Identification of modal parameters from ambient vibration data using eigensystem realization algorithm with correlation technique

An effective identification method is developed for the determination of modal parameters of a structure based on the measured ambient response data. In this study, modification to Eigensystem Realization Algorithm with Data Correlation is proposed for modalparameter identification of structural systems subjected to stationary white-noise ambient vibration. By setting up a correlation -function matrix of stationary responses, as well as by introducing an appropriate matrix factorization, modal parameters of a system can be identified effectively through singular -value decomposition and eigenvalue analysis. Numerical simulations using practical excitation data confirm the validity and robustness of the proposed method in identifying modal parameters from stationary ambient vibration data under noisy conditions.     

动力总成悬置系统隔振分析及优化

针对某皮卡车振动剧烈、噪声较大等问题,建立动力总成悬置系统多体动力学模型.通过模态分析、动力总成质心加速度和悬置支撑处响应力的仿真,优化悬置的主刚度,使其隔振效果得到明显改善,不仅提高了车辆乘坐的舒适性,而且延长了发动机与其他部件的使用寿命.     

Acoustic radiation from modal vibration of automotive brake drum

The vibro-acoustic characteristics of an automotive brake drum is studied by applying a hybrid approach, which combines a numerical vibration analysis with an analytical acoustic solution. Specifically, structural vibration of a drum is investigated with the numerical finite element analysis, and vibratory displacements of the outer surface of the drum is approximated by simple mathematical expressions. Then, radiation of sound from the drum vibration is calculated using well-known theoretical solutions based on the simplified modal displacements. Finally, the calculation results are compared with those obtained by full numerical analyses. The results show that the numerical-analytical hybrid method allows relatively accurate calculation of vibro-acoustic properties of a brake drum under realistic boundary conditions.     

Robust modal vibration suppression of a flexible rotor

This study deals with active robust modal vibration control of rotor systems supported by magnetic bearings. The inherent divergent rigid body modes are suppressed by using a dual-level control approach. Finite element method is applied to formulate the rotor model. The Timoshenko beam theory, including the effects of shearing deformations and rotary inertia, is considered in this work. Because practical control systems are often limited by its sensing, hardware, and computation speed capabilities, the reduced order approach is often used for a control system design. This study applies the independent modal space control (IMSC) approach to extract the accurate lower modes from the complex rotor systems with the gyroscopic effect considered. In practice, it is extremely difficult to model the complete dynamic characteristics of a rotor system. The model may contain unmodelled dynamics and parameter changes, which can be viewed as uncertainties of a system. As opposed to the conventional control approach, which requires fixed and accurate system parameters, this study considers robust control approach to design a controller capable of tolerating external disturbance and model uncertainties. It is demonstrated that the proposed approach is effective for vibration suppression when the system is subjected to impulsive or step loading, speed variation, and sudden loss of disk mass.     

汽车动力总成悬置系统多工况运行模态试验研究

由试验测得发动机启动、怠速和急加速三种典型工况下的振动响应,进行了动力总成悬置系统的运行模态参数识别。采用多参考点最小二乘复频域法,通过试验测得的振动响应获得系统工作振型。由于发动机激励不具备零均值白噪声的特点,运用了多种模态置信度指标进行模态验证,获得了较可信的模态参数。试验结果表明,动力总成悬置系统的运行模态参数与发动机工况有关,对于大阻尼和密集模态的动力总成悬置系统,多工况的运行模态试验可以更准确地识别悬置系统的模态参数。研究结果对悬置元件参数设计具有重要的参考价值。     

Dynamic modeling and analysis of axial vibration of a coupled propeller and shaft system

The dynamic and acoustic characteristics of a coupled propeller and shaft system which is modeled by the transfer matrix method are studied. The elasticity of the propeller is taken into consideration by employing the equivalent reduced modeling method. Thus the influence of the elastic propeller on the vibro-acoustic responses of the coupled system is investigated. To reduce the axial vibration of the coupled propeller-shaft system, the influence and location of the vibration isolator on the structural and acoustic responses is presented. Simulation results demonstrate that utilizing the relationship between the natural frequency of the propeller and the resonance frequency range of the shaft can control the vibration of the coupled system without other vibration control method. Utilizing a vibration isolator is another effective way to control vibration. The optimal position for the isolator installed between the shaft and the thrust bearing is investigated.     

空气阻尼悬置非线性动态特性建模与仿真

由于空气阻尼悬置为汽车动力总成等系统的隔振元件,其性能与成本介于橡胶悬置与液阻悬置之间,以一典型空气悬置为研究对象,建立了动力学特性仿真分析的集总参数非线性模型。对其动特性进行了数值仿真,并与实验值进行了对比分析,结果证明了所建立模型的正确性。对影响空气悬置动特性的各因素进行了趋势研究,揭示了节流孔直径、节流孔长度、初始体积、激励振幅与绝热指数等因素对空气悬置特征参数的影响规律,其中减小节流孔直径可显著提高空气悬置阻尼。此研究的建模与仿真方法有助于空气悬置产品的设计与开发。     

基于Chebyshev区间方法的动力总成悬置系统稳健性优化

汽车动力总成悬置系统是车辆的主要隔振系统之一,其性能对整车NVH体验具有重大影响。考虑到动力总成悬置刚度值存在一定程度的偏差或波动,应用Chebyshev区间方法确定动力总成悬置系统固有频率和解耦率随元件刚度值波动的区间范围,通过实例确定其计算精度。以提高悬置系统频率和解耦率的稳健性为目的,按区间优化模型对某轿车悬置系统的频率和解耦率进行稳健性优化。结果表明,基于该优化方法可获得较好的能量解耦率、较高的稳健性并可减小悬置系统振动传递率。     

Optimization Design and Performance Analysis of Vehicle Powertrain Mounting System

The design strategies for powertrain mounting systems play an important role in the reduction of vehicular vibration and noise. As stiffness and damping elements connecting the transmission system and vehicle body, the rubber mount exhibits better vibration isolation performance than the rigid connection. This paper presents a complete design process of the mounting system, including the vibration decoupling, vibration simulation analysis, topology optimization, and experimental verification. Based on the 6?degrees?of?freedom vibration coupling model of the powertrain mounting system, an optimization algorithm is used to extract the best design parameters of each mount, thus rendering the mounting system fully decoupled and the natural frequency well configured, and the optimal parameters are used to design the mounting system. Subsequently, vibration simulation analysis is applied to the mounting system, considering both transmission and road excitations. According to the results of finite element analysis, the topological structure of the metal frame of the front mount is optimized to improve the strength and dynamic characteristics of the mounting system. Finally, the vibration bench test is used to verify the availability of the optimization design with the analysis of acceleration response and vibration transmissibility of the mounting system. The results show that the vibration isolation performance of the mounting system can be improved effectively using the vibration optimal decoupling method, and the structural modification of the metal frame can well promote the dynamic characteristics of the mounting system.     

汽车动力总成刚体惯性参数的辨识

本文以某动力总成为研究对象,基于试验模态分析方法进行了动力总成惯性参数辨识。首先给出了动力总成的频响函数及其拟合方法,并推导了动力总成表面响应和激励与坐标原点之间的关系,建立了动力总成运动学方程,进而得到了刚体惯性参数的表达式;然后以矩阵条件数的方法对动力总成模态试验过程中混入的干扰噪声进行了误差分析;基于测试点的矩阵条件数对响应点的位置进行了推导,并将其表达成与动力总成表面物理参数（如长度、面积等）有关的形式,从而得到了响应点的最好和最差布置形式以及最少的测试点数目;采用捶击法进行了动力总成模态试验,并以最小矩阵条件数原则进行了动力总成惯性参数的辨识。最后,本文也给出了关于进一步消除模态试验测量误差的一些措施。     

专用喷洒车主管路的动力响应分析

采用有限元分析法对喷洒车主管路进行模态和随机振动分析，结果表明，主管路前五阶模态频率在激励谱范围内动态特性较差。用模拟方法得到车体在路面激励下的响应作为振动分析激励输入。随机振动分析表明，激励频率为24Hz时系统产生较大的动态响应。     

Decoupling and effects of the mechanical vibration on the dynamic precision for the direct-driven machine tool

The linear motor feed system realizes direct drive, and all the intermediate transmission components are canceled. The thrust harmonics and other disturbances act on the mechanical system directly because the mover is connected with the driven parts, leading to obvious mechanical vibrations. The mechanical dynamic characteristics have important effects on the thrust characteristics and dynamic precision of linear motor feed system. In this paper, the decoupling and effects of the mechanical vibration on the dynamic precision for the direct driven are researched. Firstly, the mechanical kinetic model is established considering the characteristics of the joint between the guide rail and block and servo stiffness. Then the model realizes decoupling through the modal analysis, and the vibration responses in different directions are analytically calculated. What is more, a modeling method for the linear motor feed system considering the mechanical characteristic is put forward based on the modal separation method (MSM). The effects of the mechanical vibration on the dynamic precision of feed system are discussed. At last, the experiments are carried out and the influences of the structure parameters on the mechanical characteristics and displacement fluctuations are analyzed through sensitivity analysis, which provides a theoretical basis for the mechanical active design and improvement.     

Dynamic analysis of harmonically excited non-linear structure system using harmonic balance method

An analytical method is presented for evaluation of the steady state periodic behavior of nonlinear structural systems. This method is based on the substructure synthesis formulation and a harmonic balance procedure, which is applied to the analysis of nonlinear responses. A complex nonlinear system is divided into substructures, of which equations are approximately transformed to modal coordinates including nonlinear term under the reasonable procedure. Then, the equations are synthesized into the overall system and the nonlinear solution for the system is obtained. Based on the harmonic balance method, the proposed procedure reduces the size of large degrees-of-freedom problem in the solving nonlinear equations. Feasibility and advantages of the proposed method are illustrated using the study of the nonlinear rotating machine system as a large mechanical structure system. Results obtained are reported to be an efficient approach with respect to nonlinear response prediction when compared with other conventional methods.     

Characteristic of torsional vibration of mill main drive excited by electromechanical coupling

In the study of electromechanical coupling vibration of mill main drive system, the influence of electrical system on the mechanical transmission is considered generally, however the research for the mechanism of electromechanical interaction is lacked. In order to research the electromechanical coupling resonance of main drive system on the F3 mill in a plant, the cycloconverter and synchronous motor are modeled and simulated by the MTLAB/SIMULINK firstly, simulation result show that the current harmonic of the cycloconverter can lead to the pulsating torque of motor output. Then the natural characteristics of the mechanical drive system are calculated by ANSYS, the result show that the modal frequency contains the component which is close to the coupling vibration frequency of 42Hz. According to the simulation result of the mechanical and electrical system, the closed loop feedback model including the two systems are built, and the mechanism analysis of electromechanical coupling presents that there is the interaction between the current harmonic of electrical system and the speed of the mechanical drive system. At last, by building and computing the equivalent nonlinear dynamics model of the mechanical drive system, the dynamic characteristics of system changing with the stiffness, damping coefficient and the electromagnetic torque are obtained. Such electromechanical interaction process is suggested to consider in research of mill vibration, which can induce strong coupling vibration behavior in the rolling mill drive system.     

履带车辆动力传动系统扭振的测试与分析

论述了扭振测试的两种方法,即稳态测试方法和动态测试方法.在扫频分析理论的基础上,提出了扭振实车动态试验的条件和加速时间的要求,建立了试验测试系统,并对某型装甲履带车辆的动力传动系统进行了实车道路测试试验.通过对试验数据的分析处理,得到了车辆发生扭转共振时发动机的转速和谐次,为分析、评价车辆动力传动系统扭转振动的合理性提供了试验方面的依据.     

传递矩阵法分析平面柔顺机构的振动特性

为了分析柔顺机构的动态性能和力学传递关系,提出一种新型的基于传递矩阵法的振动力学模型。柔顺机构由若干个柔性铰链与杆件顺序联接而成,采用传递矩阵法描述其力学状态量的传递关系。将柔性铰链视为拉伸和弯曲变形的弹性梁,应用材料力学理论建立反映其自振性能的传递矩阵。将杆件视为刚体,采用动量矩定理建立其动力学模型,得到描述振动刚体的传递矩阵。按照柔顺机构的联接形式,将每个元件的传递矩阵进行拼装,得到系统总传递矩阵。总传递方程以柔顺机构的边界点状态矢量为未知变量,矩阵中的元素为机构结构参数和频率的函数。应用边界条件,可得柔顺机构的特征方程,通过求解方程可得系统的固有频率和振型。将外力纳入传递矩阵,建立反映外力激励与系统的关系的扩展传递矩阵以求解系统的频率响应。通过2种常用平面柔顺机构的动态性能分析,结果表明所建立模型的正确性,能精确描述柔顺机构力学传递关系。     

Forced responses of cracked cantilever beams subjected to a concentrated moving load

An analytical method is developed to present the dynamic response of a cracked cantilever beam subject to a concentrated moving load. The cracked beam system is modeled as a two-span beam and each span of the continuous beam is assumed to obey Euler–Bernoulli beam theory. The crack is modeled as a rotational spring with sectional flexibility. Considering the compatibility requirements on the crack, the relationships between these two spans can be obtained. By using the analytical transfer matrix method, eigensolutions of this cracked system are obtained explicitly. The forced responses can be obtained by the modal expansion theory using the determined eigenfunctions. Some numerical results are shown to present the crack effects (crack extent, location of the crack) and are studied for different speeds of the moving load.     

Free vibration analysis of sandwich beam carrying sprung masses

In this paper, free vibration of three-layered symmetric sandwich beam carrying sprung masses is investigated using the dynamic stiffness method and the finite element formulation. First the governing partial differential equations of motion for one element are derived using Hamilton’s principle. Closed form analytical solution of these equations is determined. Applying the effect of sprung masses by replacing each sprung mass with an effective spring on the boundary condition of the element, the element dynamic stiffness matrix is developed. These matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the well known Wittrick–Williams algorithm. Free vibration analysis using the finite element method is carried out by increasing one degree of freedom for each sprung mass. Finally, some numerical examples are discussed using the dynamic stiffness method and the finite element formulation. After verification of the present model, the effect of various parameters such as mass and stiffness of the sprung mass is studied on the natural frequencies.     

Effects of different coupling models of a helical gear system on vibration characteristics

Time-varying mesh stiffness (TVMS) and the dynamic coupling between the helical gears have a great influence on the vibration characteristics of a helical gear rotor system. Considering the effects of TVMS and adopting two coupling models (lateral-torsional coupling model and lateral-torsional-axial-swing coupling model), the dynamic behavior of a helical gear system was studied. First, an analytical model was used to analyze TVMS of a helical gear pair where the helical tooth is simulated by many spur tooth slices along the direction of the tooth width and the mesh stiffness of each slice is calculated using the energy method. Then, considering the effects of the TVMS excitation, the finite element model of a helical gear rotor system was established. Gear mesh was simulated by the above-mentioned two coupling models to investigate the effects of coupling forms on the system vibration characteristics. The strain energy was used to distinguish the dominant mode and dominant shaft of a gear system in natural characteristics analysis. The results show that the full coupling model can analyze accurately the vibration characteristics of the system and the axial and swing motions cannot be ignored in vibration analysis. Finally, the effects of helix angle on TVMS and vibration responses of a helical gear system were also studied.