Effectiveness of a passive-active vibration isolation system with actuator constraints

In the prediction of active vibration isolation performance, control force requirements were ignored in previous work. This may limit the realization of theoretically predicted isolation performance if control force of large magnitude cannot be supplied by actuators.The behavior of a feed-forward active isolation system subjected to actuator output constraints is investigated. Distributed parameter models are developed to analyze the system response, and to produce a transfer matrix for the design of an integrated passive-active isolation system. Cost functions comprising a combination of the vibration transmission energy and the sum of the squared control forces are proposed. The example system considered is a rigid body connected to a simply supported plate via two passive-active isolation mounts. Vertical and transverse forces as well as a rotational moment are applied at the rigid body, and resonances excited in elastic mounts and the supporting plate are analyzed. The overall isolation performance is evaluated by numerical simulation. The simulation results are then compared with those obtained using unconstrained control strategies. In addition, the effects of waves in elastic mounts are analyzed. It is shown that the control strategies which rely on tmconstrained actuator outputs may give substantial power transmission reductions over a wide frequency range, but also require large control force amplitudes to control excited vibration modes of the system. Expected power transmission reductions for modified control strategies that incorporate constrained actuator outputs are considerably less than typical reductions with unconstrained actuator outputs. In the frequency range in which rigid body modes are present, the control strategies can only achieve 5-10 dB power transmission reduction, when control forces are constrained to be the same order of the magnitude as the primary vertical force. The resonances of the elastic mounts result in a notable increase of power transmission in high frequency range and cannot be attenuated by active control. The investigation provides a guideline for design and evaluation of active vibration isolation systems.     

Vibrational power-flow analysis of a MIMO system using the transmission matrix approach

The transmission matrix approach is employed in this paper for the vibrational power-flow analysis of a multiple-input/multiple-output (MIMO) system. The substructures in each subsystem are modelled as a group of general MIMO transmission elements, which are described in terms of discrete or distributed properties. The global transmission matrix of the system is formed by assembling the transmission matrices together. Using the proposed approach, the output variables of any subsystem can be expressed in terms of the input state variables of that subsystem. Hence, the proposed approach is very systematic in analysing the dynamic behaviour of a complex system with a group of elements. In the numerical example, the power flow of a multi-mount system is modelled analytically. The transmission of vibratory power flow from the vibrating rigid body into a simply supported plate through elastic mounts is studied in detail. The effects on the power flows of various factors, such as the plate thickness, loading type, mounting locations, and mass and damping properties of the mounts, are addressed.     

多层隔振系统的动力学方程

以多层隔振系统质量块（刚体）空间一般运动的坐标变换,系统的动能,势能和阻尼耗散函数,系统的拉格朗日方程为理论基础,对系统的运动微分方程进行了严格的数学推导,得出适用于质量块之间或质量块与基础之间具有６个相对运动自由度的多层隔振系统的运动微分方程组。该方程组对现有方程组有较大的改进,可应用于舰船的隔振降噪浮筏装置,也可应用于陆地上的动力机器及精密设备的多层隔振系统的设计计算。     

三维振动台的正弦扫频分析与模态分析

三维振动台采用振动方法完成对复杂异型曲面工件进行表面强化和抛光处理，为了探讨振动台的固频与振型对强化抛光的影响，本文首先对三维振动台进行Y向与Z向模态试验，得到了三维振动台的各阶模态，为了纵模态分析中确定强化抛光用模态，将模态分析中所得的各阶固频，对三维振动台进行正弦激振，同时将模态分析与正弦激振相结合，获得了适合三维振动台的抛光工艺模态。     

浮筏隔振系统功率流的另一计算方法

推导了一种用来计算输入浮筏隔振系统功率流的新方法，以便对浮筏隔振系统的隔振性能进行评估。在理论推导的基础上，运用新方法进行仿真计算，得出了输入到浮筏各子系统的功率流，初步分析了影响浮筏系统隔振性能的主要因素。     

横置动力总成悬置系统的布置设计分析

以横置的动力总成悬置系统为研究对象,系统地阐述了悬置系统的布置设计思想,解释了悬置系统中主惯性轴、扭矩轴以及弹性轴的定义,并对目前横置动力总成悬置系统的主要布置形式进行了研究与分析。在怠速扭矩激励下,悬置的安装位置应满足系统的扭矩轴和弹性轴重合,从而获得良好的隔振性能。同时对悬置系统的解耦作了相关的说明。横置动力总成悬置系统的布置设计分析,为悬置系统前期开发中悬置的安装位置和刚度的选择提供了参考价值。     

Naval-vessel on board equipment base to minimize structure-borne noise

In order to reduce the structure-borne noise of naval-vessel onboard equipment to meet imposed standards, the equipment exciting force should be restricted and additional anti-vibration devices such as resilient mounts and bellows should be applied. Since the structure-borne noise is dependent on the design of the equipment base, the realization of a low-vibration base design is important. In this study, a typical pump base is optimized using Design of experiment (DOE) and Computer-aided engineering (CAE) techniques, in order to minimize the vibration transferred from the equipment base to the floor. In addition, a sandwich panel consisting of a steel plate and rubber material is applied to the pump base between an anti-vibration mount and the base, so as to reduce the vibration transferred from the pump using the double-mounting-system principle. Consequently, the structure-borne noise reduction achieved by applying the proposed base design is verified via experiment.     

EQUIVALENT EXCITATION METHOD FOR VIBRATION ISOLATION DESIGN：THEORETICAL ANALYSIS AND EXPERIMENTAL RESULTS

In view of difficulties concerned with direct measurement of excitations inside source equipments and their significant influence on vibration isolation effectiveness, a dynamical model, for vibration isolation of a rigid machine with six-degree-of-freedom mounted on a flexible foundation through multiple mounts, is analyzed, in which the complicated and multiple disturbances inside the machine are described as an equivalent excitation spectrum. And a method for the estimation of the equivalent excitation spectrum according to system dynamic responses is discussed for the quantitative prediction of isolation effectiveness. Both theoretical analysis and experimental results are demonstrated. Further work shows the quantitative prediction of transmitted power flow in a flexible vibration isolation experiment system using the proposed equivalent excitation spectrum method, by comparison with its testing results.     

Using nonlinear springs to reduce the whirling of a rotating shaft

Vibrations in rotating machinery cause many problems such as fatigue of the rotating components, excessive noise, or transmission of vibration to the supporting structure. A major source of this vibration is out-of-balance forces and this paper proposes that the rotor response is reduced by suspending the machine on nonlinear springs. In the field of vibration isolation, nonlinear mounts have been proposed which have the same static stiffness as an equivalent linear support, i.e. load bearing capability, but at the same time offer a low dynamic stiffness, i.e. a lower natural frequency. Thus the isolator is effective over an increased frequency range. These mounts are known in the literature as high-static-low-dynamic-stiffness (HSLDS) mechanisms. In this paper, the rotor is suspended on a hardening HSLDS spring to considerably reduce the critical speeds to values far away from the operating speed. The advantages of the nonlinear supports are demonstrated using a simple two degree of freedom rotating machine model consisting of a rigid disk, and shafts, bearings and supports that are flexible but have negligible mass. Following a linear analysis to highlight the benefits of a low dynamic stiffness, an approximate analytical solution of the nonlinear equation of motion is presented. A comparison between the linear and nonlinear response shows the effectiveness of the nonlinear supports. Finally, the problems that occur if the nonlinearity is too strong are highlighted.     

复杂机械系统多维耦合振动传递矩阵分析

以特性传递矩阵描述复杂机械系统中子结构输入、输出力与速度矢量关系,提出了复杂振源激励、多弹性支承与基础板结构三维耦合隔振系统传递矩阵力学模型。考虑隔振支承多维波动效应,推证了弹性支承耦合振动传递矩阵,为复杂系统功率流特性及隔振器多维驻波效应研究确立了有效途经。数值模拟计算表明,基础板结构的前两阶弯曲共振模态是高频域系统功率流提高的主要原因。振源力矩或垂向激振力诱发的隔振器纵向谐振使系统功率流明显提高:增大基础板厚度,驻波共振峰值提高。     

弹性轮对对轮轨动作用力的影响

弹性轮对因其在减少轮轨噪声、降低轮轨间的动作用力和提高旅客乘坐舒适度方面具有明显效果而在国外轨道交通车辆上得到较为广泛的使用.利用动力学分析软件SIMPACK对采用弹性轮对的国内某城市地铁车辆进行了动力学性能方面的分析,并与采用刚性轮对的结果相比较.结果表明:当弹性轮对V型橡胶垫轴向刚度跟垂向刚度分配合理时,轻轨车辆采...     

刚散耦合振动圆锥破碎机动力学分析

将振动圆锥破碎机简化为六自由度运动的物理模型,物料层采用分段线性接触力模型来表示。应用Lagrange方程,对振动圆锥破碎机进行了建模。通过Matlab采用Runge-Kutta法对振动微分方程组进行数值计算仿真,研究了不同激振频率下系统的动力学性能。研究结果表明,物料层的作用是系统非线性的根本来源,物料层的非线性导致系统从单一频率的简谐运动变为复杂运动,为振动圆锥破碎机的参数选择提供了依据。     

非线性宽频压电振动能量采集器的研究

为改善双稳态压电振动能量采集器在基础低幅值激励条件下的输出性能,提出了一种带有线性放大器的非线性宽频压电振动能量采集器,通过线性放大器对基础低幅值激励进行一级放大后,激发双稳态压电振动能量采集器进入高能轨道的大幅值周期振动,从而提高能量采集器的输出性能。根据力学和电学平衡方法建立了非线性宽频压电振动能量采集器的两自由度集总参数模型和运动微分方程,并对系统模型进行时域和频域求解,仿真分析了系统质量比、刚度比等参数对系统输出特性(振动位移、速度、相图和输出电压等)的影响。最后,通过与双稳态压电振动能量采集器输出性能的实验结果对比分析,表明非线性宽频压电振动能量采集器在较小的激励幅值作用下具有更高的输出特性和更宽的工作频带。     

漂浮基柔性关节-柔性臂空间机器人运动非线性滑模控制及双重弹性振动主动抑制

讨论了漂浮基柔性关节-柔性臂空间机器人系统的动力学建模过程、运动控制律设计及关节和臂双重弹性振动的抑制问题。利用动量、动量矩守恒关系和拉格朗日-假设模态法对系统进行动力学分析,并建立系统动力学方程。基于奇异摄动法,将系统分解为三个相互独立的子系统：仅表示系统刚性运动的“刚性关节-刚性臂”慢变子系统、仅表示柔性关节引起的系统弹性振动的“柔性关节-刚性臂”快变子系统和仅表示柔性臂引起的系统弹性振动的“刚性关节-柔性臂”快变子系统。分别针对三个子系统设计适当的控制律,其中非线性滑模控制方法用来实现空间机器人期望运动轨迹的渐近跟踪,速度差值反馈控制器用来抑制柔性关节引起的系统弹性振动,线性二次型最优控制器用来抑制柔性臂引起的系统弹性振动。因此,系统的总控制律为三个子系统的控制律组成的混合控制律。仿真实验证明所提出的混合控制律能够保证系统的控制精度,且能够有效地抑制柔性关节和柔性臂引起的系统弹性振动。     

Optimal control of structural vibrations using a mixed-mode magnetorheological fluid mount

In this work, a mixed-mode magnetorheological (MR) mount is proposed and applied to the vibration control of a flexible beam structure subjected to external disturbances. On the basis of non-dimensional Bingham number, an appropriate size of the MR mount is designed and manufactured. After experimentally evaluating the field-dependent damping force of the MR mount, a structural system consisting of a flexible beam and vibrating rigid mass is established. The governing equation of motion of the system is derived and expressed as a state space control model. A linear quadratic Gaussian (LQG) controller is then designed in order to attenuate the vibration of the structural system. The controller is empirically realized and control responses such as acceleration and displacement of the structural system are evaluated and presented in frequency domain.     

Dynamic restoring and dissipative parameters of non-linear systems

Elastometer vibration and shock absorbing machinery mountings and package cushioning cannot be accurately modeled as linear Voigt type systems, since most of them exhibit stiffening or softening elasticity in conjunction with friction and viscous damping. Improved accuracy may be achieved by a non-linear shock or vibration loaded model, incorporating linear with non-linear elasticity and combined Coulomb and viscous damping. Formulae of such a model are compiled whereby optimal cushioning systems and mounts in shock and vibration loading may be designed. The use of these formulae requires experimental evaluation of two pairs of restoring and dissipative parameters in shock and vibration loading. Equations and test procedures for evaluating these parameters by means of shock and vibration machine tests are presented, along with a detailed discussion of properties of hysteresis loops of non-linear single degree of freedom systems in shock and vibration loading. A special test jig is described comprising a non-linear system with adjustable non-linear elasticity as well as variable Coulomb and viscous damping. This jig was used to evaluate the validity of the mathematical model by means of extensive tests on a shock and vibration machine. Programs developed for an Apple II microcomputer facilitated rapid and accurate computations whereby a numerical example is presented as an illustration of the procedure for evaluating restoring and dissipative parameters. This mathematical model and test procedures are believed to closely approximate shock and vibration isolation systems. As such, they may be conducive to developing better cushioning material and improved machinery mounts.     

弹性支承隔振和机床可移动性的试验研究

文章通过建立机床／刀困二阶振动模型及对机床不设备弹性隔／减振的试验研究和试验数据的回归分析,研究了弹性减振器的性能特点及选用原则,论证了在一定条件采用弹性隔／减振方案实现机床可移动性安装的可行性,提出一组机床重组后的安装性能评价指标。     

Generalized model of vibro-isolation systems with seated human body for single-axis transmission of vibration

A generalized model of vibration isolation systems with a human body in a seated position is developed. The system dynamics is modeled for a single-axis transmission of vibration, that is, longitudinal x, lateral y and vertical z, to limit whole-body vibration exposure. The developed model can be successfully employed to describe the propagation of vibration waves from the source to a vibrating object. The proposed mathematical model can be widely used to protect a human body against vibration.     

Free vibration analysis of a resilient impact damper

The free vibration of a vibratory system equipped with a resilient impact damper is studied. A simple model of impact damper is constructed using spring, mass and viscous damper. The important feature to be carried out in the analysis of this model is that the deformation of an impact damper during the collision with and the main mass can be formulated; therefore, the contact time is taken into consideration. This feature is important for a resilient rather than a rigid impact damper when the noise issue is concerned. The investigation showed that the effective reduction of the vibration response depends not on the number of impacts but primarily on the type of collision that the impact mass collides with the main mass face-to-face. Results also show that the clearance of an effective impact damper should be smaller than twice of the initial displacement of the main mass of the vibration system if the system is stimulated by an initial displacement only. Finally, an example of application of an impact damper on a cantilever beam is demonstrated.