Contact-impact formulation for multi-body systems using component mode synthesis

The efficiency and accuracy are two most concerned issues in the modeling and simulation of multi-body systems involving contact and impact. This paper proposed a formulation based on the component mode synthesis method for planar contact problems of flexible multi-body systems. A flexible body is divided into two parts： a contact zone and an un-contact zone. For the un-contact zone, by using the fixed-interface substructure method as reference, a few low-order modal coordinates are used to replace the nodal coordinates of the nodes, and meanwhile, the nodal coordinates of the local impact region are kept unchanged, therefore the total degrees of freedom （DOFs） are greatly cut down and the computational cost of the simulation is significantly reduced. By using additional constraint method, the impact constraint equations and kinematic constraint equations are derived, and the Lagrange equations of the first kind of flexible multi-body system are obtained. The impact of an elastic beam with a fixed half disk is simulated to verify the efficiency and accuracy of this method.

PRECISELY COMPENSATED EFFICIENT COMPONENT MODE SYNTHESIS METHOD

Based on the improved mode superposition method proposed by Z. D. Ma and I.Hagiwara, a precisely compensated efficient mode synthesis method is developed. The calculationprocedure is discussed in detail and the truncation error is also analyzed. By comparison, it isshown that this method has a higher accuracy and a less calculation time than the general used ones.

THE FREE-INTERFACE METHOD OF COMPONENT MODE SYNTHESIS FOR SYSTEMS WITH VISCOUS DAMPING

This paper presents a new free-interface method of component mode synthesis for linear systems with arbitrary viscous damping. The left and right projection matrices described by state-variable vectors are first introduced for components with rigid-body freedom. The operator function of projection matrices for state displacement and state force is proved, and then the state residual flexibility matrix and the state residual inertia-relief attachment mode are defined and employed. The results of three examples demonstrate that the method proposed in this paper leads to very accurate system eigenvalues and high mode-synthesis efficiency

Model Order Reduction of Complex Airframes Using Component Mode Synthesis for Dynamic Aeroelasticity Load Analysis

Airframe structural optimization at different design stages results in new mass and stiffness distributions which modify the critical design loads envelop. Determination of aircraft critical loads is an extensive analysis procedure which involves simulating the aircraft at thousands of load cases as defmed in the certification requirements. It is computationally prohibitive to use a GFEM （Global Finite Element Model） for the load analysis, hence reduced order structural models are required which closely represent the dynamic characteristics of the GFEM. This paper presents the implementation of CMS （Component Mode Synthesis） method for the generation of high fidelity ROM （Reduced Order Model） of complex airframes. Here, sub-structuring technique is used to divide the complex higher order airframe dynamical system into a set of subsystems. Each subsystem is reduced to fewer degrees of freedom using matrix projection onto a carefully chosen reduced order basis subspace. The reduced structural matrices are assembled for all the subsystems through interface coupling and the dynamic response of the total system is solved. The CMS method is employed to develop the ROM of a Bombardier Aerospace business jet which is coupled with aerodynamic model for dynamic aeroelasticity loads analysis under gust turbulence. Another set of dynamic aeroelastic loads is also generated employing a stick model of same aircraft. Stick model is the reduced order modelling methodology commonly used in the aerospace industry based on stiffness generation by unitary loading application. The extracted aeroelastic loads from both models are compared against those generated employing the GFEM. Critical loads modal participation factors and modal characteristics of the different ROMs are investigated and compared against those of the GFEM. Results obtained show that the ROM generated using Craig Bampton CMS reduction process has a superior dynamic characteristics compared to the stick model.

High-speed tracked vehicle model order reduction for static and dynamic simulations

In this paper, a model order reduction strategy is adopted for the static and dynamic behaviour simulation of a high-speed tracked vehicle. The total number of degree of freedom of the structure is condensed through a selection of interface degrees of freedom and significant global mode shapes, for an approximated description of vehicle dynamic behaviour. The methodology is implemented in a customised open-source software to reduce the computational efforts. The modelled tracked vehicle includes the sprung mass, the unsprung masses, connected by means of torsional bars, and all the track assemblies, composing the track chain. The proposed research activity presents a comprehensive investigation of the influence of the track chain, combined with longitudinal vehicle speed, on statics and vehicle dynamics, focusing on vertical dynamics. The vehicle response has been investigated both in frequency and time domain. In this last case road-wheel displacements are assumed as inputs for the model, under different working conditions, hence considering several road profiles with different amplitudes and characteristic excitation frequencies. Simulation results have proven a high fidelity in model order reduction approach and a significant contribution of the track chain in the global dynamic behaviour of the tracked vehicle.

基于高精度模态综合法的螺栓连接组合结构不确定模型更新

由于螺栓结构中存在复杂的微观特征,数值模型中无法避免的会引入不确定性。针对螺栓设计中参数不确定性量化问题,一种基于高精度模态综合法的螺栓连接组合结构随机模型更新方法被提出。首先考虑高阶剩余模态的影响,推导了适用于螺栓组合结构弹性交界面的高精度模态综合法;之后,在贝叶斯推理框架下,通过组合结构的自振频率和振型的概率分布,建立螺栓连接参数的后验概率密度函数,并借助DRAM(delayed rejection adaptive metropolis)抽样方法量化参数的不确定性。数值算例表明,针对各子结构之间自振频率差别较大的结构,与模态综合法相比,本研究方法在较少子结构模态参与的情形下,也可以保证良好的模型更新结果。

多级多重模态减缩策略及其在转子系统动力学特性分析上的应用

航空发动机转子部件众多,多部件高维复杂系统计算量大,导致动力学分析困难、计算时间长,进而影响转子结构设计和动力学验证的效率。基于部件模态综合方法,提出一种针对多部件高维复杂系统降维计算的多级模态减缩策略。对每个单独的子结构利用固定界面模态减缩,并行减缩各子结构的内部自由度,同时完整保留子结构间的耦合关系。通过子结构组合定义新一级的子结构,应用多级模态减缩策略提升降维减缩效果,结合多重模态减缩方法,构建界面分支模态,可显著降低转子有限元模型的维数,同时保留关键子结构的动力学特征和系统整体关键动力学特性。此计算策略被用于某弹用发动机转子系统低维减缩模型的建立,利用减缩模型提升了转子动力学分析的效率,加速轴承刚度参数的优化设计。研究结果表明,与ANSYS计算相比,转子动力学分析所需时间降低了99.5%,精度误差不超过0.1%,该计算策略可用于多部件高维复杂系统的快速分析。

Study on LQR control algorithm using superelement model

The conventional linear quadratic regulator(LQR) control algorithm is one of the most popular active control algorithms.One important issue for LQR control algorithm is the reduction of structure's degrees of freedom(DOF). In this work, an LQR control algorithm with superelement model is intended to solve this issue leading to the fact that LQR control algorithm can be used in large finite element(FE) model for structure. In proposed model, the Craig-Bampton(C-B) method, which is one of the component mode syntheses(CMS), is used to establish superelement modeling to reduce structure's DOF and applied to LQR control algorithm to calculate Kalman gain matrix and obtain control forces. And then, the control forces are applied to original structure to simulate the responses of structure by vibration control. And some examples are given. The results show the computational efficiency of proposed model using synthesized models is higher than that of the classical method of LQR control when the DOF of structure is large. And the accuracy of proposed model is well. Meanwhile, the results show that the proposed control has more effects of vibration absorption on the ground structures than underground structures.

Maneuver and vibration reduction of flexible spacecraft using sliding mode/command shaping technique

A generalized scheme based on the sliding mode and component synthesis vibration suppression (CSVS) method has been proposed for the rotational maneuver and vibration suppression of an orbiting spacecraft with flexible appendages. The proposed control design process is twofold: design of the attitude controller followed by the design of a flexible vibration attenuator. The attitude controller using only the attitude and the rate information for the flexible spacecraft (FS) is designed to serve two purposes: it forces the attitude motion onto a pre-selected sliding surface and then guides it to the state space origin. The shaped command input controller based on the CSVS method is designed for the reduction of the flexible mode vibration, which only requires information about the natural frequency and damping of the closed system. This information is used to discretize the input so that minimum energy is injected via the controller to the flexible modes of the spacecraft. Additionally, to extend the CSVS method to the system with the on-off actuators, the pulse-width pulse-frequency (PWPF) modulation is introduced to control the thruster firing and integrated with the CSVS method. PWPF modulation is a control method that provides pseudo-linear operation for an on-off thruster. The proposed control strategy has been implemented on a FS, which is a hub with symmetric cantilever flexible beam appendages and can undergo a single axis rotation. The results have been proven the potential of this technique to control FS.

On the Modal and Non-Modal Model Reduction of Metallic Structures with Variable Boundary Conditions

Vibration mode based model reduction methods like Component Mode Synthesis (CMS) will be compared to methods coming from control engineering, namely moment matching (MM) and balanced truncation (BT). Conclusions based on the theory together with a numerical demonstration will be presented. The key issues on which the paper is focused are the reduction of metallic structures, the sensitivity of the reduced model to varying boundary conditions, full system response, accurate statics and the possibility to determine “a priori” the number of needed modes (trial vectors). These are important topics for the use of reduction methods in general and in particular for the implementation of FE models in multi body system dynamics where model reduction is widely used. The intention of this paper is to give insight into the methods nature and to clarify the strengths and limitations of the three methods. It turns out, that in the considered framework CMS delivers the best results together with a clear strategy for an “a priori” selection of the modes (trial vectors).

模态综合的子结构主模态截断方法

为了减少固定界面模态综合方法中保留的子结构主模态数，分别采用频率截断和有效模态质量截断两种方法进行截断，分析两种方法的适用性，最终得到适合结构低频动态特性计算的主模态截断方法．计算结果表明：频率截断法保留的主模态不到有效质模态量截断法的1／2，采用2～3倍的最高关心频率进行主模态截断，能保证结构低频动态特性计算具有较高的精度，所保留的主模态，更能反应子结构在关心频率范围内系统振动的变形模式；有效模态质量法不能判断各子结构间主模态对系统动态特性作用的相对大小，这使小尺寸高刚度的子结构保留多余的模态，其计算效率较低．

一体化转子系统动力分析的预应力模态综合法

针对盘片轴一体化转子系统的大规模网格问题,提出用于该类结构动力分析的预应力模态综合法.对前两级整体叶盘进行静、动频分析,给出了影响一体化结构动力分析精度的模态截断数的选取原则,同时验证了本文方法的准确性.计算了盘片轴一体化转子系统的静、动频,给出了旋转作用对该系统模态的影响.比较整体叶盘与一体化转子的模态结果发现,引入转轴的作用使叶片振型对应的动频降低,且一体化转子振型中存在叶片、轮盘及转轴之间的耦合振型,这阐释了利用预应力模态综合法进行大规模网格盘片轴一体化结构动力分析的重要性.

双立柱式堆垛机碰撞振动与仿真分析

双立柱式巷道堆垛机的货笼和立柱存在间隙,在加速运行过程中发生碰撞,引起货笼和立柱的结构振动,限制了堆垛机运行速度并且降低了其安全性能。针对此问题,基于模态综合法,利用Nastran计算了立柱框架结构模态,通过锤击试验验证了有限元模型的正确性,将模型的模态中性文件(modal neutral file,简称MNF)导入到ADAMS软件中,建立了刚柔耦合的堆垛机虚拟样机。比较分析了失效模态振型与能量法进行模态截断的计算精度和适用性,并根据试验测得的加速度响应数据验证了动力学模型的准确性。在此基础上,调整货笼与立柱的间隙,再次计算了紧急制动情况下堆垛机的振动响应。研究结果表明,运用能量法进行堆垛机的模态截断能在保证精度的基础上提高计算效率,控制堆垛机立柱与货笼的间隙可以减小堆垛机的振动,对提高堆垛机的运行速度和安全性能具有重要意义。

基于模态综合技术的结构有限元模型修正

由于结构的动力分析需要大量的计算时间和占用大量的计算机内存,常规的数值迭代计算方法难以实现,提出了基于模态综合技术的模型修正方法。该方法首先得到缩减后结构模型的频率与振型,并将该振型转换为缩减前模型物理坐标下的振型。然后,用缩减后模型的频率和转换后的振型,共同构成模型修正的优化目标函数,进而通过优化求解实现结构的模型修正。该方法既保证了计算精度又提高了模型修正的计算效率,使大型复杂结构的模型修正成为可能。最后,对某吊杆拱桥模型进行了动态测试和模型修正,验证了该算法的有效性。

并联机床进给传动系统弹性动力学建模方法研究

利用动态子结构法研究一种外副驱动可实现 3平动自由度并联机床进给系统的动力学建模方法。首先将原系统分解成若干子结构 ,在建立各自动力学模型后 ,借助边界条件经综合得到系统的动力学方程。该方法手续简便、计算效率高 ,便于讨论结构参数对低阶模态的影响规律 ,故为这类复杂时变系统的动刚度预估和动态设计奠定了坚实的理论基础。

弹性管束动态特性子结构模态综合法

弹性管束换热器利用流体诱导振动强化传热,识别换热元件的模态特性对于了解其运行机理、优化结构设计有重要意义。基于此,运用子结构模态综合法,先推导出弹性管束每个部件的运动方程,然后根据相容性条件进行装配,从而得出弹性管束在模态坐标下的自由振动微分方程。用数值方法求解该方程,得出结构的固有频率和振型,并对模态频率和振型变化进行详细分析。结果表明:弹性管束既有面内振动又有面外振动。在管束内外复杂流场的宽频激励下,弹性管束的振动是各阶振型合成的复杂运动,从而初步解释了其强化传热的机理。

应用模态综合法求解自动化码头桁架桥的固有特性

应用固定界面模态综合Craig-Bampton法和双协调自由界面模态综合法求解自动化码头低架桥桁架结构刚性连接下的固有特性,比较了两种方法的优缺点,发现双协调自由界面法的计算精度高于固定界面C-B法。以3种不同的形式划分子结构,通过比较整体结构固有频率计算结果,提出若干划分子结构的原则,得出子结构的高阶主模态的频率越高则计算精度越高的结论。在此基础上,基于连接子结构可经Guyan静力变换成超单元,推导了界面位移和界面力双协调的含超单元连接子结构的自由界面模态综合法。将该法应用于含铅芯橡胶支座弹性连接下桁架桥的固有特性分析,结果表明铅芯橡胶支座对结构调频效果明显。

模态综合法在车身结构动力学计算中的应用

采用模态综合法求解车身模态、车身结构在发动机激励下的响应和车身结构与驾驶室声腔耦合的声学响应。与传统的有限元分析的对比结果表明,使用模态综合法求解时,计算时间缩短18%～40%,而车身结构模态、频响和声固耦合响应的计算偏差分别在1%、5%和15%以内。

基于有效模态质量的子结构主模态选择方法

根据建筑物抗震设计中有效模态质量计算的基本原理,推导了固定界面模态综合中子结构各阶主模态的模态参与因子和有效模态质量,以及总的有效模态质量的计算方法。根据各阶有效模态质量与总的有效模态质量之比,对某样车模型的子结构主模态进行截断。结果表明:在一定频率范围内,采用子结构主模态截断法,仅保留少数低阶主模态,即可使样车低频振动特性计算结果具有较高的精度。

含裂纹离心压缩机叶轮结构的振动局部化

针对离心压缩机在复杂运行工况下的失谐与裂纹问题,研究裂纹与失谐对叶轮结构振动响应和振动局部化的影响规律。首先,采用三维有限元模型建立具有复杂几何形状的叶轮结构的定量分析模型,并通过在裂纹界面上定义接触的形式模拟裂纹的呼吸效应。其次,通过采用混合界面模态综合法对系统自由度进行缩减,以解决了采用三维有限元模型分析非线性系统动态响应时所存在的计算量大和收敛困难的问题。最终,采用Monte Carlo方法对含裂纹的失谐叶轮结构进行统计分析,研究随机失谐和裂纹故障对叶轮结构振动局部化的影响规律。结果表明裂纹和失谐都会对结构的振动响应产生显著的影响,并会导致振动能量的集中和振动局部化现象。