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.     

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.     

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     

Motion function reliability analysis of a rotating flexible beam with random parameters

The assumed mode method and stochastic response surface method are combined to analyze the motion function reliability of a rotating flexible beam with random parameters. Firstly, based on Lagrange's equations and the assumed mode method, the rigid-flexible coupling dynamic model which takes the coupling term of the deformation in the expression of longitudinal deformation is studied. Then considering the physical and geometrical parameters under randomness, the probability analysis is made by the stochastic response surface method. The rationality and efficiency of the modeling and the method presented are verified by an example. The results demonstrate that the third order stochastic response surface method leads to good precision with acceptable time consumption compared with the Monte Carlo (MC) method, and that the randomness of density has a greater effect on the reliability of the system.     

Dynamic modeling and simulation for the flexible spacecraft with dynamic stiffening

A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system, the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystem modeling framework. 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 avoids problems which are caused by other popular modeling methods nowadays: the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can't be provided. First, the continuous dynamic models of the flexible beam and the central rigid body are established via structural dynamics and angular momentum theory respectively. Then, based on the conclusions of orthogonalization about the normal constrained modes, the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations show that: dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper, which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately, and has a clear modeling mechanism, concise expressions and a good convergence.     

Extremum response surface method of reliability analysis on two-link flexible robot manipulator

In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator, Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method. By using the Monte Carlo method, the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement, speed and acceleration. On this basis, dynamic stresses and deformations were obtained. By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities, extremum response surface functions were established. A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method. The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.     

高空作业平台臂架伸缩运动的横向振动特性

为了探究高空作业平台做伸缩运动时变幅平面内的横向振动动力学特性,针对臂架的实际搭接和支承情况,将臂架等效为根部铰接、中间弹性支承且带有集中参数的变截面变长度梁. 基于牛顿第二定律建立各臂段的运动微分方程,采用模态叠加法、结合边界条件求解臂架一系列时刻的瞬态振型函数,曲线拟合时变参数以近似表示梁的振型,并依据伽辽金截断方法,得到广义坐标下的状态空间方程. 在Matlab/Simulink环境下进行动态仿真,得到伸缩过程中臂架头部的变幅平面横向振动动态响应. 结果表明,就横向振动振幅而言,搭接简化会带来15.63%计算结果误差;支承简化会加大臂架整体刚度、减小臂架振动响应,不可取。     

基于小变形的柔性多体系统动力学建模方法研究

引入非线性变形场描述,建立了基于小变形的柔多体系统动力学模型,解决了传统动力学建模方法存在的对变形广义坐标过早线性化的缺陷。对旋转梁式构件进行了动力学仿真,仿真结果表明传统方法不适合用于高速旋转的柔性体动力学建模,本文提出的动力学模方法为解决实际工程中各种复杂结构动力学分析提供了有力工具。     

转子分布不平衡和轴承特性参数同时辨识方法

针对转子模态动平衡的关键参数转子不平衡量和轴承特性参数难以确定的问题,提出一种基于轴承处振动响应的轴承特性参数和转子分布不平衡参数的同时辨识方法。以多项式函数描述转子质量偏心曲线,表征转子连续分布的不平衡质量;以有限元法建立转子/轴承子结构运动微分方程;采用虚功原理将连续分布的广义不平衡力转化为节点处的集中不平衡力并建立其与偏心曲线系数的关系,从而推导出轴承特性参数及质量偏心曲线系数的同时辨识方程,进而实现基于不同转速下轴承处的振动响应辨识出轴承特性参数和分布不平衡参数。以一个转子轴承系统为例进行了偏心曲线阶次对参数辨识的敏感度仿真,结果表明：偏心曲线阶次对参数辨识结果影响较小。以实测轴承处响应辨识得到的参数进行一阶模态动平衡实验,平衡后轴承处振动明显降低,验证了提出的辨识方法及其在模态动平衡中的有效性。     

基于小变形的柔性多体系统运动学分析

多体系统中柔性体运动一般分为体参考系的范围运动和变形运动。在多数场合,柔性体的变形运动是较小的,可以用对变形广义坐标线性化的动力学方程描述系统动力学行为。但是,目前通用的一些动力学建模方法用于柔性体动力学建模时,存在过早线性化缺陷,导致最终的动力学方程遗失了一些重要的刚柔耦合项。本文采用非线性变形场描述,计及含有变形广义坐标及其导数的二阶小量项,将这种非线性保留到求出偏速度后,再线性化,建立了柔性     

柔性机构连接杆单元特性分析

本文介绍了机构位置变化对不同坐标系中运动参数变换的影响,对弹性杆梁单元的动能作了较为精确的计算;在未忽略惯性耦合项的基础上,导出了梁单元的运动方程式。该方程克服了目前应用的方程式的不足,可以比较全面地用来预测柔性机构系统的运动特性和动力特性。     

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...     

Dynamic reliability analysis of spacial flexible beam

In order to investigate the dynamic response reliability of the spacial flexible beam, the Monomial Cubature Rules (MCR) based Stochastic Response Surface Method (SRSM) is applied to derive the surrogate model of the nonlinear implicit limit state function. A small set of sample pairs for flexible beam dynamic response is generated by taking the integral points of MCR as sample points. Based on these sample pairs and SRSM, the surrogate model of the implicit limit state function is established. The results show that the proposed method has an excellent performance in terms of accuracy and efficiency compared with the Probabilistic Collection Method (PCM) based SRSM and Monte Carlo method, and that the dispersion of system parameters has a significant effect on the dynamic response reliability of the spacial flexible beam.     

简支柔性梁的非线性动力学和分叉

研究了轴向激励作用下简支柔性梁的非线性动力学和分叉,导出了简支梁在参数激励作用下具有五次非线性项的运动方程,分析了局部分叉和稳定性．利用多尺度法得到了柔性梁的平均方程,借助于数值方法研究了柔性梁的局部分叉．     

基于分力合成方法的航天器闭环反馈控制

为了增强分力合成主动振动抑制方法抵抗外界干扰的能力,将分力合成方法与闭环反馈控制相结合同时进行设计.用非约束模态级数方法建立解耦的姿态动力学方程和挠性附件振动方程,通过选取合适的反馈量,在设计闭环反馈参数时将挠性附件的振动和分力合成方法同时加入到约束条件中,得到最佳性能解.通过对单挠性杆模型的仿真,在满足系统各项性能指标的条件下,调整时间较分步设计方法明显减少,证明本文方法的有效性.     

Elastodynamic modeling and joint reaction prediction for 3-PRS PKM

To gain a thorough understanding of the load state of parallel kinematic machines(PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used as a case study to illustrate the process of joint reaction analysis. The substructure synthesis method is applied to deriving an analytical elastodynamic model for the 3-PRS PKM device, in which the compliances of limbs and joints are considered. Each limb assembly is modeled as a spatial beam with non-uniform cross-section supported by lumped virtual springs at the centers of revolute and spherical joints. By introducing the deformation compatibility conditions between the limbs and the platform, the governing equations of motion of the system are obtained. After degenerating the governing equations into quasi-static equations, the effects of the gravity on system deflections and joint reactions are investigated with the purpose of providing useful information for the kinematic calibration and component strength calculations as well as structural optimizations of the 3-PRS PKM module. The simulation results indicate that the elastic deformation of the moving platform in the direction of gravity caused by gravity is quite large and cannot be ignored. Meanwhile, the distributions of joint reactions are axisymmetric and position-dependent. It is worthy to note that the proposed elastodynamic modeling method combines the benefits of accuracy of finite element method and concision of analytical method so that it can be used to predict the stiffness characteristics and joint reactions of a PKM throughout its entire workspace in a quick and accurate manner. Moreover, the present model can also be easily applied to evaluating the overall rigidity performance as well as statics of other PKMs with high efficiency after minor modifications.     

空间柔性操作臂的动力学/控制耦合特性研究

采用哈密顿模型,对关节处含谐波减速器的空间柔性操作臂的动力学特性进行了研究. 在考虑谐波减速器柔性效应的前提下,分析臂杆运动过程中的动态约束类型,得到了包含系统控制参量和谐波减速器刚度系数的模态频率和振型方程. 综合关节和臂杆的柔性,建立了耦合系统控制律的动力学方程. 通过仿真计算不同控制参数下系统的动力学响应,验证所建系统动力学模型的有效性.     

非线性弹性梁的动力模型

通过弹性力学变分原理建立了大挠度非线性梁的控制微分方程组.该理论含有4个独立的自由度,能更精确描述非线性弹性梁的的力学行为.     

一种全向滚动球形机器人的动力学分析与仿真

研究了一种全向滚动球形机器人的动力学建模、分析与仿真方法．根据机器人所受的非完整约束,建立了其运动学模型．根据机器人的结构特征和Lagrange-Routh方程,建立了其动力学模型,给出了消去未知Lagrange乘子的策略．得到了该球形机器人的完整动力学模型,即控制机器人运动的强耦合二阶微分方程组．建立了描述该球形机器人完整动力学方程的仿真模型．运动实例的动力学分析和仿真结果验证了该方法的有效性．     

双层预紧式六维力传感器动态性能的理论与实验研究

对一种新型的双层预紧式六维力传感器进行了动态性能理论分析与实验研究。首先介绍了双层预紧式六维力传感器的结构特点。建立了该传感器的振动系统简化模型,基于螺旋理论和多自由度系统振动学推导了系统的运动微分方程。经过对运动微分方程进行求解,得到了传感器的各阶固有频率。最后采用阶跃响应法对传感器样机进行动态性能实验研究,经过快速傅里叶变换得到了传感器的频率响应曲线。实验结果与理论计算结果一致,从而验证了理论推导的正确性。研究结果表明,双层预紧式六维力传感器的动态性能较好,能够满足一般工业生产中对六维力测量的要求。