Dynamic modeling and simulation for the rigid flexible coupling system with a non-tip mass

The rigid flexible coupling system with a mass at non-tip position of the flexible beam is studied in this paper. Using the theory about mechanics problems in a non-inertial coordinate system, the dynamic equations of the rigid flexible coupling system with dynamic stiffening are established. It is clearly elucidated for the first time that, dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beam and the transverse vibration deformation of the beam. The modeling approach in this paper successfully solves problems of popular modeling methods nowadays: the derivation process is too complex by using only one dynamic principle; a clearly theoretical mechanism for dynamic stiffening can't be offered. First, the mass at non-tip position is incorporated into the continuous dynamic equations of the system by use of the Dirac function and the Heaviside function. Then, based on the conclusions of orthogonalization about the normal constrained modes, the finite dimensional state space equations suitable for controller design are obtained. The numerical simulation results show that: dynamic stiffening is included in the first-order model established in this paper, which indicates the dynamic responses of the rigid flexible coupling system with large overall motion accurately. The results also show that the mass has a softening effect on the dynamic behavior of the flexible beam, and the effect would be more obvious when the mass has a larger mass, or lies closer to the tip of the beam.     

在非惯性系中研究动力刚化问题

正确认识动力刚化问题,对深入研究航天器动力学和合理建立柔体动力学的数值计算模型意义重大.应用非惯性坐标系中的力学问题的理论来研究动力刚化问题,给出两类研究动力刚化问题的计算模型,明确了动力刚化问题的物理意义,探索了正确处理零次建模的途径.这样处理动力刚化问题,表现出与其他学者的研究有实质性的差异.     

含动力刚化项的一般多柔体系统动力学研究

为获取柔性体的动力刚化项,将任意形状柔性体的非线性变形场表达为直至广义坐标的二阶小量形式．在小变形条件下,用Green应变张量得到了柔性体的耦合形函数．把约束引入多柔体系统,依据Kane方程建立了包含动力刚化项的一般柔性多体系统动力学方程．通过数值仿真算例,界定了传统多柔体系统动力学建模方法的适用范围．     

基于绝对节点坐标法的三维柔性旋转梁动力特性分析

主要研究了三维柔性旋转梁的动力特性.采用绝对节点坐标法和几何非线性变形假设,基于一般连续介质理论,建立三维柔性梁的非线性动力学模型;基于摄动理论,结合浮点坐标方法,采用线性化技术,建立柔性旋转梁的振动频域分析模型.对柔性梁自由单摆进行时域仿真,并分析了不同转速下三维柔性旋转梁的频域特性.结果表明,随着转速增加梁的动力刚...     

非惯性坐标系下柔性梁的动力学分析与压缩建模

文章针对大范围运动已知的空间柔性梁结构建立其动力学方程.通过研究与分析,提出了文中精确模型,各项矩阵较原有一次耦合模型新增了2类耦合项:即变形耦合项和基点速度和角速度耦合项.通过仿真计算,比较其动力学特性与零次、一次耦合模型的差异,确定各种耦合项的作用,并进行了定性分析.最后研究了复杂系统的压缩建模问题,为工程实际和今后的研究奠定了理论基础.     

机械臂协调操作柔性负载鲁棒神经网络控制

针对多变量刚柔耦合的双机械臂协调操作柔性负载系统,基于奇异摄动理论研究该系统有限元模型的分解以及轨迹跟踪控制问题.考虑动力学模型的复杂性,通过双时标变换将协调系统分解成表征系统大范围刚性运动的慢变子系统和表征系统弹性振动的快变子系统.基于反演思想在慢变子系统中设计鲁棒神经网络控制策略,实现系统轨迹跟踪性能;针对快变子系统,设计鲁棒最优控制策略抑制系统的弹性振动.仿真研究结果表明,该控制策略增强了系统的跟踪性能和鲁棒性.     

Complete geometric nonlinear formulation for rigid-flexible coupling dynamics

A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed. Foundation item: Project(10772113) supported by the National Natural Science Foundation of China     

动力刚化系统动力学建模方法的研究

具有大范围、高速运动的柔性体，即使在小变形范围内，运动和变形的耦合将产生动力刚化现象，本文提出一种研究动力刚化系统新的方法，建立了求解动力刚化系统逆问题的数学模型，拓宽了动力刚化问题的研究范围，该项研究对以柔性体为代表的航天器中的构件、机器人和高速机构等机械诉设计、动力学仿真和减振控制，具有重要意义。     

柔性多体动力学的建模与计算

本文在对柔性多体动力学发展略作回顾的基础上，采用ｄ＇Ａｌｅｍｂｅｒｔ－Ｌａｇｒａｎｓｅ原理，对由基座、（ｎ－１）个柔性连杆及端部负载组成、相互之间由柱铰联结的柔性链式多体系统进行理论建模；柔性杆模态取三维梁单元进行有限元离散；算法上选用Ｇｅａｒ算法克服柔体动力学微分方程的刚性（Ｓｔｉｆｆｎｅｓｓ）问题。成功地进行了一种工况的失重柔性机械臂的动力学数值计算，为在其上进一步实施控制打下了良好的基础。     

刚柔耦合系统的输入成形控制

为实现对大范围运动刚柔耦合系统的振动抑制,提出基于一次近似动力学模型的输入成形控制方法.针对中心刚体-柔性旋臂梁系统,在变形位移的描述中计及纵向变形的二次耦合项,建立一次近似动力学模型用于振动控制.考虑到大范围运动刚柔耦合系统中柔性梁有别于结构动力学中定边界梁的模态特性,设计抑制柔性振动的鲁棒多模态输入成形器.仿真结果...     

直升机悬停状态下的振动计算

为降低直升机的共振危害,需要一种对直升机在空中悬停时振动特性快速计算方法.旋翼在离心力作用下,固有频率受应力刚化效应影响发生变化,同时存在旋翼桨叶/桨叶和旋翼/机身的耦合影响,动力学分析十分复杂,另一方面为提高计算效率,运动方程的低阶次、程式化成为迫切的需求.多体系统传递矩阵法(Transfer matrix method for multibody systems, MSTMM)同时解决了这两个问题.为准确快速计算悬停直升机固有频率,本研究基于MSTMM建立一种柔性四片旋翼与直升机机身耦合的动力学模型,推导出系统的动力学拓扑模型、总传递方程和特征方程.重点推导了空间旋转梁和旋转轴的传递矩阵,最终快速计算得出悬停直升机系统固有频率.研究表明:空间旋转梁MSTMM计算结果和ANSYS Workbench仿真结果对比,误差不超过2%,旋转轴MSTMM计算结果与参考文献结果基本一致;机尾固定的约束条件下,计算出36.651 9 rad/s转速下旋翼/机身耦合系统的前13阶固有频率,与ANSYS Workbench仿真结果一致,改为悬停无约束条件,计算得出悬停直升机系统前8阶固有频率,计算速度相较仿真速度提升了7.1倍,为直升机动力学分析提供一种新思路.     

Rigid-Flexible Coupling Dynamic Analysis of Sub-Launched Vehicle During the Vertical Tube-Exit Stage

During the launching stage,hydrodynamic pressure and adapters’ reaction loads can influence the vehicle’s rigid motion as well as cause its structural vibration,which is a typical rigid-flexible coupling dynamic problem. This paper presents a 2-D rigid-flexible coupling model to calculate the vehicle’s dynamic responses in that period.The vehicle was equivalent to a flexure beam with axial deformation. Hybrid coordinate and modal superposition methods were used to describe its large rigid displacement and small deformation. By the second Lagrange equation,the vehicle centroid’s displacements,rotational angle and modal coordinates were chosen as generalized coordinates and then the vehicle ’s rigid-flexible coupling dynamic equations were obtained. By numerical simulation,the results of vehicle’s motion parameters and transverse internal loads were acquired.The calculation results showed that differences of the vehicle’s motion parameters between the rigid-flexible coupling model and the rigid body assumption are noticeable and the peak magnitude of the vehicle’s transverse internal loads in the rigid-flexible coupling model is higher remarkably than that in the rigid body assumption.     

柔性机械臂的动力学模型及PD控制

应用模态控制理论，对柔性机械臂的主动控制问题中的动力学模型进行了研究，在小变形假设的前提下，考虑由于横向变形而引起的轴向位移的影响，采用拉格朗日方程建立了计及动力刚化项的动力学模型，并将ＰＤ控制理论和方法应用于该模型。最后，对一单杆柔性机械臂的振动控制进行了计算机仿真。     

压缩机振动与辐射低噪声结构分析

针对某往复压缩机噪声偏高问题,采用虚拟预测技术对压缩机进行了低噪声结构分析研究。首先建立了由柔性机体、柔性曲轴和刚性连杆、活塞及飞轮组成的往复压缩机的多体动力学模型。通过动力学仿真求解得到传递给机体的各种激励载荷,再根据直接积分法法求解出压缩机机体的振动响应结果,仿真得到的机体部分测点结果与实验结果吻合较好。最后根据有限元动态结果来预测其机体表面辐射噪声,计算出机体的辐射声功率与实测结果相一致。     

多柔体系统刚柔耦合动力学有限单元法

传统的多柔体系统动力学建模理论 ,往往基于小变形线性动力学的基本假定 ,采用线性的Cauchy应变理论描述应变—位移关系。但是 ,对于具有刚性旋转的位移场来说 ,Cauchy应变理论并不适用。本文采用Green Lagrange应变理论 ,描述有大位移运动的梁单元的非线性位移—应变关系 ,通过对应变能的分析和线性化处理 ,建立起相对变形坐标一阶精确的一致线性化的多柔体系统有限元模型 ,仿真算例的结果验证了该方法的有效性和结构中的几何非线性对系统动力学响应的重要作用。     

Dynamic modeling and analysis of 3-RRS parallel manipulator with flexible links

The dynamic modeling and solution of the 3-(R)RS spatial parallel manipulators with flexible links were investigated. Firstly, a new model of spatial flexible beam element was proposed, and the dynamic equations of elements and branches of the parallel manipulator were derived. Secondly, according to the kinematic coupling relationship between the moving platform and flexible links, the kinematic constraints of the flexible parallel manipulator were proposed. Thirdly, using the kinematic constraint equations and dynamic model of the moving platform, the overall system dynamic equations of the parallel manipulator were obtained by assembling the dynamic equations of branches. Furthermore, a few commonly used effective solutions of second-order differential equation system with variable coefficients were discussed. Newmark numerical method was used to solve the dynamic equations of the flexible parallel manipulator. Finally, the dynamic responses of the moving platform and driving torques of the 3-RRS parallel mechanism with flexible links were analyzed through numerical simulation. The results provide important information for analysis of dynamic performance, dynamics optimization design, dynamic simulation and control of the 3-RRS flexible parallel manipulator.     

多柔体系统刚柔耦合动力学有限单元法

传统的多柔体系统动力学建模理论,往往基于小变形线性动力学的基本假定,采用线性的Cauchy应变理论描述应变—位移关系。但是,对于具有刚性旋转的位移场来说,Cauchy应变理论并不适用。本文采用Green-Lagrange应变理论,描述有大位移运动的梁单元的非线性位移—应变关系,通过对应变能的分析和线性化处理,建立起相对变形坐标一阶精确的一致线性化的多柔体系统有限元模型,仿真算例的结果验证了该方法的有效性和结构中的几何非线性对系统动力学响应的重要作用。     

Evaluation of vehicle-track-bridge interacted system for the continuous CRTS-II non-ballast track slab

Considering the CRTS-II track slab, which is commonly used in the Chinese high-speed railway system, a vehicle-track-bridge dynamic analysis method is proposed in which the vehicle subsystem equations are established by the rigid body dynamics method, the track subsystem and the bridge subsystem equations are established by the FEM, the wheel-rail contact relation is defined by the corresponding assumption in vertical direction and the Kalker linear creep theory in lateral direction. The in-span spring element is derived to model the track-bridge interaction; the equal-band-width storage is adopted to fit the track structure with multilayer uniform section beam; and the dynamic equilibrium equations are solved by the inter-history iteration method. As a case study, the response of a CRH2 high-speed train transverses a simply-supported bridge with successive 31.5 m double bound pre-stress beams is simulated. The result shows that using the vehicle-track-bridge interaction model instead of the vehicle-bridge interaction model helps predict the rotation angle at beam ends and choose an economic beam vertical stiffness.     

柔性基础内燃机被动隔振系统的建模与仿真

以多体动力学为基础,结合有限元技术和实体建模技术,建立柔性基础内燃机被动隔振系统刚/柔混合仿真模型。并对支承在柔性平板结构上的某四缸柴油机隔振系统进行动力学仿真计算,静平衡及激振力仿真结果均与理论计算十分吻合。通过改变柔性平板支承刚度来改变柔性基础的边界条件,进一步获得不同刚度条件柔性基础上内燃机隔振系统的隔振特性。通过比较柔性基础上隔振器支承力和刚性基础上隔振器支承力的变化,结果表明：柔性基础对隔振器支承力有重要影响,受柔性基础弹性影响的系统自振有可能成为影响支承力变化的主要因素。     

基于刚柔耦合动力学的齿轮传动系统动态特性

为得到齿轮轴系响应的动态特性,从柔体动力学基本理论出发,系统分析了刚柔耦合动力学模型的机理,建立了多级齿轮传动刚柔耦合的虚拟样机。此模型能综合考虑传动轴各方向上的柔性特征、湿式换档离合器动态特性以及齿轮时变啮合力对轴类零件动态响应的影响。仿真结果证明了通过虚拟样机技术获取载荷谱的可行性,可用于轴的疲劳寿命预测以及齿轮箱体的振动研究。