonic balance method (HBM) and the pseudo-arc length method (PALM) to analyze the dynamic response and explore the influence of excitation and damping ratio on the response stability. In addition, the performance of equivalent linear isolators is compared, revealing significant advantages of QZS isolator in terms of isolation bandwidth and peak transmissibility. The experimental data demonstrates that QZS isolator’s initial isolation frequency (2.14 Hz) is 68.5% lower than that of linear isolators (6.79 Hz), and the isolation efficiency at 5.35 Hz can reach 90%, making it suitable for low-frequency isolation. Furthermore, experimental data validate the accuracy of the theoretical model and FEA. The static and dynamic theoretical models can optimize the structural parameters of flexible beams and serve as valuable inspiration and reference for designing and improving isolator.

Bio-inspired quasi-zero stiffness vibration isolator with quasilinear negative stiffness in full stroke

Simpler structure, better adaptability to variable loads, and wider linear stable region have always been pursued by nonlinear quasi zero stiffness (QZS) isolator. Inspired by the balancing and stabilizing effect of the leg and wing in the take-off and landing of birds, this paper proposes a novel bio-inspired QZS vibration isolator (BI-QZSVI). The BI-QZSVI is composed of two primary components: the legged negative stiffness structure, which comprises a two-link mechanism and a set of oblique springs, and a pair of vertical springs that imitate wings. A static model is established based on the virtual work principle, the nonlinear dynamic model is then constructed using Lagrangian equations, and an analytical solution is derived through implementation of the harmonic balance method. An experimental platform is established to verify the effectiveness of the theoretical results. The results reveal that the proposed isolator outperforms existing typical isolators by offering a larger quasi-zero stiffness region, as evidenced by the two proposed range and linearity indexes. The unique structure effectively tackles geometric nonlinearity to establish a linear relationship between the load and stiffness. Notably, the negative stiffness of the isolator exhibits exceptional linearity throughout the entire stroke, ensuring a broad stability region even under high excitation levels. Furthermore, the isolator demonstrates remarkable efficacy in reducing vibrations with frequencies exceeding 3 Hz. Overall, the proposed isolator is an efficient low-frequency isolator with simple structure, strong adaptability, and wide linear range.

Active Control of Quasi-Zero-Stiffness Vibration Isolator with Variable Load

Quasi-zero-stiffness (QZS) isolator has great application potential in the field of low-frequency vibration isolation due to its high-static and low-dynamic (HSLD) nonlinear stiffness characteristic, but it is precisely this characteristic that makes it very sensitive to load changes. Once the load changes, causing it to deviate from the equilibrium position, it no longer qualifies zero-stiffness characteristic, and the vibration isolation capacity will be significantly decrease. To make the QZS isolator possess variable load capacity and be more suitable for engineering practice, an active QZS vibration isolator based on electromagnetic actuator is designed in this paper, which eliminates the influence of load changes through the active force of the electromagnetic actuator. First, the dynamic equation of the isolator is established by Newton–Euler method, and the dynamic characteristic of the isolator under standard load and load variations are analyzed through improved incremental harmonic balance (IHB) method based on discrete Fourier transform (DFT). Next, the improved particle swarm optimization (PSO) algorithm are employed to optimize the Proportion Integration Differentiation (PID) controller parameters. Then, the vibration isolation performance of QZS isolator in controlled and uncontrolled and linear systems in the same control state are compared in frequency domain and time domain, respectively. Finally, the performance of active QZS isolator under load variation is discussed. The results indicate that the isolation performance of the QZS isolator under active control is significantly better than in uncontrolled conditions and the controlled linear system. When the load changes, real-time compensation through the actuator output control force can also enable the QZS isolator to achieve a better vibration isolation performance.

Theoretical and experimental study of a novel nonlinear quasi-zero Stiffness vibration isolator based on a symmetric link-rod-type structure

This study proposes a novel nonlinear low-frequency vibration isolator with quasi-zero stiffness (QZS) based on a symmetric link-rod-type structure. The principle of the isolator is analyzed, and the properties of the vibration isolator are investigated experimentally. Varying displacements with a restoring force and stiffness are acquired by a static model; thus, the QZS conditions and system contributing factors are elucidated. Various effects of the excitation amplitude, damping ratio, rod length ratio, and initial spring compression ratio on the displacement transmissibility, which are determined using the harmonic balance method (HBM), are discussed. Through a series of experiments on the isolator prototype, the performance of a QZS vibration-isolation system with a symmetric link-rod-type structure is validated. The results indicate that the presented symmetric link-rod-type QZS vibration isolator has a wider QZS interval, lower frequency of vibration isolation, and better isolation performance, providing a valuable reference for the design of QZS vibration isolators.

A nonlinear quasi-zero stiffness vibration isolator with quintic restoring force characteristic: A fundamental analytical insight

The nonlinear mechanical oscillator with X-shaped-spring suspension has attracted relevant attention in the past couple of years due to its ability to tailor the corresponding stiffness characteristic on purpose and fit diverse engineering needs. This paper deeply investigates the conditions for such a configuration to exhibit a quasi-zero stiffness behaviour with both the linear and cubic elastic term of the force-displacement curve equal to zero. The resulting quintic characteristic leads to a vibration isolator with a much larger isolation frequency band respect to the classical isolator with non-zero cubic elastic term only. A systematic comparison between the quintic and cubic characteristics is performed, emphasizing the asymptotic trends, and thus showing the fundamental behaviours. It is found that the critical damping for an unbounded response of the quintic isolator is proportional to the square of the normalized excitation amplitude, while that of the cubic isolator is directly proportional to the normalized displacement amplitude. This makes the critical damping of the quintic isolator much lower, and thus more favourable in practical engineering applications, where the values of the normalized excitation amplitude are less than one.

Bio-inspired multi-joint-collaborative vibration isolation

Inspired by the collaborative action of ankle, knee and hip joint, a novel bio-inspired multi joint structure (BIMJS) is proposed, and its favorable nonlinearity is systematically investigated for low frequency vibration isolation. Two rigid rods are adopted to imitate the femur and tibia, and three torsional springs are utilized to simulate the muscle function in each joint. Based on the principle of virtual work, a static model considering the action of three joints and leg posture is established to characterize the stiffness property. The independent action mechanism of each joint is revealed and the influence of posture adjustment on equivalent stiffness of the BIMJS is studied. By adjusting proper posture and setting reasonable stiffness of each joint, the quasi zero stiffness (QZS) can be easily obtained for low frequency vibration isolation. Dynamic model is developed and the displacement transmissibility is derived to estimate the isolation performance of the BIMJS. The experimental results confirm the advantages of realizing QZS and low-frequency vibration isolation under multiple loads. The vibrations above 2.5 Hz can be effectively isolated. The concept of utilizing the collaborative action of multi joints may provide an innovative method for the design of low frequency vibration isolators.

Load-adaptive quasi-zero stiffness vibration isolation via dual electromagnetic stiffness regulation

Conventional quasi-zero stiffness (QZS) isolators are sensitive to load variation, especially the load mismatch can severely degrade low-frequency vibration isolation performance. Herein, a load-adaptative electromagnetic QZS vibration isolator (LEQVI) is proposed. The stiffness nonlinearization for QZS characteristic is achieved by exploiting a nonlinear positive stiffness structure (a cylindrical coil and a magnet in the face-to-face configuration) to modulate a negative stiffness structure (a conical coil and a magnet in the nested configuration). Static modeling and tests reveal that the rated load of the LEQVI can be flexibly and linearly adjusted by regulating the excitation current. Dynamic modeling found that the load mismatch can narrow the vibration isolation bandwidth and deteriorate the vibration attenuation effect. A sliding mode control law considering input saturation is developed to adapt to unknown loads. Simulations and dynamic experiments are conducted to evaluate the vibration isolation performance and verify the effectiveness of the load-adaptive controller. The results demonstrate that the LEQVI can realize a wide vibration isolation band and effective vibration attenuation under various loads via dual electromagnetic stiffness regulation. The proposed LEQVI provides a novel perspective for designing load-insensitive QZS isolators and holds great promise in facilitating future engineering applications of QZS isolators.

Design and correlation analysis of quasi-zero stiffness passive vibration isolation air spring

Vibration isolation systems are widely used in high-end automobile manufacturing, precision instrument processing, building and bridge seismic resistance, ship machinery noise reduction and other engineering fields, with good development prospects. At present, the existing vibration isolation systems on the market are mainly divided into active and passive vibration isolation systems. Passive vibration isolation does not require external energy input. Its structure is simple and the control scheme is easy to implement. However, passive vibration isolation performs well in high frequency vibration but not in low frequency. As a new nonlinear low-frequency vibration isolation technology, the quasi-zero stiffness vibration isolation system has changed the traditional concept of linear system vibration isolation. In addition, compared with traditional spring, air spring as a new type of elastic vibration isolation mechanism has many excellent performances, such as high fatigue resistance and high stiffness. Therefore, this paper uses air spring to design a passive vibration isolation quasi-zero stiffness air spring structure with good vibration isolation effect, simple structure and low cost in both low-frequency and high-frequency vibration.

Further investigation and experimental study of an origami structure-based quasi-zero-stiffness vibration isolator

A quasi-zero stiffness (QZS) vibration isolator formed from a truss-spring stacked Miura-ori (TS-SMO) origami structure can provide a desired ultra-low dynamic stiffness for vibration isolation while remaining a high-static stiffness for load supporting capacity. This paper further investigates the design parameters and experimentally studies the dynamic performance of the proposed TS-SMO vibration isolation system. The effects of the spring parameters and the initial setup conditions on its static response are analysed. With the proper parameter selection, the resultant supporting force generated by the origami structure can be expressed as a polynomial containing the static force and dynamic force components which does not have the linear term. The displacement transmissibility of the proposed system is calculated to evaluate its isolation performance. Analytical and numerical results are in good agreement and both demonstrate an ultra-low resonance frequency for vibration isolation. The dynamic behaviour of the proposed system is also investigated under different conditions to enhance the vibration isolation performance. A proof-of-concept prototype is designed, fabricated and tested to verify both static and dynamic performances of the TS-SMO QZS isolator. The comparative experimental results between the corresponding linear isolation system and the proposed nonlinear QZS system validate the design of origami-inspired structure for vibration isolation and further confirm the effectiveness of the QZS vibration isolator. It is hoped that this research would provide a solid foundation for designing and modelling the TS-SMO structure adopted for vibration isolation in practical engineering applications.

Integrated vibration isolation and actuation via dual nonlinear stiffness regulation

Integrating vibration isolation and actuation is superior, enabling enhanced vibration isolation performance while attaining controllable load position and attitude. Herein, a novel actuatable quasi-zero stiffness (QZS) vibration isolator (AQVI) is proposed and systematically investigated. The stiffness nonlinearization for QZS is fulfilled by paralleling nonlinear electromagnetic negative and positive stiffness structures. This configuration gives rise to an interesting behavior, that is, the rated load and equilibrium position are tailorable via dual nonlinear stiffness regulation, rendering the load actuatable without a trade-off with the QZS characteristic. The comprehensive static investigation is implemented to fully reveal and verify the dual nonlinear stiffness regulation mechanism. Dynamic governing equations are derived and solved in the cases of dwell and actuation, and it is found that the AQVI is capable of isolating broadband vibrations and tracking prescribed trajectories. Finally, an experimental apparatus is built to evaluate the vibration isolation performance and examine the effectiveness of the load actuation. The sweep excitation test demonstrates that the AQVI has good vibration isolation performance, exemplified by a low resonant frequency of 2.5 Hz and a small isolation starting frequency of 3.6 Hz. The load actuation test validates that the AQVI under open-loop control is competent to actuate the load following the desired trajectory while retaining excellent vibration attenuation. The proposed AQVI provides a novel paradigm for devising QZS isolators that are insensitive to the load and working point, shedding promising light on applications requiring integrated vibration isolation and actuation.

A new magnetorheological quasi-zero stiffness vibration isolation system with large zero stiffness range and highly stable characteristics

Various quasi-zero stiffness (QZS) systems have been developed and applied in the vibration control domain in recent years. However, most QZS systems are usually unstable against external disturbances, and their QZS ranges are very limited. To address these issues, this study develops a highly stable QZS vibration isolation system integrated with magnetorheological fluids (MRFs). The MRFs endow the vibration isolation system with stiffness variability in vertical and lateral directions to against external disturbances, which innovatively solves the unstable problem of QZS systems. Meanwhile, the stiffness variability also makes the system adaptable to vibrations with different frequencies, so the system can deliver the best vibration isolation performance in response to various excitations. The system consists of a vertical isolation unit and a lateral isolation unit. By paralleling a nonlinear positive stiffness QZS component with a nonlinear negative stiffness QZS component in the vertical isolation unit, a large QZS range in the vertical direction and smaller stiffness are realised, thus improving the vibration isolation performance. In this study, the vibration isolation system is designed and prototyped; its QZS characteristics and adjustable stiffness features in both the vertical and lateral directions are experimentally verified; the frequency responses of the system are obtained experimentally; and the stability and the vibration isolation performance of the system are also evaluated by experiments with the designed control algorithms. This study provides a solution to overcome the unstable problem of QZS systems and extend the limited QZS range, whilst realising QZS characteristics in both vertical and lateral directions, thus broadening the application of QZS systems.

Dynamics and Stability of Magnetic-Air Hybrid Quasi-Zero Stiffness Vibration Isolation System

With the improvement of machining accuracy, external low frequency vibration has become one of the most important factors affecting the performance of equipment. The theory of quasi-zero stiffness vibration isolation shows favorable low frequency vibration isolation effect. However, the theory, mechanical properties and dynamics of the system still need to be studied and expanded. Based on our previous research on the structure of a magnetic-air hybrid quasi-zero stiffness vibration isolation system, the nonlinear mechanical expression of positive and negative stiffness structure has been analyzed in this paper, to improve application of the system and provide a theoretical basis for sequential studies of active control. To provide the judgment criteria and basis for the application of quasi-zero stiffness, a more accurate quasi-zero stiffness mechanical model was to be established, and the judgement criterion and stability of quasi-zero stiffness was to be discussed and analyzed. Then, the dynamical model based on external low frequency vibration was developed, to investigate the stability and natural frequency. At the same time, the influence of different feedback parameters on the amplitude frequency characteristics has been discussed, which provides a basis for the future study of active control. Finally, we carried out simulation and experimental analysis to verify the stiffness of high static and low dynamic and the low frequency vibration isolation effect of the vibration isolation system.

The research about application of quasi-zero stiffness vibration isolation technology in a large vehicle-mounted optic-electronic equipment

The large vehicle-borne optic-electronic tracking equipment has the characteristics of heavy inertia, complex road condition and wide vibration spectrum. In order to solve the problem of passive broadband vibration isolation for vehicle-mounted moving platform optic-electronic equipment, a combined quasi-zero stiffness vibration isolation scheme is proposed. The vibration of the engine, generator, water cooler and the remaining vibration amplitude, frequency and Yaw of the road after passing the self-vibration isolation system of the vehicle are collected and confirmed by means of calculation simulation and field test. At the same time, the effective load of photoelectric equipment is analyzed by frequency sweeping test, and the corresponding multi-mode frequency points are obtained. According to the characteristics of the special equipment, a quasi-zero-stiffness vibration isolation system is designed to suppress the wide-frequency and high-amplitude vibration and Yaw caused by vehicle-borne vibration source, ground vibration source and resonance point of the equipment, the foundation stability of load equipment under dynamic condition is realized, which provides a condition for solving the problem of high precision and stability tracking which is greatly influenced by vibration. The vibration isolation system can realize the vibration isolation efficiency of 90% in the range of 20 Hz to 2000 Hz under the condition of 60 Km/h three-class highway with 1.5 t photoelectric load, and restrain the deflection caused by unbalance torque and vibration source offset effectively. It can be concluded that the quasi-zero stiffness vibration reduction and isolation combination design can effectively suppress the vibration of the large-scale vehicle-mounted optic-electronic equipment under the condition of moving platform.