A power transmissibility method for assessing the performance of vibration isolation of building services equipment

Force transmissibility is commonly adopted in building services engineering to assess the performance of vibration isolation. However, it neglects the effect of floor mobility on structure-borne sound power transmitted from a vibratory machine to the floor/roof and the interactions among several contact points between the vibratory machine and the floor/roof. The problem that motivated this study is the occasional occurrence of unsatisfactory performance of vibration isolators observed in building services engineering. This problem may be due to the over-simplification of the vibratory problem in the usual definition of the un-damped force transmissibility or isolation efficiency commonly used in engineering practice. In this paper, use of a “power transmissibility”, which includes the effect of floor mobility and the interaction of all dynamic forces transmitted to the floor through the vibration isolators, is proposed.     

Effect of viscous damping on power transmissibility for the vibration isolation of building services equipment

Vibration isolation plays an important role in both the vibration and noise control of building services equipment. To evaluate vibration isolation performance, the force transmissibility method is commonly adopted. However, increasing the damping effect in the force transmissibility method reduces both the resonance peak value and the isolation performance in the “isolation region”. The limitation of the method is that the transmitted displacement of a floor structure and the interaction of mounting points are neglected. To include the floor displacement and the interaction of mounting points, Mak and Su recently proposed the power transmissibility method to assess the performance of vibration isolation. In this paper, the effect of viscous damping on power transmissibility is investigated. A practical procedure for experimentally determining the damping ratio is also given.     

A study of power transmissibility for the vibration isolation of coherent vibratory machines on the floor of a building

Vibration isolation is commonly adopted by engineers to reduce the vibratory effect caused by building services equipment. However, the relationship between the amount of sound power transmitted to the floor and the interaction between the mounting points of several machines is uncertain, as it is common to install several coherent machines on the same floor, for example, two water pumps of the same type in a plant room. We conduct an analytical study of the effects of the interaction between two coherent vibratory sources on the power transmitted to the floor. The study is based on two simple vibratory sources with a single contact point, two rectangular machine models of even-mass distribution with four symmetrical supports and the calculated mobilities of a simply supported concrete floor. We find that the total power obtained from coherent sources (point sources or machine models) differs considerably from that obtained from independent sources at some frequencies in a vibration isolation region. To predict the performance of isolators more accurately, the power transmissibility method proposed previously by Mak and Su should consider not only the effect of effective floor mobility and the interactions of the mounting points of the same sources, but also the interactions of the mounting points of different sources on the floor.     

Research on performance indices of vibration isolation system

Power flow transmissibility is proposed as a performance index to evaluate the performance of isolation system. It is defined as the ratio of the power flow input into the equipment and the power flow transmitted into the receiver. Based on a simple vibration isolation system, its relationship with other performance indices is given by theoretical and numerical analysis. The results show that power flow transmissibility can reflect the response characteristics of the whole isolation system effectively. In addition, power flow transmissibility can be estimated easily according to vibration acceleration level difference and does not involve the measurement of power flow. Furthermore, the influences of several parameters such as the damping, loss factor and stiffness of isolator on power flow transmissibility are analyzed.     

Nonlinear analysis,design and vibration isolation for a bilinear system with time-delayed cubic velocity feedback

This paper combines cubic nonlinearity and time delay to improve the performance of vibration isolation. Nonlinear dynamics properties, design methodology and isolation performance are studied for a piecewise bilinear vibration isolation system with the time-delayed cubic velocity feedback control. By the multi-scale perturbation method, the equivalent stiffness and damping are first defined to interpret the effect of feedback control loop on dynamics behaviours, such as frequency island phenomenon. Then, a design criterion is proposed to suppress the jump phenomenon induced by the saddle-node bifurcation. With the purpose of obtaining the desirable vibration isolation performance, stability conditions are obtained to find appropriate feedback parameters including gain and time delay. Last, the influence of the feedback parameters on vibration transmissibility is assessed. Results show that the strategy developed in this paper is practicable and feedback parameters are significant factors to alter dynamics behaviours, and more importantly, to improve the isolation effectiveness for the bilinear isolation system.     

Effects of isolators internal resonances on force transmissibility and radiated noise

Vibration isolators have been extensively used to reduce the vibration and noise transmitted between the components of mechanical systems. Although some previous studies on vibration isolation considered the inertia of isolators, they only examined its effects on the vibration of single degree-of-freedom (d.o.f.) systems. These studies did not emphasize the importance of the isolators’ inertia, especially from the perspective of noise reduction. This paper shows that the internal dynamics of the isolator, which are also known as internal resonances (IRs) or wave effects, can significantly affect the isolator performance at high frequencies. To study the IR problem, a model of a primary mass connected to a flexible foundation through three isolators is used. In this model, the isolator is represented as a one-dimensional continuous rod that accounts for its internal dynamics. The primary mass is modelled as a rigid body with three d.o.f.'s. The effects of the IRs on the force transmissibility and the radiated sound power from the foundation are examined. It is shown that the IRs significantly increase the force transmissibility and the noise radiation level at some frequencies. These effects cannot be predicted using a traditional model that neglects the inertia of the isolator. The influence of the foundation flexibility on the IRs is also investigated. It is shown that the foundation flexibility greatly affects the noise radiation level but it affects only slightly the force transmissibility, especially at high frequencies where the IRs occur.     

弹性基础隔振系统的简化性能指标和有源控制力

系统研究了基础弹性对单层隔振系统、双层隔振系统及浮筏隔振系统隔振性能的影响。分析了不同隔振系统与不同弹性基础间的振动耦合特性,讨论了不同隔振系统的振级落差和力传递率特性,给出了振级落差和力传递率的简化计算方法。针对不同隔振系统的有源隔振问题,比较了不同作动器安装方式所需的控制力。研究表明,对于所有隔振系统,增加基础的刚度和阻尼有利于提高振级落差和力传递率;对于浮筏隔振系统,增加筏架的刚度和阻尼有利于提高隔振性能和减少有源隔振所需的控制力。      

Simplified performance indices and active control force of vibration isolation systems with elastic base

Influence of the elasticity of the base on vibration isolation performances of single layer, double layer and floating raft vibration isolation systems is investigated systematically.Characteristics of vibration coupling between different vibration isolation systems and different elastic bases are analyzed. Moreover the characteristics of vibration acceleration level difference and force transmissibility of different vibration isolation systems are discussed and their simplified expressions are given. In addition the required control forces of active vibration isolation under different installations of actuators for different vibration isolation systems are compared.The results show that for all vibration isolation systems, the addition of the stiffness and damping of the base can enhance their vibration acceleration level difference and force transmissibility.Moreover for floating raft vibration isolation system, the addition of the stiffness and damping of the raft can enhance its vibration isolation performance and reduce the control force required by active vibration isolation.     

Sensor fusion for active vibration isolation in precision equipment

Sensor fusion is a promising control strategy to improve the performance of active vibration isolation systems that are used in precision equipment. Normally, those vibration isolation systems are only capable of realizing a low transmissibility. Additional objectives are to increase the damping ratio of internal vibration modes and to provide a high support stiffness. It is shown that these three objectives cannot be realized simultaneously if only acceleration or force feedback is used. An active hard mount suspension with a feedback strategy based on sensor fusion is proposed that uses the acceleration signal at low frequencies and the force signal at high frequencies. Using sensor fusion, the three objectives can be achieved simultaneously. Experiments on a single-axis setup show that this feedback strategy provides an excellent performance.     

A comparison of two nonlinear damping mechanisms in a vibration isolator

The vibration transmissibility characteristics of a single-degree-of-freedom (SDOF) passive vibration isolation system with different nonlinear dampers are investigated in this paper. In one configuration, the damper is assumed to be linear and viscous, and is connected to the mass so that it is perpendicular to the spring (horizontal damper). The vibration is in the direction of the spring. The second configuration is one in which the damper is in parallel with the spring but the damping force is proportional to the cube of the relative velocity across the damper (cubic damping). Both configurations are studied for small amplitudes of excitation, when some analysis can be conducted based on analytical expressions, and for large amplitudes of excitation, where the analysis is based on numerical simulations. It is found that the two nonlinear systems can outperform the linear system when force transmissibility is considered. However, for displacement transmissibility, the system with the horizontal damper exhibits some desirable properties, but the system with cubic damping does not.     

Design of vibration isolators by exploiting the beneficial effects of stiffness and damping nonlinearities

The present study is concerned with the design of a new type of single degree of freedom (sdof) nonlinear vibration isolation system that can deal with harmonic excitations and take advantage of both spring and damping nonlinearities. For typical design requirements expressed in terms of a transmissibility envelope, the proposed design makes use of a recently developed method called the output frequency response function (OFRF) approach, which provides a direct relationship between the system output frequency response and parameters that define the system nonlinearity. Taking all output harmonics into account, a detailed step-by-step procedure is developed to systematically determine the nonlinear parameters from a small set of simulation or experimental data. Simulation studies are conducted to verify the results and demonstrate that the design can effectively achieve all the three requirements for a vibration isolation system of a low resonant peak, low high frequency transmissibility, and a large isolation range.     

A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat

This paper designs and fabricates a vibration isolation model for improving vibration isolation effectiveness of the vehicle seat under low excitation frequencies. The feature of the proposed system is to use two symmetric negative stiffness structures (NSS) in parallel to a positive stiffness structure. Here, theoretical analysis of the proposed system is clearly presented. Then, the design procedure is derived so that the resonance peak of frequency-response curve drifts to the left, the load support capacity of the system is maintained, the total size of the system is reduced for easy practical application and especially, the bending of the frequency-response curve is minimized. Next the dynamic equation of the proposed system is set up. Then, the harmonic balance (HB) method is employed to seek the characteristic of the motion transmissibility of the proposed system at the steady state for each of the excitation frequency. From this characteristic, the curves of the motion transmission are predicted according to the various values of the configurative parameters of the system. Then, the time responses to the sinusoidal, multi frequency and random excitations are also investigated by simulation and experiment. In addition, the isolation performance comparison between the system with NSS and system without NSS is realized. The simulation results reveal that the proposed system has larger frequency region of isolation than that of the system without NSS. The experimental results confirm also that with a random excitation mainly spreading from 0.1 to 10 Hz, the isolation performance of the system with NSS is greatly improved, where the RMS values of the mass displacement may be reduced to 67.2%, whereas the isolation performance of the system without NSS is bad. Besides, the stability of the steady-state response is also studied. Finally, some conclusions are given.     

Control of a unique active vibration isolator with a phase compensation technique and automatic on/off switching

This work examines the characteristics of a unique active vibration isolator and develops a control strategy for it. The proposed active vibration isolator is introduced and its dynamic model is presented. A characterization study is conducted to identify system parameters. It is shown that with a simple proportional feedback the closed-loop system has a very narrow stability margin due to the inherent dynamics of the actuator. To improve the stability of the closed-loop system and enhance the performance of vibration isolation, a phase compensator is incorporated in the control scheme. An optimization problem is formulated to determine the optimum controller parameters by minimizing the 2nd norm of the displacement transmissibility. Both absolute position feedback and relative position feedback are considered. In real time implementation, an automatic on/off switching strategy is devised to take full advantage of both the active isolator and passive isolator. The experimental results show that with the proposed control scheme, the isolator is capable of suppressing base excitations effectively.     

A six-axis hybrid vibration isolation system using active zero-power control supported by passive weight support mechanism

This paper presents a six-degree-of-freedom hybrid vibration isolation system integrated with an active negative suspension, an active-passive positive suspension and a passive weight support mechanism. The aim of the research consists in maximizing the system and control performances, and minimizing the system development and maintenance costs. The vibration isolation system is, fundamentally, developed by connecting an active negative suspension realized by zero-power control in series with an active-passive positive suspension. The system could effectively isolate ground vibrations in addition to suppress the effect of on-board generated direct disturbances of the six-axis motions, associated with vertical and horizontal directions. The system is further reinforced by introducing a passive weight support mechanism in parallel with the basic system. The modified system with zero-power control allows simplified design of the isolation table without power consumption. It also offers enhanced performance on direct disturbance suppression and large payload supporting capabilities, without degrading transmissibility characteristics. A mathematical model of the system is presented and, therefore, analyzed to demonstrate that zero-compliance to direct disturbance could be generated by the developed system. Experimental demonstrations validate the proposed concept that exhibits high stiffness of the isolation table to static and dynamic direct disturbances, and good transmissibility characteristics against ground vibration. Further improvements of the vibration isolation system and the control system are discussed as well.     

A novel design of semi-active hydraulic mount with wide-band tunable notch frequency

Hydraulic engine mount is advanced vibration isolator with superior performance to reduce vibration transferred from engine to chassis. As the stiffness at notch frequency is small, some semi-active or active hydraulic mounts tune some parameters to let notch frequency coincide with exciting frequency for better vibration isolation performance. It is discovered the current semi-active mounts can tune the notch frequency in narrow frequency band when only one parameter is tuned. A novel semi-active hydraulic engine mount design which introduces screw thread is proposed and researched in the paper. This hydraulic mount can control both cross section area and the length of inertia track and the theoretical tunable notch frequency band is [0, ∞). Theoretical work is carried out to uncover the capability for the proposed design to tune notch frequency. Simulation work is performed to understand its high vibration isolation performance. For the purpose of energy conservation, the friction self-locking is introduced. This denotes once the mount is tuned at optimal condition, the energy can be cut off and the optimal condition will never change. We also determine the best time to tune the parameters of the proposed mount in order to decrease the acting force. The proposed semi-active mount has capability to obtain wide band tunable notch frequency and has merit of energy conservation.     

A new type of semi-active hydraulic engine mount using controllable area of inertia track

Automotive engine mounts function to constrain the engine shake motion resulting at low-frequencies, as well as to isolate noises and vibrations generated by the engine with unbalanced disturbances at the high frequencies. The property of the mount depends on vibration amplitude and excitation frequency. It means that the excitation amplitude is large in low excitation frequency range and small in high frequency range. In this paper, a new hydraulic engine mount with a controllable area of inertia track is proposed and investigated. Theoretical works with the mount model to isolate the engine-related vibrations were conducted by an optimal algorithm to control the area of the inertia track under shocks and multi-signal force excitations. This research clearly gives an analysis of the considerable changes in the mount dynamic properties according to the changes in the inertia track area. Consequently, when the inertia track area is tuned, the transmissibility of the mount is effectively reduced.     

Octo-strut vibration isolation platform and its application to whole spacecraft vibration isolation

Stewart platform is widely used for vibration isolation and precise pointing. As it is a statically determinate structure, if any strut has fault, a disaster could be unavoidable. In the present paper, an octo-strut passive vibration isolation platform with redundancy is introduced and applied to whole-spacecraft vibration isolation. This platform is modeled with the Newton–Euler method. To avoid such possibility that the spacecraft may interact with the fairing, an approach of stiffness design is proposed to reinforce the rotation stiffness of the platform. With the mathematical model, design parameters of the isolator that will affect the nature frequencies of the isolator-spacecraft system are studied. The transmissibility of the isolator topped with rigid and flexible spacecraft is also studied. Results of analytical and numerical studies show that the octo-strut platform is a reliable and effective approach to improving the dynamic environment of a spacecraft.     

On the concept of a transmission absorber to suppress internal resonance

Internal resonances within vibration isolators have been shown to increase force transmission and consequently radiated noise from supporting structures. Previous research has successfully used dynamic vibration absorbers to attenuate internal resonances. This paper introduces the term transmission absorber to describe a system that exerts both restoring and inertial forces proportional to relative motion. A novel uni-axial vibration isolator concept incorporating transmission absorbers to suppress internal resonance is proposed and theoretically compared with an isolator including dynamic vibration absorbers. The designs are optimised by using a combination of particle swarm and gradient-based optimisation algorithms. It is shown that the proposed isolator concept, incorporating transmission absorbers, has the potential to outperform previous designs, demonstrating force transmissibility levels approaching those of an ideal isolator.     

Theoretical relationship between vibration transmissibility and driving-point response functions of the human body

The relationship between the vibration transmissibility and driving-point response functions (DPRFs) of the human body is important for understanding vibration exposures of the system and for developing valid models. This study identified their theoretical relationship and demonstrated that the sum of the DPRFs can be expressed as a linear combination of the transmissibility functions of the individual mass elements distributed throughout the system. The relationship is verified using several human vibration models. This study also clarified the requirements for reliably quantifying transmissibility values used as references for calibrating the system models. As an example application, this study used the developed theory to perform a preliminary analysis of the method for calibrating models using both vibration transmissibility and DPRFs. The results of the analysis show that the combined method can theoretically result in a unique and valid solution of the model parameters, at least for linear systems. However, the validation of the method itself does not guarantee the validation of the calibrated model, because the validation of the calibration also depends on the model structure and the reliability and appropriate representation of the reference functions. The basic theory developed in this study is also applicable to the vibration analyses of other structures.     

Experimental Investigation of Nonlinear Vibration Isolator with Fluidic Actuators (NLVIFA)

This paper elaborates a nonlinear fluidic low frequency vibration isolator designed with the characteristics of quasi-zero stiffness (QZS). The existing model of QZS vibration isolator enhances amplitude of vibration and attenuating vibration frequencies. This concern with displacement plays a vital role in the performance and instability of oblique spring setup reduces the isolator performance in horizontal non-nominal loads, in this accordance; this paper associates double acting hydraulic cylinder (fluidic actuators in short) in oblique and helical coil spring. An approximate expression of unique analytical relationship between the stiffness of vertical spring and bulk modulus of the fluid is derived for Quasi – Zero Stiffness Non-Linear Vibration Isolator with Fluidic Actuators (NLVIFA in short) system and the force transmissibility is formulated and damping ratio are discussed for characteristic analysis. Modal analysis carried out and compared with analytical results and an experimental prototype is developed and investigated. The performance of the NLVIFA reduces the external embarrassment more at low frequencies and the series of experimental studies showing that the soft nonlinearity causes limitation in the resonant frequency thereupon the isolation will be enhanced and NLVIFA greatly outperform some other type of nonlinear isolators.