Recent advances in micro-vibration isolation

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Review

Recent advances in micro-vibration isolation Chunchuan Liu a, Xingjian Jing n,a,b, Steve Daley c, Fengming Li d a

Department of Mechanical Engineering, Hong Kong Polytechnic University, H.K. PR China Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, PR China c The Institute of Sound and Vibration Research, University of Southampton, UK d School of Mechanical Engineering, Beijing University of Technology, Beijing, PR China b

a r t i c l e i n f o

abstract

Article history: Received 17 March 2014 Received in revised form 13 May 2014 Accepted 20 October 2014

Micro-vibration caused by disturbance sources onboard spacecraft can severely degrade the working environment of sensitive payloads. Some notable vibration control methods have been developed particularly for the suppression or isolation of micro-vibration over recent decades. Usually, passive isolation techniques are deployed in aerospace engineering. Active isolators, however, are often proposed to deal with the low frequency vibration that is common in spacecraft. Active/passive hybrid isolation has also been effectively used in some spacecraft structures for a number of years. In semi-active isolation systems, the inherent structural performance can be adjusted to deal with variation in the aerospace environment. This latter approach is potentially one of the most practical isolation techniques for micro-vibration isolation tasks. Some emerging advanced vibration isolation methods that exploit the benefits of nonlinearity have also been reported in the literature. This represents an interesting and highly promising approach for solving some challenging problems in the area. This paper serves as a state-of-the-art review of the vibration isolation theory and/or methods which were developed, mainly over the last decade, specifically for or potentially could be used for, micro-vibration control. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Micro-vibration Vibration isolation Spacecraft applications Nonlinear stiffness and damping

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Passive isolation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. A passive viscous damping strut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Folded continuous beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Others. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Active isolation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Active damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Intelligent control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Active strut systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Active six-axial hexapods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Active–passive hybrid isolation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Active–passive hybrid struts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Corresponding author. E-mail address: [email protected] (X. Jing).

http://dx.doi.org/10.1016/j.ymssp.2014.10.007 0888-3270/& 2014 Elsevier Ltd. All rights reserved.

Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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4.2. A hybrid strut with hexapod configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.3. Hybrid isolation platforms with smart material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.4. Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Semi-active isolation techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.1. Electrorheological fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.2. Magneto-rheological fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5.3. Novel or smart materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Emerging isolation methods by employing nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6.1. Nonlinear damping isolation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6.2. Nonlinear stiffness isolation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Conclusions and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1. Introduction The term micro-vibration usually refers to low-level mechanical vibration or disturbance in the microgravity environment, typically occurring at frequency from less than 1 Hz up to 1 kHz [1]. Therefore, micro-vibration can be created by mechanical systems located on spacecraft, for example, cryocoolers, thrusters, mobile mirrors, solar array drive mechanisms, and reaction/ momentum wheel assemblies [2–5]. Due to very tiny environmental damping in aerospace, micro-vibration could persist for a long time. This will deteriorate the working environment of onboard instruments, for example, downgrading the precision of sensitive optical telescopes or the positional accuracy of space cameras. A typical example can be seen in the space interferometry mission (SIM), where a space-based interferometer with astrometry and imaging capability must meet an extremely harsh positional tolerance (of order of 1 nm across the entire 10 m baseline of the structure) to achieve astrometry requirements [6]. The main disturbance source of on-orbit spacecraft is often mechanical spinning devices such as reaction and momentum wheel assemblies [6–13]. Wheel assemblies are widely used in space technology to provide attitude control and momentum stability of a spacecraft. In general, the vibration disturbance from reaction and momentum wheels are mainly caused by static imbalance, dynamic imbalance, and bearing imperfection etc [8]. Static imbalance is caused by the offset of the center mass of the wheel spin axis, where disturbance resonant frequencies are equivalent to spinning frequencies of the wheels. Dynamic imbalance results from the misalignment of the principal axis and the rotating axis on the wheels, while bearing disturbances are caused by irregularities in balls, races and cage etc. [11]. Dynamic forces and moments generated by the imbalance and imperfection of rotating wheels can propagate in spacecraft structures. The disturbance resonant frequencies caused by the dynamic imbalance are smaller than the rotating frequencies. Compared to bearing imperfection, the imbalance of the flywheels has more impact on the generation of low frequency disturbance [11]. The main micro-vibration of onboard satellites focuses on the frequency range from 0.1 Hz to 300 Hz. Disturbances above 30 Hz are classed as high frequency whilst micro-vibration that occurs below this is deemed to be in the low frequency region [14]. The high frequency disturbance is mainly caused by momentum wheel assemblies, and low frequency micro-vibration by the reaction wheel assemblies. Due to rotating machines and their noise, micro-vibration could contain very different frequency components including harmonic, random, narrowband and broadband [15]. With the development of modern spacecraft with the characteristics of light-weight, flexible, large span and high precision, the influence of micro-vibration on the on-orbit spacecraft becomes more and more significant. Many vibration isolation methods have been designed to protect high precision payloads from the impact of micro-vibration in onboard spacecraft. Typical isolation systems for space optical telescopes, referred to as vibration isolation and suppression system (VISS) and satellite ultra-quiet isolation technology experiment (SUITE) having been developed and utilized in spacecraft, can be seen in [16,17]. The VISS and SUITE consisting of six struts in a hexapod configuration are used as the support of the sensitive payloads or the disturbance sources of onboard spacecraft. Many other isolation systems are designed as support structures of payloads, which can isolate the micro-vibration transmitted from disturbance of the spacecraft to the sensitive payloads. The suppression of micro-vibration in the propagation path of disturbances has also been studied. Overall, four kinds of isolation techniques can be classified for isolation of micro-vibrations of on-board spacecraft, e.g., passive, active, active–passive hybrid, and semi-active isolation. In this review, these four types of isolation methods will be discussed, respectively, including the isolation mechanism and characteristics, configuration design and features, advantages and disadvantages etc. Noticeably, a special section is given thereafter for some novel and emerging isolation methods by exploring nonlinear dynamics and benefits in vibration control. This review will serve as a state-of-the-art (although not comprehensive) summary of the vibration isolation theory and/or methods, that have focussed on microvibration control over the last decade.

2. Passive isolation techniques Passive isolation techniques are commonly used in aerospace engineering providing high performance and stability, and requiring no external power [18–21], where the typical passive vibration isolation system is shown in Fig. 1. Vibration Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 1. Typical diagram of passive vibration isolation systems. Implementation of passive vibration isolation needs not external power; but isolation performance in low frequency range is often not good in traditional passive isolation systems.

Fig. 2. Cross-section of the damper in the 1.5 Hz isolator struts. Source: Davis et al. [19].

energy can be dissipated by passive damping, and high frequency disturbances cannot be transmitted through installed isolators. A main part of passive isolator design is the inclusion of a high performance damper such as viscous fluid dampers [18,19] or visco-elastic composite dampers [21]. In general, the isolation performance is better if the fundamental or resonance frequency of the isolator is lower.

2.1. A passive viscous damping strut Davis et al. [19] designed a passive viscous damping strut (D-strut) with very low fundamental frequency (1.5 Hz) to isolate disturbance from a Honeywell HM-1800 reaction wheel assembly (RWA). The goal of the designed low frequency isolation device is to reduce the dynamic forces and torques emitted by the RWA with the frequency band from 2 to 300 Hz. The critical part of the D-strut is the passive damper, which can attenuate the disturbance in the frequency band and prevent high amplification at the isolator fundamental frequency. The cross-section of the damper in the 1.5 Hz isolator strut is shown in Fig. 2. The damper is composed by a viscous fluid flowing through a controlled annulus between two hermetically sealed chambers. Mechanical energy can be dissipated in the shearing of the fluid as it is pumped through the annulus by the vibratory displacements. The very important design in Fig. 1 is the secondary bellows, which enables the isolator to be tuned to provide improved performance. Due to the design of the secondary bellows, the isolator is the three-parameter configuration other than conventional two-parameter configuration, which greatly improves isolation performance. The dynamic model schematic diagram and transmissibility of the three-parameter and two-parameter isolators are shown in Fig. 3. The three-parameter configuration isolator is the critical design different from the previous passive isolators, which has high isolation performance not only at high frequencies but also at low frequency. As shown in Fig. 3, the three-parameter isolator is modeled with one spring in series with the damper, which is different from the conventional two-parameter system. The transmissibility of the three-parameter isolator with different damping factors show that it can provide low Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 3. Isolation performance and isolation models: (a) displacement transmissibility comparison between three-parameter and two-parameter isolators; (b) two-parameter isolators; and (c) three-parameter isolators. Source: Davis et al. [19].

Fig. 4. Low frequency flexible space platform consisting of folded continuous beams. Source: Kamesh et al. [20].

amplification factors at resonance. Moreover, the three-parameter isolator also provides much better isolation at higher frequencies than that of conventional two-parameter isolators. 2.2. Folded continuous beams Kamesh et al. [20] designed a low frequency flexible space platform consisting of folded continuous beams for mounting of a reaction wheel assembly, which can be effectively used to isolate the disturbance from the reaction wheel emitted into high precision payloads of onboard spacecrafts. To implement passive vibration control, the energy dissipative components such as visco-elastic materials, springs, soft materials and hydraulic dampers are commonly used in the traditional passive isolators [21]. But these passive energy dissipative components are influenced much by temperature, especially in the aerospace environment. Low frequency flexible space platforms consisting of folded continuous beams such as in [20] can provide a good suppression effect above the frequency 30 Hz without using additional energy dissipative devices as shown in Fig. 4. In the folded-beam isolator, the static stiffness is enough to support the wheel assembly, but the dynamic stiffness Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 5. Typical diagram of active vibration isolation systems: System stiffness and damping can be adjusted through various active feedback control strategies to improve isolation performance especially in the low frequency region, but external power, sensors and signal processing would be required.

is very small. Therefore, it can provide vibration isolation with a low resonance frequency. However, in the micro-vibration environment, aerospace structures are subjected to micro-gravity, where the supported static stiffness can also be designed very small. This would be beneficial to system design with a low equivalent stiffness. 2.3. Others Vaillon and Philippe [15] used elastomer material compatible with the space environment to design a passive isolator for the reaction flywheels. Compared with conventional spring dampers, the elastomer material is simple and can obtain improved isolation performance. From the experimental study, the attenuation performance of the elastomer material isolator exceeds 40 dB at the resonance and 40 dB above 50 Hz. They also employed piezoelectric wafers and dissipative shunt circuit to replace conventional damping to dissipate vibration strain energy [15]. However, the attenuation effect is not much better than that of conventional damping, and a great amount of piezoelectric wafers are needed for large structures. Zhang et al. [14] presented a cantilevered soft suspension system as supporting configuration of a flywheel assembly. Compared with traditional rigid suspension design, soft suspension design provides significant reduction of wheel-induced medium and high frequency vibration (over about 100 Hz). Passive vibration isolators have the characteristics of high reliability performance and no energy transmission, which is very satisfactory for the aerospace dynamic environment. However, low frequency vibration control effect is often not very good by using pure passive isolation techniques. Low frequency disturbance is also very important in spacecraft structural vibration, especially in modern flexible and large span spacecraft. Therefore, it is still a challenge to employ pure passive vibration isolation techniques to isolate low frequency micro-vibration onboard spacecraft. In order to suppress microvibration in the low frequency region, many researchers have investigated active vibration control techniques [22–30]. 3. Active isolation methods In active isolation techniques, external actuators and sensors are commonly used to provide control force and feedback signals such that good isolation can be obtained in the low frequency region based on different active control strategies. As shown in Fig. 5, system stiffness and damping can be adjusted to improve isolation effectiveness through active feedback control. In the literature, active damping techniques and active anti-phase control techniques etc are commonly employed to control micro-vibration of onboard crafts [15]. An active strut technique for micro-vibration isolation has been developed for a long time [26–28]. In order to suppress micro-vibration of multi-degree-of-freedom systems, active isolation platforms have also been designed [29–31]. 3.1. Active damping The active damping technique for micro-vibration control onboard satellites has been proposed in [15,22–24]. In this work, active damping is obtained by a positive position feedback on pairs of collocated sensors and actuators, which are produced by smart materials such as piezo-ceramic wafers. The dominant modes of satellite structures below 100 Hz can be damped using the local positive position feedback between sensors and actuators, and the attenuation for the best controlled modes can be improved by about 10–20 dB. The active damping isolation technique is suitable for narrow-band control, where the modal control strategy is used to achieve the damping at the given structural mode [15]. Although many modes can be damped by active damping methods, some dominant modes attenuate very little when using the positive position feedback control method above. In the active anti-phase control technique, the distributed actuators and sensors are used to implement vibration attenuation at special locations on spacecraft, i.e. the location of sensitive optical devices. The smart sensors and actuators are distributed at some specific locations, which are different from those addressed through the application of active damping. Through anti-phase compensation for the dynamic responses, the vibration Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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attenuation can be improved by about 30–40 dB [22]. The effect of the active anti-phase control technique is very good when the disturbance is harmonic for example the disturbance of a reaction wheel unbalance. Advanced composite materials with an embedded sensors and actuators (ACESA) vibration control system based on active damping techniques has been used for vibration isolation for large optical support structures [23]. The ACESA control system is composed by three tubular active members: embedded zirconate-titanate (PZTs) wafers in each strut allowing control of deformation axially and in two bending planes, a nine-channel digitally programmable with analog control electronics unit, and 400 V drive electronics for each active member [23]. Through the control strategy design, the active damping can be obtained at all modes in the frequency region up to 100 Hz. The fundamental mode damping can achieve 20%, which is about two orders of magnitude greater than the natural damping level. Moreover, piezoelectric actuators have also been used to design an image stability system for a solar optical telescope, which can minimize the jitter of image for frequencies lower than 14 Hz [24]. 3.2. Intelligent control An intelligent control strategy called the adaptive neural control (ANC) method is employed in the micro-vibration control design of large space structures in [25,26], where self-optimization, on-line adaptation and control recovery can be carried out in the ANC method. In the ANC program, an efficient and completely autonomous neural network feed-forward control strategy for the case of broadband disturbances must be developed. It is also suitable for changing conditions, and minimizing the introduction of external transmitted signals [25]. The adaptive control and tapped delay lines with static neurons performing system identification is the main feature of the ANC system, which can meet the dynamic environment of persistent plant disturbances and instrumentation noise and require no prior modeling information. It is important to develop practical neural controllers for advanced space structures in vibration control. Combining six actuation channels of the existing ACESA struts [22], an adaptive neural controller can attenuate about the 25–55 dB in the tonal disturbance of the frequency band 10–15 Hz. It suggests that micro-vibrations in precision structures can be reduced by adaptive cancellation systems without prior modeling information, and certain failures in actuators or sensors can be successfully circumvented in the ANC method [24]. 3.3. Active strut systems Vaillon et al. [26] presented a prototype of an active strut to isolate micro-vibrations along propagation paths of the disturbance in truss structures. The disturbance of micro-vibration can transmit through the primary truss structures of the satellite to the sensitive payloads. Embedding the smart material into the satellite truss structure, and using the active control algorithm, the micro-vibration onboard of the satellites can be attenuated greatly at specific frequencies. From the test, good isolation performance was demonstrated whereby the peak acceleration of the isolated part of the flexible truss structure was attenuated in excess of 25 dB in the frequency range from 40 to 160 Hz [26]. The active vibration system based on the active isolation fittings (AIFs) had been developed, which can be used to assemble into multi-degrees of freedom isolation systems. Each AIF strut is composed by a piezoceramic stack actuator and accelerometers at top and bottom. The piezoceramic stack actuator is preloaded with springs, and thus it is a stiff actuator with no passive isolation capability [27]. A purely active vibration control system is presented to provide the isolation of micro-vibration under the micro-gravity environment, which was developed for experiments on the international space station [28]. 3.4. Active six-axial hexapods An active isolation platform has been developed to implement micro-vibration attenuation of high precision instruments for instance space-based optical interferometers [29,30] and solar optical telescopes [24]. The Stellar Interferometer Mission requires 10-nm level stabilization of optical elements distributed across a 10-m flexible structure under the disturbance of the spinning reaction wheel assemblies [29]. The six-axial hexapod vibration isolation platform with each strut having the active optical control strategy can present vibration attenuation for six degrees of freedom not only in the high frequency range but also in the low frequency region. The active vibration control is performed by a voice coil actuator. The isolation platform can be used as the mounts of the payloads or the disturbance source, which consists of six identical active struts in the hexapod configuration as shown in Fig. 6. Each active strut contains a diaphragm allowing motion only in the axial direction, where a voice coil actuator is in parallel with the diaphragm. The reaction wheel attitude control torques can be passed through the diaphragm. Each strut is connected to the structure in series with an axial force sensor and two axially cross-blade flexures serving to reduce coupling between struts [29]. The detailed active strut design is described in Ref. [30]. Ideally, only the axial force can transmit through the strut. However, each strut also passes nonaxial vibrations due to imperfect cross-blade flexures, which creates the coupling between the struts. The feedback loop is single input–single output, and each loop is decoupled from the other five loops. Combining the fringe tracker optical control systems [31], the six axial hexapod active isolation platform can satisfy the requirement of 10 nm level stabilization for the space-based optical interferometers. Except for the adaptive control method, many other control algorithms such as classical, multivariable, robust control approaches can be chosen for the control of the six-axis hexapod isolation system. The decoupled design method is used in Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 6. The six-axis hexapod active isolation platform and cut away view of a single active strut. Source: Hauge and Campbell [33].

Fig. 7. Soft isolation Stewart platform with six active actuators. Source: Preumonta [34].

the process of six-axial controller design that the full six-axis controllers are combined by the designed single-axis controller [32]. The linear quadratic Gaussian (LQG) control method is used to design the controller in the active six-axial isolation platform as shown in Fig. 6. Due to the coupling effect existing among the struts in the six-axis hexapod isolation platform, the isolation effect will become poor. The main cause of the coupling among the struts is the imperfect cross-blade flexures in the strut. Hauge and Campbell [33] designed an improved six-axis hexapod isolation platform for the spacebased payloads. The two-sensor control architecture is designed for each active strut other than the traditional one-sensor control. Compared with traditional six-axis hexapod isolation platforms, the active struts with two-sensor are suitable for the performance and robustness requirement of new-type space optical interferometers which can achieve vibration attenuation about 3 dB up to 1.5 Hz and 20 dB in frequency region for 5–20 Hz [33]. Moreover, Preumonta et al. [34] designed the stewart isolation platform based on the active control method for micro-vibration in the micro-gravity environment as shown in Fig. 7. In the active isolation stewart platform, micro-vibration in the frequency region from 5 to 400 Hz can be well reduced, and a vibration attenuation of about 40 dB in the 50–200 Hz region can be obtained. 3.5. Problems Micro-vibration of spacecraft structures can be effectively controlled by active vibration methods especially in the low frequency range. Different active control methods can be developed for this purpose [117]. However, in the implementation of active vibration control, external energy is required for driving numerous actuators and sensors. It may suffer serious spillover (e.g., actuator saturation) and stability problems, and obviously increases the weight of payloads. Therefore, in combining the advantages of pure passive isolation and active isolation techniques, active–passive hybrid isolation methods could be an alternative way to solve micro-vibration problems of on-orbit spacecraft [35–38]. 4. Active–passive hybrid isolation techniques Active–passive hybrid isolation methods are usually developed with the one part either active or passive as a master system and the other part as a slave independently but being combined together to achieve an overall objective. This could be used to roughly differentiate from semi-active isolation where some components of an isolation system will be actively controlled. As shown in Fig. 8, the passive isolation system and active control system in a typical hybrid vibration isolation system are carried out simultaneously. Micro-vibration of spacecrafts in the whole frequency domain (including low frequency Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 8. Typical diagram of active–passive hybrid vibration isolation systems, which combine the advantages of both the active and passive isolators, and could minimize their disadvantages, where the one part either active or passive is as a master system and the other part as a slave independently but being combined together to achieve an overall objective.

Fig. 9. Schematic of second-generation AD-Strut. Source: Davis et al. [36].

and high frequency) can be well suppressed through some active–passive hybrid isolators. Hybrid isolation systems combine the advantages of both the active and passive isolators, and could minimize their disadvantages in practice. Some active– passive hybrid struts and hybrid isolation platforms have been developed for micro-vibration isolation of onboard spacecrafts.

4.1. Active–passive hybrid struts Davis et al. [35] designed a hybrid D-strut based on a traditional D-strut as shown in Fig. 2 with active control, which can be used to suppress micro-vibration of high performance optical payloads. The advantage of hybrid isolation is that the passive part is designed for dissipating vibration energy with viscous damping and the active part is designed to degrade the disturbance in low and high frequency regions [35]. Even if the active control system is not powered, the microvibration of sensitive instruments can still be reduced with the passive part. The second generation of hybrid D-struts combining the viscous damping D-strut with electromagnetic actuators was designed in 1995 as shown in Fig. 9, which can be referred to as AD-strut [36]. The passive damping part consists of an intervening damping orifice, primary and secondary bellows. The primary bellows are connected to the payload on one side and to the base on the other side, and the secondary bellows are linked to the base on one side and is free at the other end. Passive damping results from the viscous shear in the orifice with fluid through between the two bellows. The active device is attached to the free ends between the secondary bellows and base. The linear voice coil is used as the active actuator which can produce the Lorentz force with a linear relationship to applied current over a wide frequency range (0–20 kHz). The force constant variation can be obtained less than 1% by proper magnetic design, which is dependent on stroke and current. The active part is used to enhance the low-frequency isolation performance of the isolator by lowering the break frequency of the passive system through degrading its stiffness. In the approximate lumped parameter model of the hybrid AD-strut as shown in Fig. 10, an active control force along the axial direction can be provided by the voice coil, where it is different from the three-parameter model of the pure passive damper (as shown in Fig. 4). The hybrid AD-strut isolator can be used for isolation of microgravity, spacecraft disturbance and payload [36]. The hybrid AD-strut system can be designed as a stable ultra-quiet base for high precision pointing payload in satellites or aircraft, and it has obvious advantages over pure active or passive isolation systems, which can be effectively utilized to reduce vibration of entire payload racks produced by forces and torques from machinery or astronauts. If the external power fails, the hybrid control system still shows good performance of vibration suppression. The isolation effect in microgravity environment can achieve about 10–30 dB of acceleration attenuation from 0.1 to 300 Hz [36]. Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 10. Lumped parameter model of AD-strut. Source: Davis et al. [36].

4.2. A hybrid strut with hexapod configuration Another active–passive vibration isolation platform was developed by the Jet Propulsion Laboratory for space borne interferometry missions [37]. The isolation system consists of six active/passive hybrid struts in a hexapod configuration. Each hybrid strut contains a voice coil actuator in parallel with a soft spring, which is a passive isolator with 3 Hz break frequency. Even if the active power fails, the isolation system is still operated by the passive part. The feedback sensor used for active vibration control is the load cell mounted in the hybrid strut, which is not suitable for significant payload wiring harness stiffness. It can be effectively used to isolate the disturbances from the reaction wheels and momentum gyroscopes propagated to the satellite. However, it is difficult to use as a stable isolation platform for micro-vibration of high precision optical and communication devices for large wiring harnesses. An active–passive hybrid isolation platform referred to as vibration isolation and suppression system (VISS) was designed based on the new-type hybrid isolation strut above, which was employed to protect high precision payloads from on-board disturbances (Fig. 11) [16]. The new-type of hybrid isolation strut can provide active control force and passive damping, but the design and configuration is different from the conventional AD-strut in Ref. [36]. The key component of the VISS system is a new-type hybrid D-strut, where the cross-section of the hybrid D-strut is shown in Fig. 12. Compared with the AD-strut in Fig. 9, the configuration design of the new-type hybrid D-strut is compact and practicable. The hybrid D-strut is a singleaxis device operating along the stinger, which has the capability to endure a poor dynamic environment without obvious isolation performance degradation. The passive part is composed by viscous fluid in two primary bellows, which are interconnected by a narrow orifice between the payload and the base [16]. The main features of the passive part of the isolation system are that the damping is independent of stiffness, has no wear mechanism and exhibits large stroke. The passive isolation part is designed to soften the isolation system with a low break frequency, and can obtain good isolation over a broad frequency region. The voice coil motor is used for the active part, which is connected to the stinger and primary bellows [16]. The carbon fiber composite material is employed to produce the voice coil bobbin, which has the features of high strength and excellent thermal conductivity. The isolation performance of the VISS as the support for space optical telescopes can achieve about 20 dB over the frequency region from 5 Hz and above. A low cost passive and active hybrid isolation system for micro-vibration suppression of space high precision payloads is developed as the Satellite Ultra-quiet Isolation Technology Experiment (SUITE), which was designed and manufactured by CSA Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 11. VISS hexapod configuration with model of MWIR telescope. Source: Cobb et al. [16].

Fig. 12. Cross-section of the new-type hybrid D-strut. Source: Cobb et al. [16].

Engineering, Inc. [17]. Similarly, the SUITE isolation system is composed by six active–passive hybrid isolation struts arranged in the Stewart configuration to provide isolation in six degrees of freedom of sensitive payloads. Each strut in the SUITE system contains passive and active elements, different with the hybrid D-strut in the VISS system as shown in Fig. 13 [38]. The passive damping is provided by the viscoelastic damping material laminated connected to the flexures, and the active control force is provided by the piezoelectric ceramic stacks mounted on the geophone. The piezoelectric ceramic stack is used as the active actuator, where the hybrid struts have much larger stiffness than that of the VISS system. Due to the system stiffness, the passive isolation performance of the SUITE system is less effective than that of the VISS system. The technical objective of the SUITE system is to achieve attenuation of vibration transmissibility from base to payload with 20 dB in the frequency region from 5 Hz to the above [17,38]. 4.3. Hybrid isolation platforms with smart material Another active–passive isolator for the micro-vibration of satellites is proposed with the folded continuous beams combining with piezoelectric actuators and sensors as shown in Fig. 14. It is used to isolate micro-vibration from the reaction wheel assemblies in six-degrees-of-freedom [39]. The passive isolation is performed by the folded continuous beam configuration, which has a low dynamic stiffness. A Low corner frequency can be obtained by increasing the number of folds and decreasing the thickness of the vertical beams. The piezoelectric layer materials bonded on the vertical beams are Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 13. Active–passive isolation struts in SUITE. Source: Anderson [38].

Fig. 14. Hybrid isolator consisting of folded continuous beams and smart material. Source: Kamesh et al. [39].

chosen as active actuators and sensors as shown in Fig. 15, and the optimal control algorithm is employed to design the control strategy. The disturbance of harmonic and impulse loadings can be well suppressed by the active isolation system. Moreover, a similar low frequency flexible intelligent isolation platform is used for micro-vibration isolation of the onboard reaction wheel and momentum wheel assemblies [40]. It is shown that the passive isolation part is effective to isolate high frequency micro-vibration of momentum wheel assemblies, and the intelligent active part is effective to suppress low frequency disturbance of reaction wheel assemblies. 4.4. Problems Active–passive hybrid isolation systems combine the best of both the passive and active isolation techniques. They are effective to isolate micro-vibration of on-orbit spacecrafts both in high and low frequency range. However, implementation of active–passive isolation systems still requires many other accessory devices such as sensors, actuators, feedback control and power systems, which share the same drawbacks as pure active isolation systems. Semi-active isolation methods could solve some of the problem here, but the most preferable approach would be novel passive isolation systems with advantageous isolation performance in practice. 5. Semi-active isolation techniques Semi-active isolation is an effective approach for micro-vibration isolation/suppression in aerospace engineering. It could provide a much better solution for vibration isolation than pure passive isolation systems, and could be more reliable than pure Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 15. The typical piezoelectric layer beam. Source: Kamesh et al. [39].

Fig. 16. Typical diagram of semi-active vibration isolation systems, which could provide much better isolation performance than pure passive isolation systems, and be more reliable than pure active isolation systems, where tunable system stiffness or damping can be implemented through active control techniques in the context of passive vibration isolation.

Fig. 17. Cross section of an ER-fluid variable damper. Source: Onoda et al. [48].

active isolation systems, and the tunable system stiffness or damping can be implemented through active control techniques in the context of passive vibration isolation as shown in Fig. 16. Usually, semi-active methods are stable even if active elements are in illcondition. Some typical semi-active methods with different mechanisms have been developed for vibration suppression of space truss structures, for example, semi-active systems with hysteretic variable stiffness system in [41–43], variable-friction devices in [44], and dashpot type variable viscosity dampers in [45]. So far, semi-active techniques using electrorheological fluids, magnetorheological fluids, and some smart materials have been extensively investigated. 5.1. Electrorheological fluids As a variable damper, electrorheological (ER) fluids have caught much attention in the literature, where damping features can vary according to a change of the applied electric state strength [46]. The characteristics of ER-fluid dampers are modeled and Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 18. Equivalent model of the ER-fluid variable damper. Source: Onoda et al. [48].

Fig. 19. Block diagram for semi-active vibration suppression experiments for truss structures. Source: Oh et al. [49].

measured in detail in Ref. [47]. An ER-fluids based variable damper is designed as shown in Fig. 17, which is composed by two variable-volume chambers filled with particle-dispersion type of ER-fluids and a bottleneck connecting them [48]. The ER-fluids damper can be used in a vacuum space environment, since it is sealed by bellows. The damping characteristics can be varied as the characteristics of the ER-fluids between the electrode in the bottleneck and the casing of the bottleneck change according to the external voltage applied to the electrode. A simple mathematical model of the ER-fluid dampers was proposed [48], which consists of two springs, a variable coulomb frictional element and a viscous damping element as shown in Fig. 18. Some semi-active on–off control laws are employed to suppress vibration of space truss structures. It is shown that all the semi-active on–off control laws are effective to control the single mode vibration. It is also shown that the semi-active vibration strategy is effective both for free and forced vibration under random excitation. Oh et al. [49] presented a liquid-crystal type ER-fluid variable damper to isolate the vibration of space truss structures in a semiactive manner, which is a single-phase ER-fluid with the characteristic like Newtonian fluid. The configuration of the damper and damping variation principle are basically the same as that for the particle-dispersion type ER-fluid variable damper as shown in Fig. 17. The mathematical model is also the same as that of the particle-dispersion type ER-fluid variable damper as shown in Fig. 18. However, the variation of the variable viscous damping element is much larger than that of the variable Coulomb frictional element as changing the external applied voltage, which is different from that of the particle-dispersion type ER-fluid variable damper in Ref. [48]. Semi-active on-off control laws have been derived for the liquid-crystal type ER-fluid variable damper, and the experiment on the semi-active vibration suppression for the ten-bay space truss structures was performed as shown in Fig. 19. It indicates that the liquid-crystal variable damper can be effectively used to suppress vibration of space truss structures, especially for large amplitude vibration. The damping performance caused by semi-active control laws is much better than that achieved by the optimally-tuned passive control [49]. In order to improve pointing precision of spacecraft payloads, a semi-active isolator filled with liquid-crystal type ER-fluid is designed to suppress high frequency disturbance of onboard momentum wheels in [50]. The liquid-crystal type ER-fluid with nematic phase is fulfilled in the two variable volume chambers connected to each other by a cylinder. Two control strategies are employed to implement the semi-active control of the ER-fluid isolator, which can provide much better isolation performance than that of a pure passive system. However, the disturbance in multi directions and different type of excitations of momentum wheel assemblies are not investigated with semi-active ER-fluid variable isolators, and sufficient power is required in the operation of ER-fluid based components. Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 20. Cross sections of the electromagnets: (a) the conventional electromagnet and (b) the designed electromagnet. Source: Oh [52].

5.2. Magneto-rheological fluids The main features of the MR fluid are essentially similar to those of the ER fluid. MR fluids can have superior and stable properties in a wide temperature range (
40 to 150 1C) and the control of MR fluids is easy to implement in practice without too much external power [51,59]. Therefore, MR fluids have been extensively studied and used in various semiactive vibration control systems. A magneto-rheological (MR) fluid variable damper with semi-active vibration control laws is designed to suppress vibration of space truss structures in [51]. The basic configuration and mathematic model of the MR fluid variable damper are the same as those of the ER fluid ones as shown in Figs. 17 and 18. From the experimental investigation on vibration suppression of ten-span truss structures, the disturbance can be well suppressed by the MR fluid variable damper, and the isolation performance of the semi-active MR fluid damper is much better than that of the ER fluid damper [51]. The MR fluid based semi-active isolator with supplementary permanent magnets is also presented to isolate micro-vibration of space sensitive instruments due to the on-orbit momentum wheel and reaction wheel assemblies. The best permanent magnet arrangement can also provide the prevention of the alignment shift for spacecraft equipment as a result of shock and vibration during lift-off [52]. For example, in [53], a novel MR fluid variable damper is designed to control vibration of space flexible structures. Compared with conventional MR and ER fluid variable dampers, the new one can show both semi-active and optimal passive damping characteristics. The novel designed electromagnet consists of a permanent magnet and blocks with various gap sizes as shown in Fig. 20. With the novel electromagnet design, the semi-active control can be quickly implemented with low power consumption, with optimal passive damping in fault conditions. Moreover, MR fluids can be flexibly used Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 21. (a) The schematic structure of the MrEPI and (b) its equivalent mechanical system. Source: Zhu et al. [57].

for different isolation tasks such mount or shock absorber systems in practice [54,55]. Recently, Zhu et al. [56,57] designed an MR fluid damper allowing independently adjustable stiffness and damping by means of the semi-active control strategies, which consists of an adjustable nonlinear pneumatic spring and a MR damper as shown in Fig. 21. Through passive adjustment of the pneumatic spring and semi-active control of the MR damper, favorable vibration isolation performance can be achieved, with flexibility in switching between different vibration control modes. MR fluid dampers are highly nonlinear elements and thus the control of MR fluid dampers is an interesting topic. A novel MR fluid damper is effectively used to suppress vibration of a Macpherson suspension system based on the H1 robust control theory, which can be adopted to deal with model uncertainty and implementation limits of the suspension system [58]. A nonlinear active vibration control methodology is used to design the semi-active control of MR fluid dampers for suspension systems, which employs an adaptive back-stepping technique with some H1 constraints [59]. From MATLAB/ Simulink results, both semi-active MR fluid controllers have good isolation performance for worse-case dynamic environments. The control of MR fluid dampers also depends on specific structure design of the damping system. Zhu et al. [60] reviewed the structural design for MR fluid variable dampers. Two MR fluid isolators with different structural design are investigated based on a non-dimensional analytical method as shown in Figs. 22 and 23, where the optimal MR control valve design can be determined by considering the magnetic flux conservation and mechanical flow characteristics in valve materials and MR fluids [61]. Compared with pure active and pure passive isolation systems, the semi-active MR fluid variable isolators have many advantages such as fast reaction time and very low power requirements. However, very few semi-active MR dampers are applied in space structures [53] due to the weight increase. 5.3. Novel or smart materials A variable damping isolator based on the bio-metal fiber (BMF) valve is proposed to isolate vibration of optical instruments of spacecrafts from the disturbance of reaction wheel assembly in [62]. The variable damping can be operated by opening and closing the valve through the electric current in the bio-metal fiber, which is produced by the Ti–Ni shape memory alloy. Compared to the conventional variable damper such as ER-fluid variable dampers, the variable-damping BMF valve isolator consumes less electric power. A new semi-active control strategy is thus proposed to suppress the chattering effect caused by sudden variation of damping force in semi-active isolation system to enhance the pointing performance of the payloads [63]. The light weight semi-active isolators are studied by using smart materials such as piezoelectric materials [64–67] and electromagnetic transducers [68–72]. The smart semi-active controllers consist of smart material actuators and switching shunt electrical circuits. Mechanical vibration energy can be dissipated in the process of switching between the open-circuit and resistive-circuit states [64]. Onoda et al. [73] presented an energy recycling technique with piezoelectric transducers embedded to implement semi-active vibration control of space truss structures. Structural vibration energy can be Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 22. Two structure configurations of MR control valve with one coil: (a) separate wire placement and (b) conventional wire placement. 1: annular duct; 2: valve core; 3: magnetic pole; 4: electromagnetic coil; 5: outer housing; and 6: nonmagnetic bobbin. Source: Zhu et al. [61].

Fig. 23. Different configurations for the MR control valve: (a) integral configuration and (b) bypass configuration. Source: Zhu et al. [61].

Fig. 24. The momentum wheel and isolator on observation satellites. Source: Makihara et al. [74].

converted to electric charge by the piezoelectric transducer and thus be suppressed with no energy dissipation and also no external energy required. Although the energy recycling semi-active vibration isolation system is good and stable, many sensors and a huge calculation cost for vibration control are required, especially for complex structures. The reliability of energy recycling semi-active systems could thus be affected by the sensitivity and reliability of sensors and circuit systems. Makihara et al. [74] presented a self-sensing method for an energy recycling semi-active vibration control system to suppress vibration of space truss structures as shown in Fig. 24. The self-sensing method can be operated with a Kalman filter rather than the conventional bridge circuit technique. The latter has a serious drawback for its highly sensitive variation of parameter. A novel energy recycling semi-active isolator is designed to suppress the micro-vibration of payloads in observation satellites from the momentum wheel assembly disturbance in [75]. The isolator consists of piezoelectric material and switch controlled passive circuits as shown in Fig. 25. Unlike conventional energy recycling semi-active isolator systems, this isolation system is simple and practical in that it requires only one velocity value for feedback rather than the full states of the isolation system and thus achieves improved reliability. The isolation performance of this isolator system is Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 25. Electric circuit of energy-recycling semi-active isolator. Source: Makihara et al. [74].

Fig. 26. Typical diagram of nonlinear vibration isolation systems: both stiffness and damping characteristics are nonlinear functions of system states, which could be inherent nonlinearity or intentionally-introduced nonlinearity, to drive system dynamic response in a desired nonlinear manner. Nonlinear vibration isolation techniques are more and more shown to have advantageous isolation performance over the linear counterparts at both low and high frequencies.

very good with respect to the disturbance of momentum wheels in medium and high frequency regions, and the attitude control with the momentum wheel assembly is not affected by the semi-active isolator. However, low frequency microvibration isolation performance of these semi-active isolation systems still need to be improved, and isolation platforms for six degrees of freedom are yet to be developed. 6. Emerging isolation methods by employing nonlinearity Some novel isolation methods have been developed based on nonlinear dynamics theory for example nonlinear damping, and quasi-zero stiffness. These isolation theories or methods have excellent isolation performance and good stability, and especially are suitable for vibration isolation over a wider frequency range or perform well at low frequency. Some earlier examples can be seen in [76–78] and some recent results can be seen in [79,83–85,118,119], where a systematic frequency-domain method for nonlinear analysis and design is established with the concept of nonlinear characteristic output spectrum (nCOS). A typical nonlinear vibration isolation system is shown in Fig. 26, in which both stiffness and damping characteristics are nonlinear functions of system states, which could be inherent nonlinearity or intentionallyintroduced nonlinearity, to drive the system dynamic response in a desired nonlinear manner. In order to design advanced micro-vibration isolators for modern onboard spacecraft, these isolation techniques could play an important role. 6.1. Nonlinear damping isolation techniques Viscous damping systems are widely used to design the passive isolators to suppress structural vibration. As the viscous damping is a linear function of velocity, the vibration amplitude at resonant frequency can be reduced by increasing the damping, while isolation performance over the whole frequency range (especially at high frequency) could degrade greatly. In order to solve the dilemma above presented by viscous damping, nonlinear viscous damping theory has been developed [79,83–90]. Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 27. Single degree of freedom isolation system with a cubic nonlinear viscous damping. Source: Jing and Lang [79].

Fig. 28. The experimental isolation system for the SDOF system with cubic viscous damping. Source: Laalej et al. [87].

The nonlinear viscous damping isolation system can be analyzed and designed with an output frequency response function (OFRF) approach [79–82]. Jing and Lang [79,83–85] proposed a novel design of nonlinear damping systems to suppress periodic disturbance. As shown in Fig. 27, which is a typical single degree of freedom (SDOF) vibration isolation system, the damping f(.) is designed as a cubic nonlinear function of velocity. The force transmissibility of the SDOF isolator can be derived using the OFRF method [83] and theoretical understanding of nonlinear damping in the frequency domain is given in [84]. The main characteristics of cubic nonlinear viscous damping are: (1) it has a minor effect on the transmissibility of SDOF vibration isolators over the frequencies which are much lower or much higher than the resonant frequency; (2) the force transmissibility nearby the resonant frequency region can be reduced with increasing the cubic nonlinear viscous damping [84,85]. The features of the cubic nonlinear viscous damping are very significant and suitable for designing ideal passive or semi-active vibration isolators, where the dilemma for the vibration isolators based on the linear viscous damping can be well resolved. The isolation performance of the cubic nonlinear viscous damping for force vibration and displacement vibration of SDOF systems are also studied by using the traditional Ritz–Galerkin approach in [86]. The results indicate that the vibration of the SDOF system can be much more effectively isolated by the nonlinear viscous damping than the linear damping in the whole frequency range, and the isolation performance under different loading conditions can also be improved by appropriately designing nonlinear damping coefficients. Although the analysis methods for the cubic viscous damper in [86] are different from the OFRF based method in [83,84], the main characteristics of the isolation performance of the cubic viscous damping are almost the same with these different approaches. Experimental investigation is carried out to verify the vibration isolation performance of SDOF systems with cubic nonlinear viscous damping based on the OFRF method as shown in Fig. 28 [87]. The implementation of the cubic viscous damping is very simple (with semi-active MR dampers), and the vibration in whole frequency region can be effectively reduced by the cubic viscous damper. Different cubic nonlinear damping is also studied in [88] for typical SDOF systems based on the OFRF. As shown in Fig. 29, the nonlinear damping can not only be a function of velocity but also displacement, which is different with the results Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 29. A SDOF isolation system with novel cubic nonlinear damping: (a) isolation model and (b) force transmissibility with different linear damping coefficients and different cubic order nonlinear terms. Source: Xiao et al. [90].

Fig. 30. MDOF systems: (a) MDOF system with one a cubic viscous damping and (b) multi-storey shear building model with fitted additional damping devices. Source: (a) Peng et al. [88] and (b) Lang et al. [89].

in [83,84,86–88]. The isolation performances with stiffness-related cubic nonlinear damping are very good both at resonant frequency and over a wider frequency range subjected to force and base excitations, while the isolation performance of the nonlinear viscous damping as a function of pure velocity is limited for the base displacement excitation [90]. Nonlinear viscous damping isolators are extended to the multiple degrees of freedom (MDOF) systems in [87,88]. The force transmissibility of MDOF systems in series with one cubic nonlinear viscous damper on the support is studied as shown in Fig. 30(a). Good isolation performance can be obtained nearby all resonant frequencies, but the MDOF system in series in [87,88] with only one cubic nonlinear viscous damping can be easily coupled within the system. The displacement transmissibility of a multi-storey shear building with nonlinear viscous dampers at each storey is investigated based on the OFRF as shown in Fig. 30 (b) [88]. It demonstrates that good isolation performance over wider frequency range around the fundamental frequency of the MDOF system under harmonic excitation and earthquake loadings can be achieved based on the OFRF concept. Due to the ease of implementation and excellent isolation performance as discussed above, cubic nonlinear viscous damping systems should be able to play a significant pole in micro-vibration isolation and control for onboard spacecraft. Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 31. SDOF system with a horizontal linear damper. Source: Tang and Brennan [93].

Fig. 32. Schematic representation of the simplest system with quasi-zero stiffness mechanism. Source: Carrella et al. [95].

Besides the nonlinear damping above, isolation systems with geometrical nonlinear damping is also studied in the literature [91]. The isolation performances of SDOF passive isolation systems with two different type of nonlinear damping are investigated in [92,93]. The first nonlinear viscous damper consists of a cubic viscous damping in parallel with the spring similar to that in [82–86]. The second damper is composed by a linear viscous damping perpendicular to the spring as shown in Fig. 31. Due to the geometrical configuration, the damping force due to the linear viscous damper is nonlinear. The isolation performances of these nonlinear dampers are much better than that with pure linear damping, and the isolation system with horizontal linear damping has some better properties than that with cubic nonlinear damping in displacement transmissibility [93]. The nonlinear damping characteristics can be designed by geometrical configuration, which provide good applications of using linear vibration systems to achieve nonlinear dampers with excellent isolation performance. Although the dynamic responses at or above natural frequency can be much attenuated with the nonlinear damping methods above, it may not be useful to isolate vibration at lower frequency. Therefore, isolation techniques with nonlinear stiffness have also attracted attention of researchers.

6.2. Nonlinear stiffness isolation techniques Vibration systems are composed by mass, stiffness and damping elements, and the latter two elements play a crucial role in vibration isolation performance. Besides the nonlinear damping techniques discussed in the previous section, many researchers have investigated nonlinear stiffness characteristics to improve isolation performance. It is very significant and meaningful to use these novel methods in the design of micro-vibration isolation systems for on-board spacecraft. To have a good isolation performance, system stiffness should be as small as possible. However, isolation performance of a vibration isolation system is always limited by the mount stiffness which should provide enough static load support. Recent advances indicate that an isolation system can be designed by exploring nonlinear stiffness to achieve low dynamic stiffness but high static stiffness to realize excellent isolation performance (e.g., quasi-zero or negative stiffness) [94]. Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 33. A QZS isolator in the static equilibrium position with different springs. Source: Carrella et al. [97].

Fig. 34. Schematic of the isolation system with QZS model. Source: Le and Ahn [98].

The quasi-zero-stiffness (QZS) mechanism is presented to design nonlinear stiffness vibration isolators with large static stiffness but very small dynamic stiffness, which can be achieved by combining positive stiffness elements with negative stiffness elements [95–97]. A simple QZS configuration design consists of three linear springs with one vertical spring connected with two inclined springs as shown in Fig. 32, where these springs can be linear or nonlinear. The negative stiffness effect can be obtained by installing springs in the horizontal direction as shown, which can counteract the effect of positive stiffness due to the springs in the vertical direction. With the mass loaded on the vertical spring, the static equilibrium position with the oblique springs in the horizontal direction can be determined by the geometry configuration. The zero stiffness at the static equilibrium position can be obtained by the optimum geometry configuration design. As the disturbance is applied in the vertical direction, the system dynamic stiffness will vary nearby the zero stiffness except for some ill conditions [95,96]. The dynamic stiffness of the QZS system changes in the process of system vibration, which is different from that of nonlinear viscous damping system. The force transmissibility and the jump-down frequency of the simple QZS system with different spring stiffness shown in Fig. 32 can be studied by the harmonic balance method [95]. The optimum geometry configuration design for the QZS isolator can be determined by the static equilibrium analysis as in Refs. [95,96], and the static equilibrium position configuration is shown in Fig. 33. The vertical spring is linear, and three kinds of springs are used in the horizontal direction as follows: the linear springs in case I, the linear springs with pre-stressed in case II, and the softening nonlinear springs with cubic polynomial nonlinearity in case III. The stiffness is zero for all the three different cases at the static equilibrium position, but the dynamic stiffness of the QZS isolator is governed by the oblique springs. The dynamic stiffness for case I increases rapidly as increasing the dynamic displacement, and can be bigger than the vertical spring stiffness. The dynamic stiffness characteristics of case II are much better than those for case I. The dynamic stiffness features with the nonlinear springs with softening characteristics are the best, and the jump-down frequency for case III is the lowest in the three cases. As the excitation force meeting certain conditions [97], the maximum transmissibility and jump-down frequencies for the three cases are always less than the maximum transmissibility and natural frequency of the linear system, and the isolation performance of the QZS isolator will always outperform corresponding linear systems. The nonlinear characteristics of the QZS system consists of two nonlinear pre-stressed oblique springs and a vertical linear spring are further studied in the reference [97]. Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 35. Schematic of geometric nonlinearity QZS system attached to a linear system. Source: Gatti et al. [101].

Fig. 36. Vertical QZS isolator using the flexures. Source: Kim et al. [103].

Fig. 37. Schematic of a QZS isolator with the buckled beams formed negative stiffness corrector. Source: Liu et al. [105].

Based on the concept of the QZS mechanism presented in Refs. [95–97], a novel vibration isolation structure composed by two negative stiffness structures (NSS) and a positive stiffness structure is designed to improve the isolation performance of vehicle seats in the low frequency region (0.5–10 Hz) as shown in Fig. 34 [98]. Through the appropriate design and analysis, the low equivalent dynamic stiffness can be obtained by the negative stiffness acting in parallel with the positive stiffness spring, and the resonant value of frequency response can be shifted to the left. It shows that the effective frequency region for the isolation system with the NSS is much larger than that without NSS, and the isolation performance for the system with NSS is much better than that without NSS subjected to various external loadings [98]. The primary resonance response characteristics of a QZS single degree of freedom system composed by cubic nonlinear stiffness and no linear stiffness with the change of the static force are studied with the harmonic balance method. As static force increases from zero, the system dynamic characteristics change from three states: firstly the purely hardening characteristic, then the mixed softening and hardening characteristic and finally a purely softening characteristic [99,100]. The dynamic characteristics for the specific two degrees of freedom system are studied with the average method, where the system consists of a linear system and a QZS nonlinear oscillator with the geometric configuration as shown in Fig. 35. As the mass in QZS system is much smaller than that of the linear system, the nonlinear system has little influence on the forced vibration of the linear system but some special nonlinear dynamic phenomena appear under the forced vibration of Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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Fig. 38. Isolation performance comparisons among different QZS isolators. Source: Sun et al. [116].

the linear system [101]. A QZS isolator based on the magnetic levitation system is designed and analyzed to isolate vibration of precision structures with low resonant frequencies [102]. Kim et al. [103] used the flexures and springs to design a QZS isolation system for a wide range of payload, which consists of vertical and horizontal springs, flexures and vertical gravity compensator as shown in Fig. 36. From the optimal parameter design, the QZS isolator suitable for payloads with different weight can be obtained. The QZS mechanism is the same as that in Refs. [95–97], but it provides the actual and novel configuration design of the QZS isolation system for the payloads. The active control technique is used to improve the isolation performance of the vertical QZS isolator designed in Fig. 36 [104]. The voice coil actuator applied on the horizontal direction provides the nonlinear active control to compensate for vertical vibrations. It shows that the isolation performance for the active QZS isolator is very good for the force transmissibility as well as the base disturbance. Liu et al. [105] employed two horizontal Euler buckled beams as the negative stiffness corrector to design the QZS isolator as shown in Fig. 37, which is different from using the springs in the previous studies [95–102]. The Euler buckled beams can provide negative stiffness to the positive supporting stiffness, and the isolation performance of this QZS isolator can be improved by adjusting the configurations of the beams. For excitation under certain conditions, the isolation performance outperforms the equivalent linear isolator in a wide range of working frequency. Xu et al. [106] used permanent magnetic springs to design the QZS isolator based on the QZS mechanism in [95–97], where the novel QZS isolation system can be adjusted with the change of loading mass. The isolation performance is much better than that of the equivalent linear isolator, especially in the low frequency range [106]. The QZS isolation systems above with low dynamic stiffness and high static stiffness have good isolation performance. Some other high-static-low-dynamic (HSLD) stiffness isolators have also been developed and studied based on different mechanisms [107–112]. These HSLD stiffness systems have, nonlinear stiffness characteristics so that the natural frequency can be shifted to left or jumped down by appropriate parameter design. The transmissibility will be reduced in a wide frequency region due to the lower natural frequency incurred by the nonlinear stiffness characteristics. [112–115]. Noticeably, isolation techniques combining the nonlinear damping and nonlinear stiffness could provide a much more powerful isolation system. A novel nonlinear vibration isolation system by employing a scissor-like structure is studied recently in [116], which demonstrates advantageous HSLD property by exploiting nonlinear benefits both in stiffness and damping but using only linear and passive elements as shown in Fig. 38. In micro-vibration environment onboard spacecraft, the gravity is almost zero, and thus the static supporting stiffness of isolation systems can be small. The excellent isolation performance of nonlinear stiffness and damping methods in HSLD systems above can be very helpful for the design of novel micro-vibration isolators to achieve high stability and excellent isolation performance both at low and high frequencies. 7. Conclusions and discussions With the development of aerospace engineering, the control of micro-vibration onboard spacecraft is a challenging and hot topic in the area. Different isolation techniques have been developed for micro-vibration suppression onboard spacecraft for a long time, including passive, active, active–passive hybrid, and semi-active isolation methods, and some emerging nonlinear isolation techniques. Passive isolation techniques are commonly used for high reliability and low cost both in development and energy. However, the micro-vibration in the low frequency region cannot be well attenuated with traditional pure passive isolators. Therefore, novel structures or materials are required for better isolation performance such as those emerging methods exploring nonlinear benefits in vibration control. Active isolation techniques can be effectively used to suppress microvibration onboard spacecraft, especially in the low frequency range if energy cost and weight increase are acceptable. The active damping and active anti-phase control techniques are mainly employed for spacecraft micro-vibration control. Multiple degrees of freedom isolation platforms can also be developed with active isolation techniques. Active–passive hybrid isolation systems have advantages over pure passive isolation and pure active control techniques, and can be effectively used to isolate micro-vibrations of on-orbit spacecraft over a narrow band, a wide band and in the low frequency range. However, micro-vibration isolation in the low frequency region is mainly enabled by active isolation parts, Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i

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which could result in degradation of reliability. The Semi-active isolation technique is another effective approach for microvibration suppression in space engineering, which can provide much better isolation performances than those achievable by pure passive or active isolation systems. The semi-active MR fluid variable damping isolator has many advantages such as fast reaction time and very low power requirements, but very few semi-active MR fluid isolators are applied in space structures due to the weight limitation. Using controlled smart material, mechanical vibration energy can be dissipated or converted in an appropriate manner, which has advantages in micro-vibration isolation. Noticeably, some advanced nonlinear isolation methods such as nonlinear damping and nonlinear stiffness techniques have been developed for vibration isolation of low frequency and/or in a wide frequency range, which have excellent isolation performance and reliability, and could be of great potential in the area. Nonlinear viscous damping is easy to implement, outperforms linear ones over a wide frequency range, and may play an important role in designing microvibration isolators in the future. The nonlinear stiffness isolation systems such as QZS systems or HSLD systems can be used by combining with nonlinear damping systems to achieve an advantageous vibration isolation performance with only pure passive components, and thus could be of much greater significance to the general field of vibration isolation/suppression/ control.

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Please cite this article as: C. Liu, et al., Recent advances in micro-vibration isolation, Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.10.007i