Two-stage Vibration Isolation Research Articles

Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness

A quasi-zero stiffness (QZS) vibration isolator outperforms other passive control strategies in vibration attenuation especially in a low-frequency band, but it also has an intrinsic limitation of low roll-off rate in the effective frequency range of vibration isolation. To overcome this limitation, a two-stage QZS vibration isolation system (VIS) is proposed, in which the QZS feature is realized by combining a vertical liner spring with two parallel cam–roller–spring mechanisms. Considering a possible disengagement between the cam and the roller under large amplitude vibration, a piecewise nonlinear dynamical model is developed and approximately solved by the averaging method. The analytical solutions for amplitude–frequency relationship and force transmissibility are derived. The results reveal that the two-stage QZS VIS has both advantages of low-frequency vibration isolation and high roll-off rate. It is also found that the second resonance can be eliminated when heavy damping is present in the upper stage, and hence, a broader effective frequency range of isolation can be achieved. High intermediate mass and soft vertical springs in the lower stage are also found to result in high-quality isolation performance.

Dynamic modeling and simulation of a two-stage series-parallel vibration isolation system

A two-stage series-parallel vibration isolation system is already widely used in various industrial fields. However, when the researchers analyze the vibration characteristics of a mechanical system, the system is usually regarded as a single-stage one composed of two substructures. The dynamic modeling of a two-stage series-parallel vibration isolation system using frequency response function–based substructuring method has not been studied. Therefore, this article presents the source-path-receiver model and the substructure property identification model of such a system. These two models make up the transfer path model of the system. And the model is programmed by MATLAB. To verify the proposed transfer path model, a finite element model simulating a vehicle system, which is a typical two-stage series-parallel vibration isolation system, is developed. The substructure frequency response functions and system level frequency response functions can be obtained by MSC Patran/Nastran and LMS Virtual.lab based on the finite element model. Next, the system level frequency response functions are substituted into the transfer path model to predict the substructural frequency response functions and the system response of the coupled structure can then be further calculated. By comparing the predicted results and exact value, the model proves to be correct. Finally, the random noise is introduced into several relevant system level frequency response functions for error sensitivity analysis. The system level frequency response functions that are most sensitive to the random error are found. Since a two-stage series-parallel system has not been well studied, the proposed transfer path model improves the dynamic theory of the multi-stage vibration isolation system. Moreover, the validation process of the model here actually provides an example for acoustic and vibration transfer path analysis based on the proposed model. And it is worth noting that the proposed model can be widely applicable in mechanical systems.

On the transmissibilities of nonlinear vibration isolation system

Transmissibility is a key parameter to quantify the effectiveness of a vibration isolation system. Under harmonic excitation, the force transmissibility of a linear vibration isolation system is defined as the ratio between the amplitude of the force transmitted to the host structure and the excitation force amplitude, and the displacement transmissibility is the ratio between the displacement amplitude of the payload and that of the base. For a nonlinear vibration isolation system, the force or the displacement responses usually have more frequency components than the excitation. For a harmonic excitation, the response may be periodic, quasi-periodic or chaotic. Therefore, the amplitude ratio cannot well define the transmissibility. The root-mean-square ratio of the response to the excitation is suggested to define the transmissibility. The significance of the modified transmissibility is highlighted in a nonlinear two-stage vibration isolation system consisting of two linear spring connected linear vibration isolators with two additional horizontal linear springs. Harmonic balance method (HBM) is applied to determine the responses with the fundamental and third harmonic. Numerical simulations reveal that chaos may occur in the responses. In both cases, the modified transmissibility works while the original definition cannot be applied to chaotic response.

Multi-objective optimization of composite two-stage vibration isolation system for sensitive equipment

Purpose The purpose of this paper is to propose a novel strategy of optimal parameters configuration and placement for sensitive equipment. Design/methodology/approach In this study, clamped thin plate is considered as the foundation form, and a novel composite system is proposed based on the two-stage isolation system. By means of the theory of mechanical four-pole connection, the displacement amplitude transmissibility from the thin plate to precision equipment is derived. For the purpose of performing optimal design of the composite system, a novel multi-objective idea is presented. Multi-objective particle swarm optimization (MOPSO) algorithm is adopted as an optimization technique, which can achieve a global optimal solution (gbest), and selecting the desired solution from an equivalent Pareto set can be avoided. Maximum and variance of the four transmitted peak displacements are considered as the fitness functions simultaneously; the purpose is aimed at reducing the amplitude of the multi-peak isolation system, meanwhile pursuing a uniform vibration as far as possible. The optimization is mainly organized as a combination of parameter configuration and placement design, and the traversal search of discrete plate is performed in each iteration for the purpose of achieving the global optimum. Findings An important transmissibility based on the mechanical four-pole connection is derived, and a composite vibration isolation system is proposed, and a novel optimization problem is also defined here. This study reports a novel optimization strategy combined with artificial intelligence for parameters and placement design of precision equipment, which can promote the traditional view of two-stage vibration isolation. Originality/value Two-stage vibration isolation systems are widely applied to the vibration attenuation of precision equipment, but in these traditional designs, vibration participation of foundation is often ignored. In this paper, participation of foundation of equipment is considered, and a coherent new strategy for equipment isolation and foundation vibration is presented. This study shows a new vision of interdisciplinary including civil engineering, mechanical dynamics and computational science.

Self-synchronization theory of dual motor driven vibration system with two-stage vibration isolation frame

This paper studies self-synchronization and stability of a dual-motor driven vibration system with a two-stage vibration isolation frame. Oscillation amplitude of the material box large enough can be ensured on the vibration system in order to screen materials. Reduction of the dynamic load transmitted to the foundation can also be achieved for the vibration system. A Lagrange equation is used to set up the motion differential equations of the system, and a dimensionless coupled equation of the eccentric rotors is obtained using a method of modified average small parameter. According to the existence condition of zero solution in the dimensionless coupled equation of the eccentric rotors, the precondition for commencing self-synchronization motion is achieved. The stability condition of self-synchronization is obtained based on the Routh-Hurwitz criterion. The theoretical analysis is validated by simulations and experiments.

Advanced LIGO two-stage twelve-axis vibration isolation and positioning platform. Part 2: Experimental investigation and tests results

This paper presents the results of the past seven years of experimental investigation and testing done on the two-stage twelve-axis vibration isolation platform for Advanced LIGO gravity waves observatories. This five-ton two-and-half-meter wide system supports more than a 1000kg of very sensitive equipment. It provides positioning capability and seismic isolation in all directions of translation and rotation. To meet the very stringent requirements of Advanced LIGO, the system must provide more than three orders of magnitude of isolation over a very large bandwidth. It must bring the motion below 10−11 m/Hz at 1Hz and 10−12 m/Hz at 10Hz. A prototype of this system has been built in 2006. It has been extensively tested and analyzed during the following two years. This paper shows how the experimental results obtained with the prototype were used to engineer the final design. It highlights how the engineering solutions implemented not only improved the isolation performance but also greatly simplified the assembly, testing, and commissioning process. During the past two years, five units have been constructed, tested, installed and commissioned at each of the two LIGO observatories. Five other units are being built for an upcoming third observatory. The test results presented show that the system meets the motion requirements, and reach the sensor noise in the control bandwidth.

Influence of equipment excitation on flexible carbody vibration of EMU

To study the vibration transmission characteristics of a flexible carbody and its suspended equipment, a vertical mathematical model of high-speed electric multiple unit was established with equipment excitation considered. And the dynamic unbalance and impact turbulence excitation from equipment were taken into account in a single-stage and two-stage vibration isolation system, respectively. Results show that the excitation transferred to carbody increases with suspension stiffness but decreases with the equipment mass increasing; the vibration transmission can be reduced by increasing the equipment mass or reduce the suspension stiffness. To avoid vibration resonance, the dynamic unbalance frequency of equipment should be out of the possible range of the carbody flexible modes, and a small stiffness should be applied to reduce the impact turbulence. A small stiffness, however, would result in a large movement of the equipment which is limited by the static deflection requirement, while a great stiffness will transfer high frequency vibration. Therefore, a preferred stiffness should make the suspension frequency of equipment a bit greater than the first bending mode of carbody. Additionally, a 3D rigid-flexible coupled dynamics model was built to verify the mathematical analysis, and they show good agreements. Results show that a two-stage isolation could reduce the excitation transmission and make the vibration of carbody and equipment acceptable.

On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness

Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.

Fuzzy Logic Controlled Semi-Active Floating Raft Vibration Isolation System

A warship may be detected in hostile waters because of its unique acoustic signature. A typical two-stage passive vibration isolation system used on ships and submarines to isolate onboard machinery is the floating raft isolation system. The passive isolation system, though robust, may result in substantially high transmission of forces to the foundation at certain excitation frequencies, adversely affecting the ship's stealth. This paper highlights the results of a simulation study aimed at the design of a semi-active floating raft vibration isolation system with the objective of mitigating the acoustic signature of a warship by minimising the transmission of forces, resulting from operation of onboard machinery, to the foundation. A semi-active control scheme with variable damping has been proposed for the floating raft, the variable damping being achieved by means of an electrorheological (ER) damper. A fuzzy logic controller has been designed to achieve the best isolation effect by analysing the characteristics of the frequencies in the excitation signal. The designed semi-active control system is subjected to a time-varying signal, each time-segment corresponding to a different optimal damping ratio. The MATLAB simulation results indicate that the proposed fuzzy logic control method is more effective in vibration isolation than the passive method thereby indicating the potential of the designed semi-active control system in reducing a ship's acoustic signature.

Active structural acoustic control of an elastic cylindrical shell coupled to a two-stage vibration isolation system

Abstract An analytical study of active structural acoustic control of an elastic cylindrical shell coupled to a two-stage vibration isolation system is presented. An analytical active–passive model is developed in order to attenuate sound radiating from the base shell structure, which consists of a rigid-body machine, an intermediate rigid mass, and a supporting cylindrical shell, all connected by a combination of passive and active isolators. Various active control strategies are considered and the corresponding optimal control forces are formulated, including (a) minimizing the vibratory power transmitted to the foundation, (b) minimizing the structural kinetic energy of the supporting shell, (c) minimizing the sum of the square accelerations at the isolator locations on the supporting shell, and (d) minimizing the acoustic power radiated from the supporting shell. Numerical results are presented and discussed in detail. The control performance of all control strategies and system configurations are evaluated and compared in terms of acoustic power radiating from the supporting shell. The effects of key system parameters, i.e., the number and location of the actuators, and the fact that the output forces from the actuators are limited in engineering applications, are also considered and discussed. Finally, some concluding remarks and general design principles for the active control system are also discussed.

An investigation of a two-stage nonlinear vibration isolation system

This paper investigates the most desirable configuration of a two-stage nonlinear vibration isolation system, in which the isolators contain hardening geometric stiffness nonlinearity and linear viscous damping. The force transmissibility of the system is used as the measure of the effectiveness of the isolation system. The hardening nonlinearity is achieved by placing horizontal springs onto the suspended and intermediate masses, which are supported by vertical springs. It is found that nonlinearity in the upper stage has very little effect and thus serves little purpose. The nonlinearity in the lower stage, however, has a profound effect, and can significantly improve the effectiveness of the isolation system. Further, it is found that it is desirable to have high damping in the upper stage and very low damping in the lower stage.

Dynamic behaviour and active sound radiation control of a two-stage vibration isolation system equipped on a flexible plate

This paper presents a general model of a two-stage vibration isolation system involving a flexible base plate with arbitrary boundary conditions. The dynamic behavior of the coupling system was obtained by using an impedance method in which the impedance matrix of the base plate was derived from a combined use of an improved Fourier series expansion and the Rayleigh-Ritz method. Subsequently, with the purpose of attenuation of sound radiation from the base plate structure, the optimal force information is formulated under various active control strategies including: 1) minimizing the total vibratory power of the coupled structure, 2) minimizing the sound power radiation from the base plate, 3) minimizing the vibratory power transmitted to the base plate, and 4) minimizing the mean square velocities at the isolator locations on the flexible plate. Numerical results were presented and discussed in detail. Finally, some concluding remarks are made.

Adaptive Detection of Sinusoidal Signal Based on Adaptive Iir Notch Filter

Adaptive tracking sinusoidal signals with time-varying frequency buried in white noise presents a great interest in engineering applications. A simple approach of application of adaptive notch filters (ANFs) in recursive identification was presented. The use of adaptive infinite impulse response (IIR) notch filters is exploited to detect the sinusoidal components in noise as far as the two-stage vibration isolation system. Computer simulations and experiments on real signals generated by the two-stage system vibration isolation demonstrate the advantage of this method in terms of estimation variance, convergence speed, and the capability of tracking the signals.

Power Flow Method Used to Vibration Transmission for Two-stage Vibration Isolation System

Two-stage vibration isolation system,which is divided into substructures and dynamic transfer matrixes of those substructures are constructed,is the objective system,average vibration energy is adopted as objective function and power flow method is used to assemble transfer matrix of system,thus realizing vibration transmission mechanism investigation of passive vibration isolation.Based on passive vibration isolation process,actuator is installed between upper vibration isolator and intermediate mass,and vibration transmission mechanism investigation of active and passive vibrations isolation of the objective system is realized by optimizing quadrics objective function.By considering the parameters of practical two-stage vibration isolation system,numerical simulation and experimental research are carried out in order to obtain multi-vibration transfer path energy distribution and realize investigation of vibration transmission properties of the system,whose results show that the dominant modes,dissipation characteristics of coupling and damping,and disturbing excitation,determine multi-vibration transfer path energy distribution and vibration transmission properties.

Semi-Active Static Output Feedback Variable Structure Control for Two-Stage Vibration Isolation System

Abstract A semi-active static output feedback variable structure control (VSC) strategy is presented to control a two-stage vibration isolation system in this paper. A continuous output feedback VSC controller which utilizes the measurements from a limited number of sensors installed at strategic locations is designed and a bypass electrorheological (ER) damper is applied to achieve the best control effect more rapidly and accurately. The determination of sliding surface in terms of the Routh-Hurwitz stability criterion is combined with continuous controller design such that the control law is completely decoupled from external excitations, which are hard to measure or estimate. The self-adaptability of the vibration isolation system with respect to external disturbances, the robustness of the control method with respect to parameter variations and the effectiveness of vibration isolation are demonstrated by numerical simulation results. It showed that the designed semi-active static output feedback VSC strategy realized by the ER damper can achieve better performance than those of optimally passive damping and maximum damping variety even if system parameter uncertainties exist.

Signal frequency-based semi-active fuzzy control for two-stage vibration isolation system

In this paper, a novel feed forward control scheme with a fuzzy controller, based on the identification of the signal's main frequency, is proposed to control a semi-active two-stage vibration isolation system such as the floating raft isolation system, whose excitation signal changes regularly. A fuzzy controller is employed in this method to achieve the best isolation effect by analyzing the main frequency's characteristics of the excitation signal, such as amplitude and position, and a bypass electro-rheological (ER) damper is applied to achieve the best control effect more rapidly and accurately. The inputs of the fuzzy controller are the characters of the signal's main frequency and the output is the effect coefficient of the main frequency. Then, the optimal damping ratio of the ER damper and the appropriate voltage could be obtained. The experimental results indicate that the proposed feed forward control method is more effective in vibration isolation in comparison with the passive optimal system.

A Two-Stage Vibration Isolation System Featuring an Electrorheological Damper via the Semi-Active Static Output Feedback Variable Structure Control Method

In this paper, we present a semi-active static output feedback variable structure control (VSC) strategy for vibration isolation. The control concept is based on the fact that, for a practical vibration isolation system subject to external disturbances, all state variables are hard to measure on-line and variations of system parameters frequently exist. A bypass electrorheological (ER) damper is designed and manufactured by incorporating a Bingham model of ER fluids. After the voltage-dependent damping characteristics of the ER damper are evaluated, the dynamic model of a two-stage vibration isolation system with one ER damper is derived. Using only the measured information from sensors installed at strategic locations, continuous output feedback VSC controllers are presented, which do not have possible chattering effects. The continuous control law is decoupled from external disturbances by combining controller design under a meeting sliding mode reachable condition with the choice of sliding surface gradient parameters under a guarantee of the Routh-Hurwitz stability of reduced-order sliding mode dynamics. The saturation of the actuator is also incorporated into the controller, showing no adverse effect. The self-adaptability of the vibration isolation system with respect to external disturbances, the robustness of the control method with respect to parameter variations and the effectiveness of vibration isolation are demonstrated by numerical simulation results in the frequency and time domains. It is illustrated that the performance of the presented semi-active static output feedback VSC system is superior to those of optimally passive damping and maximum damping variety even if system parameter uncertainties exist.

A scanning tunneling microscope adapted to a 3-in. molecular-beam-epitaxy system

The combination of a custom-made scanning tunneling microscope with a commercial molecular-beam-epitaxy (MBE) system for 3-in. wafers is reported. The design of the microscope allows the exchange of the tip and piezo scanning unit in ultrahigh vacuum, thus offering the possibility to apply various local probe techniques with the same instrument. The tip can be cleaned by baking and by Ar+-ion sputtering. Good thermal stability and stiffness of the microscope is obtained by a lever-type design using two similar parallel piezo tubes for the scanner and for a mechanical contact close to the tip, respectively. A two-stage spring vibration isolation with internal viscous damping is used to achieve good mechanical stability for atomic-scale resolution without any further vibration isolation of the MBE system.

Adaptive control of a two-stage vibration isolation mount

An adaptive control system has been developed that may be used for active noise and vibration control problems involving one-dimensional propagation. Based on the least-mean-squares (LMS) algorithm, the adaptive controller performs both system identification and control in real time, without the need for a priori measurements of the system. Since the controller is adaptive in nature, it is possible to track changes in the system while maintaining optimal control. In the present application, the adaptive control system was applied to the problem of minimizing the force transmitted through a two-stage vibration isolation mount. The control system was implemented in real time using a Motorola DSP56000ADS signal-processing board and applied on a physical vibration isolation mount. For periodic excitations, the adaptive controller was capable of providing 30- to 40-dB attenuation of the transmitted vibration. For broadband excitation, some limitations exist, but the controller was still capable of providing about 20-dB attenuation over the lower frequency range. The controller also demonstrated the ability to track changing system parameters to maintain optimal control of the system.